PNNL-14256
O
          Model Documentation
          The Second Generation Model
Antoinette L. Brenkert
Ronald D. Sands
Son H. Kim
Hugh M. Pitcher
          October 2004
          Prepared for the United States Environmental Protection Agency under
          Contracts AGRDW89939464-01 and AGRDW89939645-01
          Joint Global Change Research Institute, College Park, MD
          Pacific Northwest National Laboratory
          Operated by Battelle for the US Department of Energy

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                             Printed in the United States of America

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Executive Summary
For a full overview of the model see the "SGM Model Overview".

Briefly, the Second Generation Model (SGM) is a computable general equilibrium model
designed specifically to analyze issues related to energy, economy, and greenhouse gas
emissions. It has 14 global regions, multiple greenhouse gas emissions, vintaged capital stocks,
explicit connections between technology and the economy, disaggregated to reflect the relative
importance of sectors in determining greenhouse gas emissions, and explicit treatment of energy
and land stocks. Model development began in 1991. The first model design paper was published
in 1993 (Edmonds, et al.,  1993). The SGM was developed to complement the "first generation
model," referred to as the MiniCAM. The MiniCAM was also explicitly designed to address
long-term, strategic, issues related to energy, economy, and greenhouse gas emissions (Edmonds
and Reilly, 1983)1 and continues to be used for that purpose2. In contrast the SGM was designed
to address transitional energy-economy-technology-greenhouse-gas-emissions issues.

The detailed documentation below presents the SGM 2003 version. The SGM was developed at
the Pacific Northwest National Laboratory (PNNL) and is maintained by the PNNL Joint Global
Change Research Institute (JGCRI)3.
1 The MiniCAM evolved to include agriculture, land-use, terrestrial and ocean carbon cycle, radiative forcing, sea level
rise, and climate change.
2 For a brief comparison between the SGM and MiniCAM see Appendix D
3 The JGCRI is a collaboration between the PNNL and the University of Maryland at College Park. The JGCRI is
located on the campus of the University of Maryland in College Park, MD.
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Acknowledg merits

We want to thank Elizabeth L. Malone for steadfast support and for editing the document.
We want to thank Marshall Wise and Joe M. Roop for their peer review. We want to thank the
Economic Analysis Branch of the Office of Atmospheric Programs of the Environmental
Protection Agency's Climate Change Division for making this documentation become reality.

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Table of Contents
LEGAL NOTICE	2
Executive Summary	2
Acknowledgments	2
     Table of Contents	2
     List of Figures	2
     List of Tables.	2
Chapter 1. The Second Generation Model	2
Chapter 2. The modeling framework: economic input-output and energy balance tables	2
     Production and input-output tables in the SGM	2
     Investment and capital stocks	2
Chapter 3. Production functions	2
     Production functions, vintages, and the input-output matrix	2
     CES production by vintage	2
     Long-and short-run elasticities	2
     The Leontiefor fixed coefficient production function	2
Chapter 4. Prices and expected prices	2
     Base year prices and initial future prices	2
     Determining prices paid for supplies by producers, prices received for produced
     commodities, and policy potential	2
     Expected prices	2
Chapter 5. Technical change	2
     Input-output coefficients and their relationship to the technical scale coefficients.	2
     How technical change is operationalized in the SGM.	2
     The technical coefficients (o^j) in the CES production function	2
     The technical coefficients (A,~j) in the Leontief production function	2
Chapter 6. Profits, demands,  expected profit rates, and the operation of capital	2
     Profits and the production functions	2
        Profits and the CES production function	2
        Profits and the Leontief production function	2
     The relationship between profits and demands	2
        Demands and the CES production function	2
        Demands and the Leontief production function	2
     Expected profit rates	2
     Operation of capital stock in the SGM: determining production and interindustry demand. 2
        Old vintages	2
        New vintages	2
        Demands by production sectors and cost calculations	2
        Additional costs when operating any of the active vintages	2
Chapter 7. Carbon policies	2
     Carbon prices  and revenue cycling	2
     Carbon permit trade	2
     Carbon policy  impacts	2
Chapter 8. The final demand sectors	2

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     Investment	2
     Households	2
     Government.	2
     Imports and exports	2
Chapter 9. GNP accounting	2
Chapter 10. The solution procedure	2
Chapter 11. Calibration procedure	2
Chapter 12. The energy balance and emissions	2
     Fossil fuel emissions	2
     Other greenhouse gas emissions and non-greenhouse gases	2
     Mitigation and marginal abatement cost curves	2
     Display of results	2
Chapter 13. Reference case results	2
     Projections/Validation/Calibration for the USA	2
References	2
List of Equations	2

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List of Figures

Figure 1 The flow of goods and services in SGM	2
Figure 2 Typical input-output table	2
Figure 3 Typical energy balance table	2
Figure 4 Basic flowchart of the SGM model	2
Figure 5 Annual investment: paper making and paper products in China	2
Figure 6 Putty-semiputty isoquants	2
Figure 7 Putty-clay isoquants	2
Figure 8 Neutral technical change when the elasticity of substitution coefficient (cr) equals 0.5... 2
Figure 9 Biased technical change when the elasticity of substitution coefficient (a) equals 0.5.... 2
Figure 10 Investment into production sectors over time	2
Figure 11 Investments in fossil fuel related production over time	2
Figure 12 Investment in electricity production over time	2
Figure 13 Quantities of uninvested depletable resources and invested capital in depletable
     resources for one region in a case other than the reference case illustrating the well-behaved
     nature of the SGM	2
Figure 14 Marginal abatement cost curves for the United States energy system generated with a
     series of constant-carbon-price experiments	2
Figure 15 Historical and projected normalized GNP	2
Figure 16 CO2 emissions in units of million tons of carbon in the reference case with a zero
     carbon fee and the responses of CO2 emissions to carbon fees of $10, $50, $100, and $200
     per ton carbon	2
Figure 17 Response of CC^and carbon-equivalent emissions in units of million tons of carbon to
     carbon fees of $100 per ton carbon	2
Figure 18 Response of CC>2 emissions in units of million tons of carbon from oil, gas, and coal
     combustion to carbon fees of zero versus $100 per ton carbon	2
Figure 19 Response of carbon-equivalent emissions in units of million tons of carbon from energy
     production, energy transformation, agricultural and other production processes to carbon
     fees of zero versus $100 per ton carbon	2
Figure 20 Response of carbon-equivalent emissions in units of million tons of carbon from
     agricultural processes to carbon fees of zero versus $100 per ton carbon	2
Figure 21 Carbon-equivalent emissions in units of million tons of carbon from industrial
     processes responding to carbon fees	2
Figure 22 Emission stabilization levels in units of million tons of carbon set exogenously and
     reached as model output	2
Figure 23 Market prices for carbon when exogenously set emission stabilization levels are
     attained. Note that the steep curve is for the carbon price when only energy production and
     agricultural carbon-equivalent emissions are mitigated but for landfills;  no industrial
     emissions are mitigated	2
Figure 24 Emission pathways due to the energy sectors when carbon-equivalent emission limits
     are imposed	2
Figure 25 Emission pathways due to the agricultural sector when carbon-equivalent emission
     limits are imposed	2

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Figure 26 The vintage-specific (vin-3 through vin-0) technical scale coefficients over time that
     relate the agricultural input to production in the reference case	2
Figure 27 The vintage-specific technical scale coefficients (vin-3 through vin-0) over time that
     relate the agricultural input to production. The vintage-specific technical scale coefficients
     are shown (1) when all sectors are impacted by a carbon price and all carbon-equivalent
     emissions are mitigated (CE_all) and (2) when all sectors are impacted by a carbon price
     and the energy production sectors and a limited number of agricultural processes are
     mitigated (CE_ind) (no landfill mitigation and no industrial processes mitigation)	2
Figure 28 Historical and projected electricity generation in the USA. in billion kilowatt hours.... 2
Figure 29 Historical and projected CC>2 emissions in units of million tons of carbon from the
     combustion of fossil fuels from electricity generation	2
Figure 30 COj emissions in units of million tons of carbon from the combustion of fossil  fuels
     from electricity generation	.'	2
Figure 31 CO2 emissions in units of million tons of carbon from the combustion of fossil  fuels
     from electricity generation when carbon fees are imposed of $100 per ton carbon	2
List of Tables

Table 1 Regions in the SGM	2
Table 2 Production sectors and sub-sectors in SGM 2003	2
Table 3 Relationship between vintages (v) and times of operation (t)	2
Table 4 Variable values at the end of the last iteration of the market solving algorithms when
     carbon policies are based on carbon emission limits	2
Table 5 Emissions sources, drivers and control options	2

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Chapter 1.  The Second Generation  Model

The Second Generation Model (SGM) is a computable general equilibrium model designed
specifically to analyze issues related to energy, economy, and greenhouse gas emissions. It has
14 global regions, multiple greenhouse gas emissions, vintaged capital stocks, explicit
connections between technology and the economy, disaggregated to a degree to reflect the
relative importance of sectors in determining greenhouse gas emissions. The SGM is maintained
at the Joint Global Change Research Institute, operated by Pacific Northwest National Laboratory
and the University of Maryland. .

The SGM projects economic activity, energy consumption, and greenhouse gas emissions for
each region in five-year time steps from  1990 through 2050. It is designed specifically to address
issues associated with global change, including (1) projecting baseline carbon-equivalent
emissions over time for a country or group of countries; (2) determining the least-cost way to
meet any particular emissions constraint; (3) providing a measure of the carbon price, in dollars
per metric ton carbon; and (4) providing a measure of the overall cost of meeting an emissions
target.

Below we present a quick overview of the chapters that follow. The chapters describe in detail all
model processes simulated in SGM 2003.

Chapter two explicates two basic features of the SGM: the basic structure of the SGM, that is, the
regional hybrid commodity-by-commodity input-output table and a summary of the SGM's
approach to investments and capital stock. The SGM data requirements are such that for
timesteps of five years a regional hybrid commodity-by-commodity input-output table can be
solved for a set of prices that clear the markets. The table is hybrid in that it expands a traditional
economic input-output table to account for an energy balance. Data on the relationship between
monetary units and energy units is therefore a prerequisite, as are base year data on capital stock.

As in a typical computable-general-equilibrium (CGE) model, each commodity produced is
associated with a production sector represented by a production sector "column" in SGM's input-
output table. In Chapter three we describe the production functions employed so that future
values in the input-output tables can be projected. All production in the SGM takes place with
either a constant-elasticity-of-substitution (CES) production function, or a fixed-coefficient
(Leontief) production function. These  are constant-returns-to-scale production functions, but they
are operated with one fixed input, capital.

Chapter four describes the price calculations. The model must find a set of prices for which
demands by producers and consumers for goods, services and primary factors of production are
consistent with domestic production and imports/exports. These price calculations need to  work
not only for base case scenarios but also under large changes in relative prices induced by carbon
management strategies. Chapter four also describes how price expectations over the lifetime of
plant and equipment are formed and used.

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Chapter five describes how technical change is implemented in the SGM. In brief, technical
change is imposed on the scale coefficients of the input-output table that relate the supply sectors
to the production sectors. In addition, we describe how autonomous efficiency improvements are
imposed on energy use in households and the government.

Chapter six contains an explanation of how the production functions relate to profits and demands
and how they are operationahzed in the SGM, that is, how the operating vintages relate to the
technical scale coefficients and elasticities of substitution, including a description of how
elasticities of substitution are reduced between ex ante investment decision and ex post operating
decisions.

The model's representation of the competition among different technologies for fuel-specific
electricity generation is based on a logit share equation, which is also described in this section, as
are different aspects of depletable resources.

Chapter seven describes carbon policy options that can be implemented in the SGM. An
important consideration for any climate policy is the time it takes for capital stock to turn over.
The five-year time steps and capital vintages hi SGM allow simulation of important dynamics
with the introduction of a carbon price and the corresponding changes in relative energy prices.
Depending  on what carbon policies are implemented, investments, households, government
and/or trade flows may be affected. SGM regions are operated together when a carbon emission
target is set for a group of regions and carbon emission permits are traded between those regions.
Carbon emission permits are traded at base year market exchange  rates.

Chapter eight describes the final demand sectors: investments, household consumption,
government consumption and trade.

In the SGM, capital may be allocated to new production activities  in one of two ways. The first
allocates capital as a function of the expected profit rate and previous investment. The second
allocates capital based on the expected profit rate and previous output.  Chapter eight also
describes how capital goods are produced by a Leontief production function.

The representative consumer (households) in the SGM supplies labor and land to other sectors,
and also acts as the owner of all capital stocks.  Income from labor, land, and retained earnings,
adjusted for taxes and government transfers, becomes household income. Income is split between
savings and expenditure, with a savings function that depends on the interest rate. Demand for
each good by households is calculated as a function of expenditure, income elasticity, own-price,
and price elasticity (the constant elasticity equation).

Government activity purchases goods and services.

Each region has a trade-balance constraint that must be satisfied within each model time step. In
the model base year, the trade-balance constraint is the same as the historical trade balance. The
model user has a choice as to whether this trade balance goes to zero over time or is kept qt the
base year level.
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Chapter nine summarizes the major aspects of the economy simulated in the SGM. GNP can be
calculated either as the sum of final demand or as payments to primary factors of production.

Chapter ten describes the solution procedure and illustrates how the SGM solves for excess
demand - the difference between demand and supply, and the market prices.

Chapter eleven contains a brief description of the calibration procedure that is employed for
calibrating SGM's outputs.

Chapter twelve contains a description of how emissions are calculated. Emissions are calculated
based on a production sector's emission activity, which is the product of the total demands by a
production sector and a conversion factor that converts monetary units to energy units. Carbon-
equivalent emissions are then calculated based on these emission activities' emission coefficients
and the emissions' global wanning potential coefficient.

In Chapter thirteen we provide for some results for the reference case for the USA as region.
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Chapter 2.  The  modeling framework: economic input-
output and energy  balance tables

The Second Generation Model (SGM) is a set of 14 regional computable-general-equilibrium
dynamic recursive (CGE)4 models, with an emphasis on energy transformation, energy
consumption, and greenhouse gas emissions. Regional models may be run independently or as a
system with international trade in greenhouse gas (GHG) emissions permits. Table 1 lists the
regions.
Table 1 Regions in the SGM
Annex I
United States
Canada
Western Europe5
Japan
Australia6
Former Soviet Union
Eastern Europe
Non-Annex I
China
India
Mexico
South Korea
Middle East
Rest of World
Brazil (as stand
other regions is
alone region; its trade with
not yet implemented)
Many of the 14 regional models, including Japan, China, India, South Korea, and Brazil, were
developed along with local institutions using local data. The models are then available to those
institutions for their own analysis. For example, SGM-Japan has been used within Japan in a
model comparison exercise of the cost of reducing GHG emissions.
4 Two types of CGE models exist: inter-temporal optimization and dynamic recursive. The SGM is an example of a
dynamic recursive model. The 2 types of CGE models differ primarily in the treatment of savings and gross investment.
Both types of models must allocate investment across sectors within a time period, but inter-temporal models also
determine an optimal time path of capital accumulation. Inter-temporal optimization creates an additional
computational burden, because all time periods are solved simultaneously; that burden usually limits the amount of
sectoral detail in a model with many regions. Savings and investment decisions are endogenous in inter-temporal
optimization models, making it possible for the trade balance to be endogenous. A dynamic recursive model is in a
narrow sense a sequence of static models with rules for determining the amount of savings and therefore the total
amount of new capital constructed in each time period. The SGM, is however, not simply static in that its decisions
involving capital investment and resource base utilization are explicitly carried forward to subsequent periods. The
trade balance must be exogenous in a recursive CGE model. In the SGM base year of 1990, each region is given its
historical trade balance for 1990. In subsequent model years, the modeler can either leave the trade balance at its 1990
level or bring the trade balance gradually to zero.

5 Germany can be run as a separate region

6 Australia can be replaced with an Australia /New Zealand composite region in SGM 2003.
PNNL11819: JA Edmonds, SH Kim, CN MacCracken, RD Sands, MA Wise. October 1997.
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Figure 1 illustrates in general terms the flow of goods and services in the SGM. Goods are
produced in the production sectors, which use the three primary factors of production: land, labor,
and capital.
                                                   Supply of Land, Labor, & Capital
                                                       Final Demand Sectors:
                                                        Government
                                                        Households
                                                        Investments
     Iroduction Sectors:
Intermediate Goods
                                 Product Markets:
                                  Energy
                                  Industry
                                  Transportation
                                  Agriculture
                                  ETE
Figure 1 The flow of goods and services in SGM


The flow of goods between industries and consumers in an economy can be described by means
of an input-output table in value terms {see Figure 2), which maps directly onto Figure 1. An
economic input-output table has three major sections: inter-industry flows, value added, and final
demand. An input-output table is organized with inputs as rows and activities (production) as
columns. Inputs include direct inputs and intermediate  (inter-industry) inputs (those derived from
a production process) and primary factors of production. The primary factors of production are
rental of land, labor income, other value added, and indirect business taxes.7 Activities that use
inputs are industries, and consumption by the final demand sectors: households, government,
investments, and net exports (exports minus imports).
7 Indirect business taxes, less subsidies, are modeled as a proportional tax on production.
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               Production Activities  Trade Inv Gov Hh
  Intermediate
  Inputs
 Primary
 Factors
                 Interindustry
                 Flows
Value Added
Figure 2 Typical input-output table


In the SGM, regional economic input-output tables are combined with regional energy balance
tables to create regional hybrid input-output tables (see also Miller and Blair 1985). Economic
input-output tables alone are not sufficient to determine the quantities of oil, gas, coal, electricity,
and refined petroleum that are produced and consumed. Supplemental information on energy
quantities is required to map monetary units from an input-output table to energy units needed to
calculate levels of greenhouse gas emissions.

                      Energy Inputs

   Production
   Imports
   Exports
   Electricity
   Oil refining
   Coking
   Agriculture
   Industry
   Transport
   Everything
   eIse(ETE>
     Sources
     Energy
     Final
Figure 3 Typical energy balance table
The International Energy Agency (TEA) compiles annual energy balance tables for both OECD
and non-OECD countries. These national energy balance tables show the basic supply and
demand data for all fuels expressed in common physical units. Moreover, these tables provide the
necessary information on the fuel interrelationships (see Figure 3) through conversions of one
fuel into another (IEA 1997) and they provide a consistent energy balance table format across
countries. Energy balance tables may be summed across countries to form energy balance tables
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for multi-country regions. The SGM uses IE A energy balances for all of the multi-country SGM
regions, and uses local energy data for all of the following single-country regions, United States,
Canada, Japan, China, India, Mexico, South Korea, and Brazil, given that the IEA energy
balance tables are not as detailed as may be obtained from these local governments.
Table 2 Production sectors and sub-sectors in SGM 2003

Everything Else (ETE)
Energy Production
Energy Transformation
Industry or Manufacturing
Transportation
Agriculture
Carbon
Sector
No.
2
3
4
5
9
10
6
8
11
12
13
14
15
16
17
18
1
19
20
21
22
23
24
' 25
26
SGM 2003
Sector / Markets
EveryThing Else sector
Crude oil production
Natural gas production
Coal production
Oil refining
Distributed gas production
Coke production
Electricity generation
Paper and pulp
Chemicals
Cement
Primary metals
Non-ferrous metals
Other industry and construction
Passenger transport
Freight transport
Other agriculture
Grains and oil crops
Animal products
Forestry
Food processing
Carbon prices and/or GHG emissions
Subsectors


Oil (8.1)
Gas (8.2)
Coal (8.3)
not active
Nuclear (8.5)
Hydro (8.6)


Land (Factor market)
Labor (Factor market)
Capital (Factor market) also called "other value added" or OVA
Economic input-output tables contain varying amounts of sectoral detail, depending on the
country, with anywhere from 30 to over 500 producing sectors. The tables are aggregated to the
level of detail that best matches the structure of SGM. Usually, an input-output table contains the
same number of producing sectors as there are intermediate inputs. This does not have to be the
case however because some industries may produce more than one product and some inputs
might not be produced domestically and must be imported. The number of production sectors and
markets simulated in the SGM is flexible. In the reference case, production sectors with markets
are implemented for the so-called "Everything Else" sector or ETE, three energy production
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sectors, four energy transformation sectors, five agriculture sectors, six industrial sectors, a
passenger transport sector, a freight transport sector, and a carbon sector (see Table 2).

Since the SGM is an energy model as well as an economic model, attention is paid to maintaining
energy balances as the model operates through time. An energy balance table is used for base
year calibration of energy production and consumption. Original units might be tons of coal
equivalent (China), tons of oil equivalent (International Energy Agency statistics), or calories
(Japan). The SGM uses joules for all energy units, expressed as either petajoules (PJ) or exajoules
(EJ).

The merging of an economic input-output table with an energy balance table presents a special
problem: oil and natural gas are a joint product from a single industry in input-output tables,
producing a single composite product. This is one area where energy balance tables provide
essential information to maintain a clear distinction between oil and natural gas consumption.


The following steps are used to create a hybrid commodity-by-commodity input-output table
from an economic input-output table and energy balance table (Sands 2002).
    1.   Put the economic input-output table in a format suitable for SGM. This involves
        aggregation across producing sectors and possible conversion to a 1990 base year.
    2.   Obtain 1990 energy balance table and convert units to joules.
    3.   Aggregate energy balance table across fuels to match the SGM format.
    4.   Rearrange activities (rows) within the energy balance table to match those of the
        economic input-output table.
    5.   Transpose the energy balance table so that rows correspond to fuel inputs and columns
        correspond to energy-consuming activities.
    6.   Create a hybrid input-output table where the energy rows (inputs) come from the
        transposed energy balance table and all other rows come from the economic input output-
        table. This table is no longer in value terms but is now considered to be in quantity terms
        with units of joules for the energy  rows and units of 1990 dollars (or other local currency)
        for all other rows.
    7.   Find a set of prices for all intermediate inputs that will rebalance the hybrid input-output
        table in value terms. By rebalancing, we mean that the value of output in each producing
        sector is equal to the total value of inputs.  A linear equation may be derived for each
        producing sector, resulting in a system of equations that can be solved to obtain a price
        for each intermediate input8. It is important to note that these prices are derived from the
        calibration process and are not historical prices. This reflects the SGM modeling
        philosophy  that assumes that technology characteristics, represented by the input-output
        and energy balance data, should determine relative prices in the  model, and not the other
        way around.
    8.   Finally, create a new hybrid (economic and energy information) input-output table in
        value terms by multiplying all quantities by their respective prices (paid). The resulting

8 These linear equations are sometimes referred to as zero-profit conditions.

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       commodity-by-commodity table elements represent quantities expressed in 1990 million
       dollars.9
    9.  Units for the non-energy inputs in the hybrid input-output table are usually redefined so
       that prices equal one in the base year.
    10. Thus, baseline information obtained consists of
       o  the regional commodity-by-commodity hybrid input-output tables, including land,
           and labor prices, information on capital for production sectors and taxes imposed
           (e.g., Appendix A)
       o  information on final demand sector supply and demands in the form of domestic
           consumption by households, domestic consumption by government, domestic
           investment, poss exports, and gross imports
       o  initial market prices are set to one (see Appendix A)
       o  energy price-converters (EJ per million 1990 regional currency; see Appendix A).

The final hybrid input-output tables provide regional representations of the economy that are
completely consistent with base year (1990 for SGM 2003) energy balances. Energy production
and consumption for each fuel will exactly match the quantities in the base year energy balance
table, and emissions can be calculated (Sands 2002).
Production and input-output tables in the SGM

Each region's base year input consists of a commodity-by-commodity hybrid input-output table.
Each column in the table represents a production process in the SGM, either represented by a
constant-elasticity-of-substitution (CES) or a fixed-coefficient (Leontief) production function.

Through changes over time in population and labor productivity, and through autonomous time
trends governing the efficiency of inputs in production processes projections can be made and
historical changes in GDP, fossil fuel consumption and electricity generation can be calibrated
against.

The hybrid commodity-by-commodity input-output table provides information on the use of
produced commodities in the production of other commodities. These interdependencies are the
basics in the computation of each production sector's production function technical scale
efficiency coefficients (Fisher-Vanden et al. 1993:6), along with value-added information in the
form of land and labor prices, and capital and tax information. Calibration of the production
function coefficients allows observations of benchmark years to be reproduced. When anticipated
technological change is incorporated in these coefficients, the model produces long-term
projections.

Appendix A shows an complete example of the input-output elements^Yy^v for all input supplies
(rows) and all production sectors (columns), including the electricity production subsectors, the
carbon sector and all final demand sectors, where; indicates the row number of the input in the
input-output table,./ represents the column number or production sector in the input-output table,
9 Appendix A provides essential information about transforming energy units (Joules) into monetary values (1990
dollars).
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jj represents the production subsector column in the input-output table, and v represents the
actively operating vintaged capital (technology). The input-output table represents a one-year
snapshot of the economy at time t; for the base year inputs v =/. Units are quantities in monetary
values. The summed input values XSiiV (Equation 1) for each of the regions are shown in Table 2
of Appendix A, showing the different regions' input breakdowns. Total production is the sum of
the intermediate products that are produced in a production sector / of technology vintage v
(A5^v); this summed production is the gross production of a commodity/ When subsectors jj are
simulated, as in electricity generation, commodity /' is calculated as the sum over the subsectors
(Equation 2).

         22
                                                                               Eq. 1
         26
         V
         2-
                  i,J,D,v
Eq.2
where
   i indicates the row number of the input in the input-output table,
   j represents the column number or production sector in the input-output table,
   jj represents the production subsector column in the input-output table,
   v represents the actively operating vintaged capital (technology),
   n is the number of active production subsectors where n < jj,
   Xijjj>v are die input-output table elements, which for the base year values are called Xyjj>v in the
documentation and when the model procedures are described are referred to as EDVyjj-v (vintage
v, production sector j, or subsector jj, and supply sector i, demands), and
   Xi-27jjj,v is the production sector or subsector indirect business tax; note that these are added
only for the production sectors (j=l:22), and not for the final demand sectors 0=24:27).

When equilibrium conditions exist, supplies (inputs) meet demands, and excess demand - the
difference between demand and supply - equals zero for all markets.

Besides input-output tables, key parameters needed are base year capital, elasticities of
substitution for the production sectors, and income and price elasticities for the final demand
sectors. Individual sector and subsector technologies are characterized by the annualized cost of
providing an energy service. Thus, additional data needed to determine the annualized cost
include in addition to capital cost, equipment lifetime, annual fuel requirements, the interest rate,
and other annual maintenance and operating costs.
 Investment and capital stocks

 The SGM operates in five-year time steps and keeps track of capital stocks in five-year vintages.
 At the end of each SGM time period, the model converts investment for each producing sector
 into capital stock, with the capital stock defined to be five-years' worth of investment. Each
                                            18

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4»
capital stock has a specified lifetime typically of four time periods or 20 years, the so-called
nameplate lifetime of a technology10; the vintage indicator v of a technology keeps track of the
operating technology capital stock's age. Four vintages are operating simultaneously at each point
in time, representing three operating old vintage technologies and one new technology that do
differ in efficiency. Once capital is created it remains with its original sector, subsector and
vintage until its planned retirement or when its profits are insufficient in meeting certain criteria.
Vintage-specific capital stock is operated across its lifetime without change in technical
efficiency.

Thus, the SGM in effect operates as a hybrid commodity-by-commodity input-output table that
gets solved by "clearing" its markets after supplies and demands are summed over its vintage-
specific determination of supply and demand. In the SGM production of supplies and demands
for consumption are determined separately, and the model has therefore has to reach equilibrium
through a solution algorithm that adjusts  market prices until excess demand — the difference
between demand and supply, is less than the solution criteria, which is typically a small number
(less than one but greater than zero). The solution algorithm needs only to access information on
price, supply  and demand to operate. SGM 2003 s solution  algorithm first uses a bisection routine
to bring individual markets closer to equilibrium and then uses a Newton-Raphson procedure for
final convergence (see also Appendix B). Newton-Raphson relies on partial derivatives of supply
and demand with respect to the unknown prices. Once the set of unknown prices is close to its
final solution, Newton-Raphson converges very quickly. Prices adjusted by the iterative solution
algorithm determine technology costs, demand for inputs, and sector outputs for a point in time.

Old capital has limited ability to respond to changing prices; this is implemented by imposing
short-run elasticities of substitution on the operation of old capital. New capital is assumed to be
more flexible than old capital in its response to prices. Long-run elasticities of substitution, with
values greater than short-run elasticities,  allow for this greater flexibility. Long-ran elasticities of
substitution are imposed when investment decisions are made and when new capital is operated.

Most production sectors use a single production function for each capital vintage. The electricity
sector, however, is divided into subsectors that represent alternative processes for generating
electricity such as gas-turbine, coal-steam, nuclear, or hydro. Market share within the electricity
sector is based on expected the rate of return to new investments. Technologies with the highest
expected rate of return receive the greatest market share.

The major behavioral components of the SGM model thus describe the relationship between
prices, production, and consumption of goods and services.  Prices that are solved for are
consistent with demands by producers and consumers for goods, services, and primary factors of
production. Energy production and consumption balance, such that emissions can be accounted
for. The behavioral components of the system are shown in  Figure 4.
                  10 The modeler has the option changing any capital stock's lifetime. The SGM has mostly been run with capital stocks
                  lifetimes of 20 years.
                                                             19

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                               H Prices: Current & Expected Future
Figure 4 Basic flowchart of the SGM model

Base year calibration of the SGM requires that we determine the quantities of capital needed for
all producing sectors by vintage. For a 1990 base year and a capital lifetime of 20 years, we need
four capital stocks which equal investment during the time periods 1971-1975, 1976-1980,1981-
1985, and 1986-1990. The following steps are used to create capital stocks for  a region.

    1.   Obtain historical time series of investment data for each producing sector (e.g., Figure 5).
    2.   Fit an exponential curve to the investment data for each producing sector. This provides
        for smoothing out the effects of recessions or other temporary deviations from a long-
        term trend. This also provides a way to extrapolate data backwards in time  if the
        historical time series of investment is not long enough to create all of the needed capital
        stocks.
    3.   Convert investment data to real 1990 currency (e.g.,  1990 US dollars) using a time series
        of GDP deflators.
    4.   Sum investment by sector across each five-year time period to create capital stocks with
        units of 1990 currency.

Figure 5 provides an example of annual investment data available for papermaking and paper
products sector in China. An exponential line is fit to the historical data for China to smooth out
the effects of a recession around 1990. The smoothed data are summed over five-year intervals to
create capital stock vintages.
                                            20

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 100 million yum
  (1290 yuwi)
~2
                                               ~

            1980    1982    1984    1986    1988    1990    1992    1994


Figure 5 Annual investment: paper making and paper products in China
                                              21

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 Chapter 3.   Production functions

 A basic concept in the economic theory of production is the production function. A production
 function is a quantitative abstraction of a technology's - or industry's - productive operations. A
 typical industry transforms inputs (capital, labor, energy, materials, and land) into output. The
 production function relates the maximum output q, to any given vector of inputs x,: that is,
 qj=f(Xi,t), where / is time, implying that the maximum output qj from a given set of inputs xt can
 change with time. Technological change  can increase the maximum output. Natural resource
 exhaustion or environmental constraints can decrease the maximum output (Reister et al.)

 All goods in the SGM are produced with either a Constant-Elasticity-of-Substitution (CES)
 production function or a fixed-coefficient (Leontief) production function. These are constant-
 returns-to-scale production functions11; they are operated with one Fixed input, capital in SGM
 2003. Thus, among the key parameters needed for the SGM are elasticities of substitution for the
 production sectors.12

 Oil refining is represented by a fixed-coefficient production function, as is electricity generation
 from its various energy sources, while most other production sectors are based on the CES
 production function.

 The production functions are described below. We describe in Chapter four "Prices and expected
 prices" and in Chapter five describe how operating vintages relate to the technical scale
 coefficients and elasticities. That information is required to understand the way in which the
 production functions relate to profits and demands as described in Chapter six.
 Production functions, vintages, and the input-output matrix

 The hybrid commodity-by-commodity input-output table, excluding the final demand sectors,
 provides representations of the inputs i (rows), to a production process in any sectory or subsector
jj (columns). For each input there is an associated price and quantity. Each production process is
 tracked for its lifetime by vintage v; each vintage is the accumulated capital stock over 5 years of
 investment. Once capital is created, it must remain within its original sector or subsector and can
 be operated until its retirement.

 The primary advantage of this vintage structure is to better describe technical change over time
 and provide the option for putty-semiputty and putty-clay behavior in capital stock (Kim 1995:37)
 (putty for flexible; clay for fixed). Because capital stock cannot shift from one  sector to another,
 new technologies affect productivity only at the margin; once a technology is installed, capital
 11 " 'Returns to scale' describes the output response to a proportionate increase of all inputs" (Henderson and Quandt
 1971:79).

 12 The elasticities of substitution for the reference case for the USA for the production sectors and the income and
 price elasticities for the final demand sectors can be found in Appendix A.
                                            22

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                  costs no longer matter. To operate or idle a technology depends solely on the ability of the
                  technology to recover its current operating expenses plus taxes less subsidies.

                  Vintaging is associated with the SGM's five-year time steps (Nstep), that is, each vintage
                  represents 5 years of investment. For the base year 1990, v equals zero, implicitly representing
                  investments from 1986 through 1990, while older vintages are represented by negative integers.
                  Vintage v~-I represents investments from 1981 through 1985, etc. Table 2 illustrates the
                  relationships between SGM's four vintaged production sectors and subsectors that are operating
                  and the 12 time steps the SGM executes after the base year13.
                  Table 3 Relationship between vintages (v) and times of operation (t)
o

Year
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
t=
0:12
I
Q
1
2
3
4
5
6
7
8
9
10
11
12
Operating new vintage
(new vintage operates
with long-run elasticities
of substitution)
att=0forv=0
att^l forv=l
att=2forv=2
att=3forv=3
att=4forv=4
att=5forv=5
att-6 forv=6
att=7forv=7
att=8forv=8
att=9forv=9
att=10forv=10
att=ll forv=ll
att=12forv=12
Operating old vintages
(old vintages operate
with short-run elasticities
of substitution)
at t=0 for v=-3. -2, -1
att=l forv=-2, -1,0
att=2forv=l,0, -1
att=3 forv=2, 1, 0
att=4forv=3, 2, 1
at t=5 for v=4, 3, 2
at t=6 for v=S, 4, 3
at t=7 for v=6, 5, 4
at t=8 for v=7, 6, 5
at 1=9 for v=8, 7, 6
att=10forv=9, 8, 7
att=ll forv=10, 9, 8
att=12 forv=ll, 10,9
                  CES production by vintage
                  The Constant-Elasticity -of-Substitution (CES) production function is a well-behaved
                  homogenous, generic function that enables minimum coding for a wide range of analysis (Kim
                  1995:37). The CES production function has a constant return to scale;14 that is, output response is
                  proportional to an increase of all inputs. Total factor production is determined by a growth rate
                  applied to the technical scale coefficient (oo^yand cfyj/.v) of the CES production function,
                  affecting all factor demands equi-proportionally.15
                  13 The model is structured such that nameplate lifetimes of various sizes can be input and additional vintages are
                  simulated.

                  14 "If output increases by the same proportion, returns to scale are constant for the range of input combinations under
                  consideration" Henderson and Quandt 1971:79.

                  15 "A production function which belongs to the CES class has 2 major characteristics:
                      (1)  it is homogeneous of degree one, and
                      (2)  it has a constant elasticity of substitution."  Henderson and Quandt 1971:85
                                                              23

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Sands (2002), Kim (1995) and Edmonds et al. (1993) formulate the CES production function16 in
the SGM as follows:
                  'N-l
                      Xfy      Y
                        i.j,j}.>   iJJ.
                                                                 lip
                                                                                      Eq. 3
where for each production sector/, or subsectorjy and each operating vintage v,
   qjjj(V is the output or gross production of commodity j or jj produced by vintage v capital stock,
which is stored in array PROV,^ in the SGM computer code and referred to as such in the
documentation,
   i is an indicator of an input to vintage v's production of commodity j or jj,
   N is the total number17 of inputs i (26) in SGM 2003; if i equals 26, then i, in our case, refers
to the one fixed factor in the model, capital,
   N-l is the number of variable inputs,
   
-------
   X,jjjiV is demand for input i in vintage v's production of commodity j or jj; this demand is
denoted by X^ in the base year in the documentation and stored in array EDVijjj>v in the SGM
computer code and denoted as such in the documentation when not referring to the base year,
   Xj_26jjj,v is the demand for the fixed (capital) input in vintage v's production of commodity j or
jj, and
   p is a function of the elasticity of substitution parameter, a, where p = (a-l)/a and a=l/(l-p).
Long- and short-run elasticities

The output of a CES production function is dependent on the elasticity of substitution, as shown
in Equation 3 (see also Henderson and Quandt 1971: Chapter 3). In the SGM, when capital is
operated as a CES production function, new capital operates under long-run elasticity, and all
older vintages of capital operate under short-run elasticity. This means that new capital (new
vintage) has a higher elasticity of technical substitution among inputs in response to changes in
prices than old capital (old vintage). The type of technology simulated in the SGM in that case is
so-called putty-semiputty technology.18

Sands (2002) summarizes how elasticities of substitution, a, must satisfy the following
relationship

 0
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isoquant is tangent to a line showing all combinations of equal expenditure on inputs. The slope
of this line is the ratio of prices for the two inputs. A representative line of tangency is also
shown.
                                         Input 1
Figure 6 Putty-semiputty isoquants


During each SGM time period, new capital is formed. At the time of capital formation, the
isoquant with the greater elasticity of substitution is used. However, at the end of the SGM time
period, capital is converted from a higher to a lower elasticity of substitution. Once capital is
constructed in SGM, substitution possibilities between inputs are limited.

A putty-clay technology assumes that old capital is fixed-coefficient and the input-output
coefficients do not respond to price. The input-output coefficients reflect relative prices that were
in effect when the capital was new. Therefore, new capital is responsive to prices (putty), but
input-output coefficients are locked into place as the capital is converted from new to old (clay).
Isoquants for a putty-clay technology are  shown in Figure 7.
                                          Input 1 -
Figure 7 Putty-clay isoquants
                                            26

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The Leontief or fixed coefficient production function

Some technologies are considered to be fixed-coefficient19 and have a Leontief functional form
whether new or old, and their mix of input factors of production is not responsive to prices. This
technology is referred to as clay-clay or simply clay. This assumption is sometimes used in the
energy transformation sectors, especially oil refining, where the ratio of energy input to energy
output is fixed in advance by physical processes and cannot respond to changes in price. All
electricity subsectors are fixed coefficient.

When a Leontief production function is implemented, an industry/ oijj chooses the minimal
amount of all intermediate and primary inputs / to produce output, leaving quantities of the inputs
beyond the minimal amount idle (Chung 1994:170; Henderson and Quandt 1971:336).
The Leontief production function can be described as follows:
mmfe^
    V'
                                 y
                                 ^
                                                                                 Eq.5
where for each production sector j, or subsector jj and each operating vintage v,
   qj jj,v is the output or gross production of commodity j or jj produced with vintage v capital
stock, later in the documentation denoted by PRDV,jj,v,
   i is the input to vintage v's production of commodity j,
   N is die number of inputs i (N=26); if i equals 26, then i refers, in our case, to the one fixed
factor in the model, capital,
   Vjjj,v is a technical scale coefficient in vintage v's production of commodity j or jj reflecting
the overall production efficiencies of die vintages of production sectors j or jj,
   0 indicator denotes that the parameter (in this case the technical scale coefficient X) impacts
the production sector as a whole,
   X;j jj v represents the technical scale coefficients, and
   X,jm>v is demand for input i in vintage v's production of commodity j or jj; mis demand is
denoted by XyiJJiV in the base year and by EDV,jjjiV in the forecasts, where jj denotes a production
subsector.
19 The elasticity of substitution (a) in CES production functions has a practical lower bound of 0.05 in economic
models such as SGM. Elasticities less than 0.05 result in numeric overflows or underflows in double-precision. Fixed-
coefficient production functions in SGM have an elasticity of substitution of exactly zero. Therefore, there is a range of
substitution elasticities between zero and 0.05 that the SGM can not simulate.
                                            27

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Chapter 4. Prices and  expected prices

The model must find a set of prices that is consistent with demands by producers and consumers
for goods, services, and primary factors of production. In Chapter ten we detail the market price
solution process, but here and in Chapters five through nine we describe the details of the costs of
operating capital and the various aspects of demand simulated in the SGM,

Base year prices and initial future  prices

In the SGM 2003 model runs, the base year market prices are set to one (Pu=0=/), given that base
year input is based on equilibrium and Walras' Law  guarantees that (1) if an equilibrium set of
prices exists, any positive scalar multiple of each of those prices is also an equilibrium set of
prices and (2) any commodity can be chosen as  a numeraire,21 which in the SGM is the
commodity of the Everything Else sector. Future prices are determined relative to the price of the
Everything Else sector, for which market prices remain one in the projections.

Initial, base year capital interest rates  (J=2<5) equal 0.06; land rental prices (i=24) do not play a
role in the example data set and prices are set to zero. When land plays a role in SGM, the initial
market price of land rental, Pi~24-is,t, is calculated based on the total land available as supply and
land demand (i=24; see Equation 6).
p     = _   i-2^i.
ri=24=U,t  pp.
         C'Li=24=ls,j=27=hli
where
   XSj=24-isis the summed (total) demand for supply of land in the base year and
               as the total demand for supply of land (see "Households").
Similarly, the initial market price for labor, Pt=2}-a>s,t — the cost of by ing a year's worth of one
laborer's time, i.e., the average annual wage of labor— could be calculated 0=25; see Equation 7)
and should deliver the same results as the input parameters listed for the reference case; thus,
labor's market rental price is not set to one.
where
   XSj-25-ibsis tile total demand for supply of labor in the base year, and
   EDi=.25=ibsj=27=hhis the total demand for supply of labor (see "Households").
20 "If all the commodities in an economy are included in a comprehensive market model, the result will be a Walrasian
type of general-equilibrium model, in which the excess demand tor every commodity is considered a function of the
prices of all the commodities in the economy" Chiang (1967:52).

21 Numeraire: " A unit of account, or an expression of a standard of value. Money is a numeraire, by which different
commodities can have values compared" (Pearce 1992); Oxford: Numeraire - good used as a standard value for other
goods. The price of the numeraire is defined to be 1.

                                            28

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O
                 In the base year market prices equal one (Pif,=l), with the exception of labor; market prices in the
                 projections result from the market solution processing but can be set exogenously. The prices for
                 crude oil, land rental and the Everything Else sector are set exogenously in the reference case; the
                 gas market price is also set exogenously, assuming that they are set globally and not regionally as
                 in the example carbon policy run to be discussed in Chapter thirteen. When market prices are set
                 exogenously they retain their exogenously set value in the market solution process.

                 For the base year, prices received for commodity/ produced in a production sector are calculated
                 from the difference between the total demand for / inputs minus the  indirect business taxes paid
                 (/=/:27~1:N+1), divided by the total demand for / inputs. Prices received for a production sector
                 commodity/are identical for all subsectorsj/.
                          N+l

Pr    —-tl-
rrj,t-o —
                                N+l
                                                                                               Eq. 8
                                IX,
                                     1.J.JJ."
                 where
                    ZXjjjj,v is the summed over N+l demands for inputs i in the production of commodity j or jj
                 (see Equation 2), which includes
                    Xj-N+ijjj.v, the indirect business tax from the hybrid commodity-by-commodity input-output
                 table, which is a production sector- or subsector-specific input parameter which needs to be
                 substracted.
Determining prices paid for supplies by producers, prices received
for produced commodities, and policy potential
                  For a closed economy, the price paid by producers for supplies at each point in time includes
                  transportation costs, taxes and adjustments.

                  Prices paid for the variable inputs (1=1:23) from the »'* supply sector for each of the actively
                  producing vintages v for sectors/=7:22 and subsectors jj=l:6 at time t are calculated as follows:
                                                        ijjj +Txadd,ijLj +CpfJ
                                                                              Eq. 9
                 where
                    adjijaj,t, is a time-period-dependent adjustment factor that reflects markups and intra-regional
                 transport costs; these adjustment factors can be input i and sector j or subsector jj specific; adj,
                 is further described in Equation 1 1,
                    P1>tis the market price; in the base year Pjit equals one; in the forecasts P(,tis calculated during
                 the model solution process and is supply and demand dependent,
                    Exlm, is a transportation cost multiplier, a rate parameter,
                    Txpro,jjj is a proportional tax rate on the i* product,
                            j is an additive tax on the i* product, and
                                                           29

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   Cpfj, is a carbon permit fee on inputs, i, per dollar of production based on the global warming
potential and the emission coefficient of a fuel; thus

   Cpfi = P,=23,i • ExchRateregion • ]T EMCfn • PRconvrt; • GWPfn                 Eq. 1 0
                                  fn
   where
      fn stands for oil, gas. or coal within a production process for which the energy supply
   carbon fee is calculated,
      Pj-23,t is the carbon price, which, dependent on if and which carbon policy is implemented
   may equal the market price during the model solution process, or may be fixed,
      ExchRatercgjon the monetary exchange rate,
      EMCfois the fuel-specific carbon content in million tons C per exajoule of the energy
   source; fn stands for oil, gas, or coal within a production process for which the energy supply
   carbon fee is calculated,
      GWPfn is the global warming potential; GWPfll=l for carbon,
      PRconvrti is the energy conversion factor, converting the relative prices in monetary units
   to physical energy units.

Note that PRconvrt for each supply sector in each region is expressed in energy units produced
(EJ) per million 1990 regional currency (that is, per gross production of a commodity j, which is
the sum of all intermediate products in the base year in 1990 million regional currency). Also
note that the final conversion factors are the results of base year calibration.

A time-dependent adjustment factor, adj,JJJ:S, reflects markups and intra-regional transport costs;
these adjustment factors can be input i and sector y or subsectorj/ specific. A (sub)sector-specific
price adjustment factor is calculated as a time-dependent interpolation of initial and terminal
values when fas number of time periods t times the time step of five years (Nstep) is smaller
than
where
   Adyjj, Tadjzyjj, and Adjzgj are input parameters and T is the number of time periods
multiplied with the time step (t*Nstep).

In most cases adj equals one. However, adj is included in the equation calculating the price paid
by the producer for inputs (Equation 9) to provide the model with increased flexibility in
describing the purchase price.

The proportional tax, Txpro, and additive tax, Txadd, can be input and (sub)sector specific; they
are presently only supply-price-specific, however.

By changing the different rates in the above price-paid equation, researchers can evaluate policy
scenarios. For example, carbon prices and energy excess fees can be imposed in the model by
                                            30

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changing Txaddar applying a carbon fee Cp/on the appropriate products whether they are fossil
fuels or energy services.
Technology specific discount rates Pii^apitaijjj,t may be adjusted over time as follows:
 Pi;
    =capital,j,jj,
Ljjj.t  = wedSej
i=capita!,j,jj,l
                                  li=26
                                                           Eq. 12
The wedge component of the technology specific discount rate can be considered an interest rate
wedge or discount rate. They can be calculated in the base year in a spreadsheet model for each of
the sectors and subsectors. A target profit rate for each (sub)sector is calculated based on
    o   all active capital (KA), and
    o   an expected profit rate weighed against zero profit by the sector where the expected profit
        rate calculations are based on the CES production function and long-run elasticity, a, and
        inputs from the IO table, which are based on base year information

The wedge component of the technology specific discount rate can be modified over time as part
of the calibration process (see also Chapter eleven).

Calculation of prices received (Pr^ for the production sector-specific commodities produced, in
relation to the market prices (P^, are first steps in the model evaluation, since they determine
operational and investment decision-making.

Prices received for a production sector commodity are identical for all subsectors. For the
projections they  are calculated as follows:

       P:, +Tri( • Exlm,
pr  = -*	1!	L                                                        Eq.  13
   '•'       1 + TxIBTj
where
   Pi>t are the market prices which are updated during the model solution processing and are
therefore time-period-specific,
   Exlntj is the transportation cost rate parameter (these input parameters equal one in the
reference case),
   TxIBTj is the production sector indirect business tax; these input parameters are constant over
time in the reference case, and
   TrJ-t is a time-period-dependent transportation cost factor.

The region-specific transportation cost factors are calculated as time-dependent interpolations of
initial and terminal values as long as T, which is the number of time periods multiplied by the
time step (T=t*Nstep, where Nstep equals 5 years), is smaller than TVz,.

TrA, = Tri. . (1 - —-) + TrZj • JL                                          Eq. 14
                  Ttrz'
            Ttrz;
where
   Trij, Ttrzj, and Trz, are input parameters.
                                            31

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The equations above are cycled through each row / and column./ and.// element of the input-
output matrix, and each of the vintage-specific Pi^t matrices are filled for each element of the
matrix at each point in time for each of the operating vintages. The model is solved after
summing the vintage-specific inputs to production and vintage-specific calculated demands.  Note
that prices for input to production are identical for all operating vintages and will be only
differentiated among production sectors by the adjustment factors adjij^, that reflect markups and
intra-regional transport costs, the proportional tax rates Txpro^ and the additive taxes
Expected prices

The simplest rule for projected future prices is to set them equal to current prices. Alternatively,
projected future prices can be based on a previous model run. A third option is to determine
expected prices as projected future prices discounted to the present. In the SGM expected future
prices for all variable inputs 0=7:25) are  calculated such that investment decisions based on
expected profitability can be made. The expected prices paid Pie^ (i=l:2S) for the next point in
time are calculated based on prices paid by producers for inputs (see Equation 9). These prices
are production sector- and production subsector-specific.22
                                                                                    Eq. 15
Expected prices received for the commodities produced by the production sectors and subsectors
are based on the prices paid for inputs (see Equation 9) and the prices received for commodities
produced (see Equation 13).
                                                                                    Eq. 16
where
         is the prices paid by the producer for supplies (see Equation 9),
   Prj>tis the price received for a commodity produced (see Equation 13),
   Pii-26jjj.i is the interest rate, which is production sector- and subsector-specific (Equation 12),
   Texp is the nominal life of the investment (years) and a parameter of technology, and
22 Note that the equations as described here are easily solved analytical equations and replace the original equation that
had to be solved iteratively (eq. 15 in Edmonds et al. 1993). The original equations were described as follows: Pej, for
time / is calculated as discounted price for product j (either an input or an output) by
where Texp is the nominal life of the investment; r} is the rate of expected price change; and dis is the discount rate.
The nominal life of the investment is a parameter of the technology. This parameter value may be different from the
maximum potential life of the technology. Both the rate of expected price change rt and the discount rate dis are
behavioral variables.
                                              32

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   Texp equals t»Nstep, where t is the number of time-step periods the investment is operational;
thus Texp=20 when t=4, given that SGM's timestep (Nstep) equals five years.

The difference between the expected prices for input supplies Pie^ and the expected prices for
the output products Pe^ is thus based on the difference between the price paid for input P;'
the price received for a commodity/ produced Pr^t at time t.
                                          33

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Chapter 5. Technical change

Technology is a central feature shaping anthropogenic greenhouse emissions. Given that
technology is "the broad set of processes covering know-how, experience and equipment, used by
humans to produce services and transform resources" (Edmonds and Moreira, 2004), technology
is a central issue in understanding climate change. Technology unifies the elements of the
system. Technology shapes many elements of SGM design. This chapter describes how technical
change is implemented in the SGM. In brief, technical change is imposed on the scale coefficients
of the input-output table that relate the supply  sectors to the production sectors.  In addition, we
describe how autonomous efficiency improvements are imposed on energy use in households and
the  government and the changes over time.

Input-output coefficients and their relationship to the technical scale
coefficients

The SGM keeps track of capital stocks in five-year vintages. Vintage-specific capita) stock is
operated across its lifetime without change in technical efficiency. The four vintages operating
simultaneously at each point in time represent three old vintage technologies and one new
technology. Old and new vintages may be characterized by different elasticities (denoted by "a")
of substitution given that new capital can be expected to be more flexible than old capital and its
elasticity of substitution will therefore be greater than or equal to the corresponding elasticity of
substitution for old capital.

The SGM's framework is a hybrid commodity-by-commodity input-output table in monetary
values where for energy the input-output dollar values remain related to the per-joule cost of
energy.

The relationship between input-output coefficients (denoted by "a") and the technical scale
coefficients (denoted with "a" for a CES production function and with "A" for a Leontief or
fixed-coefficient production function) that are implicit in an input-output table was described by
Sands (2000) and can be summarized as follows. The physical input-output coefficients can be
derived from a hybrid input-output table for each combination of input and production processes.
An  input-output coefficient is the quantity of input divided by the quantity of output. The quantity
of output is found by dividing the value  of output by its price. Similarly, the quantity of input is
found by dividing the value of input by its price.

In the special case of fixed-coefficient production, the technical coefficients of the production
function are related to input-output coefficients in a very simple way which is independent of
price:

^.±

where
    Xoj are production sector-specific technical coefficients,

                                          34

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   Xjj are technical coefficients that can incorporate technology-specific (i.e., non-neutral)
technical change parameters.

In general though, input-output coefficients are related to the technical coefficients of production
functions through prices. The production process should substitute away from inputs that become
relatively more expensive. The rate at which one input is substituted for another, relative to the
rate of change in prices of those inputs, is accomplished through the implementation of the
elasticity of substitution among inputs in production. In a constant-elasticity-of-substitution
(CES) production function, this elasticity of substitution remains constant across changes in price.
Equation 18 shows the dependence of input-output coefficients on CES technical coefficients,
relative prices, and the assumed elasticity of substitution. In the SGM we invert this relationship
and solve for technical coefficients as a function of input-output coefficients, prices, and the
elasticity of substitution.
                                                                                 Eq. 18
where
   3ij is the amount of input i required per unit of output j; aij is called the input-output
coefficient when dealing with input-output matrices,
   
-------
The SGM contains a large set of parameters that can be used to simulate technical change over
time for any given production sector. Separate parameters are available for each input to each
production process (and each vintage)24. The rates of change in input efficiency can be varied at
each five-year time step in the SGM. For example, we could assume that energy efficiency in
coal-fired electric generating plants is improving at a rate of 0.5% per year for 10 years, with no
change after that. These technical change parameters are very powerful in determining energy
consumption and emissions in a reference case, the impact of which is similar to the Autonomous
Energy Efficiency Improvement (AEEI) that is used in some other energy models. In the SGM,
exogenous rates of technical change can be specified for all inputs to production, not just energy.

In the case of Hick's neutral technological change, all  of the a or technical scale coefficients (the
parameters that relate the inputs to the production processes) within a production function are
assumed to change at the same rate. Isoquants for the case of two inputs with neutral technical
change are shown in Figure 8. Note that as technology improves from Ta to T2, the isoquant
moves inward toward the origin, showing that less of each input is required to produce one unit of
output.
                           Input 1
Figure 8 Neutral technical change when the elasticity of substitution coefficient (a) equals 0.5


Instead of adjusting OQ to represent technical change, each of the av parameters can be adjusted
with its own technical change parameters. If the rale of change in efficiency varies across inputs,
then technical change is said to be non-neutral or biased.

Figure 9 provides an example of biased technical change, with the isoquant shifting in towards
the origin, but at different rates for different inputs. For example, we could have a technology for
which labor productivity is improving at a faster rate than energy efficiency. In this case the
amount of labor needed per unit of output is falling faster than the amount of energy needed per
unit of output.
24 The technical scale coefficients remain constant over the lifetime of the vintage, while they differ among vintages.
                                           36

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                               Labor -
Figure 9 Biased technical change when the elasticity of substitution coefficient (a) equals 0.5


If the production process is fixed-coefficient, then these technical change parameters A can be
used to precisely control input efficiency. However, most production processes are not fixed-
coefTicient, at least in the long run as old capital is replaced by new capital. Most production
processes respond to changes in prices of inputs by substituting away from those inputs that are
relatively expensive. In this case, input efficiency is affected by both the exogenous technical
change parameters described in this section and by changes in relative prices. Changes in input
efficiency are a combination of exogenous technical change and price-induced technical change.25
Exogenous technical change is represented by a shifting isoquant; price-induced technical change
is represented by shifts along an isoquant.

Besides production efficiency, there are parameters that determine land, labor, and capital
productivity. Labor productivity parameters are the primary determinants of economic growth in
SGM and are used to influence the time path of GDP in a reference case. Both energy efficiency
and labor productivity assist in constructing reference scenarios. The labor productivity
parameters are used to determine a time path for GDP and the energy efficiency parameters are
used to determine consumption efficiency of energy by fuel (see also Chapter eleven).
How technical change is operationaiized in the SGM
For each region technical change parameters for each sectary, each subsectorj/, and each time
period t determine the efficiency improvements in energy production, energy transformation (e.g.,
oil refining, gas processing, coal and electricity generation), industry, transportation and
agriculture, and the efficiency of labor productivity, land productivity, and capital.

The TECHNN parameters or y parameters are set to identical values for all industries, while coal
production, gas production and distribution, oil refining and electricity production have their
25 Note that the SGM does not attempt to simulate induced technical change. In that case, an isoquant would shift
inward in response to a change in prices or some other policy signal, perhaps with a time lag.
                                           37

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unique efficiency parameters (see Appendix A for example values). Technical change over time
is calculated as a multiplier called Factor of the technical scale coefficients a for the CES
formulation and A for the Leontief formulation.

Factoi^, = Factor, j^., • (1 + TECHNN)N"e>'                      (unitless)   Eq. 19

where
   Nstep is the time step of 5 years,
   t denotes the number of 5 year time steps since the base year; in the base year t=0,
   Parmname (TECHNN or y) indicates the sector-, or subsector-dependent regional technology-
dependent technological rate change (unitless).

Technical change parameters are also implemented for household and government fuel use such
that improved energy-use efficiency can be simulated.

Household (j~hh) fuel-use changes over time are calculated by means of the following factor, the
implementation of which is discussed under "Household Demands":

Factor,.,,, = (1 + HHAEEI^-


where
             , is a technical change parameter for household fuel use.

Government (/=gv) fuel-use changes over time are calculated by means of a similar calculation:

Factor. vt =(1 + GVAEEL  )N'tep
       '>gv''                1>g                                       (umtless)    Eq. 21
where
   GVAEEIi,gv is a technical change parameter for government fuel use.

Implementation of me government fuel use factor is discussed under "Government Demands."

Technical change as described above is implemented in exactly the same way for all production
functions in me SGM. Thus, Factor is used as a multiplier of a technical coefficient such that a
change over time in technology is simulated.


The technical coefficients (ay) in the CES production function

The technical scale coefficients (cty) are extracted from CES production functions for the base
year as follows:
                              £
                             V    p:.
                                                                            Eq. 22
          v         /P          P
          yVi=ETE,j,iJ,v ' ri=ETE,t )    ri=ETE,t
                                         38

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where
   v equals zero for the base year,
   Oijjj>v is the technical coefficient of the invariable input in the production of commodity j or jj,
   i denotes the variable input (i=l :22),
   j or jj denotes the production (sub)sector commodity output,
   Xjjjj,v is demand for the i* input in the production of commodity j or jj {each X,^ is a value of
the input-output table in the base year, which comprises the input-output values within the
regional hybrid commodity -by -commodity input-output table in value terms (in monetary units)
by row i, column j, subsector {column jj) for electricity, and region L,
   Pj,t is the market price, which equals one in the base year,
   Xi-ETEjjj.v is the demand for the Everything Else sector input in the production of product j or jj
in the base year,
   Pi-ETB.1 for the base year is the market price of the Everything Else sector and equals one,
   p is a function of the elasticity of substitution parameter a, a unitless input parameter that is a
base year  long-run elasticity of substitution for each production sector, where p = (cr-l)/a and n if
expressed in terms of o then p. =  a-1; thus, p/|J. = I/a.

Note that the alphas are extracted without consideration of vintage. The vintage indicator is set to
zero (v=t=0). It is assumed that total output from production sectors is produced from one
vintage (i.e., total production can be described by one CES production function) rather than from
a summation of multiple vintage-specific CES production functions in the base year (Fisher-
Vanden 1993: 14). Formulation of that assumption is a normalization of the technical scale
coefficients after the the fixed factor capital stock technical scale coefficient is calculated based
on data on prior active vintage stock.
The production sector-specific technical scale parameters
The production sector- and subsector-specific efficiency coefficients (aojj;,v) are calculated for the
base year as follows:
an
                                                                                 Eq. 23
where
   v=0 for the base year,
   Pojjj/Pi-ETE,t is the normalized price index for commodity j or jj,
   Pi-EiE,tis the market price of the numeraire sector ETE, which equals one,
   £Xijjj,v is the summed over N+l base year demand (variable plus fixed factors + the indirect
business taxes) for the inputs i in the production of commodity j or jj (see Equation 2),
          j.v is demand for the ETE input in the production of commodity j or jj,
          the price received for commodity j produced in a production sector. These sector prices
are calculated from the difference between the total demand for inputs i minus the indirect
business taxes paid (i=l :27=1:N+1), divided by the total demand for inputs i for the base year:
                                            39

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        N+l
           'X-    —'
      	  i=l                                                                       T-*  * A
  O.JLJJ	N+i	                                                   Eq-24
where
   v=0 for the base year,
   ZXjjjj>¥ is the summed over N+l demands for the inputs i in the production of commodity j or
jj (see Equation 2) in the base year, which includes
   Xi-N+ijjj.v. the indirect business tax from the hybrid commodity -by -commodity input-output
table, which is a production sector- or subsector-specific input parameter which needs to be
substracted.
The fixed-factor-specific scale coefficients for ca
The fixed-factor-specific scale coefficients for capital stock (Oi-26-cVitaijjj,v) for each production
sector./ and subsector // for the base year are calculated in steps and are a direct result of SGM's
profit-making assumption:
            / N+l                          \P
ai=26,j,ii,v
                          V=:-3
                                                                                 Eq.25
where
   ZXijjj,v is the summed demand for the inputs i in the production of commodity j or jj in the
base year and v equals zero for the base year,
   KApriorjjjiV is the vintage capital stocks that is active prior to the base year 1990, and
   Zjjj(V is calculated as follows for the base year when no or zero profit expectations are
incorporated:
                                                                                     26
                                .=1 V.     U-i=ETE,j,jj,v
   where
      v equals zero in the base year,
      POJJJ is the price received for commodity j or jj in the base year (see Equation 24),
      aojjj,v reflects the overall production efficiency of the vintage,
      Pi,tis the market price, which equals one in the base year,
      
-------
Ct;
         N=26
                        fori=l:26andj=l:22
                                                                                  Eq. 27
          i=0
The production sector-specific efficiency parameters,
                     \i/p
                                                        are re-calculated as follows:
an
              O.J.JJ.V
           N=26

         V  i=0
                                                                                 Eq. 28
The vintage alphas and incorporation of technical change
The vintage alphas are calculated in three steps:

(1) First, assumed future technical change is incorporated. All alphas (i=0:26;j=]:22;jj=I:6),
from the oldest vintage (v=-5) through the time zero vintage (v=t=0), o^v-j.-o, are set equal to
fXijjj^o, which are calculated as shown above (Equations 22 through 27) and all alphas for the
variable factors and for capital stock are projected into the future (t=l:12) as follows:

                   >FaCt0r
                          '.J.JJ.t
                                                                                  Eq. 29
where
   v equals t-3:t,
   ai,j,jj,v-i,the previous vintage-active alpha, is updated for each time period by implementing the
technological change assumptions:
    Factor , js .  = Factor; ; „ , , • 0 + Tech s ( .... ) Nstep     ,    _    .    , _.
          i,j.jj.t          '.j.jj.i-1   v         '.jjj'        (see Equation 19)
   where
      Nstep is the time step of 5 years, and
      Techi j jj  is the production sector-dependent regional technology -dependent technological
   rate change, which for aij jj,v is referred to as Parmname, and
      p is a function of the production sector-specific long-run elasticity CT.
Note
                    1 in the base year when t-0.
(2) Second, the overall production efficiency, a
-------
where
   p is a function of the long-run elasticity of substitution and equals (o-l)/o.

(3) Third, the alphaos (oo^v) for all production (sub)sectors (/' and //), all vintages (v) and time
periods are set to one after being "used" in the equation above. This allows alphao to be used for
energy supply calibration.
and

                   r*"=1                                                         Eq.33
Imposing changes in elasticities of substitution
When capital becomes "old vintage" the technical coefficients' long-run elasticity v=KApriorjjjiV and in the projections KA^is set equal to the linearly interpolated annual
capital investment flow over a five-year period (from the current point in time back to the
previous model solution-point in time [see Equation 118]).

    KAjJJV=KApriorj>JJ;V                                                       Eq.35

The vintaged-specific production sector or subsector-specific technical scale coefficients (for
i=l:25 and j= 1: 22; foTjj=I:6 if active) for old vintages are calculated as follows:

                              [•v(

                        rPH
                        rliJ,JJ.'- J
where
   v equals  t-3:t,

                                             42

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                     a, jjj>v, is based on the calculation in Equation 28,
                     Piyjj,t are the prices paid by the producer for supplies (see Equation 9),
                           the price received for a commodity produced (see Equation 13).
                   All alphas, including alpha for capital interest (/=2<5) are then once more transformed before
                   being used in the calculations when operating old vintages (see "Profits, demands, expected profit
                   rates, and the operation of capital").

                   acst^^fa^J170-^                                                       Eq.37
                   where
                     v equals t-3:t,
                     a0j,jj,v equals one,
                     ayjj.v is based on its last transformation in Equations 34 for capital costs and in Equation 36
                   for the variable factors, and
                     er2 is the short-run elasticity of substitution, which can also be expressed as
                   l/(l-p2)
                   and
                  where
          a0>J,v     -1                                                          %38

   p2 is a function of the short-run substitution elasticity [p2=(cr2-l)/ o2].

Note that after the transformation processes the adjusted aoj,v for each production sector is set to
one.

The technical coefficients (Ay) in the Leontief production function

For potential substitution of each of the production functions' technical coefficients based on the
CES production function (ODJ^V', &ijjj,v', M,V, ^f-capuaij^, the Leontief technical
coefficients are calculated. These Leontiefs are, as are the alphas, calculated from the hybrid
commodity-by-commodity input-output table values and prices. Base year computations are
given in Equations 39-32, projections in Equation 43.

For the base year the technical coefficients for the Leontief production function (Aj.jj,v for i=l:25
and/=/:22 and./j=/:(5 when active) are computed as follows:
                   1
                                   /p:
                                   ' rl
                                       i.J.jj.t=0
                    LJ.JJ.v


                                                                                Eq. 39
                            1=1
                  where
                     v=0 for the base year,
                     N equals the variable plus fixed factors,
                                                              43
i»

-------
   Xgjj is base year demand for the i* input in the production of commodity j or jj (each Xyj is a
value within the regional hybrid commodity-by-commodity input-output table),
   £XjjjjiV is the summed base year demand for the inputs i in the production of commodity j or
jj.
   Pij,jjj,t are the prices paid by the producer for supplies (see Equation 9), and
   Prjrtis the price received for a commodity produced (see Equation 13).

For the base year the production sector-specific efficiency coefficients for the Leontief production
function AOJJJ,V are set to one.

X0>JJJV=1                                                                      Eq.40

The capital cost technical scale coefficients 0=26) for the base year are calculated as follows:
                                                                                 Eq. 41
where
   KApriorjjj,v is the capital stock vintage that is active for a production sector in the base year,
   ZXyjj>v is the summed base year demand for the inputs in the production of commodity j in the
base year,
   Prjjt is the price received for commodity j at time t.

Note that the vintaged and projected technical coefficients /L are only calculated when the
elasticity of substitution for the production sector equals or is smaller than 0.05. Note that these
elasticities are inputs for each production sector (for an example, see Appendix A). Vintaged
production sector or subsector-specific efficiency coefficients AOJJJ.V for a Leontief production
function are always set to one in the reference case.
Implementation of technical change is formulated as follows:
 X....  =     ^'-1                                                               Eq.43
  >,J,JJ,t   «+  -vNltep


 thus, with large values of yt, ly gets smaller and demand decreases, or differently put, supplies
 are used more efficiently. For the technical coefficient of capital any value besides zero, of y, will
 result in more costly capital over time.
                                            44

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In the case of putty-clay behavior a sector's vintaged and projected technical coefficients for the
Leontief production function (Aj,jj/,v for i=l:25 and j=1:22) are based on the vintage technical
                                                                                Eq. 44
coefficients calculated for the CES production function.

                     „  f          Pr,,   ***

                       •{•*»•„*
where
   aoj)V equals one,
   pi isa function of the long-run elasticity al which equals less or equal 0.05,
   (Xjjjj,v  is based on long-run elasticity and has technological change incorporated,
   Pitjjj.i are the prices paid by the producer for supplies (see Equation 9), and
   Prj>tis the price received for a commodity produced (see Equation 13).

And the Leontief vintaged and projected technical coefficients for capital are then also based on
the vintage technical coefficients calculated for the CES production and on the profit rate:
 1
  i=26=
                                            Pr.
      capital,j.jj.v
                   Oj.jj.v
                                                                                Eq. 45
where
   aojjj,v equals one,
   ai-26-capitaijaj,v will be based on long-run elasticity and has technical change incorporated,
   Prj_t is the price received for the commodity j produced at time t,
   Kajj|,v is the capital stock vintage that is active,
   Wj jj>v are profits for which the calculations are described in "Profits, demands, expected profit
rates, and the operation of capital."
                                            45

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Chapter 6.  Profits, demands, expected  profit rates,  and
the operation of capital

Profits equal the residual payments to owners of capital; alternatively defined, profit is the
difference between total revenue and the summation of all variable costs. Profit rates equal the
annual return per dollar of invested capital and profit maximization implies that the value of the
additional output (marginal revenue) from increasing input / by one unit should be equal to the
price of that input.

Capital is the only fixed input in SGM. With one or more fixed factors of production, a profit
function can be derived.

The relationship between profits and demands is addressed in the next two sections, followed by a
description of expected profit rate calculations. Next, operation of old and new vintages in
relation to production of supplies, demand, profit and cost as simulated in the SGM is described.
Profits and the production functions

Payments to owners of capital at a point in time, i.e., profits are the difference between total
revenue and the summation of all variable costs.
                      N-l
* j,ii,v  = Prj,t • q j,jj,v -    Pl i.j, j|,t • XU,ii,v                                   Eq. 46
                       i--i
where
   jji refers to the total profit in the production of sector commodity j or subsector jj,
   Piijji,t are the prices paid by the producer for supplies (see Equation 9),
   PrJ-tis the price received for a commodity produced (see Equation 13),
   Ojjj.v is the gross output of the production process in production sector] or jj by operating
vintage v at a point in time (see Equations 3 and 5), later referred to as PRDVj^v,
   Xijjj,v is the amount of input i demanded in the production of commodity j or jj at a point in
time, later referred to as  EDVjj jJiV,
   N is the number of variable plus fixed inputs (N=26) where capital is the only fixed input in
SGM.

Profit maximization implies that the value of the additional output (marginal revenue) from
increasing input / by one unit should be equal to the price of that input (ffPpers) in a perfectly
competitive market; thus,
                 i.J.JJ.v
where the variables are defined above.
                                         46

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Profits and the CES production function
Through algebraic manipulations of Equations 46 and 47 and the CES production equation
(Equation 3), profits can be expressed as a function of price and the quantities of M non-variable
or fixed factors of production (M=l  in the SGM) captured in Yj^iV, and the quantities of variable
factors, captured in Zy,>
                  "r
                                         1/p
                    j,t
                                     J,JU,v
            Eq. 48
where for each operating vintage v
   OQJJJ.V equals one (see "Technical change"),
   Prj_t is the price received for the commodity produced in sector j at a point in time,
   M- and p are functions of the elasticity of substitution a where l/n=l/(cj-l) and l/p=o/(c-l),
   Zjjj.v denotes the participation of the variable factors at a point in time and is calculated as
follows:
                                       N-M

                                                                                    Eq.49
    where
      M=l, since the SGM has one fixed factor supply, capital,
                                                            26
      Pijjjj,t are the prices paid by the producer for supplies (see Equation 9), and
      acstj,jjj?vis the transformed and vintaged technical scale coefficient between a supply and
   production sector; note that this coefficient incorporates the technical change ocoj^v
   coefficient; short-run elasticities may be substituted for the long-run elasticities when old
   vintage is operational (see Equations 22-38), and
      aojjj,v is a potential energy supply calibration parameter, presently set to one.

Note that Zyj> is for each point in time t for each production sector/, production subsector^/',
vintage v-specific; v and t may be suppressed for simplicity.
26 Note that if only one fixed factor, capital, is simulated Equations 47-49 are as follows:
YjJ.v =,


for acst equations see Equations 20-36 Section 2.5.2:
                                or
  i.J.JJ,v
                     Pi;
                                       and
/0-p2)
                                             47

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The last part of the profit equation J^,v denotes the participation of capital,

                                                                                 Eq.50
        i=N-M>l
where
   Kajjjj,v is the demand of the fixed factor input (capital) in the production of commodity j or jj
of vintage v at time t (denoted by Xi=26Jvii,v in the base year) and
           is the fixed factor technical scale coefficient (see Equations 22 through 38).
Profits and the Leontief production function
Through algebraic manipulations of Equations 46 and 47 and the Leontief production equation
(Equation 5), profits can be expressed as a function of price and the quantities of M non-variable
or fixed factors of production (M=I). Profits are not dependent on the quantities of variable
factors, which are in the CES production function captured in 2, ^ >. Thus, the Leontief profit
function is simply revenue27 less variable costs. Profit based on prices received and prices paid
and on the fixed factor of production (capital) is calculated as follows:
                             N-l
                                      ',J.JJ.V
                                                         • KA
                                                             J.JJ.V
Eq.51
                                  S=capilal>j,jj,v
where for each operating vintage v at each point in time
   KAjjj,v is the vintage-specific capital stock,
   P'ijjj,t a16 the prices paid by the producer for supplies (see Equation 9),
   PrJ|tis the price received for a commodity produced (see Equation 13), and
   Xojaj,v, ^ijjj,v and ^,-26=capitayjj.v are the Leontief technical coefficients.
The relationship between profits and demands

Retelling's Lemma states that the partial derivative of the profit function with respect to the price
of the /* input results in negative profit-maximizing total factor demand (A^;v) for that input:
               i.J.JJ.v
                                                                                 Eq. 52
where
   v indicates the active vintage,
   rtjjj,v is the vintage-specific profit in the production of commodity j or jj,
   Piijjj,t is die price paid by the producer for input at time t, and
   X,jjji¥ is the demand of the im input in the production of commodity j or jj.

Demands are thus partial derivatives of the profit function with respect to prices.
27 Revenue equals the product of output (PRDV) and the price received (PR/). Variable costs equal the product of
demand (EDV) and the price paid for supplies (Pi).
                                            48

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Demands and the CES production function
The demand for the /* factor input to the production process28 in relation to the technical scale
coefficients (the individual supply-to-production sector technical scale coefficients o^v and the
overall production technical sector scale coefficient ao^.v) can therefore be calculated directly if
the production function is a CES production function as:
                                         Y;
                                           J.JJ.V
                          Pi
                                                                                 Eq. 53
                            i.j.jj.t .
where for each vintage v at each point in lime
   otoj,j,>v is a potential energy supply calibration parameter, presently set to one,
   p and M. are functions of the elasticity of substitution parameter a, where p = (CT-!)/CT and
   Zjjj.y denotes the participation of the variable factors (see Equation 49), and
   Yjjj,v stands for the (single) fixed factor part (capital) of the profit calculation,

    Y»J,V  = acst,=26,J,Jy,v * Xi=26,J,Jy,vP    (see Equation 50)
   where
      acsti.26-capitaijjj,v is the fixed factor capital scale coefficient, and
                 j.vis the demand of the fixed factor inputs (in SGM, capital).
Demands and the Leontief production function
When the production function represents a Leontief technology, demand is independent of the
variable factors and die expression for profit is linear. Demand for the Ith input in the production
process/ mjj by operating vintage v at time / is described as follows:
            '.J.JJ.v
   1.J.JJ.V
           OJJj.v    i=26,j,
                             >KA
                                         4.J.JJ.V
                                 J.JJ.v
                                                      J.JJ.v
Eq. 54
                        J.JJ.V
where
   KAjjjjV is the vintage-specific investment capital, and
   AOJJJ.V, ^ijjj.v and X,-26=«apjtaioju,v are the Leontief technical scale coefficients.
Expected profit rates

One way in which economic growth is achieved from one model period to the next is through
investments in new production capacity. Demand for investment in new technology is determined
28
see Equations 61 & 76
                                            49

-------
                          -
EraAJM =ao,jj,v •-- — - •ZJ,Ji,v •alXjj.v                         Eq. 55
by the expected profit rate. Once expected prices of supplies and expected prices to be paid for
commodities produced are calculated, expected profit rates for new capacity can be calculated by
substituting expected future prices into the profit rate function. The results are sensitive to the
interest rate as well as other model prices. Decision-making on investments is part of the iterative
process of (1) determining supply prices and prices received for commodities produced based on
the operation of the active capital stocks, and (2) of determining expected prices and expected
profit rates.

Expected profit rates and the CES production function
The expected profit rate is calculated based on expected prices and current technology. The
expected profit rate Exr^, relative to capital  cost /£4J(^V_, is based on long-run elasticities of
substitution. The vintage subscript for the expected profit rate is denoted not by v but by t, given
that the operating vintage will have a vintage v=t for the time period at hand.
                        Pe-
    AJM      o,jj,v   -
                        i=ETE,j,jj,i
where
   Oojjj,v equals one and remains one over time,
   Pejjj is the expected price to be received for a commodity (see Equation 1 6), which changes
over time,
   Piei-ETEjj),t is the price of the numeraire Everything Else sector, which remains one over time,
   ai-26-capitaijjj,v is the technical scale parameter for capital costs; this is  the transformed capital
stock  scale coefficient based on long-run elasticities of substitution (see  Equations 25, 27 and 34),
   p and p. are functions of the long-run elasticity of substitution, and
   ZjjjiV denotes the participation of the variable factors as described above (Equation 49) and is
calculated for each production sector j, based on active technology and expected prices as
follows:

    Ziii.v=, = 1 -Ki.ii.v •Peiii)"*-rt •Z(acst,,,v • Pie,;/™)            Eq. 56
                                        i=!
   where the variables are defined above, and
      acstyjj_v is the technical scale coefficient described in Equation 3 1 and
      Pieijjj is the expected price paid (Equation 15).


Expected profit rates and the Leontief production function
Based on the Leontief production function the expected profit rates based on expected prices and
the technical scale coefficients of capital.
          Ai=26=capilal,j,jj,v            1  ^ /Vri=26=capiUl,j,jj,v
where
   v equals t,
   Xojjj,v, Xijjj.v, and X,-26=espitaUjj,v are the Leontief technical coefficients (Equations 39-45),
   Pe^ is the expected price received for commodity j or jj (Equation 16), and
                                            50

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   Pie,jjj is the expected price to be paid by the producer j or jj for input i.

Note that the elasticity of substitution cris not less than 0,05 for any of the production sectors or
subsectors (see Appendix A for the list of the sigmas for the production sectors and subsectors)
with the result that expected profit rates are always based on the CES production Function in the
reference case. Investment is based on expected profit rates and one may assume some price
elasticity with regard to investment choices.


Operation of capital stock  in the SGM: determining production and
interindustry demand

As was stated above, profits Trare the difference between total revenue and the summation of all
costs; demand is the amount of input i demanded in the production of commodity./ orjj by
operating vintage v (denoted by £DK^.vand, as previously discussed, the same as the Jfyj,-
elements of the hybrid commodity input-output table in the base year); supply is the gross output
of the production process in production (sub)sectory aijj by operating vintage v (PRDV^or as
previously denoted by <£,>).

Excess demand is the difference between demand and supply. For each of the market
commodities excess demand is  calculated when operating either old or new capital. An
equilibrium solution requires the absence of excess demand for each and every commodity
included in the model. When the model solution is reached there will be a set of prices and
quantities of the w-commodity market such that all n equations in the equilibrium condition will
be simultaneously satisfied.29

When  operating old vintages in the base year, vintages v=-3 through v=-/ are operated. When
operating old vintages in the years following the base year, three vintages v=t-3 through v=t-I are
operated given that in the reference case the expected lifetime of a vintage is 20 years, the time
step is five years and a vintage in its first time period is operated as new vintage, v=/. The time
step indicator / is therefore, at each time step, three steps ahead of the oldest vintage and one step
ahead of the latest vintage and with new vintages the time step t and the vintage v are identical.

All production activities, regardless of vintage, have a fixed input. First, profits and profit rates
are calculated. Second, input demands are calculated. Third, output is calculated by substituting
input demands into the production function. We first describe operation of old vintages, where the
capital stock is known in advance.
Old vintages

Operating old vintage and the CES production function
29 "If all the commodities in an economy are included in a comprehensive market model, the result will be a Walrasian
type of general-equilibrium model, in which the excess demand for ever,' commodity is considered a function of the
prices of all the commodities in the economy" Chiang (1967:52).
                                           51

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Before profits are calculated from the operation of old capital, its lifetime is checked to determine
if it should operate at all (see Appendix A for examples of nameplate life of capital). If the
vintage-specific capital stock (KAjj,.v) exceeds its nameplate life, that capital will be scrapped. If
capital is not scrapped, the profit rate for each operating old vintage is calculated. When a profit
rate is negative, capital stock is retired and production for that vintage is set to zero.

The fixed input for old vintage profit is the industry- and vintage-specific capital stock carried
over from the previous time step. In the case of a CES production function, profit is calculated as
follows:


•Ojji.^M = «W • V(Zj,j)/1V))a~'" •k^,,, 'KA^/r              Eq. 58

where
   v equals t-3 through t-1,
   oojjj,v equals one,
   Prj?t is the price received for the commodity produced in sector j,
   Zjjj,v is described in Equation 49 and implemented in Equation 58 with long-run elasticities for
old vintages older than the base year of 1990; in the base year and in the projections, short-run
elasticities are implemented when vintages are old capital,
   p is represented by long-run elasticity for vintages older than the base year and p is
represented by short-run elasticity for old vintages for the base year and beyond (then p=p2),
   KAjjj>v is the vintage-specific capital stock,
   ai,-26-capitaijaj,v is the vintage-specific capital stock technical scale coefficient in which technical
change is incorporated; short-run elasticities are implemented when calculations are made for old
vintages (Equation 34); however, when vintages are older than the base year of 1990, long-run
elasticities are implemented (see Equations 25 and 27).

Operating old vintage and the Leontieffixed factor production
For old operating capital, profit based on the Leontief production function is calculated as
follows:
 TlO
    j,jj,v=t-3.t-l
•KAJ>JJjV              Eq.59
where
   v equals t-3 through t-1,

   KAjjjpV is the vintage-specific capital
   ^Ojjj,v, ^ijoj,v, and X,-26-capiiaij1ij,v SK the Leontief technical coefficients (Equations 39-45),
   Piijji,t are the prices paid by the producer for supplies (see Equation 9), and
   Prj>tis the price received for a commodity produced (see Equation 13).

Note that only in the cases of operating old capital for electricity generation and for refining oil,
the Leontief production functions are actually implemented in this SGM's documented version.

                                            52

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Profit rates — that is profits relative to capital cost, or annual return per dollar of invested capital
— are calculated by production sector or if subsector production takes place, as follows:
           7lO|jjv
          	WtT-                                                               Eq. 60
           KA:
    J.JJ.V
               J.JJ.V
When a profit rate is negative, that is when payments to owners of capital can not be met, capital
stock is retired and production for that vintage is set to zero.

Old vintages, demand, and gross production
Demands by production sectors y or subsectors.//, when operating old vintages, are calculated as
in Equation 61 when the production function is a CES production function. A multiplicative
factor reduces output smoothly to zero as profit rate goes to zero. This isfac in the equation for
input demands (EDV^^. The same factor is applied when calculating production or output
(PRDVjjj^ in the operation of old vintages. This tsrmfac is used to ensure that input demands are
continuous as  relative prices change.
 EDV
      i.j.j,.v=,-3:t-]
                                          '.J.JJ.v
                                        Pi
                                          1.J-JJ.I,
                                                                                  Eq. 61
where
   i is the supply sector indicator (i= 1:25), j the production sector indicator (j=l:22),jj the
production subsector indicator (j < 6), and v the vintage indicator,
   v equals t-3:t-l,
   fac is a scaling factor described below,
   ZJ(ijiV is described under Equation 4930 and used in Equation 61 with long-run elasticity of
substitution for the base year's old vintages and short-run elasticity of substitution for 1990 and
beyond; it is similarly calculated for subsector production,
   [a^jj v 1/(1"p)] is described as acsti_jjj,v in Equation 31 with long-run elasticities and in Equation
37 for old vintages with short-run elasticities,
   p is a function of the long-run elasticity of substitution for the base year's old vintages and
short-run elasticity of substitution for 1990 and beyond,
   Piijjj.i are the prices paid by the producer for supplies (see Equation 9),
   Prjtis the price received for a commodity produced (see Equation 13), and
   fac represents a sealer also to be applied to the production sector's productivity (Equation 61
and 63). This sealer may be applied when the profit rate is less than a threshhold profit rate of
0.01 (see Equation 62 for the calculation of the sealer in that case). Alternatively, the threshold
can be set such that for depletable resources one makes sure that production does not exceed
available optimal production levels from resources through the calculation of the total amount
30
                                             53

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(integrated over the five-year time period) of resources needed to meet expected demand. Under
one more alternative, production sectors may be idled based on emission limitations.
                                                                                 Eq.62
               0.01              0.01
The annual vintage-specific gross production by the production sectors and subsectors through
the CES production function is calculated as follows:


                                                                                 % 63
where
   fac is described above,
   a0jjj,v equals one,
   Zjjj>v is described under Equation 61,
   ai,-26jjj,v is described under Equation 61,
   KAjjj>v is the vintage-specific capital, and
   p is a function of the elasticity of substitution.

When the production function represents a Leontief technology - that is, when the elasticity of
substitution a2 is smaller than 0,05 - demand is calculated as follows:
      ,^.^ = PRO V^ •      -                                            Eq. 64
                               'Vj.jj.v
where
         and A-ijjj.v; are the Leontief technical coefficients, and gross production by the
production sectors or subsectors is calculated as follows:
                                                                                 Eq. 65
                            /1=26,jjj,v
   where
      fac is described above, and
      KAjjjrV is the vintage-specific capital.
Checks on depletable resources after calculations regarding operating old vintages
Oil, gas and coal production sectors involve depletable resources. Therefore, available resources
have to be checked against desired investments.
The sum of linearly interpolated annual energy consumption PRDV^v for the five-year period
starting with the current model period T (which is t*Nstep) and going back over the previous four
years can be shown to equal two times the annual flow at time T-5 plus three times the flow at
time T. The anticipated consumption or depletion potential of an energy source over a five-year
time period based on anticipated energy production is calculated as follows:

                                            54

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DepletCj  = ((2 • PRDVj jjv) + (3 • PRDVj _- v)) • PRconvrtj                       Eq. 66
where
   v equals t-3 through t-I,
   PRDVj jj,v-t-3:t-i is the annual anticipated gross production of the oil, gas, and coal production
sectors, and
   PRconvrtj is the energy conversion factor, converting the relative prices in monetary units to
physical energy units.

If, over the next five-year investments, the required energy production exceeds the oil, gas, or
coal supply available, demand for production is decreased (Equation 68), as are the related
anticipated profits (Equation 69). Thus,


                           'Deplete,                                           Eq'67

       jji.v.t-31-i = PctDeplete* PRDVjoj,                                       Eq. 68
where
   DrsVtmpjjj v is the energy resource available at a point in time initiated with the energy
resource data information (see Appendix A) and calculated through resource investment
calculations in the projections (Equations 119-132) and updated through Equation 70.

Profits would be reduced accordingly:

ftOj jj v=t_3l_, = PctDeplete* 7tj>ijjV                                             Eq. 69

The energy sources are reduced by the amount of energy consumed as follows:

DrsVtmp- -t. = DrsVtmpj (j, - Deplete,                                       Eq. 70
          jtjji1             JiJJi1      1   J

Analogously, capital investment demands into fossil fuel production would be reduced (Equation
71). This demand Kdem^ will be described under "Investments" in the "Final Demand" section
(see Equation 133 where capital demand, Kdem, is set equal to the flow of capital Kaflow when
investment into depletable resources is described).
Note that Kajlawi&i refers to the yearly capital flow of investments into vintage production sectors
or subsectors while KAj&v-i refers to the total capital investments or capital stock over the five-
year time period t simulated (see Equation 118). '

       y = PctDeplete* Kdem^                                              Eq. 71
31 Given that Kaflowj^y,, refers to an investment flow at a certain point in time when new capital investment is
calculated, the vintage indicator v equals /. Kaflow has, in effect, in the SGM code, at times a v subscript and at other
times a / subscript.

                                           55

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New vintages
New vintages differ from old vintages in two important ways. First, capital stock is not known in
advance and must be provided by an investment mechanism {see "Investments"). Second, new
capital has an elasticity of substitution that is equal to or greater than old capital in that sector or
subsector. Therefore, new capital has more flexibility than old capital to respond to changes in
relative prices of inputs. Equations for input demands and output for new vintages are identical to
equations for old vintages.

Operating new vintages and calculating profit rates
When new capital with a vintage notation of v-t is operating at the first iteration of finding a
model solution, the profit rate or profit per unit of capital is calculated as follows when calculated
by means of die CES production funcion with long-run elasticities:
          =<*
              0.j.jj.v
                                                          Eq.72
where
   v=t denoting new vintage investment,
   aOjjj,v =1,
   PrJ>t is the price received for the commodity produced in sector j at a point in time,
   Zjjj,y is described in Equation 49, and is implemented with long-run elasticities in Equation 72,
   H is a function of the long-run elasticity crl,
   a,,=26=capitai,jj],v is the vuitaged capital stock scale coefficient in which technical change is
incorporated (see Equation 27, which provides for a normalized value of Equation 25; see
Appenxix A for an example of capital alpha transformations for j=l), and
   p is a function of the long-run elasticity al.

Similarly, at the first iteration of finding a model solution, the profit rate or profit per unit of
capital if calculated by means of the Leontief production funcion is as follows:
                              N-l
             A
Pr,<- Z
              i=26,j,jj,v
                                                li,j.Jj,l
                                                                                  Eq. 73
where
   v=t,
   Xojjj.v, ^ijjj,v, and Ai=26=caPiuijjj.v are the Leontief technical coefficients (see Equations 39-45),
   Piijjj,t are the prices paid by the producer for supplies (see Equation 9), and
   Prj,tis the price received for a commodity produced (see Equation 13).

Operating new vintage and profit
Profits, after the first iteration of finding a model solution when operating new capital, are
calculated based on the CES production function with long-run elasticities:
                                                                                  Eq.74
                                             56

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o
                  where
                     v=t
    =t,
   p is a function of the long-run elasticity CT! ,
   ZjJJiV is described in Equation 48, and is implemented with long-run elasticities in Equation 74,
    -i,=26jjj,v is the vintaged capital stock scale coefficient in which technical change is
    porated (see Equation 28 in "Technical change"), and
    A    is the vintae-secific caital stock.
                     a-i,=26jjj,v is the vintaged capital stock scale c
                  incorporated (see Equation 28 in "Technical ch
                      KAjj,.v is the vintage-specific capital stock.
                   If the long-run elasticity of substitution is smaller than 0.05 and new capital is operating, profit is
                   calculated based on the Leontief production function:
                                 >               N-lf  1
                      j,)J,v=t
                                1
                                /vi=26,j,jj,v
•Pi.
                                                                          •KA;
                                                                               J.JU.v
                                                                                  Eq. 75
                  where
                     v=t,
                     KAjjjiV is the vintage-specific capital,
                     Xo,jjj,v, ^ijjj.v, and ^^e-capiuyjj.v are the Leontief technical coefficients (see Equations 39-45),
                     Pijjj,,t are the prices paid by the producer for supplies (see Equation 9), and
                     Prj,tis the price received for a commodity produced (see Equation 13).

                  New vintages, demond,and gross productivity
                  When new vintages are operating and the production function is a CES production function,
                  demands by production sectors and subsectors are calculated as follows:
EDY.U.v-,
                                                                                                     Eq- 76
                   where
                      i is the supply sector indicator (i=l :25), j the production sector indicator (j=l:22), jj the
                   production subsector indicator (j < 6), and v the vintage indicator,
                      v=t,
                      Zjjji¥ is described in Equation 49 and implemented with long-run elasticities in Equation 76,
                      [aijjj,v 1/(1"p)] is described as acst in Equation 31 with long-run elasticities,
                      Piijjj.t are the prices paid by the producer for supplies (see Equation 9), and
                      Prjjtis the price received for a commodity produced (see Equation 13).

                   The vintage-specific gross production through the CES production function is calculated as
                   follows when new vintage is operated (v=0:
                                                                                                     Eq. 77
                   where
                                                               57

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   Zjjj.y is described in Equation 49 and implemented with long-run elasticities in Equation 77,
   a,i=26Jjj,v is the vintaged capital stock scale coefficient in which technical change is
incorporated,
   KAjjj>v is the vintage-specific capital,
   p is a function of the long-run elasticity of substitution.

When the production function represents a Leontief technology demand is calculated as follows:

EDVi>jtAvMl = PRDVjijjtv • -j^Z-                                               Eq. 78

where
   AOJJJ,V and ^,j^v are the Leontief technical coefficients,

and gross production is calculated as follows:
                   A   .
             ,=.  = -,  ''^  >KAj.ii,v                                            Eq.79
                  /ti=26j,ii,v
Checks on depletable resources after calculations regarding operating new vintages
New vintage capital in the oil, gas and coal production sectors, like old vintage capital in these
sectors, use depletable resources when operating. Resource consumption and potential depletion
is again calculated by linear interpolation of annual flows for the five-year period starting with
the current model period T and going back over the previous four years. If the  consumption of
resources is larger than or equals the resources available, the resources are exhausted and set to
zero, and consumption  is set equal to the available resources (Equations 66-71).
Demands by production sectors and cost calculations
To obtain production sector demands, the vintage and subsector demands are summed over the
operating vintages and subscctors if active:
                    _                                                         Eq. 80
               v=t-3
where
   EDVjjjjiV denotes demand by a vintaged production sector or subsector,
   n is the number of subsectors where n < jj, and
   v denotes the operating vintages.

When production is simulated, costs for each vintage-specific production sector and subsector are
calculated based on the vintage sector or subsector demands and prices paid at time t of the model
solution; costs are here expressed as the product of quantity produced in units of 1990 millions of
dollars and the relative purchase price paid accounting for transportation costs, taxes and
adjustments.

                                            58

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C°Sti,j,Jj,v=t-3:t-l =
'Pi;
Eq. 81
where
   EDVijjJ>v denotes demand by a vintaged production sector or subsector, and
   Piijjj,t are the prices paid by the producer for supplies (see Equation 9).

Note that these cost calculations are performed for model output only.

Additional costs when operating any of the active vintages
Adjustment factors WHSLit representing distribution and markup factors for the supply sectors
— that is, for the variable factor inputs — are calculated next. The same adjustment factors are
calculated for household distribution and markup costs (see Equation 193). The summations of
both costs are used when calculating Everything Else sector demands32 (Equation 137). All
variables in this equation are described above. The adjustment factors WHSLj will be factors with
values that equal zero, given that in our reference case adfijj-it=l for all supply sectors (see
Equation 11). For all supply sectors (i=I:25), for each production sectary and subsector jj, the
adjustment factor WHSLj is calculated as follows:
 WHSL,=|;
               v=t-3
                                                               Uij +TxaddI>JJj]«
                                    'Pi
                                       i=ETE,j,jj,t
                                                                                 Eq. 82
where
   v refers to all actively operating vintages (v=t-3 :t-l for old vintages and v=t for new vintages),
   n is the number of subsectors with n < jj,
   j is the number of production sectors,
   i refers to input sectors,
   adjjjjj.t, is a time-period-dependent adjustment factor that reflects markups and intra-regional
transport costs; these adjustment factors can be input- (i) and sector- (j) or subsector- (jj) specific,
   Pu is the market price; in the base year P, equals one; in the forecasts Pi is calculated during the
model solution process and is supply and demand dependent,
   Tr,|t is a time-period-dependent supply sector transportation cost factor,
   Exlm, is the transportation cost rate parameter,
           j is a proportional tax rate on the i* product,
         jjjj is an additive tax on the i* product,
   EDV,jjj,y denotes  demand by a vintaged production sector or subsector (see Equations 61 and
64 and 76 and 78), and
   Pii=ETEjjj,t is the price paid by the producer for Everything Else input.
32 Equations described in this section are calculated separately when operating old vintages (v=t-3:t-l) and new
vintages (v=/). Given that these equation in both subroutines in the SGM code are the same we describe them here once
for v=t-3:t.
                                            59

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Transportation costs (TRNPj) for markets with imports and exports for all variable factor inputs
are calculated in Equation 83. They are calculated in a similar fashion based on demands by
households (Equation 196). The summation of both costs are used when calculating Everything
Else sector demands (Equation 137).
              v=t-3
                                                    *i=ETEJ,ij,t
                                                                             Eq. 83
Taxes on production (TcKt] for i=l :22) are summed over all supply related transfers and for
electricity generation over the subsectors:
         22
            v=t-3
                      M + Tr; t • Exlm,. EDV1>WJ>v=t_3:t).
                                                            Eq. 84
Taxes on labor (Tax2J for /=2J) for each production sector/ are kept separate in Tax2ti. These
taxes are for the v=/-specific production sectors and summed for electricity generation over the
subsectors:
TaX2,j =
         v=t-3
  u*.t + Tr,=25,t • Exlmi=25. EDVi=2Uiiv=l_3:t).
  Eq. 85
where
   Pj-25)tis the market price for labor rental during the model solution process.

Supply subsidies Subsidi equals the production taxes Taxij for i=l:25:
Subsid,=£
              -'•I
          (P,t + Ti;,, • Exlm,. EDy, , v=l.3:t)• (Txproufi -1)
 Eq. 86
Taxes on production per unit production and subsidies to supplies per unit supply TaxpU,j
are only calculated when the additive taxes are greater than zero,
 TaxpUy =
            i=i
                v=t-3
                                                            Eq.87
Taxes on labor TaxpU2j (for i-25) for each production sectory per unit labor supply are kept
separate in TaxU2j:
 TaxpU2>J =
            v=t-3
Z(T*addi=2Uij • EDY^,^^ J
Eq.88
                                          60

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Subsidies per unit supply SubsidpUt (for i-1,25) equal the taxes on the production (sub)sectors.
Subs.dpU^f
                  -1. X
                      v=t-3
                                                                            Eq. 89
Final carbon permit fees CPermFSj are a function of the energy demands by the production
sectors and the carbon fees per dollar of energy production, which are a function of the global
warming potential and the emission coefficient of the fuel combusted. Thus,

                                                                               Eq.90
                    v=l-3
where
                        _jj=i

              . • ExchRate  •
                           region
   where
      fn stands for oil, gas, or coal
                                     !fn • PRconvrt; • GWPfn  (see Equation 10),


   	—, D^, „. —„, within a production process for which the energy supply
carbon fee is calculated,
   Pj«23,t is the carbon price, which equals the market price during the model solution process,
   ExchRatCregion the monetary exchange rate,
   EMCfnis the fuel-specific carbon content in million tons C per exajoule energy of the
energy source,
   GWPfn is the global wanning potential, which equals one for carbon,
   PRconvrtj is the energy conversion factor, converting the relative prices in monetary units
to physical energy units.
                                          61

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Chapter?. Carbon policies
The SGM may impose carbon fees to provide an economic incentive for the economy to
substitute away from carbon. Revenues obtained from the carbon fee can be large, and how the
revenues are recycled or redistributed to the economy makes a difference in the economic costs.
The GHG market operates using the same mechanism as each of the other markets in the  SGM.
Implementation of a carbon market can be achieved by (1) imposing a global or regional carbon
price and have the model solve for additions in prices paid with the objective of emission
reductions, or (2) imposing an emission limit or target and have the model solve for the necessary
carbon price to reach that target. We describe the different options in the next section.

For the cases in which emissions permits are traded between regions, each SGM region is
allocated an initial number of carbon emission permits based on the stated mitigation policy (e.g.,
1990 emissions levels). Carbon permits can then be traded between countries at a price that clears
the global market in these permits.
Carbon prices and revenue cycling
Carbon policies in the SGM can be expressed in a number of different forms. Sets of switches
(CarbFeeP and PolType) activate the no-policy or policy -specific options. Appendix A lists the
first set of switches. To implement any carbon policy the CarbFeeP / switch has to be set to one.

Appendix A also lists the second set of switches (PolType) and the different sets of input data
(CarbVar) that are required under the different policy options that can be implemented in the
SGM.
A. Under Policy type zero (PolType^ 0) carbon prices are fixed; CarbFeeP 3 is set to  zero which
   implies that there are no carbon emission limits (CarbonLim = 0.0); the fixed price switch is
   set for carbon (IPfix^i ='• True) and carbon prices are input (CarbVar >) such that

    P,=*»,t = CarbVar,                                                          Eq. 91

   If, in addition to CarbFeeP t^ I, CarbFeeP «has a value larger than the base year (where t=0),
   then the time period of implementing the carbon price is determined by the value t of
   CarbFeePe.

Alternatively, under other types of policies, a set of switches can be set to solve for a market price
for carbon in response to emission limits. The carbon price is then initially set to a small number:
e.g., Pi-23,i,m=0. 1 and the model is allowed to solve for the carbon price; the CarbFeeP / and
CarbFeeP2 switches have to be set to one.

    Pi=   = 0.1                                                               Eq.92
B. Under Policy type one (PolType = /) external carbon emission limits are set; CarbFeeP; is set
   to one; carbon emission limits are then equivalent to Carb Var,.
                                          62

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   CarbonLim, = CarbVart

   where
                                                                              Eq. 93
      CarbVart values are externally set emission level limits illustrated in Appendix A (e.g.,
   1429 mt C/yr in year 2000; 1345 mt C/yr in 2005, etc.) and
      Pi-23=c«t>on is set initially to 0.1 or one (Equation 91) and when solving the model becomes
   the market price.

C. Under Policy type "larger than 1990 an internal carbon emission target is determined; both
   CarbFeeP2 and CarbFeeP< are set to one and CarbFeePs is set to a number of time steps
   (t=(year-1990)/5) into the future to function as the initial year for an internal carbon emission
   target to be reached. Thus,
   CarbonLim, = EmTot, • CarbVar,
                                                                              Eq. 94
   where
      EmTott is total emissions (Equation 247),
      CarbVart values are endogenously set emission level limits {e.g., 1.1 times the year 2005
   level in 2010; 1.2 times the 2005 level in 2015, etc.), and
      Pi-23=cari»n,t is set initially to 0.1  or one (Equation 91) and when solving the model becomes
   the market price.

Ensuring that the model runs contain relevant data is dependent on the relationships between the
switches and values listed above. These relationships are summarized in Appendix A.

When the switch CarbFeePi is set to one - that is, when a carbon policy is to be implemented -
all demands (Edj,23~carb
-------
values of the different gases with the type of gases emitted (as related to their emission
coefficients, EMC) and their conversion factors of monetary units to energy units (PRconvrf)

EDu23,H:22 = EmissionsJ = ^TotDem^PRconvrtj • GWP, • EMC,              Eq. 98


Carbon permit trade
If carbon permits are traded, the value of CrbTrade, can be set exogenously in the base year
(variable CrbTrExo,).

Alternatively, under each of the carbon policy implementations listed in the previous section,
CrbTrade, may be based on a fixed permit price (Pj~23,i) or a market price for carbon and on a
carbon emission limit set exogenously or endogenously. Carbon permit trading only takes place
when regions are linked through trade markets.

CrbTrade, = P1=231 • ExchRatereglOT*(CarbLimt-EmTot,)                        Eq. 99

where
   Pj=23,t is the carbon price at time t
   ExchRatd is the exchange rate,
   CarbLimt is the emission limit, and
   EmTott is total  carbon emissions, which are calculated in Equations 244-247.
Carbon policy impacts
Impacts of carbon policies can include the following: (a) energy prices are impacted by adding
the carbon fee to the energy price (see Equation 10); and (b) household, government and
investment demands are impacted by accounting for a carbon fee per dollar of energy demand
(see Equations 205, 206, and 140).

Carbon fees collected can be recycled as revenue in various ways, described below.

If carbon prices are market-based then the household, government, and investment carbon permit
fees are part of a carbon market. If carbon trade is implemented and the market demand and supply
are determined by emissions (see the previous section) the domestic carbon price receipts have to be
taken out of the carbon trade estimate. The costs of carbon prices are recycled as revenue when
carbon prices are market-based and when they are fixed. If no carbon trade is implemented, the
CrbTrade, variable will equal zero (Equation 100). The carbon fees imposed on investment,
households, and government are based on carbon prices (see Equation 10 for determining the Cpf
values). The carbon  fees to be recycled as  carbon revenue within a region are the carbon fees traded
and corrected for the carbon fees levied on households, government and investments. Appendix A
summarizes the carbon policy option impacts through the recycling of the revenues obtained from
the carbon fees and, if active, from carbon permit trade. The details of the revenue recycling are
described in the investment, household and government sections in this document.

CrbTradet = CrbTradet - CPermF5 Ji25=raiex -CPermF5  J=:26!=gv - CPermF5 j=27ihh    Eq. 100

                                          64

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where
   Carbon fees on fuel combusted and demanded by households (CPermFSj,27) is calculated in
                               24  .               .
Equation 199:   CPermF5 j=27=hh = 2^(Cpf, • ED;j=27=hh) where Cpfi is a carbon fee per doll:


of energy demand.


   Carbon fees on fuel combusted and demanded by government (CPermF^^f) is calculated in

Equation205:   CPermF5 J=26=gv = j^Cpf, .ED,J=26=J


   Carbon fees on fuel combusted and demanded by investment (CPermFi^s) is calculated in
                                22 .                .
Equation 140:   CPermF5 J=25=mex = £(Cpf; • ED, J=25=inv)
                                         ar
where

   Cpf,=P1=23,t»ExchRateregion.
fn • PRconvrt; • GWPfn (see Equation 10)
CrbFeeTot, = CrbFeeTot, +CrbTradet

where

   CrbFeeTott are the summed carbon fees:  CrbFeeTot, = ^CPermF5_-}
                                   Eq. 101
              27
 65

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Chapter 8. The final  demand sectors

The four final demand sectors that demand and produce goods and services are
    •  investment
    •  households
    •  government
    •  net exports.

The final demand sectors are integrated with the rest of the system (see Figure 1) through their
demand for final goods from the production sectors and their supply of land, labor and capital33.
Below we describe investments followed by sections on government and household supply and
demand and finally by a section on imports and exports. The export/import aspects of the final
demand are integrated with the product markets by including the changes in inventory as net
exports to eliminate the need for modeling inventory fluctuations.
Investment
The SGM requires a fixed factor, that is, the amount of capital to be known before production can
take place. To close the model, an investment mechanism is required to determine how much
capital is to be allocated to each of the sectors and subsectors. New capital requirements, in turn,
determine the inputs necessary to produce new capital. Capital required for new production can
be determined in two ways. New investment can be determined as a function of expected profit
rate and investment in the previous period. Alternatively, new investments can be based on
expected profit rates and the gap between expected production levels and the potential output by
existing capital stocks.

Whenever a distinct product is being produced, it is represented by means of a production sector.
Subsectors represent different ways of making that product. Subsectors are implemented in the
SGM for electricity generation. The competition among the technologies based on expected profit
rates determines the relative contributions (shares) the technologies make towards electricity
generation investments and this is formulated by means of the logit share equation after
McFadden (1981). In that formulation the shares of the competing fuels add to one, and are
33 Demand sector indicators
Final demand sectors (j)
J


24
Investment
inv
25
Net Exports
imex
26
General Government Consumption
Gv
27
Household Consumption
Hh
Primary factor supply indicators
1
24
25
26
Primary factor supply sectors
Land
Labor
Capital or OVA
la
Ibs
capital or capital cost

27
Indirect business taxes or IBT
ibt
                                          66

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dependent on an assumed base share value for each of the competing fuels and on the elasticities
of their prices. Thus, more than one fuel source and its accompanying technology (oil-fired, gas-
fired, coal-fired, nuclear, and hydro in SGM 200334) can meet the electricity generation demand.

Delays with regard to investments that take more than one period before coming on line are not
simulated in SGM 200335.

New investments based on expected profit rates and investments in the previous period
Investment  as a function of expected profit rate Enr^., and investment in the previous period
KAflo\vt.t is described first.

Initial annual investments KAflow for the base year (v=t=0) and old vintages (v=-7) are input
parameters, as are initial expected profit rates. Thus,
                   .i.ii.t
                                           for the base year
                                        Eq. 102
 E7n-JJ]t=0=EXPPROF
                         JJJt=0
for the base year
Eq. 103
When based on expected profit rate and investment in the previous period, sector-level
investment in the projections for all production sectors is a function of a base rate of growth, the
growth in working-age population, and the expected return to capital. This investment is
calculated in relation to what the marginal dollar should earn under perfect competition
(margvalue=l); the production sector-specific variable Tempj determines the earnings and K,,,
denotes the potential  investment into a production sector./ at time t.36 The investment calculation
is then
 KJt ^
where
                              rhoinv+1
                   JJ=1
                              ihoinv
                                        Eq. 104
    Ejiry>t is a sector or subsector's expected profit rate at time t (see Equations 55 and 57),
    n denotes the number of active subsectors where n < jj; the summation over jj takes place
only when subsector production takes place,
    rhoinv is the expected profit rate exponential, which equals one in the reference case, and
34 Presently (October 2004) renewables (biomass, waste, solar, geo, wind-on shore, wind-offshore) and new
technologies (coal IGCC with and without carbon sequestration and disposal, gas NGCC with and without carbon
sequestration and disposal, pulverized coal with carbon sequestration and disposal are implemented in various nesting
structures to achieve optional knife-edge investment behavior in the model).

35 Presently (October 2004) delayed investment is a viable option in the model and implemented for new technologies
to come on line.

36 calculations concern generating a new vintage v with an indicator value of v-t
                                             67

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    rinv is the expected profit rate function exponential, which equals one in the reference case,
and
    Tempj is the variable denoting investment dependency on the change in demography, the
marginal value of the dollar, and some basic assumption with regard to annual investments for all
production sectors.
          = basekaj} •sealer*
                              working_age_pop,
                                              •marg value"1
Eq. 105
                             working_ age _popl_,
    where
      basekapj is a production sector-specific annual investment which may be based on various
assumptions:
    a.   basekap may be based on the production-sector-specific annual investment (KAflow)
        from the previous time-period, thus,
       basekapj = KAfloWj u ,._, , or
    b.   when the annual investment is very small, basekap is 1% of the total available annual
investment into all production sectors, thus basekap j -O.
                                                                               ,,, , or
    c.   when subsectors are involved (electricity generating subsectors), basekapj is the summed
        annual investments over the subsector previous time-period's investments:

       basekapj = £KAflowjJJ(_,
                    jj
    sealer — an investment accelerator — is a scale coefficient and has a value of 1.2,
    working_age_populationt at a point in time is the number of people in the working age
bracket,
    accinv is the working age population ratio exponential, which equals one in the reference
case, and
    margvalue is the marginal one dollar.
New investments based on anticipated output
As an alternative, the model can determine demand for capital based on (he expected profit rate
Enr^t and the gap between gross output PRDj and the potential output by existing capital stocks.

When old and new vintages are operated, vintage-specific gross production PRDVjjjiV is calculated
for each operating vintage for each production sector/ and subsector jj. Total gross production,
PRDf1 is die summed vintage-specific production.

                                                                                 Eq. 106
         v=t-3
37 In the SGM code Salexl] is set equal to PRDj at this stage, and the ED matrix at a certain stage has diagonal
elements calculated as Ed,j-PRD/, in this documentation the Safest'' vector is only initialized when describing the
solution algorithms (see Equation 239) and the Ed,j matrix always refers to the demand matrix. Appendix A shows
complete Ed,j-PRDj matrices which solve to (close to) zero for the base year (/=0) and for year 1995 (t-1).
                                            68

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PRDVjjjiV calculations are either based on CES or on Leontief production functions, dependent on
the elasticity of substitution parameter of the production sector or subsector.

Anticipated increases in investments for all production sectors are in this formulation determined
by an exogenous parameter in SGM 2003 (Qprojt). This parameter functions as a multiplier to the
production sector's gross production of the previous point in time. Output needed from the to-be-
invested-in new vintage Qnewj is calculated as the difference between die summed active vintage-
specific production sector output and  the anticipated needs calculated as the summed previous
vintage-specific operating production sector output multiplied by the desired increase in
production.  This is expressed in the following equation:
         = Qproj, •
                    v=t-4
 -I
   v=t-3
                                                JJ=1
                                                          J.JJ.V
Eq. 107
A testable demand for capital TestKjto produce output needed from new vintages is calculated as
the product of the desired investment Qnewj and the calculated capital-to-output ratio Capq if no
subsector production takes place:
TestKj =Capcjy
forjj=l
Eq. 108
where
    Capqjj is the capital-to-output ratio.

The capital-to-output ratio is calculated based on the CES production function given that one may
assume some price elasticity with regard to investment choices. Therefore, investment decisions
in the SGM are based on the CES production function assumptions and not on die Leontief
production function assumptions where price elasticities are zero38.
                                                 ,1/0-p)
                            i=26J,jj(v
                                       TiNr,
                                           Eq. 109
                                           J,JJ.v=t
where
38 When the elasticity of substitution (crl) is less than 0.05 this intermediate step could be calculated based on the
Leontief production funcion coefficients:
This is not implemented, however.  This is for theoretical reasons: one may assume some price elasticity with regard to
investment choices. Therefore investment decisions in the SGM are based on the CES production function assumptions
and not on the Leontief production function assumptions where price elasticities are zero.
                                             69

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      ij jj,T-t is the profit rate calculated based on active prices and long-run elasticities, which in
the CES formulation is as follows (see Equation 72)
and for the Leontief formulation as (see Equation 73):


    jrNr      = _ °-J'Jj'v  .pr
    "^j.jj-v^   -,           rrj.t
                Ai=26.j,jj,v

These calculations are more complex, however, when subsector production is simulated.
Subsector investment is simulated as a shared investment. This logit sharing is only relevant to
electricity production given that this sector is the only production sectors with subsectors in the
reference case. Before 2040 hydropower and nuclear power-generated electricity are determined
by exogenously determined investments39. Hydropower and nuclear energy produced electricity
take part in the electricity generation share equation after 2035.

To  calculate the investment in each of the electricity technology subsectors, the expected profit
rates for the fixed (hydro and nuclear) electricity subsectors are set to zero. Then, investment is
allocated at the remaining subsectors through the logit function. The logit function calculates the
sectoral investment shares based on the ratio of the relative expected profitability of each of the
subsectors. As a consequence, subsectors with the highest expected profit rates Enr^^, receive
the largest share of that sector's investment. The investment subsector shares sum to one for each
production sector. The logit share equation at time t is formulated as follows:

                   rhoinv
                   j j: ,
                               forj=8andjj=l:6                                   Eq. 110
where
   EOTjjjjis the expected profit rate at time t (Equation 55),
   rhoinv is the logit share exponential, or elasticity, a parameter that controls the rate that
investment shares change in response to changes in expected profit rates, and
   n denotes the investment demands for oil, gas and coal generated electricity.

Next, the inverse of capital to output ratio QCap is calculated:
39 The history of hydroelectric and nuclear generation installations over the last two decades indicates that factors
other than the cost and performance of these technologies and the demand for electricity are the main drivers
determining electricity capacity installed. The penetration of these technologies is therefore modeled exogenously.

                                             70

-------
                                                                               Eq. Ill
And TestKj-s is corrected for the revised capital demands:
                     2»K.aflo\vJijt_1   3»ExoEle
-------
electric and nuclear generated electric production and the subsector annual investments that are
set exogenously. Thus, the annual subsector investments, KAfloWj for the electricty sector for
hydro and nuclear and the annual sector investment K} =«„/ denoting the potential investment into
the electricity sector have to be set (Equation 115). and the recalculated shares determine the
remaining subsector investments, given that those shares equal one when no subsectors are active.

 KAflow j=8(jjjt = ExoElec ^        for j=8 and jj=5 or 6                           Eq. 1 15

The investment into electricity is updated with the exogenously set investments.
 Kj=8 , = K j=8 , +    ExoElec^                                                   Eq. 1 16
                   JH
where
   n < jj and denotes the exogenously set investments, e.g., nuclear and hydro power generating
electricity.

Capital investment for all production sectors and subsectors besides the exogenously set
investments is then re -calculated as:
            , = Share, ^ • K . t                                                    Eq. 1 17
where
    Shareware the calculated shares which equal one when there are no subsector production
sectors, and
    Kj,t is the potential investment into production sector j.

Finally, the actual annual investment in the form of capital flow is retained as total capital stock
over the five-year time period as KAjjjitfoi each production sector and subsector through linearly
interpolated annual flows starting with the current period and going back to the previous model
solution-period:

 KAijit =  2» KAflow jiiM_, + 3 • KAflow j ^ ,                                       Eq. 1 18
Investment in energy production
The investment in energy resources is more complicated. A set of triggers function as indicators
for the oil, gas, and coal production sector implementation of resource-related investment
functions.

At the start of the model run, fossil fuel resource and reserve40 variables for a region are
initialized:
40 http://www.eere.energy.gov/: "Known resources can be classified from two standpoints: 1) purely geologic or
physical/chemical characteristics - such as grade, tonnage, thickness, and depth - of material in place, and 2)
profitability analysis based on costs of extracting and marketing the material in a given economy at  a given time. The
former constitutes important objective information of the resource and a relatively unchanging foundation upon which
the latter economic delineation can be based".  " For mineral resources, the reserve chosen for this index is the reserve
                                             72

-------
           jj = Drscej(jj
DrsVtmpj ^ t = Drsve} ^
                         } ^ t
                                  Eq. 119

                                  Eq. 120
Over time, oil, gas and coal investments are turned into into available reserves (Reserveyin energy
units) that can be consumed; these are calculated as follows based on investments in monetary
values (Eqdepj):

 Re servej  = PRconvrtj  • Eqdepj                                                 Eq. 121
where
   v=t,
   jj equals one, given that no subector production is active for fossil fuel production,
   PRconvrtj is the energy  conversion factor, converting the investment costs in monetary units to
physical energy units, and
   Eqdepj is the investment in fossil fuel production, where
                               Z AjjiV
>KAJJ,«
                                                                                     Eq. 122
   where
      xnpj equals the product of the nameplate lifetime of the technology (4 in the reference case
   for oil, gas and coal production) and the timestep (five years for SGM 2003),
      Oojjj,v equals one,
      oti,-26jjj,v is the vintaged capital stock scale coefficient in which technical change is
   incorporated (see normalizalion in Equation 27 of Equation 25 in "The vintage alphas and
   incorporating technical change").
      KAjjj,v is the active vintage-specific production sector or subsector capital, and
      Zjjj,v  incorporates the participation of the variable factors, where
                                       N-l,                     v
       Zj,;j.v = ! - KJJ.V * Peu)M * 2>csti.iii.v • Pie,,,,"'1)  which is calculated with
                                       i=i
   expected prices in the expected profit equation and implemented with long-run elasticities (see
   Equation 56),
      PeWJ is the expected commodity price (see Equation 16),
      Pie,jjj is the expected price paid (see Equation 15),
      p and M. are functions of the long-run elasticity ol,
      acstijjj.v equals (
-------
Note that the investments into available energy reserves are calculated with the CES production
function with long-run elasticities ol. The values of Ot-j^vused in calculating the reserves cab
be found in Appendix A. Also note thatj/" equals one in the reference case.

The quantities of uninvested depletable resources Drsce^ change over time, because of a
combination of resource growth and investment into reserves, that is, into energy for
consumption. Thus,

Drscejt& = DrsCtmpj l} + Drsces^ • ((1 + ResgrOj JJn'*Ns"!p) - (1 + ResgrOjiii°*~l)n*l'p))
                                                                                Eq. 123
where
   DrsCtmpjjj is an exogenous value in the base year and updated after reserves are calculated
(see Equation 126),
   Drscej j is the uninvested depletable resource for which the initial value is an input parameter
value (Equation 119 for the initial value),
   ResgrOjjj is the calculated growth in the resource base for depletables (oil, gas, coal) as a time-
dependent interpolation of initial and terminal values, as long as T, which is 5 times the number
of time periods (Nstep*t), is smaller than Tresgrz,.
        ResgrO", =
       where
                  , Trcsgrzjjj, and Resgrzjjj are input parameters.

Calculated reserves associated with desired investment are checked to see if they exceed available
reserves.
 DrsVtmpjjjt = Re serve,
                          - Reserve
Eq. 125


Eq. 126
where
   DrsCtmpjjjare the available energy resource at a point in time, which are updated during the
iterations finding the model solution,
   DrsVtmpjjj,t is the energy resource available at a point in time initiated with the energy
resource data information (Equation 120 for the base year value) and calculated through resource
investment calculations in the projections and updated through Equation 70.

Resources are decreased as long as the amount of production Reserve j is less than the resources
available.

Note that the iterative model results for one region for each of the 12 time steps (1990 through
2050 in five-year time steps) are shown  in "The solution procedure" for the resource reserves
invested in to be consumed, as well as for the depletable oil, gas, and coal resources.
                                           74

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The ratio of available reserves and desired reserves is calculated as

_  _           DrsCtmpjh/
Pet Re serves =          J-%
                          /Reserve.
                                                                             Eq. 127
Energy sources available for consumption are set equal to the calculated available reserves, which
in turn are checked for depletion when vintages are operated. (See "Checks on depletable
resources" after the calculations regarding operating old and new vintages.)
           jj, = Reserve^
                                                                             Eq. 128
If the ratio of available reserves and desired reserves is smaller than one, investment is scaled
down:

Eqdep joj = Pet Re serves • Eqdepj -a                                          Eq. 129


KAflowjjj( = Pet Reserves* KAflowJJJt                                    Eq. 130
and the previously calculated investment capital over the last five years into the production
sectors for oil, gas and oil is updated based of resource availability as follows:
    j jjv=t = PctReserves«KAjjJV=l

and the investment into reserves is set to the maximum available:
Re serve j = DrsCtrnp^
                      ^
                                                                             Eq. 131
                                                                             Eq. 132
Figure 10 illustrates investment in production sectors over time in the USA. The highest level of
investment is in the Everything Else sector; coke production shows the lowest level of
investment. Note that the vertical axis is logarithmic-transformed. The horizontal axis shows the
time line; for 1990 t=0 and for 2045 t=ll.
                                          75

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          Investments into Production Sectors other than Energy in the
                                  Reference Case
  10000000
  1000000
   100000
    10000
     1000-
      100

  - Other Ag.
  -ETE
  -Wood Prd
  "•Chemicals
HH-Cement
--»-• Steal
  -NFMetate
  -Othlnd
  — PassTran

-------
              Investments in Fossil Fuel Related Production in the
                                 Reference Case
  30000-,
  20000
  15000
  10000
   5000
  -Crude Oil
  -Natural Gas
  -Coal
  -Cokel
Hit-Oil Refining
  -GasT«D
        1990 1995 2000  2005  2010 2015 2020  2025  2030 2035 2040  2045  2050

Figure 11 Investments in fossil fuel related production over time

           Investments in Electricity Production in the Reference Case
  70000 i
  60000
  50000
  30000
  20000
  10000
        1990 1995 2000  2005  2010 2015  2020  2025 2030 2035  2040  2045 2050
Figure  12 Investment in electricity production over time
Demand for capital
                                                77

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As part of the iterative model solution, where annual capital flow is the result of the investment
equations described above, demand for annual capital Kdem^ by each of the production sectors
and subsectors is set equal to the annual capital flow
 Kdem. •• = KAflow
                                                                            Eq. 133
Intermediate capital goods (i~l:22) are produced as £Dy-/m. using a fixed coefficient or Leontief
production function, whose coefficients are the CapMatij matrix whose row values i are the
Sharelnv coefficients which are inputs (see Appendix A).
              n
             :V
                     Kdem ^ • CapMatirj
                                                                            Eq. 134
Given that Kdemjj, is the capital demanded by a production sector./ or subsector jj and CapMaty,
are the fixed coefficients of a fixed coeficient production function, the demand equation for
capital (Equation 134) can be mapped onto the Leontief demand equation (see Equation 54)
                                        A,
                                         ,
                                         !iM
                                               KA- -u . The quotient of the scale factors of
where demands are described as ED  =
the inputs to production and capital kjj/h-2fjjjis equivalent to the elements of the
vector for each of the inputs, and KAjj, is equivalent to the (demanded) investment capital
Total (summed over all production sectors) capital investment (i=2<5) demand is the summed
demand for all capital inputs multiplied by the relevant supply prices paid:
ED
CL/i-26,j-
     26,j-25-inv
                22
             -V
             ~
                       22
ijpjj • CapMat,_2(M-Pi1>J>JJit i
Eq. 135
Total investment demand needed for GNP accounting is
          22 f n [~_22                      1
                           ^ • CapMatij
                                                                            Eq. 136
Additional costs towards demands
Transportation demands and distribution costs, WHSL, and TRNP,, are added to the final
Everthing Else demands;

 EDi=E1E)j = EDi=ETC j + £ WHSL( + f) TRNP;                             Eq. 137
                        i=l           i=l
where

                                          78

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   WHSLi is the summed over all adjustment factors to the supply sectors calculated when
operating production sector vintages (see Equation 82) and when household consumption is
calculated for j=27 (Equation 193 for j=27, v=t, and n=l):
 WHSL-f
               Y = t-3
                    Jj=l
EDV.
         'Pi
                                    i=ETE,j,jj.t
                                              i.,)« ExIml.TxproiJ>Jj + TxaddiijJ«
                                                ij^hM-i + TxaddlJ=27=hh>JFl].
  EDi
where
             'i=ETE,j=27=hh,jj=l,t
                                                                                Eq. 138
   v refers to all actively operating vintages (v=t-3:t-l for old vintages and v=t for new vintages),
   n is the number of subsectors with n < jj,
   j is the number of production sectors,
   i refers to input sectors,
   adjijjj.t, is a time-period-dependent adjustment factor that reflects markups and intra-regional
transport costs,
   P^tis the market price,
   Trijt is a time-period-dependent supply sector transportation cost factor,
        j is the transportation cost rate parameter,
          j  is a proportional tax rate on the i* product,
   Txadd,jjj is an additive tax on the i* product,
   EDVyjj.v denotes demand by a vintaged production sector or subsector, and
   Pii-ETEjjj,t is the price paid by the producer for Everything Else input.

and

   TRNPj is the summed over all supply  sector transportation costs calculated when old vintages
are operating (see Equation 83) and when household consumption is calculated forj=27
(Equation 194 forj=27, v=f, and «=/):
              v=t-3
                                      EDV.
                                                  Ii=ETE,j.jj,t
                            li=ETE,j=27=hh,jj,t
                                                                                Eq. 139
Final carbon permit fees, CPermF^, are a function of the energy demands and the carbon fees
per dollar of energy use, which are a function of the global warming potential and the emission
coefficient of the fuel combusted and demanded by investments (see Equation 10 for the
calculation of Cpfy. Thus,
                                           79

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 CPermF5 J=25=inv =


Households
Eq. 140
A great many operations are carried out in the model's household sector. The household sector
concerns
    •  Labor supply
    •  Land supply
    •  Household savings
    •  Household demand for final products.

Demographic characteristics are the basis for household behavior as a representative consumer
with regard to labor supply, land supply, savings, and demand for final products. Household
income is derived after adjusting for taxes and government transfers. Income is then split between
savings and expenditure, with a savings function that depends on the interest rate. Labor supply,
land supply, household income and savings, and household demand for final products are
described below. In the subsequent discussion, personal income in the household sector is the
regional population's total income, and households are the total regional population. The
household demands include demands for land and labor, and household consumption.

Labor supply
Labor supply depends on regional demographics. The SGM tracks population within each region
by gender and five-year age cohort. Population data may be read in directly, using projections
from either the World Bank or the United Nations for the model base year and for all future SGM
time steps. This is the usual way of specifying population in the SGM (see Appendix A for data
used).

Alternatively, a demographics module that uses an age-cohort method of calculating population
by age and gender for each region can be incorporated. The required input variables are fertility,
migration, and mortality rates. The demographics module keeps track of population within each
region by gender and five-year age cohorts.  Base year populations may evolve by applying
assumptions with regard to survival rates, fertility rates, and migration rates.
For any time period, total population (of a region) is given by
         NAOR
 POPU*  =
where
Eq. 141
              is the number of males in age group age,
               is the number of females in age group age, and
   NAGE is the number of age groups defined, which equals 16.
                                           80

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The fraction of the population that is either over 15 years old or under 65 is calculated to obtain
the fraction of the population potentially in the labor force as wage earners. Thus,
                                          Eq. 142
                                          Eq. 143
working_age_poplot      (POP,^.. +POP3ge>femaks)
or
                          ;«=] 3,
working _ age _ pop^ =
where
   the male and female population is summed between ages 16 and 65, that is age groups 4
through 13, and
   ng is either the male or female population.

Labor supply is gender-specific, which is denoted by the subscript ng. Labor supply for the
projections is calculated in the SGM using the following equation:
EDi=25=!bS)J=27=hh = -] • Z working _ age _popng • LB0iBg • [1 - expCLE,,*  .  '=25='bs-'  )]
                       ng                                                *"i=ETE,j=27.jj.t
                                                                               Eq. 144
where
   when j equals 27, representing the household sector, jj equals one by definition,
   ng is either male or female,
   LBo,i^is the maximum potential share of the gender-specific working age population
employed in any given year,
   working_age_popng is the gender-specific working age population (ages 15 to 64) (calculated
from the age-specific numbers of people, (see Equations 145 and 146 or read in), and
                      i=2S=lb»,t

                     i=BTE,j=27,ij,t
                                   denotes the labor supply responsiveness,
   where
      P,.25,i is the average annual wage rate (calculated initially from the input-output table by
dividing total labor supplied (Pi=
                               i=25=|bs ,
     XS
= - '-
                                                     see Equation 1 and 7) and equals the
   market price wage rate during the model solution process, and
      Pii-ETEj-27jj,t denotes the price of the numeraire sector.

The labor supply function parameters LB are determined as follows: the maximum potential share
of the gender-specific population in the labor force for the base year LBo,ng is either fixed by an
exogenous parameter or calculated from data:
LB
    0,ng
       _ working _ age _popng
                 POP,,
                                          Eq. 145
                                           81

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LBi,ng is a labor supply function coefficient in the labor supply responsiveness equation, which
can be formulated as follows and although gender-specific is equal in this case for both male and
female:
                 (workmg_age_popt>LB0,
                                            0,n
 LB1>ng =
                          i=2J=Lbs.t
where
   Edi=25-ibsj-27=hh is the total demand for labor supply (see also Equation 152 below), which is set
exogenously for the base year, and calculated for projections as in Equation 147.

Alternatively, to make calibration to a prescribed path simpler, the labor supply function coefficient
LBi,ng can be calculated as a ratio of the labor supply and the working-age population. Under this
alternative labor supply elasticity is in effect eliminated.
LB, „. =
    ' *
where
            ED'=25=lbaj'2?=hh
         working _ age __ popl
                                                                                Eq. 147
                 tota^ labor supply to be provided by households and is determined by the wage
rate (see Equation 144).
Labor produced, SalesV^^ibs, is set equal to the negative value of labor supply demand such that
the market calculations can be performed when solving the model for supply and demand
Sales^=2fclbs = -1 • EDi=25=lbsJ=27=;hh
                                                                                Eq. 148
The fraction of labor demand that is the demand for household's own labor LB2,2 is calculated as
follows:
LB   =
    •
where
                        - p
                  ,j=27=hh   ri=25=lbs,t
                                                                                E   149
   X,-25j-27is labor demand by households in the base year,
   Edi-2sj«27is total labor supplied by households, and
   P^s.t is the market price of the average annual wage rate during die model solution process,
and Edi-25j-27* Pi=2s,t is total payment for labor.
The number of households, Nhh, in a regional population can be calculated based on the average
number of people per household, pphh, as input, in the following equation:

                                                                                Eq. 150
                                           82

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where
   Nhh is the number of households,
   POPsoiis the total population in a region, and
   pphh is the average number of persons per household.

Alternatively, if the number of households, Nhh, are known, the number of people per household,
LB2j, can be calculated:

                                                                                 Eq. 151
          Nhh

Note that next the LBu, LBij, LB2,j, and 182.2 values are set constant over time, initially (after the
base year calculations), but are then recalculated when projections are made.

Land (agricultural land) supply
Households supply land on the basis of a land rental rate, where the land supply denotes the total
land area that could be managed for agricultural or other purposes. SGM 2003 has one land
type.4' Demand for land supply in the base year is regional input data (see Appendix A for data
examples) and is calculated for projections in a parallel fashion to the demand for supply of
household labor:
         ,^^ = -1 • TLA • R0 • [1 - exp(R, •      -24°M	)]                 Eq. 152
                                               "1i=ETE>j=27=hh,jj,t
where
   TLA is the total land area that could be managed for agricultural or other purposes,
   RO is the maximum potential share of land supplied to the market for the base year, and
l-exp(R,
                    P.
                  .
                * 1i=ETE,>=27=hh,jj,t
                                 denotes the land supply responsiveness,
   where
      P,-24,t is the average annual rental rate of a unit of land, initially calculated from the input-
                                       XS
   output table information (Pi=Ms=u, =	E2^!l—; see Equations 1 and 6), and equals the
                                    k'-'i=24=!j,j=27=hh
   market price land rental during the model solution process, and
      Pii=ETEj=27=hhjj,tis the price of the numeraire sector.

The land supply function coefficients/? are determined as follows:
The maximum usable land, expressed as a fraction of land in a region R0 is input data for the base
year (see Appendix A for values).

RI is a land supply function coefficient in the land supply responsiveness equation.
41 The land supply coefficients R have, therefore, no/ subscripts
                                            83

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      log
   FD
1      '=34- l».j'27f hit
      TL
              P
              r=
                                                                              Eq. 153
where
   TLA is total regional available land area,
   RO is the maximum useable land for the region, which is input data for the base, and
   Pi=24,tis the market price of the land rent during the model solution process,
   EDi=24=isj=27=hh represents the demand for land use or land supply, which for the base year is
regional input data, and is calculated for projections as described above (Equation 152).

Produced availability of land, SalesVM4-tn is set equal to the negative value of the demand for
land supply such that the market calculations can be performed when solving the model for supply
and demand.
SalesV
        24=ls
= -UED,
                                                                    Eq. 154
When land rental income is calculated, the relationship, R2, between land demanded and land rental
price is important; R2is calculated as follows from the initial elements of the input-output matrix:
    =
      Nhh»P1=24=lM
                                                                              g
where
   Xi-24j =27 is the land demanded by households in the base year,
   Nhh is the number of households at time t and
   Pj=24,tis the market price of land rent during the model solution process.

Note that the R0, RI, and RI values are set constant over time, initially (after the base year
calculations), but are then recalculated when projections are made.

Personal income or household income
Personal income Pine (Equation 156 and updated in Equations 171-175 and 188) equals the sum
of retained income HHincl (Equations 157-160), labor income HHinc2 (Equation 166) and land
rental income HHincS (Equation 168) minus personal income tax (calculated fay means of the tax
rate coefficient PItr) to which government transfers GovTr (Equation 170) are added and personal
savings (Equation 179) are subtracted (Equation 180).  Personal income calculated thus, is saved
in a household consumption variable Cons, (Equation 181) to be part of GNP balancing at time t
(Equation 236).

Personal income, government transfers and savings are calculated sequentially, starting with
personal income based on retained income HHincl, labor income HHinc2, land rental income
HffincS and taxation on personal income PItr (Equation 157). Retained income HHincl may be
impacted by the recycling of carbon revenues, depending on if and which carbon policy is
implemented (Equations 171-175). Next, government transfers are calculated based on this
                                           84

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income, but without taxation (Equation 170). Depending on if and which carbon fee policies are
implemented, household income is updated based on recycling of carbon revenues. Household
savings HHincS are calculated based on taxed income; they are in effect demand for capital by
households (Equation 176) and dependent on the capital interest rate P,=26  Savings are subtracted
from income. After these updates, household consumption is set equal to household income.
Household income is once more updated in Equation 188 by labor (HHinc9) and land (HHinc 10)
expenditures (see Equations 189 and 190).  A budget constraint calculation based on that updated
household income (Equation 191) limits all household demands £Z),j before a model solution can
be sought.

Thus, the first step in calculating household income is as follows:

Pine = (HHinc, + HHinc2 + HHinc3) • (1 - PItr) + GovTrt                       Eq. 156
where
   PItr is the personal income  tax rate,
   HHinc 1 is retained household income,
   HHincl is labor income,
   HHinc3 is land rental income, and
   GovTr, are government transfers in the base year,
which are all explained below.

HHinc, is the retained household income, which in me base year (see Equation 157) is calculated
from the production sector- and subsector-specific retained household earnings parameters REoj
and the demands by the production sectors and subsectors for capital X^ejjj, restrained by taxes
Citr said XitCj and the market interest rate Pi-is- In the projections retained income is based on
profits in the production sectors (see Equation 160).

For the base year:
           22
                            (0 - Citr) + XitCj )• (l - (REOJ • (1 - exp(RE,,J
                                                                              Eq. 157
where for each production sector
   ZXi-sejjj is the summed subsector demand for capital by the production sector in the base year,
   Citr is the corporate income tax rate (see Appendix A for values),
   XitCj is the production sector and/or subsector tax credit rate or dividend, which can be
initiated by setting a switch and which impact is dependent on demand. Tax credits are not
activated in the reference case. The equation is shown for potential implementation, replacement
or elaboration:
                                                                              Eq. 1 58
j = ]T [xiTCratej jj • Kdem^ ]
   JH
   where
      XITCrate jsthe investment tax credit rate (set to zero), and
                                          85

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             j is the sector and subsector specific demand (see Equation 133 when final capital
   demand for each production sector and subsector has been determined and Equation 71 under
   "Checks on depletable resources,")

   Pj=26,tis the capital cost interest rate,
   REoj is the maximum retained earnings for the base year, which is a production sector-specific
input parameter,
   REi j is the production sector-specific retained household earnings parameter, which is (for the
base year 1990) calibrated against input data (through the Total corporate Retained Earning
parameter, TREte).
           log
                                TREte
   RE,, = —t	>-	=1                            Eq. 159
                              * i=26
   where
      TREte is the total corporate retained earnings, which is read-in for calibration in the base
   year and calculated for the projections (see Equations 161-164 below),
      Xj_26j denotes die demand for capital by each production sector, and demands by
   investment, households, government and trade in the base year.

The REojSndREij values are set constant over time after the base year calculations but are then
recalculated when projections are made.
For projections, retained income HHinci is based on profits in the production sectors:
           22
HHinc, =
           H
  >
ij U ((1 - Citr) + XitcJ- (l - (RE0-J • (1 - exp(RE:)J * P!=26,,))))
Eq. 160
where
   Tt jjj is the production sector or sufasector profit summed over the actively operating vintages:
           t-i
   7Iiii= SPctDep'ete*7t°j.JJ.v +7tNijj.v
          v = t-3
   where
      PctDeplete is calculated as not equal to one (see Equation 67) if depletable resources have
   reached a depletion level when old vintages are operated,
      7tOjjj,v is the profit from operating old vintage production sectors or subsectors (see Equations
   57 and 58),
      JiNjjj v is the profit from operating new vintage production sectors or subsectors (see Equation
   72),
and

-------
   REi j are the production sector- and subsector-specific retained household earnings, which are
recalculated through Equation 159 with a recalculated total corporate retained earnings (TREte)
where
             22 ,     ,
   TREte = £[REtej]                                                       Eq. 161
   where
REteJ =
                           ~Citr).XitCj
                                           (RE0;J • (1 -exp(RElo • Pl=26-t»    Eq. 162
Retained income HHincI might be impacted by the recycling of carbon revenues, depending on if
and which carbon policy is implemented (Equations 157-160).

If carbon pricing is simulated, corporate earnings have to be adjusted in accordance with the carbon
policy implemented. Among the options explored are die impacts of carbon policies on corporate
earnings, e.g., carbon revenue recycling of 60% towards industry and 40% to households
(ICRBfeeOPT=4) or all are recycled to industry (ICRBfeeOPT^ff).
      TREte = TREte + 0.6 • CrbFeeTot, + 0.6 • ExIBT,
Case 4: 60% of the domestic carbon fees are recycled towards industry and 40% to households.

                                                                             Eq. 163

Case 6: all of the carbon fees are recycled to industry if the CrbFeeRcyPctsis on,

      TREte = TREte + CrbFeeRcyPct3«CrbFeeTot, + CrbFeeRcyPct3»ExIBT,  Eq. 164

where
   CrbFeeRcyPctj refers to a fraction.
   CrbFeeTot is based on domestic carbon fees and carbon permit trade (see Equation 101),
   ExIBT is the amount of IBT tax collected above the base year, which remains independent of
any carbon fee  recycling. No increases in IBT taxes occur if TxIBT is constant over time.
             22  ,                              .
   ExIBT, = £(SalesPj • (TxIBTJt -TxIBT,_,,„)) (see Equation 209) and

   where
      TxlBTj is the production sector-specific indirect business tax, and
      SalesPjis gross production summed over all active vintages and production subsectors in
   monetary terms: SalesPj =
                           v=t-3
                                                     (see Equation 208).
The tax on profits produced in the production sectors Tax3j,i:22 is kept track of in a tax array as
follows:
Tax3,j=i:22 - Citr • ttj - XitCj
where
                                                                             Eq. 165
                                          87

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   Xitej is production sector and/or sub sector tax credit rate or dividend (see Equation 158), and
   Citr is the corporate income tax rate, and
   it, are die production sector profits after summing over the operating vintages and subsectors.

HHinc2is labor income, which is estimated based on demand for labor supply, social security
taxes and the market price for labor:

HHinc2 = (I - SStr) • -1 • ED1=25=lhs J=27=hh • P1=25=lbs t                          Eq.  166
where
   SStr is the social security tax rate, which is a regional input parameter for the base year,
   EDj-2sj-27 is the labor supply demanded, which is described above, including its changes when
projections are calculated, and
   P,=2s.tis the market price of labor rental.

The social security tax is kept track of in a tax array as Tax2j-27 and is also called HHinc}

Tax2>J=27=hh = [SStr . -1 • ED1=25=lbSiJ=27=hh • P1=25=lbs,J                             Eq.  167

HHinc3 is land  rent income, which is calculated based on demand for land supply £4-2^-2?
(Equation 152) and the market price of land rental Pi-u-i* Land supply may change over time
through the land-use modifying parameter/?2 (see Equation 155) as do the number of households
Nhh  (Equation 150). Note that SGM 2003 has one land type.

HHinc3 = -1 • ED1=24=lsj=27=hh • Pi:=24=ls>t                                       Eq.  168
where
   Edj-24j-27is the demand for land supply, which is described above (Equation 152), including its
changes when projections are calculated,
   Pj_24i,is the market price for land rental during the model solution process,
   Nhh is the number of households, which may also change over time, and
   R2 is a parameter that is based on land demanded by households and land rental price (see
Equation 155), which determines land rent income.
The personal income tax Tax3j^7 is also called HHinc4.

 Tax3 j=27=hh = (HHincl + HHincl + HHinc3) • Pitr
where
   Pitr is the personal income tax rate.
Eq. 169
G0v7>,are government transfers in Equation 156, which are either input parameters (see
Appendix A for base year values) or calculated. GovTr are also called HHincg.

When government transfers are calculated for the base year (for (=0) and for projections, they are
calculated based on per capita income Pine (Equation 156), percent of population in young and
                                           88

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o
                 old age groups YngOld, and the fraction of the population working working_age_pop.
                 Government transfers are assumed to be untaxcd.

                                                  t ( (HHinq + HHinc, + HHinc,) Y' %
                                                               POP.
                                     -NED.
                                            i=25=lb».j=27;
                                      Y
                                   r=hh
                                     working _ age _ pop )
                                                           • YngOld83
                                                                                              Eq.170
where
   the exponents gl, g2, and g2 equal zero in SGM 2003, and
   YngOld denotes the non-employable population, that is the population under age 15 and over
age 65, and the other parameters are described above.

Depending on if and which carbon fee policies are implemented, household income is updated
based on recycling of carbon revenues. If carbon pricing is implemented household income has to
be adjusted in accordance with the carbon policy. CrbFeeTott represents the carbon fee at time /.
The different carbon policy case impacts on household income (ICRBfeeOPT=case) are shown
below:

Case 3: all carbon fees are returned to household income.

      Pine = Pine + CrbFeeTott                                               Eq.  171

     where
        CrbFeeTott is based on domestic carbon fees and carbon permit trade,

Case 4; 40% of the carbon fees are returned to household and 60% to industry.

      Pine = Pine + 0.4 • CrbFeeTot,                                          Eq.  172

Case 5: domestic fees are returned to consumers, permits are returned to the deficit
    (a) if carbon trading is implemented and carbon trade provides for revenue households will
       receive the  difference between domestic carbon fees and the carbon trading fees.

       Pine = Pine + CrbFeeTot, - CrbTrade,                                  Eq.  173

     where
        CrbFeeTott is based on domestic carbon fees and carbon permit trade,
        CarbTradet refers to the carbon permit trade.

    (b) If carbon trading is a net loss, households receive the domestic carbon fees.

       Pine = Pine + CrbFeeTot t                                              Eq.  174

Case 6: all of the carbon fees, determined by CrbFeeRcyPct2, are recycled to households.

       Pine = Pine + CrbFeeRcyPct2»CrbFeeTott                               Eq.  175

      where

                                          89

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         CrbFeeRcyPct2 refers to a fraction.
Savings supply
The savings supply or capital supply requires the determination of personal income Pine, which
includes the income from (a) providing labor services, (b) land rental, (c) retained corporate and
personal earnings, (d) government transfers, and (e) possibly, recycled carbon revenue.
Household saving supply for the base year is an input parameter, and changes over time are
determined by using a simple exponential model. Thus,

ED1=26J=27=hh = -1 • Pine • S0 • (1 - S, • exp(S: • Pl=26))                         Eq. 176

where
   Pine is personal income (see Equation 156),
   So is die household savings function coefficient in the base year, and
    [l - Sj • exp(S2) • Pi=26 1 J denotes the saving supply responsiveness, where
   Si and 82 are described below, and
   Pi-26,tis the capital cost interest rate and equals the market price during the model solution
process.

The savings function parameters are determined as follows:

So = the household function coefficient in the base year
S, = 1                                                                          Eq. 177
and

                P
                ri=26,t
where
   EDi-26j-2?is the household saving supply (Equation 176),
   Pine is the taxed personal income to which government transfers are added (Equation 156),
   So is the household savings function coefficient in the base year, and
   P;=26,tis the capital cost interest rate which equals the market price during the model solution
process.

Note that the S0, Si, and S2 values are set constant over time, initially (after the base year
calculations), but are then recalculated when projections are made.

Household Saving (=HHincs) is set equal to (negative) household savings.

Saving = -1 • EDi=26=capilal)j=27=hh                                              Eq. 179

where
   EDi=26j-27isthe household savings supply (see Equation 176).

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Personal income is updated next for savings expenditures. After this update, the variable
represents consumption expenditures.

Pine = Pine - Saving                                                         Eq. 180

Household consumption, Cons,, particpating in the GNP accounting as illustrated in Equation
236 below, thus accounts for personal (household) income that can be used for commodity
consumption including land and labor expenditures, given that they are not subtracted as of yet
(see Equations 188- 190 below).

Cons t= Pine                                                                Eq. 181

To obtain the total demanded savings supply, the corporate retained earnings are added.

EDi=26=caplUU,j=27=hh = EDi=26=caplta!J=27=hh ~ TREte                                Eq. 182

Production of capital by households SalesV,,26 is set equal to the updated produced savings
supply.
SalesVt=26 = -1 • ED1=26=
                           capltelj=27=hh
                                                                               Eq. 183
Total household demand for variable factor inputs
Household demands will be constraint by prices paid for the household variable factor inputs
(/=! :22) at time / and by household income after accounting for (subtracting) household
expenditures for labor and land (Equation 188). The total costs of meeting these variable-factor
household demands are therefore calculated next:

DemTot^^ =|][ED,i)=27=hh -Pi1-J=27=hhjjt]                                   Eq. 184
                  1=1
These summed household demands as calculated in Equation 184 are to be used to scale the
demands for inputs by households (see the budget restraints simulation expressed in Equation
191).

Household demand projections
Each consumption good (each/) in household consumption (demand) is assumed to have an
income and a price elasticity of demand42;
                        Pi
                        rii=ETE,j=27=hh,jj,l
where
42 The constant elasticity equation is found in Edmonds and Reilly (1985:248-249).
                                           91

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   Pine refers to the updated, by savings expenditures, personal income (see Equation 180),
   ED., >s a sealer for household demand for supplies (i) which incorporates income and price
elasticities:
where
      Xij-27-hh is the household demand for supplies in the base year,
      Pine is household income (Equation 180),
      P'i-ETEj-27jj,t is the price of the numeraire sector,
      Piij-27jj,t is the price of paid for inputs with regard to the household sector,
      P,,t is the market price, which equals one in the base year and equals the market price
   during the model solution process,
      ei j is the income elasticity,
      E2j is the supply price elasticity.

Note that the Eo,i values are set constant over time first; then household (J=27=hh) fuel use
changes of oil, gas, coal and electricity (i=3,  4, 5, 8) over time are calculated by means of the
updated sealer which is calculated as follows:
 E0hht=     ''                                                   (unMess)    Eq. 187
   •  '    Factorihh-t
where
   Factor, u,, = (1 + HHAEEI; ihh ) Nstep     (see Equation 1 9)
   where
      HHAEEIi,hh is a technical change parameter for household fuel use.

Labor, HHincy, and land, HHincjo, expenditures are subtracted from personal income such that
personal income Pine denotes personal income available to purchase produced commodities.
Note that consumer purchases of housing are not subtracted from income in SGM 2003.

 Pine = Pine - HHinc9-HHinc10                                               Eq. 188
where
    HHinc9 =  - 1 • Pi1=25=lbS;J=27=hh,JJ,t • LB2 2 • ED1=25=lbs-J=27=hh                   Eq. 189

are the labor expenditures, and

    HHinc10 = (Pii=M=UJ=27=iih.iJ., • R2 • Nhh)                                   Eq. 190

are the land expenditures,

    where
      Pii=25j=27jj,t is the price of labor rental with regard to the household sector, and
                                           92

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                                      the price of land rental with regard to the household sector.
                   Budget constraints need to be satisfied before a model solution can be sought. Therefore,
                   household demand is restrained by the summed shared demands of all inputs as follows:
                   ED
                      i=l:22,j=27=hh
     EDu»Pinc
     DemTot;.
                                                 Eq. 191
                                            j=27
                   where total demand by the household sector from the production sectors DemTotj was calculated in
                   Equation 184, total household income Pine was calculated in Equation 156 and updated in Equation
                   182, and demand by the household sector £Dy for industry goods was calculated in Equation 185.

                   Finally, the demand for household labor, as determined by the household labor fraction LB2i2 is
                   subtracted from the total labor supply Edi=2sj-27 such that the labor supply available to the rest of
                   the economy is determined.
                   ED;
     = EDi=25=lbs,J=27=hh.(l-LB2,2)
                                                 Eq. 192
                   Additional household expenditures
                   Adjustment factors, WHSL,, for the supply sectors (representing distribution and markup
                   factors) are calculated. All variables in this equation are described above.
                   WHSL, =
i.t +Tru
                                                   +Txadd
                                                           lj_27
                                                                                              _hh]«
ED
                                  i.j-27-hh.
                                        'Pi
                                           i=ETE,j=27=hh,jj,t
                                                  Eq. 193
                   where
                      v refers to all actively operating vintages (v=t-3:t-l for old vintages and v=t for new vintages),
                      n is the number of subsectors with n < jj,
                      j is the number of production sectors,
                      i refers to input sectors,
                      adjijjj,t, is a time-period-dependent adjustment factor that reflects markups and intra-regional
                   transport costs,
                      Pi>t is the market price;,
                      Trj,t is a time-period-dependent supply sector transportation cost factor,
                      Exlm, is the transportation cost rate parameter,
                            jj is a proportional tax rate on the 1th product,
                            ijjj is an additive tax on the i* product,
                          jjjj.v denotes demand by a vintaged production sector or subsector, and
                      Pii-ETEjoj,t is the price paid by the producer for Everything Else input.

                   Transportation costs for the household market for imports and exports TRNP, are calculated
                   as follows:
                                                              93
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                        ED       /
 TRNP; = Tr{ t • Ex Im, •    '>J=27=%;                                        Eq. 194
                                / rIi=ETE,j=27=hh,j].t

Taxes on households Fox j,/^? are calculated as follows:
              24 ,                                 .
 T«i.j=27=hh = £(PLt + Tri,t * Exlnv abs(ED(.j=27=hh))» (TxproM=27=hh -l)      Eq. 195
              1=1

Household subsidies Subsit equal household taxes Taxtj but for the sign of household demand:

 Subsid; = -Tax, J=27:=hh                                                       Eq. 196

Taxes on households per unit production TaxpUj^7=M, and subsidies to supplies per unit supply
are calculated when the additive taxes are greater than zero.
                24  .                        .
 TaxpUj=27=hh = X (jxaddlj=27=hh • ED, J=27=hh)                                Eq. 197
                ;=i

Subsidies per unit supply StibsidplJ, equal the taxes on the household sector:

 SubsidpU, = SubsidpU, - Txadd; j=27=hh • ED, J=27=hh                        Eq. 198

Carbon permit fees CPermFsjare a function of the energy demands and the carbon fees per
dollar of energy use, which in turn are a function of (1) the global warming potential and (2) the
emission coefficient of the fuel combusted and demanded by households (see Equation 13 for the
calculation ofCpfy. Thus,
CPermF5 =27=hh =    cPf, - ED,_=27=hh                                       Eq. 199
I5,j=27=hh - ^V-*"! ~ i-i-'i,j=27=hh
          i=l
Government

Production of government services
The government is modeled as potentially producing up to three government services in a nested
production function hierarchy:
   •  general government sen-ices,
   *  national defense, and
   •  education.
The number of government services modeled in an SGM region is determined by regional data
availability.

Government services are assumed to be produced with fixed input-output coefficients.

                                         94

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The reference case of SGM 2003 contains only one general government service and the
government preference function GFis, consequently, set to one, given that no government
subsectors are simulated. In the equations below we show, however, the potential implementation of
different government subsectors.
GF0i=l
Eq. 200
Government taxes and subsidies TaxGov/tf=i,.saK calculated in a manner analogous to taxes and
subsidies related to the production sectors. However, they are applied in a model solution
iteration as paid to the government sector itself.

TaxGovltc =£(p. t +Tri>t .ExIm.-ED. J=26=gv • (ixpro,J=26=gv -l))             Eq. 201
             i=l
where
   when j=gv equals 26 and jj equals one by definition,
   itc is the indicator for 5 potential taxes,
   TxprOg-26-gv is a proportional tax rate on the government sector which equals one for all
supplies in the reference case, resulting in zero taxes in the reference case (note that when j equals
26, jj equals one by definition),
   P,,(is the market price, which equals one in the base year and equals the market price during
the model solution process,
   Tr, t is the time-dependent transportation cost factor (see Equation 9)
   Exlnii is the transportation cost rate parameter (these input parameters currently equal one,
   ED(j=26-gv is the demand by the government sector for capital supply.

Government supply subsidies SubsidGov equal government production taxes TaxGovitc.

SubsidGov=-TaxGovilc                                                    Eq. 202

Taxes on production per unit production TaxGovpUiteand subsidies to supplies per unit  supply
are calculated when the additive taxes are greater than zero,
                25
TaxGovpUltc =£(Txadd,J=26=gv »ED1)J=26=gv)
Eq. 203
where
   Txaddjj=26=gV is an additive tax on government supplies.

Government subsidies per unit supply SubsidpU equal the taxes on the government sector.

SubsidpU = TaxGovpUj(£                                                    Eq. 204

The carbon permit fee CPermFsj^t is a function of the energy demand by government and the
carbon fee per dollar of energy production, which is a function of the global warming potential
and the emission coefficient (based on the carbon content) of the fuel combusted (see Equation 10
for the calculation of Cpfy- Thus,

                                         95

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 CPermF5 j=26=gv = f](cpf: • ED, j=M=gv)                                       Eq. 205
                  1=1

Total government taxes are the summed production sector taxes to which various other taxes are
added as described in detail below:
             27
 TotTax, = ^ (Tax,j + Tax2 j + Tax3 j + Tax4 • + CPermF5j)              Eq. 206

where
   Taxq-i ^for production sectors are calculated when operating old and new vintages (Equation
84forv=t-3:t),
   Taxij-26 equals TaxGovi (see Equation 201) calculated during the previous model solution
iteration, (Tax2j-26 equals TaxGov2 which equals TaxGovi
   Taxq-27 equals taxes on household related to exports and imports (Equation 195),
   Tax2j-i 22 for production sectors when labor taxes (i=25) are calculated (Equation 85 for v=t-
3:t),
          ;is me labor income tax related to the social security tax rate (Equation 167),
            is the production sectors (j) tax on profits (Equation 165),
   Tax3j=27 is the tax on personal income and personal income tax rate (Equation 169),
   Tax4j-i:22equals the taxes on the production sector-specific sales:
   Tax4 j = Sales' • TxIBT,                                                    Eq. 207
   where
      TxIBTj is the production sector-specific indirect business tax, and
      SalesPjis gross production summed  over all active vintages and production subsector in
   monetary terms.
                  t
      SalesP =
     l(pRDVJJJ>v.PrJt)
Eq. 208
      where
         PRDVjjj.v is vintage and sector (and subsector, if active) specific gross production,
         Prj>t is the price received for the commodity produced.

      The amount of 1BT tax collected above the base year (ExIBTt) is based on changes in the
   production sector-specific business tax. If no changes in these taxes occur the ExIBTt values
   are zero.
 22
£
 j-i
                22 ,                               ,
      ExIBT, = £ (SalesP; • (TxIBTj _, - TxIBTiu0))                             Eq. 209
                   carbon fees calculated for old vintages and new vintage production sectors
when fossil fuels are produced (Equation 90 for v=t-3:t),
   CPermF5j-2s are carbon fees based on the per dollar energy use as a function of energy demand
for investments and Cpf,,, a carbon permit fee on supplies per dollar of production based on the
global warming potential and the emission coefficient of a fuel (see Equation 140).
                                           96

-------
   CPermF5j=26are carbon fees based on the per dollar energy use as a function of energy demand
by government and Cpf,,, a carbon permit fee on supplies per dollar of production based on the
global warming potential and the emission coefficient of a fuel (see Equation 205).
   CPermFsj^are carbon fees based on Ihe per dollar energy use as a function of energy demand
by households and Cpf,,, a carbon permit fee on supplies per dollar of production based on the
global warming potential and the emission coefficient of a fuel (see Equation 199).

Total government subsidies are calculated by summing the supply sector subsidies towards
operating old and new vintages and the government subsidies:
           22
Subsid  =
-'•I
                   v=t-3
.i +Triit •ExIm1.EDVUjjiV).(TxproijijJ -l)
                        .JH
 £(Pu + Tr.,i • Ex Im, • ED, J=26=gv )• (Txpro, J=26=gv -1)
                                                                             Eq. 210
j=26
where
   the potential subsidies to the supply sectors for operating old vintages and new vintages are
summed, v=t-3:t=l (see Equations 86 for v=t-3:t), and
   the last part of the equation are the government and household subsidies (is SubsidGov which
are the government production taxes (see Equation 202)).

Government transfers are calculated based on per capita income, percent of population in young
and old age groups, and the fraction of the population working. Government transfers are
assumed to be untaxed (see Equation 170 under "Household demands")

Government deficits are input data with negative values. Deficits are calculated relative to the
price of the numeraire:

GovDeft, = GovDeftt • Pii=ETC>j=26=gVijj,t                                       Eq. 211
where
   GovDeft are input data (see Appendix A), and
   Pii-ETEj-26-gvjj.iis the price of the numeraire sector.

Government resources GovMt can now be calculated as equal to tax collections plus a
government deficit less government transfers. In the base year this amounts to the sum of all
inputs (supplies)
              22  i
GovMtt=0  = X! Z Xj=26=8v,ii=8vii                                              Eq. 212
              i=0 gvjj=l

In the projections at each point in time / the government balance is calculated. This government
balance at time / is part of the GNP accounting
                                          97

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 GovMt, = TotTax, - Subsidy, - GovTtr, + GovDeft,                      Eq. 213
where
   TotTaxt denotes the summed taxes on active old and new vintage production sectors in
combination with various other taxes, e.g., investment, government and household taxes (Equation
208),
   Subsidyt denotes the summed supply sector subsidies (Equation 86 for old vintages and new
vintages production sectors) in combination with household subsidies (Equation 196 and
government subsidies (Equation 202 (see Equation 210; summing takes place over the 26 supply
                   26
sectors:  Subsidy, =

   GovTrt denotes the demographics and income dependent government transfers (Equation 170),
and
   GovDeftt denotes the government deficits, which have negative values (Equation 211).

Depending on if and which carbon fee policies are implemented, government income is updated
based on recycling of carbon revenues.

If carbon pricing is implemented the government deficits GovDejl, and government resources
GovMff have to be adjusted in accordance with the carbon policy. The variable CrbFeeTott
represents the carbon permit fees at time t. The  different carbon policy case impacts on the
government deficits and resources ICRBfeeOPT=case 2 through 6 are shown below:

Case 2: all carbon fees produced from government resources are returned to deficit reductions.
Government deficits have negative values and carbon fees and therefore have to be subtracted.

      GovMt, - GovMt, - CrbFeeTot,                                       Eq. 214

      GovDeftt = GovDeftt - CrbFeeTot,                                     Eq. 215

     where
         CrbFeeTott is based on domestic carbon fees and carbon permit trade,

Case 3 and 4: All carbon revenues taken  from government resources are returned to other sectors.

      GovMt, = GovMt, - CrbFeeTot,                                       Eq. 216

Case 5: Domestic carbon fees are returned to consumers and permits are returned to the deficit.
   (a) If carbon trading is implemented and carbon trade provides for revenue, government
deficits will receive the carbon fees traded in order to reduce these deficits and carbon domestic
fees will be subtracted  from government resources to provide for the carbon fees to be returned to
households.

      GovMt, = GovMt, - CrbFeeTot,                                       Eq. 217

      GovDeft, - GovDeft, - CrbTrade,                                     Eq. 218
      where
         CrbFeeTott is based on domestic carbon fees and carbon permit trade,
                                          98

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         CarbTradet refers to the carbon permit trade.
   (b) If carbon trading is a net loss, government resources provide for the domestic carbon fees,
but deficits cannot be reduced.
      GovMt, = GovMt, - CrbFeeTott                                         Eq. 219
Case 6: Government resources will produce part of the carbon fees (see also Equation 165 where
CrbFeeRcyPct2*CrbFeeTott is added to household income).

      GovMt, = GovMt, - (CrbFeeRcyPct2 + CrbFeeRcyPct3) • CrbFeeTott     Eq. 220

Demands for goods and services by the government
Calculation of government consumption GCi>grtor the base year of each supply and
government sector interaction is determined by government demand and is calculated as follows:
1
gvjj=l
fx / \
i,j=26=gv.gvjj /
/> x
/ ^j 'rvi,j=26=gv,gvjj
/ i
PM
                                                                              Eq. 221
Note that next the Gdigv values are set constant over time first and then government (gv=j-26)
fuel use changes for oil, gas, coal, and electricity (i=3, 4, 5, 8) over time are calculated as
follows:
    i,j=26=gv,t ~ _   ,
              Factor; j=26=g¥,
                                                                  (unitless)   Eq. 222
where
   Factor, j=gvl = (1 + GV AEEI 1-j=gv )Nstep   (see Equation 2 1 )
   where
      GVAEEIjj-gv is a technical change parameter for government fuel use.

Expenditures by the government subsectors g^y towards government consumption is calculated as
follows when based on fixed government subsector weights:
                   25
i=26=capital,j=26=gv,gyjj
                                       '.gYJi    i,j=26=gv,gyiiv=t /
                   GC
                      •i=2fccapit4j=26=gv,gyij  ' 1i=ETE,j=26=gv,gyiJ,v=t
                                                                              Eq. 223
The scheme for allocation of the subsector purchases across production sectors is simulated as
follows:
                                          99

-------
                       PGC~S'8      • GFsig
 GEgvJJ = GovMtt
                                           f 26=gv,gvjj
                    BYJ.H
where
   GovMtt is the government resource balance (Equation 220),
rho equals zero resulting in a value of PGC~rilo*!l6of one,
   sig equals one,
   PGCj^gvjj denotes the government expenditures (Equation 223), and
   GFj-26,gV,gvjj, the government preference function, equals government one, given that there are
no government subsectors.

Government demand for each supply sector EDM:2ij.gv is then calculated based on government
purchases. Capital demand EDM6j-gv by the government is treated separately. Note that in that
case the price of the numeraire sector is required. Also note that government saves automatically,
so government capital does not, in this version, increase demand for savings.
                gvjj=l

and add government deficit to the demand for savings

                       i
EDi=26=«**,j=26=iv  = £ (GEj=26=gv,gvjj * G^ capital, j= 26, gv,,^ * PGCj=26=gVigvjj)
                     gyii=i
                                                                               Eq. 226

and update the demand of the Everything Else sector

                                    i
                            g-gv + 2L(GEj=26=gvgyij • GCi=ETE j=26=gv,gvjj)       Eq. 227
                                   gxij=i
Imports and exports

Trade is kept track of as an demand array element denoted as EDjj-u-ma,. If trade is fixed, trade
quantities can be input values (Trade0:i,23 data are in Appendix A), and trade demand can be set
equal to these initial trade values. The SGM offers users the option to "read in" carbon trade (into
either Trade0,i-2i or into an additional trade vector Trade;.(=^).

                          =1:26                                                  Eq. 228
                                          100

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                  Over time or with open markets, trade may be assumed to be the difference between production and
                  summed domestic demand (see Equation 231), although this assumption remains part of the market
                  solution process. In the reference case markets are not open across the regions and trade is fixed for
                  the base year, but trade in oil and gas is calculated as in Equation 229 as the difference between
                  demand and supply for the projections.
                                  27
                  where
                     Edy represents the demand matrix43 (see Equation 80), and
                     PRDj represents the production vector (vector of outputs j) (see Equation 106).

                  To calculate the trade balance, the relevant exchange rates have to be used:
                                            • ExchRat^
                                                                                                  Eq. 229
                                                        egion
                                                                               Eq. 230
                  and/or Trade, i=1:25 = Trade, i=125 • ExchRat^^                                  Eq. 231

                  The export-import balance will be determined by calculating the monetary equivalent.
o
25


i=l
Exp Imt = £ [Trade0;i=1:25 • P;, ]

and/or
                              25
                                                                               Eq. 232
                                                                                                  Eq. 233
                  If carbon pricing is simulated, the export-import balance has to be adjusted in accordance with the
                  carbon policy implemented. This implies that the carbon trade has to be subtracted from die net
                  exports
                  Explm, = Explm,- Trade, i=23 • Pi::23,
                                                                               Eq. 234
                  and the carbon traded has to be converted back to tons of carbon TgC (from Equation 232):
Tradeu_23 =
                                          ExchRate
                                                   reglonI
                                                                    Eq. 235
                  43 In the SGM code the ED matrix at a certain stage has diagonal elements calculated as Edtj-PRDj; in this
                  documentation the Edjj matrix refers to the demand matrix.
                                                             101

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Chapter 9. GNP accounting

To ensure that the production and demand are consistent throughout the model, the SGM relies on
simple economic relations for the accounting framework. GNP can be given as the price weighted
sum of net production of all products, which in turn is equal to the disposition of net output
among final demand sectors (Edmonds et al.  1993:303; Kim 1995:36)
GNP =
PRDj ~ Z ED> .1  = KTott + Const
              ''
, + Ex Imt
                                                                            Eq. 236
where at each point in time t
   i is an input product identifier,
   j is the output product identifier,
   N is the number of factors of either i or j; N=27 for inputs (22 variable inputs plus a carbon
option (i=23) plus land, labor, and capital as fixed inputs (M=3) and indirect business taxes and
subsidies as final input; N=22 for outputs (22 production sectors; sector 23 is the carbon market);
   Piy is the price paid by producers for inputs,
   PRDj is gross domestic production,
   ED,j is the demand for product i in the production of product j,
and
   Ktott is total investment demand (see Equation 136)
   Const  is household consumption, which is based on retained income, labor income and related
costs, land rental income, government transfers and with savings subtracted (see Equation 181),
   GovMtt is government consumption, which is based on taxes, subsidies, government transfers
and government deficits (see Equation 220),
   Explmt is net export, which is based on exogenous input, energy balances and time-dependent
market prices (see  Equation 234).

Alternatively, consistent with the input-output accounting framework, GNP can be expressed as
the sum of payments to the factors of production (Edmonds et al. 1993:303; Kim 1995:36):
GNP =
                     =     TXibt
 Pi,. •
                                                                             Eq. 237
where
   i is a row factor identifier (input),
   j is a column factor identifier (output),
   Prj is the price received for commodities produced,
   PRDj is gross domestic production,
   Piy is the price paid by producers for inputs,
   ED.j is the demand for product i in the production of product j,
and in the last part of the identity ;
   TXibti is the indirect business tax,
   HI represent the profits including net interest and capital consumption allowances,
   M is the number of primary factors of production (labor, land, capital).
                                         102

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Chapter 10. The solution procedure
The fundamental problem that the model must address is finding a set of prices that is consistent
with demands by producers and consumers for goods, services, and primary factors of production
when assumptions about change are made in forecasting.

Thus, for any period, equilibrium will exist when a set of prices is found for which all excess
demands are zero. This set of prices is not unique. Walras' Law guarantees that if an equilibrium
set of prices exists, any positive scalar multiple of those prices is also an equilibrium set of prices.
Any commodity can be chosen as a numeraire, and its price can be determined arbitrarily; in
SGM the commodity of the Everything Else sector is the numeraire, and its price is set to one.
The number of independent market prices is always one less than the number of markets.
Similarly, since the unit of measure chosen for commodities is also arbitrary, units can be chosen
such that all equilibrium prices are unity in one period.

When the model solution is reached, there will be a set of prices and quantities of the n-
commodity market such that all n equations in the equilibrium condition will be simultaneously
satisfied.

At each step in the solution process, trial prices are already known because they are set by the
previous time-period prices. To calculate excess demand - the difference between demand and
supply - both demand and supply are determined iteratively. Demand EDY^? by  a vintaged
production sector or subsectorj ory; for input; is calculated, if the production function is
assumed to be a CES function, as dependent on the variable inputs (expressed in the variable Zjj),
prices (prices received for the commodity Prjit and prices paid for supplies Pi'y^v), capital KA^
and the various technical coefficients (osj^v and acstij^) and the production sector-specific
elasticities (expressed as a function of a, in the form of por //),
                         •Z;;;
                                          -Up
                                                 a  ••
                                                   >,J,JJ,v
                                                 pii/0-A
                                                \   i.J,JJ,t
                                                             (see Equations 61 and 76)
for the CES production function implementation for old and new vintages, respectively)
                               'N-l
where
= 1 - (ao>¥ •
                                £acstijjj>v • Pi^     (see Equation 49)
The annual vintage-specific gross production PRDV^by a production sector or subsector is
calculated through the CES production function as dependent on the same variables.

 PRDVj jj v  = #o,j,jj,v * ^j,ij,v     * \ai=26j,jj,v * KAj j(V J    (see Equations 63 and 77 for the
CES production function implementation for old and new vintages, respectively)

Demand is calculated, if the production function represents a Leontief technology (in the SGM
when the elasticity of substitution (cr2) is smaller than 0.05) as dependent on gross production and
the Leontief technical coefficients,
                                          103

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 EDY
                I.J.JJ.V
      l.J,U,V
•KA;
(see Equations 64 and 78 for the Leontief production
function implementation for old and new vintages, respectively)

where the annual vintage-specific gross production (PRDV^) is calculated as dependent on the
Leontief technical coefficients and capital.
                             j jj v   (see Equations  65 and 79 for the Leontief production
function implementation for old and new vintages, respectively).

In the case of putty-clay behavior a sector's vintaged and projected technical coefficients for the
Leontief production function (A^V for /=7:25 andj=l:22) ate based on the vintage technical
coefficients calculated for the CES production function.

                         (          Pr    Y''°"P)
                pi/0-pi)              rrj)t
  U,Ji.v  = ao,j,ij,v       *  ai,j,ij,v * ^	         see Equation 44 for the variable factors
                                  /U-pi)
and Equation 45 for the fixed factor capital


 ),             _~pi'(i-pi).  rt
• /v'i=26=capital,j,jj,v ~ "'OJ.jj.v     "-i=26.j,ij.
Vintage and subsector-production-specific demands were summed over the operating vintages
and subsectors (if operating) (i=l:25\j=l:22). Thus, EDi,,:2sj-i^ represent the demands44 by the
production sectors/ for inputs, /, and those for carbon (i=23), land (i=24), labor (i=25) by each
production sector.
                                    (see Equation 80)
               v=t-3
where n is the number of subsectors with n 
-------
   EDi-26j-2S-inv represents demands for capital by investment (Equation 135),
   EDj=2-ETE,r25-inv represents demands for the Everything Else sector after adjustments for
supply sector transportation costs and additional adjustment factors (Equation 137),
   EDi-i 25j-26-sv represents demands by the government sector (Equation 225), including those
for carbon, land, and labor,
   EDj-2-ETEj-26=gv represents demands for the Everything Else sector by the government sector
(Equation 227)
   EDj=26j=26=gv represents demands for capital by the government sector (Equation 226)
   EDj.) 22j-27-hh represents demands for supplies by households; these are income- and price-
elasticity dependent (Equation 185 and constrained for overall budget: Equation 191),
   ED,-24=isj=27-hhrepresents demand for land supply by households (Equation 152)
   EDi-25-ibsj-27-hh represents demand for labor supply by households (Equations 144 and 192),
   ED.^-capiiaij-^-hh represents demand for saving supplies by households (Equations 176 and
corrected for retained income: Equation 182).

Budget constraints for households with regard to demands are expressed in Equation 191.

Gross production for each sector summed over active vintages and active production subsectors
was retained in a production sector vector to be part of the model solution algorithms.
         , 23 = PRDH 23 = £
                          v=l-3
1LPRDVr-
(see Equation 106)
Eq. 238
where
   j=i=l:23 denote the product markets (see Figure 1) Note that when carbon prices are zero a
market for carbon (for j=23) is not operated.

Supplies of land, labor and savings were set equal to the negative values of the demands for land,
labor and savings when describing the household sector and retained in SalesV. SalesVj,^^
denotes the supplies to the factor markets provided by labor, land and Oher Value Added (see
Figure 1):

SalesVi-24-b       (i=24; m=23; land supply: see Equation 154);
SalesV,,25-ibs       (i=25; m=24; labor supply: see Equation 148);
SalesVj-26-capiiai    (i=26; m=25; savings supply: see Equation 183)

These production sector vector elements are multiplied by conversion vectors and stored as the
market-supply vector:
MrkPrdm = SalesV, • PRconvrt;
                          Eq. 239
where
   PRconvrt converts monetary values to energy quantities such that an energy balance will be
obtained in the market solution.
                                           105

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Excess demand is calculated across all markets as the difference between demand and gross
production, which determines the supply to the demand sectors, and stored as a market-excess
demand vector (MrkEdm)
             27  .
 MrkEdm = £ (fid^ • PRconvrt;)- Mrk Pr dn
                                                                            Eq. 240

where the supply sector indicators, i=J:23, and the production sector indicatorsj=/:25, map on
the market indicator m.

Note that the market solutions are calculated in either monetary or energy units through
PRconvrt; in addition, if exchange rates are involved due to trade or multiple interacting regions,
demand EDy and gross production PRDj are converted by the appropriate exchange rates
ExchRate,
        region-
Both demands and supplies are stored after a log transformation in a vector Xvecintvl to be
checked if they fall within the elasticity bounds and meet the solution criteria for convergence.
Xvecmewt = Log(MrkEdm + Mrk PrdJ - Log(Mark Pr dm)
                                                                            Eq. 241
If not, then for the next iteration a ff matrix is inverted to calculate the new prices based on the
necessary delta of the price perturbation.
        DemTmp - (MrkEdm+Mrk Pr dm)   SupTmp - Mrk Pr dm
              Mrk£dm + Mrk Pr dm               Mrk Pr dm
                                                                      delta
                                                                    Pi t-delta
                                                                            Eq. 242
where
   DemTmp equals MrkEdra+MrkPrdn, and
   SupTmp equals MrkPrdm which are values from the previous solution attempt.

The new prices feed back to the demand and supply equations and the process is reiterated until a
price perturbation is found for an equilibrium solution. The process is a derivative-based Newton-
Raphson search procedure (see Appendix B). The procedure converges very quickly once prices
approach their equilibrium values.  A simple sector-by-sector line search is used first to bring
prices that are far from equilibrium close to their equilibrium values (see Appendix B).

Figure 13 illustrates, for one region, the extent to which the model solution searches for the
solutions of fossil fuel investments. Table 4 illustrates the variable values at the end of the last
iteration of the market solving algorithms when carbon policies are based on carbon emission
limits at randomly chosen time period 7.
                                         106

-------
      Oft OiijDtity of Uniiwe ssteil Pftplrtnble
                 Re««ui'c««
       fr»m 1»H «=«) through ?*5« 
                                                          Gas Reserve*
                                                         Ca»I Reserves
Figure 13 Quantities of uninvested depletable resources and invested capital in depletable
resources for one region in a case other than the reference case illustrating the well-behaved
nature of the SGM
Table 4 Variable values at the end of the last iteration of the market solving algorithms when
carbon policies are based on carbon emission limits
For t=7 when carbon
policies are based on
carbon equivalent
emissions and carbon
Mrk
(m)


0)



MrkEd
=
Excess
Demand
MrkPrd
(note
energy in
ExaJoules)
Pi



SalesV
(note
energy in
monetary
                                              107

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fees of $100 ton C
(see Figure 18)
Region = USA
Other Ag.
C.Oil Prd.
N.Oas Prd.
Coal Prd.
Coke Prd.
[empty]
Elec Gen.
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains and Oil Seeds
Animal Products
Forestry
Food Processing
Carbon market for
fixed carbon fee of
$100 per ton carbon

Land
Labor
OVA (other value
added)

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26

1
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
2

0.02328
0.00000
0.00000
0.00000
0.00000
0.00000
0.00003
0.00000
0.00001
0.14703
0.29714
0.01484
0.02649
0.03776
6.44723
0.92306
0.55866
0.05353
-0.04671
-0.21275
-2.90778
0.00081
0.00000
-0.00001
71.01880
0.00000

138868.0
20.8
21.8
27.8
1.2
0.0
20.7
41.9
36.9
439236.0
616838.0
143155.0
153190.0
128960.0
5948400.0
3285080
425260.0
99969.7
1968590
9553.9
1038580.0
2440.6
0.0
170365.0
2269550.0
14169100.

0.91327
1.00000
1. 00000
0.89636
2.17083
1.00000
1 .38707
1.72712
1.59899
0.83425
0.85995
0.91768
0.90411
0.76174
0.85386
1.00436
0.95212
0.84195
0.67687
0.84770
0.72144
165.66
0.00000
60.62
0.08938
1.00000
values)
138868.0
47777.9
50024.8
27122.8
5933.4
0.0
425025.0
176722.0
176302.0
439236.0
616838.0
143155.0
153190.0
128960.0
5948400.0
328508.0
425260.0
99969.7
196859.0
9553.9
1038580.0
2440.6
0.0
170365.0
2269550.0
14169100.
108

-------
Chapter 11. Calibration procedure

All SGM regions are calibrated to match base year energy consumption, carbon emissions, and
economic activity.  1990 is the current model base year, and one model diagnostic is the
comparison between base year model output and base year data. Base year model output should
exactly match base year data from energy balance tables and input-output tables (see also
Appendix A).

Some SGM regions are also calibrated to match external projections on energy consumption and
economic output, usually from an official government source, from the present to 2020 or
beyond. This is especially true of SGM-USA, where the Annual Energy Outlook, published by
the US Energy Information Administration, provides projections to 2025. We use a sequential
procedure for baseline calibration of gross national product (GNP), electricity generation, and
fossil fuel consumption.

Various technical parameters are available in SGM to influence the time path of model output,
especially autonomous time trends governing the efficiency of inputs in production processes.
The first step in baseline calibration is to match GDP projections by adjusting an autonomous
labor efficiency improvement parameter. The second step is to match projections of electricity
generation, in units of billion kilowatt-hours, by adjusting an autonomous electricity efficiency
improvement parameter in all model activities that use electricity. Third, the mix of fossil fuels
within electricity generation is adjusted by varying the time path of the cost to produce electricity
using oil, natural gas, or coal. Fourth, fossil fuel consumption outside of electricity generation is
adjusted using fossil fuel efficiency improvement parameters in all model activities that use fossil
fuels. These adjustments in efficiency and cost parameters arc not independent, so the baseline
calibration process is repeated at least once.

This calibration process is used for baseline energy consumption and carbon emissions, but
another set  of parameters governs the slope of the marginal abatement cost curves. For all
production  processes in SGM except electricity, the elasticity of input substitution determines the
rate that other inputs can substitute for carbon-intensive fuels, as the price of carbon changes
relative  to other prices. The electricity sector in SGM is actually a collection of production
processes that represent different ways of generating electricity. A parameter in the logit sharing
mechanism, that determines the market share of generating technologies, governs the rate that one
technology  can substitute for another as relative costs change. A set of marginal abatement cost
curves is constructed by running a series of constant-carbon-price  experiments in SGM, with a
carbon price introduced in the 2005 time step and held constant  thereafter. If any of these
parameters  are changed, they will affect baseline calibration and the baseline calibration process
must be repeated. Conversely, some of the baseline calibration parameters mentioned earlier,
especially cost parameters in the electricity sector, influence the slope of the marginal abatement
cost curves.
                                           109

-------
Chapter 12. The energy balance and emissions

One of the main functions of the SGM is to balance energy demand and supply and quantify the
resulting emissions by
    •   accounting for baseline greenhouse gas emissions over time for a country or group of
       countries;
    •   finding the least-cost path to meet any particular emissions constraint;
    •   providing a measure of the carbon price, in dollars per metric ton;
    •   providing a measure of the overall cost of meeting an emissions target.

Fossil fuel emissions
Emission calculations, in the SGM, are based on the amount of fossil fuel combusted and fuel-
specific emission coefficients.

Total demand for each of the fossil fuels is calculated first. These total demands for each region
need to account for trade, for both raw fuels (oil, coal, and gas) and for refined fuels (refined oil
and Gas T&D). The product of fuel-specific total demand and related emission coefficients and
global warming potential (GWP) results in total carbon emissions after accounting for the fixed
factor energy trade when regional markets are closed (EDi=126,j=24=exim ~ Trade0 i=] 26; see
Equations 228). Thus,

TotDem1=1 ;22 = f]EDM - ED, j=24                                            Eq. 243
                j=i
where
   Edy represents the demand for supply i by production sector j which equals the summed over the
subsectors and its operating vintages' demands (see Equation 80).
Emissions for oil combustion are calculated as follows:


EmissionsCJ=3=oll = EMQ • GWPI=, •
(0.97 • PRconvrt^ • TotDem^ - PRconvrtfn=9 • Trade0-i=9=refinedoil)
Eq. 244
where,
   EMCjis the oil-specific carbon content in million tons Carbon per exajoule of the energy
source,
   GWPi is the global warming potential,
   TotDemi is the oil-specific total demand,
   PRconvrtfa is the energy conversion factor, which converts the relative price in monetary units
to physical energy units; the factor of 0.97 accounts for the fact that not all oil products are
combusted, e.g., tar and lubricants; PRconvert for each supply sector in each region is expressed
in exajoules per million 1990 regional currency, and
                                         110

-------
   Tradeo,,=9 is either a fixed trade amounts (net exports) or calculated as the difference between
production and the summed domestic demand.

Emissions for gas and coal combustion are calculated similarly, but for the 0,97 factor:


EmissionsCj=4^as = EMC, • GWP1=4 •
Eq. 245
 /                                                              \
 (PRconvrtfn=4 •TotDem,=4 - PRconvrt^o •Tradeb>i=u>=OM_T«J

where
   EMCiis the gas-specific carbon content in million tons C per exajoule of the energy source,
   GWPj is the global warming potential,
   TotDem, is the gas-specific total demand,
   PRconvrtj is the energy conversion factor, which converts the relative price in monetary units
to physical energy units, and
   Tradeo,j=io is a fixed trade amount (net exports) or calculated as the difference between
production and the summed domestic demand.45


 EmissionsCJ=5=coal = EMC5 • GWPi=5 • (PRconvrtfn=5 • TotDem1=5 )            Eq. 246

where
   EMC5 is the coal-specific carbon content in million tons Carbon per exajoute of the energy
source,
   GWP; is the global warming potential,
   TotDem, is the coal-specific total demand, and
   PRconvrt; is the energy conversion factor, which converts the relative price in monetary units
to physical energy units.

The summed CC>2 emissions are then
           5
 EmTot, = £ EmissionsC,                                                    Eq. 247
           j=3

Other greenhouse  gas emissions and non-greenhouse gases
All other potential emissions (CH4, N2O, HFC, PFC, andSF6) are calculated based on "emission
activities".  "Emission activity" or EmAc!* is a term used to describe the potential of emissions to
be generated during a production process either as an industrial or an energy production process,
or in agriculture. Emission activities are directly related to demand. Thus,

 EmActix= PRconvrt^TotDem^                                               Eq. 248

where
45 In the code the calculations are made twice: in the energy balance subroutine and in the GHG emissions subroutines;
in the energy balance subroutine oil emissions are calculated by multiplying with the 0.97 factor, which accounts for
the fact that some oil products are not combusted, e.g., tar, lubricants, etc.; in the GHG emission subroutine emissions
are calculated without that factor.
                                          Ill

-------
   ix is mapped on the supply sector index i,
   PRconvrti is the emission activity energy conversion factor, which converts the relative price
in monetary units to physical energy units, and
            is emission activity demand (see Equation 243).
With correct mapping of EMC, GWP and PRconvrt parameters towards the emission activities,
emissions of non- greenhouse gases and other than CO2 greenhouse gases can be calculated. Total
demand for each region accounts for trade. Thus, carbon-equivalent emissions are calculated
based on a production sector's emission activity, which is the product of the total demands by a
production sector and a conversion factor that converts monetary units to energy units (see
Equation 248), multiplied by the emission activities' emission coefficient EMC and the
emissions' global warming potential coefficient GWP:
Emissions, = EMC, • GW^ • (PRconvrt, • TotDem.;)
Eq. 249
If these emissions are greenhouse gases, they can be added to the total emissions. If they are non-
greenhouse gases they are kept separate.
Emissions of gases, like CO, NOx SOX, VOC, PMIO and emissions of black carbon can
potentially be simulated in a similar fashion if and when necessary data are available linking
production processes and related emissions.
Mitigation and marginal abatement cost curves
The SGM has options of calculating consequences of mitigation policies. For carbon dioxide and
carbon-equivalent emissions we have obtained marginal abatement cost curves (MACCs)46.
These marginal abatement curves are generated exogenously, based on the relationships between
carbon prices and the percents reduction in emissions, which are specific to each source and type
of emission. Cost curves are defined for a variable number of points relating the carbon price
(level) to a corresponding percent (fraction) reduction in emissions. The model finds the
percentage reduction in emissions through linear interpolations between carbon prices. Thus,
when testing the impacts of carbon prices, the SGM solves for the emission levels. Alternatively,
when setting carbon dioxide emission limits or carbon-equivalent emission limits as model input,
the SGM market calculates the carbon fees. Obtained revenue, in both cases, can be recycled to
government, households and/or industry1. These options are explained in "Carbon policies" and
summarized in Appendix A. Table  5 lists the  relationships between emission sources, the drivers
and the control options.

Table 5 Emissions sources, drivers  and control options
Activity
Oil Combustion
Gas Combustion
Coal Combustion
Coal Production
Emission
CO2
CO2
C02
CH4
Driver
Total Combustion
Total Combustion
Total Combustion
Coal
Mitigation option
Endogenous
Endogenous
Endogenous
MAC
4S DeAngelo et al. (2004); Delhotal et al. (2004); Schaefer et al. (2004); Scheele and Kruger (2004)
                                          112

-------
Enteric
NatGasSys
OilSys
Manure
OthAgMeth
ManureN
SoilN
Landfills
OthNonAgMeth
Wastewater
HFC23
ODSSub
IndProcsN
MobileN
StationaryN
Aluminum
Semiconductor
Mg
ElecDist
Soil and Forest
Sequestration
CH4
CH4
CH4
CH4
CH4
N2O
N2O
CH4
CH4
CH4
HFC-23
HFC's
N2O
N2O
N2O
PFC's
PFC's
SF6
SF6
CO2
Ag Production
Gas Trans & Dist
Oil Production
Ag Production
Ag Production
Ag Production
Ag Production
Everything Else
Everything Else
Everything Else
Everything Else
Everything Else
Everything Else
Every thingjilse
Everything Else
Everything Else
Everything Else
Everything Else
Electricity
NA
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
MAC
Sequestration
function47
The SGM modeling team has experimented with regard to joint product production in the gas
production sector (methane and natural gas).  Emission mitigation technology involves multiple
sectors in this case. The level of mitigation might be determined by an expected profit rate
calculation done on the margins between mitigation levels provided (Mark Jacobsen 6/12/00 &
7/13/00). The energy sectors are made to bear the mitigation costs. In the joint-product mitigation
case only activities in the left column (see lists below) are mitigated and the ones in the right
column are not mitigated. The fact that the industrial processes and landfills are not undergoing
mitigation in this case drives the price for mitigating other sectors up when emission constraints
are severe (see Figure 23 in Chapter thirteen).

 Mitigated activities  No mitigation
 Oilcomb
 Gascomb
 Coalcorrtb
 CoalPr
 Enteric
 NatGasSys
 OilSys
 Manure
Landfills
OthNonAgMeth
Wastewater
HFC23
ODSSub
IndProcsN
MobileN
StationaryN
47 In SGM 2004 sequestration offsets are an option based data thanks to personal communication with Bruce A.
McCarl: mccarl@tamu.edu
                                           113

-------
 OthAgMeth
 ManureN
 SoitN
 ElecDist
Aluminum
Semiconductor
Mg
Display of results
For carbon dioxide and carbon-equivalent emissions, we usually display the results as marginal
abatement cost curves (MACCs). To calculate marginal abatement curves as output, the simplest
method is to obtain a reference case through calibration without carbon fees imposed, and then
setting carbon permit fees exogenously and evaluating the results with regard to GHG emissions.
The marginal abatement curves can be generated by plotting emissions over time for each of the
imposed carbon fees, e.g. Figure 14, Alternative ways of displaying results are shown in Chapter
thirteen.
    180


    160
  a
  o
   L120-
   1100
   t

   - 80
   I
   I

   •SO
   I
   I

   ' 40


    20
                              start     *5 years  +10 years
                                                   tag run
      0%        5%       10%      15%      20%
                       Reduction from Baseline Emissions
                                                  25%
                                                           30%
Figure 14 Marginal abatement cost curves for the United States energy system generated with a
series of constant-carbon-price experiments.
                                           114

-------
Chapter 13.  Reference case results

Projections/Validation/Calibration for the USA

This chapter contains reference case results and briefly reviews calibration and validation.
In addition, selected results of carbon policy implementations are presented. The simulation
results are not analyzed in depth.

The first step in baseline calibration is to match GNP projections to an exogenous source (usually
the Annual Energy Outlook) by adjusting the autonomous labor efficiency improvement
parameter. GNP projections obtained from the SGM simulations can also be evaluated against
historical data for validation. Results for the reference case for the US are shown in Figure 15.

                       Historical and Projected Normalized GNP
                                (against 1990 values)
  3.0 i
  2.5
  2.0
  1.5
  1.0
  0.5
-SGM 2003


 Historical (CEA 2002)


- AEO 2003 (linked to CEA)
    1980     1990     2000     2010     2020     2030
Figure 15 Historical and projected normalized GNP
A set of curves can be constructed by running a series of constant-carbon-price experiments in the
SGM, e.g., with a carbon price introduced in the 2005 time step and held constant thereafter. COa
emissions in units of million tons of carbon in the reference case and as response to carbon fees
are shown in Figure 16.
                                        115

-------
                Response of Carbon Dioxide Emissions to Carbon Prices
      4000
      3500
      1000
                                                                           -$0 per ton
                                                                             C
                                                                         -«™ $10 per
                                                                             ton C
                                                                           i-$50 per
                                                                             ton C
                                                                           |-$100 per
                                                                             tonC
                                                                         -*-$200 per
                                                                             tonC
Figure 16 CO2 emissions in units of million tons of carbon in the reference case with a zero
carbon fee and the responses of CO2 emissions to carbon fees of $10, $50, $100, and $200 per ton
carbon
The SGM has the option tracking GHG emissions from processes in the agricultural sector, the
Everything Else sector, from the electricity generation and distribution sector, and from the
distributed gas production sector (see Table 65). In that case, not only carbon dioxide emissions
are calculated, but also methane, nitrous oxide, HFCs, PFCs and SF6 emissions in units of
carbon-equivalents. Carbon-equivalent emissions are calculated based on a production sector's
emission activity, which is the product of the total demands by a production sector and a
conversion factor that converts monetary units to energy units, multiplied by the emission
activities' emission coefficient (EMC) and the emissions' global warming potential coefficient
(GWP) (see Equation 249).

Figure 17 illustrates the response of the total of carbon-equivalent (CE) emissions to a carbon fee
of $100 per ton carbon compared to the response to a carbon fee of $100 per ton carbon when
only CC>2 emissions are impacted.

Figure 18 illustrates the primary fossil fuel-specific carbon dioxide emission responses to a
carbon price of $100 per ton of carbon. Coal emissions respond most strongly, followed by
emissions generated from oil combustion; emissions due to gas combustion are least affected.
                                           116

-------
           Response of Carbon Dioxide and Carbon-Equivalent Emissions to
                                  Carbon Prices
Figure 17 Response of CO2and carbon-equivalent emissions in units of million tons of carbon to
carbon fees of $100 per ton carbon
                                       117

-------
            Response of Carbon Dioxide Emissions from Oil, Coal, and Gas
                             Combustion to Carbon Fees
                                                        -•-emissions from oil if $0 per
                                                           tonC

                                                        -»- emissions from oil if $100
                                                           per ton C

                                                        -*-emissions from coal if $0
                                                           per ton C

                                                        -*- emissions from coal if $100
                                                           per ton C

                                                        -*- emissions from gas if $0
                                                           per ton C

                                                        -•-emissions from gas if $100
                                                           per ton C
            omoiooiooioomomo
                SroOO^^fMlNlrOrt^j^lO
                0)  ^3  ^3 ^T*  ^3  f^  ^5  ^3  ^3  ^^ ^5  ^"^
            •^•f-rM(MCNCMCM{N«
-------
           Response of Carbon-Equivalent Emissions by Various
                   Processes to Carbon-Equivalent Prices
   *
   I
   •I
1600 n

1400

1200

1000

 800

 600

 400

 200
                      ^^ C)  O  G)  ^3 C^  C5
                giA
                0»
            00)
                                                CM  (N
    oil

    coal

    gas

    gasT&O

    coal production

    oil refining

   from oil if $100 per ton CE

   from coal if $100 per ton CE

   from gas if $100 per ton CE
  ~from gasT&D if $100 per ton
   CE
    from coal production if $100
   per ton CE
	from oil refining if $100 per ton
   CE
Figure 19 Response of carbon-equivalent emissions in units of million tons of carbon from energy
production, energy transformation, agricultural and other production processes to carbon fees of
zero versus $100 per ton carbon
When agricultural practices respond to carbon prices, the largest response is due to nitrous oxide
emissions from fertilizer application, followed by methane emissions from enteric fermentation,
followed by manure management. In addition landfill management impacts overall carbon
equivalent emissions greatly (see Figure 20). Figure 21 shows the responses of the various
industrial processes to carbon prices.
                                         119

-------
Response to Carbon Prices of Carbon-Equivalent
                     Agricultural Practices
                                  toon-Equivalent Emissions from
                                   Practices             ,	•	
                                                         -+- Landfills

                                                         -s~ Enteric

                                                            SoilN

                                                            Manure

                                                            ManureN

                                                            OthAgMeth
                                                          •from Landfills if $100 per ton
                                                           CE
                                                          •from Enteric if $100 per ton CE

                                                          •from SoilN if $100 per ton CE

                                                          •from Manure if $100 per ton C

                                                        -Q-from ManureN if $100 per ton
                                                           CE
                                                           from OthAgMeth if $100 per ton
                                                           CE
                                                                                 >nCE
            ocnooooooooooo      CE
            •«--«-INJCM(S|CM  '	


Figure 20 Response of carbon-equivalent emissions in units of million tons of carbon from
agricultural processes to carbon fees of zero versus $100 per ton carbon
                                         120

-------
  Response to Carbon Prices of Carbon-Equivalent Emissions from
                     Various Industrial Processes
                                  O  if)
           cncnoooooo
           ••-••-CMCMCMCMCMCM
                      in  o  in
o  m   o   to   o
CO  f)   ^   ^   IO
o  o   o   o   o
CM  CM   CM   CM   CM
-«-MobileN
—*-lndProcsN
—6— StationaryhJ
 :••• • OthNonAgMeth
HK-HFC23
^^ Aluminum
-+- EtocDist
—- Mg
	Semiconductor
   Wastewater
   ODSSub
-*-from MobileN if $100 per ton CE
-*-from IndProcsN if $100 per ton CE
—«— from Stationan/N if $100 per ton CE
-•!••• from OthNonAjMetn if $100 per ton CE
- -from HFC23 if $100 per ton CE
—"••from Aluminum if $100 per ton CE
	from BecOist if $100 per ton CE
•••*•• from Mg if $100 per ton CE
• •••-••from Semiconductor if $100 per ton CE
-ft from Wastewater if $100 per ton CE
-.•••• from ODSSub if $100 par ton CE
Figure 21 Carbon-equivalent emissions in units of million tons of carbon from industrial
processes responding to carbon fees

The SGM has the option of setting emission limits and letting the model solve for the carbon fee
that would need to be imposed to reach that goal. Figure 22 illustrates stabilization of GHG
emissions. Figure 23 illustrates the carbon fees (market prices of carbon) calculated.
To meet desired carbon emission targets, three options can be exercised: (1) reduce carbon
dioxide emissions from primary fuel combustion, (2) reduce emissions through mitigation of all
carbon-equivalent emission processes, (3) reduce emissions dirough mitigation of a limited
number of carbon-equivalent emission processes, that is from energy production processes and
agricultural processes only (see list below).
Carbon prices respond accordingly. Figure 23 shows all three responses. The high carbon price
is paired with carbon-equivalent emissions that exclude those of landfills and industrial processes
such that the burden of emission reductions falls on the energy sector and the remaining
agricultural processes. When the carbon-equivalent emission reduction burden is spread over all
carbon-equivalent emissions the resulting carbon price is very similar to when only carbon
dioxide emissions are targeted. Note that after the year 2045 emission restraints were allowed to
be relaxed resulting in an immediate decrease of the carbon price.
                                             121

-------
 Mitigated activities
 Oilcomb
 Gascomb
 Coalcomb
 CoalPr
 Enteric
 NatGasSys
 OilSys
 Manure
 OthAgMeth
 ManureN
 SoilN
 ElecDist
No mitigation
Landfills
OthNonAgMeth
Wastewater
HFC23
ODSSub
IndProcsN
MobileN
StationaryN
Aluminum
Semiconductor
Mg
         Attaining Emission Stabilization Levels of Carbon Dioxide and Carbon-
                                Equivalent Emissions
£OUU
9fiftn .

2400 -
-yynn .

(0
C r»AAA
o 2000 -
"55
to
"£. 1 floo -
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ifioo -
1400 -
1900 -
innn -
*
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/
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      '-T-c'J
      OOO
                 OO
                 tMC>I
                                                ^-
                                                O
                                                        O
                                                        CM
Figure 22 Emission stabilization levels in units of million tons of carbon set exogenously and
reached as model output
                                        122

-------
             Market Prices for Carbon to Attain Emission Stabilization Levels
     700 -I
     600
                                                                -»-CEstabilization


                                                                -«~ CEstabilizationMitgas


                                                                -*- CEstabilizationCC


                                                                -*-CO2stabilization
            O>(T>OOOOOOOOOOO
            ••-••-CVICMfMCMCMCMCM	
        in
_   _   s   _
CM   CM   CM   CM
Figure 23 Market prices for carbon when exogenously set emission stabilization levels are
attained. Note that the steep curve is for the carbon price when only energy production and
agricultural carbon-equivalent emissions are mitigated but for landfills; no industrial emissions
are mitigated.

Figure 24 illustrates the various emission pathways resulting from the carbon-equivalent
mitigation strategies for the energy-production sectors.  Figure 25 illustrates the emission
pathways resulting from the carbon-equivalent mitigation strategies for the agricultural processes
                                           123

-------
           Pathways of Mitigation Through Inclusion or Exclusion of Various
                                       Sectors
      1600
   O
HK~ Gas
-*-Coal
 •-•: • oil under targets
-*- gas under targets
-•- coal under targets
-+- oil under mitigation
— gas under mitigation
•-	coal under mitigation
Figure 24 Emission pathways due to the energy sectors when carbon-equivalent emission limits
are imposed
                                         124

-------
      Response of Carbon-Equivalent Emissions from
           Agricultural Practices to Carbon Prices
      350 i
            oinoinoin
                       oT-i-
                       OOO
-*- Landfills
••«•• Enteric
-— SoilN
- v, - Manure
-*- Manure N
-»-OthAgMeth
-J— Landfills under targets
—— Enteric under targets
	SoilN under targets
   Manure under targets
   Manure N under targets
   OthAgMeth under targets
 •••-••• Landfills under mitigation
 -• Enteric under mitigation
••*•• SoilN under mitigation
-a- Manure under mitigation
—-ManureN under mitigation
	OthAgMeth under mitigation
Figure 25 Emission pathways due to the agricultural sector when carbon-equivalent emission
limits are imposed
Thus, when mitigation is implemented in the energy sectors and some of the agricultural sectors
and not in landfill management nor in the other sectors, we find the energy sectors and the
mitigation-active agricultural sectors much more impacted compared to when all mitigation
options are activated.  A considerably higher carbon price results.


Technical scale coefficients (aiJiV) that relate "inputs to production" and the "production process"
are partially determined by the elasticities of substitution in the production equations and partially
dependent on the market prices resulting from solving for excess demand close to zero in the
model solution process (see  section on "Technical change"). Figures 26 and 27 illustrate both
aspects for «*=/,/-/ - that is, for the technical  scale coefficient that relate agricultural input to
agricultural production. In the reference case, the technical scale coefficients are vintage
dependent. When carbon prices change over time due to imposed carbon emission limits, the
technical scale coefficients are affected due to changes in prices paid. Note that when emission
limits are relaxed from year 2045 to 2050, responses can be  seen in the technical scale
coefficients as illustrated in Figure 27.
                                           125

-------
           The Technical Scale Coefficients over Time That Relate Agricultural
                        Input to Production in the Reference Case
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 0.11
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 0.09
0.085
 0.08
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O
CM
O
CM
                                                  in
                                                  CM
O
Cst
                                                            CM
                                                                 CM
tno
^-WI
OO
CJCM
Figure 26 The vintage-specific (vin-3 through vin-0) technical scale coefficients over time that
relate the agricultural input to production in the reference case
                                            126

-------
           The Technical Scale Coefficients When Mitigation Is Applied for All
                          Emitting Sectors or for Industry Only
Figure 27 The vintage-specific technical scale coefficients (vin-3 through vin-0) over time that
relate the agricultural input to production. The vintage-specific technical scale coefficients are
shown (1) when all sectors are impacted by a carbon price and all carbon-equivalent emissions
are mitigated (CE_all) and (2) when all sectors are impacted by a carbon price and the energy
production sectors and a limited number of agricultural processes are mitigated  (CE_ind) (no
landfill mitigation and no industrial processes mitigation).

The second step in the calibration process is to match projections of electricity generation, in
units of billion kilowatt hours, by adjusting an autonomous electricity efficiency improvement
parameter in all mode! activities that use electricity.  The results, shown in Figure 28 illustrate a
combination of validation against historical data and the results of calibration of projections in
model-to-model output comparisons.
                                           127

-------
               Historical and Projected Electricity Generation in the U.S.A.
                                      (bilion KWh)
      6000
      5500
o
= 4000
15
   3500
                       ,'S
                                                               • Annual Energy Review
                                                                 (total)

                                                               •*•• AEO (total)
                                                               a Annual Energy Review
                                                                 (electric power)

                                                               x AEO (electric power)
                                                               * SGM2003
          1980     1990     2000    2010     2020     2030
Figure 28 Historical and projected electricity generation in the USA. in billion kilowatt hours
The total amount of CO2 emissions generated by the electricity production sector is directly
related to the total amount of electricity generated, but more specifically by what fuels are
combusted. The mix of fossil fuels within electricity generation is adjusted by varying the tune
path of the cost to produce electricity using oil, natural gas, or coal in the calibration process.
Consequences of these adjustments manifest themselves not only in the total amount of COa
emitted but also in the fuel-specific emission balance (see Figure 29). Moreover, when carbon
fees are imposed, this emission balance is affected also. Figures 30 and 31 illustrate the CO2
emissions over time from the combustion of fossil fuels for electricity generation for the reference
case and  for when $100 per ton carbon fees are imposed.
                                           128

-------
     900 i
     800
   750-
«o
o  700
'35
0)
'£  650
UJ
   600
     500
             Historical and Projected Carbon Dioxide Emissions from the
                 Combustion of Fossil Fuels for Electricity Generation
                      A  /
                 Z
                                                          • SGM2003
                                                           -AEO2003
- Historical reconstruction
 with EIA data

 Emissions of GHG in the
 US 2000
         198 199  199  200  200 201  201  202  202 203
          5050505050


Figure 29 Historical and projected CC>2 emissions in units of million tons of carbon from the
combustion of fossil fuels from electricity generation
                                        129

-------
          Carbon Dioxide Emissions From the Combustion of Fossil Fuels for
              Electricity Generation When No Carbon Fees Are Imposed
     1800 -r

     1600
        1990 1995 2000 2005 2010 2015 2020 2025 2030 2035 2040 2045 2050


Figure 30 CO2 emissions in units of million tons of carbon from the combustion of fossil fuels
from electricity generation
                                       130

-------
          Carbon Dioxide Emissions From the Combustion of Fossil Fuels for
           Electricity Generation When Carbon Fees Are Imposed of $100 per
                                   Ton Carbon
  1600 i
  1400

  1200

  1000

   800

   600

   400

   200-
     1990  1995 2000 2005 2010  2015 2020 2025 2030 2035 2040 2045 2050


Figure 31 CC>2 emissions in units of million tons of carbon from the combustion of fossil fuels
from electricity generation when carbon fees are imposed of $100 per ton carbon
                                       131

-------
 References

 Chung, J.W. 1994. Utility and Production Functions. Blackwell Publishers.

 Chiang, A.C. 1967 Fundamental Methods of Mathematical Economics McGraw-Hill Book
 Company.

 DeAngelo, B. J., DelaChesnaye, F. C.. Beach, R. H.( Sommer, A. and Murray, B. C. (2004).
 Methane and nitrous oxide mitigation in agriculture. Energy'Journal (forthcoming).

 Delhotal, K. C., DelaChesnaye, F. C., Gardiner, A., Bates, J. and Sankovski, A. (2004).
 Mitigation of methane and nitrous oxide emissions from waste, energy and industry. Energy
Journal (forthcoming).

 Dervis, K, J. De Melo and S. Robinson. 1985. General equilibrium models for development
policy. Cambridge University Press. Cambridge, London, New York, New Rochelle, Melbourne,
 Sydney.

 Edmonds, J. and Moreira (2003), Cross Cutting Theme:  Technology in AR4,
 http://www.ipcc.ch/activitv/cct7.pdf. accessed 10/13/04.

 Edmonds, J.A. and J. Reilly.  1985. Global Energy: Assessing the Future. Oxford, New York.

 Edmonds, J.A., H.M. Pitcher, D. Barns, R. Baron and M.A. Wise. 1993. 'Modeling Future
 Greenhouse Gas Emissions: The Second Generation Model Description,' in Modelling Global
 Change, Lawrence R. Klein and Fu-chen Lo, eds. United Nations University Press, New York.

 Edmonds, J.A., J.M. Roop and M. J. Scott 2000. Technology and the Economics of Climate
 Change Policy. Pew Center on Global Climate Change, Washington, DC.

 Edmonds, J.A., SH Kim, CN MacCracken, RD Sands, MA Wise. Return to 1990: The Cost of
 Mitigating United States Carbon Emissions in the Post-2000 Period October 1997. PNNL11819

 Fisher-Vanden, K.A., R. Baron, J.A. Edmonds, H.M. Pitcher, R.D. Sands and M.A. Wise. 1993.
 Calibration of the Second Generation Model, draft report. Pacific Northwest National Laboratory,
 Washington, D.C.

 Henderson, James M. and Richard E. Quandt. 197L. Microeconomic Theory: A Mathematical
 Approach. McGraw-Hill Book Company, New York.

 International Energy Agency (1EA). 1996. World Energy Outlook:  1996 Edition. Organization for
 Economic Cooperation and Development, Paris, France.
                                         132

-------
International Energy Agency (IEA). 1997. Energy Balances for OECD andNon-OECD
Countries, data provided on floppy disk. Organization for Economic Cooperation and
Development, Paris France.

Kim, Son Hwi 1995. Stabilization of carbon emissions: a viable option for the Republic of South
Korea. Massachusetts Institute of Technology, Cambridge, MA.

Miller, Ronald E., and Peter D. Blair. 1985. Input-Output Analysis: Foundations and Extensions.
Prentice-Hall, Inc., Englewood Cliffs, New Jersey.

Reister, David B., James A. Edmonds, Richard W. Barnes, The Oak Ridge Industrial Model
Volume II - Mode! Description ORNL/Con-56/V2

Sands, R.D. 2002. SGM2000: Model Description and Theory. Draft report. Joint Global Change
Research Institute, College Park, MD.

Schaefer, D. O., Godwin, D. and Harnisch, J. (2004). Estimating future emissions and potential
reductions of HFCs, PFCs and SF6. Energy Journal (forthcoming).

Scheele, E. A. and Kruger, D. (2004). Global antropogenic methane and nitrous oxide emissions.
Energy Journal (forthcoming).

"United States Department of Energy, Energy Information Administration (EIA). December
1996. Annual Energy  Outlook 1997: with Projections to 2015. DOE/EIA-0383(97), Washington,
D.C.

United States Government. May 1997. Economic Effects of Global Climate Change Policies:
Results of the Research Efforts of the Interagency Analytical Team, draft report.
                                         133

-------
List of Equations
        22
      =
26

I
i=l
           JH
            JH
•x.
                N-l
                                  Eq. 1
                                          Eq. 2
                                  Eq. 4
                                                               Eq.3
            JJ
            'l.J.JJ.
                     .J.JJ.v
           f~is2S=l!_
        N+l

  j,t=o
              N+l
                          Eq.6
                                  Eq. 7
                                       Eq. 8
                                                  Eq. 5
piu,Ji,. = adJi, j,ii, • (pi,« • Ex Inii.Txpr0ii j;jj + Txadd.. ^ + Cpf,)        Eq. 9
Cpf, = P1=23>t • ExchRateregion • ^ EMCfn • PRconvrtj • GWP^      Eq. 10
pii=capiu,i,j.ij,t = wedge1=capltalj]jt + Pi=26          Eq. 12

           + TxIBT

Trit=Trij«(l
   J>t      J
                                      Eq. 14
                                        134

-------
                                ,0.5
      -Pi
      - "
                                                      1-
                             ,0.5
                                      Pi
                                        i=26,j,jj,t
                                                   I-
                            Eq. 17
                            Pi
                                                Eq. 18
Factor, JJJt = Factor, Jjyt., • (1 + TECHNN)Nstep       (unitless) Eq. 19
Factor^,  = (H-HHAEEI1>hll)N8tep
Factor, gvt  = (1 + GVAEEI,igv)Nslep
                                         (unitless) Eq. 20
                                         (unitless) Eq. 21
Ot:
a,,
                              r.-L
           C         /P           P
           k'i=ETE,j,jj,v ' ' i=ETE,l )    l i=ETE,t
                                                  Eq. 22
       _   ^
                 s-l/P
         /i=ETE,t
                                         X
                                          •i=BTE,j,j).v
                                           [i=ETE,t
                                                             Eq. 23
       N+l
             N+]
                                        Eq. 24
ai=26,j,jj,v -
             N+l
                         V=-J
                           N-l/
                                            *ZJ,ii,v
                                      a
                                        '.J.JJ.V
                                                          Eq.25
                                                        Eq. 26
a;
        N=26
                     f°r i=1 :26 Snd J=1 :22
                                                  - 27
         i=0
                                                                                Eq. 15
                                                                             Eq. 16
                                          135

-------
             a
              'O.J.JU.V
           N=26
          V i-O

                                        Eq. 28
acst0 j jj v = ao j jj v



ft         = «5I-p2.:)/(1"pl)
  i=26,j,jj,v   ^1=26,.!,^. v
                                              Eq.29


                                            Eq. 30
                              Eq. 32


                       = 1              Eq. 33

                                           \(pl-p2)/(l-p1)
                                 Pr,
                                                                Eq. 34
a     = aO-p2)''(i-p« .
                          Pr
acst0 j ¥  = ar0_j>vij,v >J
2—t ',.
i=l
X0 • -v =1
I . ^'•J'JJ>t-1

j,jj,v ' rrj,t

Eq.42

                                                Eq.41
                                    Eq.43
        _
    Ji-v ~ ao,j,jj,v
                                      Pr
                            a
                                         j,t
                              "•"•*   Pi,,,,,
                                                            Eq.44
                                              136

-------
                                                                   /0-pi)
I
/Vi=26=
                 _~P1/0-P1)
       capital,j,jj,v    "'O.j.jj.v       **i=26,j,jj,v
                            N-l
71 AJfcv  = Prj,t • q j,J|,v - S Pi i,J,JM * XUJH,v             Eq. 46
«iii.v = ao,j,ji,v •
                                                                Eq. 48
ZJ,i,v = 1 - («.JA
                        v
          i=N-M+l
            "k
            ^i=capital,j,jj,v
                                      *       acstU,ii,v
                                             i
                                           i=capiULj.)j,v


                                                                            Eq. 49
                                                                                      Eq.51
                                        Fn
 V
   i,J.JJ,v
                                                        vl/p
                                                                       Eq. 53
                         =26.j.jj.v
                                                (p-D/p ._.I/P
                                                       ._.
                                                         a
                                                           i=26,j,ij)v
                                                                              Eq. 54
                                                                             Eq. 55
                                                                                     Eq. 56
             Ai=26=capital,j,jj,
                     pital,j,jj,v
                =«o,j,JJ,
        v=t-3't-l
                     ^•i=26,j,ij,v
                                                i=26=capital,j,jj,v
                                          N-i
                                                               >,J.JJ.«
                                                                                        Eq. 58


                                                                                        Fa  59
                                                     137

-------
                             Eq.60
                                     ',j,JJ,t
    Eq. 61
           0.01
                          0.01
                                           Eq.62
PRDV
      i,Ji,v=.-3:«-.

     ,,^^.^, = PRDVj!jJ-
                                           Eq.
                                KAjJiV         Eq. 65
       JJj¥=t.3 ,., = PctDeplete* PRDVj>J]|V            Eq. 68
   j,ji.v=t-3:t-i = PctDeplete* 7CjiJJ-v          Eq. 69
DrsVtmpj •• t = DrsVtmpjiJjfl - Deplet^          Eq. 70
Kdenij ^ = PctDeplete* Kdem- ^          Eq. 71

         = Oo.j.ij.v • Prj,t« Zj.jj-v"1"1 * al             Eq. 72
PRDVjJ,v=l_3:t_! = fac. -
                      /(
Deplet^ = ((2 • PRDVj dj v ) + (3 * PRDV^, )) • PRconvrtj       Eq. 66
            i=26,j,jj,v
   j,jj,v=t
                       J'1   i  Ui-26 jjj-
Eq. 73

     Eq. 74

,,,v     Eq. 75
PRDVJ,ii,v=, = "
                                                               77
                                                                         Eq. 76
                                       138

-------
                                           Eq.78
PRDV;
       J,J),=1
                             J,0),v
              v=t-3
                         Eq.79






                           Eq.80




                            Eq. 81
          22
     Eq. 82
          22
         22
              v=t-3











              t
              :=(






             t
                      EDV
                                    li=ETE.j,jj,t
                   JJ=1
                                     EDV
                                           l.j.jj,V=t-3:ty
                                                    'i^ETE.j.jj.t
                                                                     Eq. 83
     M + Tr,, . Exlm,. EDVM>JJ-v=(_3:t). (ixpro,,^ -1)
         v=t-3
           22
Subsid =
              -"I
                   1





                t
            ,t + Tr, t
                                                    J ,
                v=t-3
             t
TaxpU2 j =





SubsidpLT =
            v=t-3



              22
                           i.25,j.ii - EDV1=25,J,Jy.v=t-3:t)
                      v=t-3
-"I
     v=



   I
                    v=t-3
                         JJ=1
Pi=23, = CarbVar,
             Eq. 91
                      Eq. 92
                                                                            Eq.84
'(Txproi=2Ujrl)Eq.85






>(Txpr0]jJj-l)  Eq,86
                                                            Eq. 87
                                          Eq. 88
                                                                 Eq. 89
                                                           Eq. 90
                                          139

-------
CarbonLim, = CarbVai;        Eq. 93
CarbonLim, = EmTot, • CarbVar,       Eq 94
EDi=23>J=23= -CarbLin\            Eq. 95
PRDJ=23= CarbLim,             Eq. 96
EDi=23>J=3>4 5= EmissionsCj=3 4,           Eq. 97
   Wo H 22 = Emissions j = ^TotDem, •PRconvrt, • GWP; • EMC;     Eq. 98
                         i
CrbTrade, = Pi=23, • ExchRateregloll»(CarbLimt-EniTott)       Eq. 99
CrbTradet = CrbTradet - CPermF5J=25=imej[ -CPerrnF, j=26,gv - CPermF5 J=27=hh   Eq. 100
CrbFeeTot, = CrbFeeTot, + CrbTradet         Eq. 101
       n
Kj t = ]T KAfloWj jj t       for the base year    Eq. 102

EOTjJjjt=0 = EXPPROFjJj]t=0     for the base year    Eq. 103
                              Nrinv
                         rhoinv+1
                         liioinv
                                           Eq. 104
                     f working, age_popt
Temn =basekao • sealer* 	—	
     '         '       I n>r\r-is«n n  or>»  «^r\«%
        v=t-3
      j = Qprojt •
                v=t-4
\_ working_ age_popt_,
               Eq. 106

             -t
                                            •margvalue™"     Eq. 105
                                    v=t-3
                                                           Eq. 107
TestKj = Capqy • QneWj     forjj=l      Eq. 108
                                 TiNr
                                                     Eq. 109
                                    J,J),v=t
Share = ;i =
            Far
            H/il: ::
                rhoinv
          n=3
                          forj=8andjj=l:6   Eq. 110
                                      140

-------
             Share
                   J.JJ
               n
             -I
                                 Eq. Ill

                                3»ExoEleJB t = Share JJJt * Kjit   Eq. 117
KAJ J} t = 2 • KAflow jjj>t_, + 3 • KAflow^  Eq. 118
DrsCtmpjjj = DrsceJij            Eq. 119
DrsVtmpJ)Jt=DrsveJJJt           Eq. 120
Re serve j = PRconvrtj "Eqdepj          Eq. 121
Eqdepj=xnpj«a0iAAv»Zjj&v
Drscej ^ = DrsCtmpj jj + Drsce^
    Eq. 123
                                                          forj=8 Eq. 112
                                                       122
                        Tresgrz^'      "  J>JJ  Tresgrz
DrsVtmpjJjpl = Re serve •           Eq. 125
DrsCtmp: - - DrsCtmpj t  - Re serve:          Eq. 126
                                                          Eq. 124
                                                     j.jj
„   „         DrsCtmp,..
Pet Re serves =         J|JJ
          ]} t = ReservCj
                         Reserve:
                                           Eq. 127
                                 Eq. 128
                                     141

-------
        i = Pet Re serves • Eqdep
KAflowjjjt =PctReserves»
KAj jj v=t = Pet Re serves*
Reservej = DrsCtmp
Kdem = == =
                                         Eq. 129
                                              Eq. 130
                                         Eq. 131
ED1>J=25=mv=
                 22
      Eq. 132
      Eq. 133

> CapMatj j
                                               Eq. 134
                     22
                                                          Eq. 135
            ii=i
                 22
                j=i
                                                 Eq. 136
EDi=ETOJ = EDi=ETCJ + £ WHSLt + ^TRNP,        Eq. 137
                     i=l           i=l
          -   .    .. [(adi.ijit -1)* [(pi,« +Trl,.)* ExIm,«Txpro,vy + Txadduij]»
WHSL;=£  ^  ^ — -
             v-t-3
                 JJ-1
                     EDV,
                               li=ETE,j,jj,t
 (adji,j_27_hhJ.M -l)«[(Pi,t +Trit)»ExImi«Txproi].27.hhi_1 +Txadd. ^^^.J.
         /Dj
          rli=ETE.j=27=hh,jj=1,l
    Eq. 138

            v=t-3
                 JJ=1
                                  EDV
                     Triit»ExImi«      1>M)V'
                         i=ETE,j=27=hh,jj,t
                                            li=ETEJ,jj,t
                                                           Eq. 139
CPermF5>J=25=inv =
        NAO
                       ; • EDi>J=25=inv)
                      +
                                            Eq. 140
                                           Eq 141
working_age_poPtot =    (POP^^, + POPagB>females)      Eq. 142
                      age=4
                                      142

-------
working_age_popng =
                                            l 143
ED1=25,lbs>J=27=hh = -1 • X working_age_popng • LB^ « [1 - exP(LB.
                                                                    "25-lb5't
                    ng
LB0,ng -
    Eq. 144
        working _ age _ pop v
               POP.,
                                      Eq. 145
        logl-
LBl,ng =
              (working _ age _ poptot )• LB0
                                       0,ng
                                                   Eq. 146
          ED;
>ng  working _ age _ popl(


         X.
SalesM=25=lbs = -1 • EDi=25=)bs j=27=hh
                     * "
                                     Eq. 147


                                          Eq. 148


                                        Eq. 149
                        i=25=lbs,l
               Eq. J50
LB  -POP«
L-D-> I —
        Nhh
                            Eq. 151
ED1=24=ls,J=27=hh = -1 • TLA • R0 • [1 - exp(R, • -
                                             ri=2-f=ls,t

                                                      -)]     Eq. 152
                                           i=ETE,j=27=hh,jj.t
     log
         1--
              TLA
SalesY.24.,, =-l«EDi=

     X,
                     Mrllij±27=hh
                                    Eq. 153


                                       Eq. 154
RI   Nhh •*_„_,
                              Eq. 155


Pine = (HHinc, + HHinc2 + HHinc3) • (1 - PItr) + GovTr,       Eq. 156


HHinc, = ]T

    Eq, 157
            (ZXi^jVfO-Citr^^
            \JH       )
                                                                             )]
                                      143

-------
Xitc =
                   j u • Kdem}11 ]        Eq. 1 58
       log
                         TREte
                                                  Eq. 159

                 ui  • (d - Citr) + Xitc> (l - (REOJ • (1 - expCRE,, * P1=26,t))))
                                                                       Eq. 160
TREte =
REt6j =
                            Eq. 161
                  (l-Citr).XitCj
                                           - exp(REKj « P1=26,t>)   Eq. 162
TREte = TREte + 0.6 • CrbFeeTott + 0.6» ExIBTt       Eq. 163
TREte = TREte + CrbFeeRcyPct3«CrbFeeTott + CrbFeeRcyPct3«ExIBTt   Eq. 164
TaX3.j=l 22 = Citr * *j ~ ^^j               E(l- 165
HHinc2 = (1 - SStr) • -1 • ED1=25=lbs_J=27=hh • P1=25=lbs t       Eq. 166
Tax2>J=27=hh  = [SStr •-! • ED,^lbs j=27=Wl • P1=25=lteJ       Eq. 167
HHinc3 = -1 • ED1=24=ls J=27=hh • Pi=24=ls t         Eq. 168
Tax3j=27=hh = (HHincl + HHinc2 + HHincS) • Pitr       Eq. 169
GovTi; =
                                '=hh
                                      • YngOld63
                 ^working_age_pop/
Pine = Pine + CrbFeeTott           Eq. 171
Pine = Pine + 0.4 • CrbFeeTot,          Eq. 172
Pine = Pine + CrbFeeTott - CrbTrade,         Eq. 173
Pine = Pine + CrbFeeTot,           Eq. 174
Pine = Pine + CrbFeeRcyPct2»CrbFeeTot,        Eq. 175
EDl=26(j=27=hh = -1 • Pine • S0 • (1 - S, • exp(S2 • Pi=26))
S,=l               Eq.  177
                                                       Eq. 176
                                                                  Eq. 170
                                      144

-------
    logl i   "•"i-ae.c^ij.n.hh
        1        Pinc»Sn
                                        Eq. 178

                                           Eq. 179
Saving = -1 • EDi=26=capital j=27=hh
Pine = Pine - Saving              Eq. 180
Const = Pine               Eq. 181
EDi=26=capitai.j=27=hh = ED1=26=capita) j=27=hh -TREte
                                                     Eq. 182
SalesV1=26 = -1 • ED1=26=capltalJ=27=hh           Eq. 183

DemTotj=27=hh = £ [EDio=27=hh • Pi,,j=27=hh, J        Eq. 184
                            Pine
                                               "1i.j=27=hh.jj.t
                       Pi
                       rli=ETE,j=27=hh,jj,t
                                                                    Eq. 185
 J   -    '.J=27=hh
 'w"l   Pine
P    _   ^O.hh,t-l
•^O.hh,'
        Factor
                                    Eq. 186
                             (unitless) Eq. 187
              i.hh.t
Pine = Pine - HHinc9 -HHin c, 0          Eq. 1 88
HHinc9 = (- 1 • Pi^^^HH,,, • LB2>2 • EDl=25=lbsJ=27=hh )      Eq. 189
                  u.j^hh,*, • R2 • Nhh)        Eq. 190
HHinclo =  Pi
ED
   i-l:22,j-27-hh
                ED, ;• Pine
                DemTot j=27
Eq. 191
WHSL =
                = ED1=25=lbsj=27=hh • (l - LB2,2 )        Eq. 192
                             Vt +Tri,t •ExIm1)»TxPr°1>J=27=hh +Txaddlj=27=hh]»
           ED
              i,j=27=hh>
                    'Pi
                       i-ETE,j-27-hh,jj,l

TRNP, = Tri-t • ExIm, • ED^27=bh/n-
                                                                             Eq. 193
                                                       Eq. 194
Taxu=27=hh = £(pi-t + Tr, t • Exlm,. abs(ED, J=27=hh))« (ixpro, J=27=hh -1)    Eq. 195
Subsid, =-Tax1>j=27=:
                    hh
                                  Eq. 196
                                        145

-------
              24
                                               Eq. 197

SubsidpUj = SubsidpUj -Txaddlj=27=hh »EDij=27=hh       Eq. 198
CPermF
       5J=27=hh
GF  = 1
   ftt
                      ; • ED, J=27;=hh)         Eq. 199

                     Eq. 200
TaxGovlte = £(pi-t + Tr( t • Ex Im, • ED, J=26=gv • (ixpro, >j=M^ - 1))    Eq.
                                                                201
SubsidGov = -TaxGov;,,
                                 Eq. 202
TaxGovpU,,, = £ (ixadd; J=26=gv • ED1>j=26=gv )        Eq. 203
SubsidpU = TaxGovpUit
CPermF5,j=26=gv =
                                 Eq. 204
                        ED1J=26=gv
                                          Eq. 205
           27
TotTax. = V  (Tax, • + Tax,, + Tax,, + Tax., + CPermF, f)    Eq. 206
       1   mimmft      *> J       * J       *J       >J           *J
Tax4 ^ = SalesPj • TxIB^
SalesPj =
        v=t-3
         22
                               Eq. 207
                                       Eq. 208
ExIBTt = J (SalesPj • (TxIBTj, - TxIBT* >t.0))      Eq. 209
         22
Subsid =
                v=t-3
£(PM +TrM .Exlm,. ED; J=26=gv).(Txpro10=26=gv -l)
j=26
GovDef^ = GovDeft, • Pii=ETBii=2fcBViijil         Eq. 211
            22   1
GovMt,=0 = J] ZXJ=26=gv,ii=gvjli          Eq. 212
            i=0 gvjj=l
GovMt, = TotTax t - Subsidy, - GovTtr, + GovDeft,      Eq. 213
GovMtt = GovMtt - CrbFeeTott         Eq. 214
GovDeft, = GovDeftt - CrbFeeTott        Eq. 215
                                                                   Eq.210
                                    146

-------
GovMt, = GovMt, - CrbFeeTot,          Eq. 216
GovMt, = GovMt, - CrbFeeTot,          Eq. 217
GovDeft, = GovDeft, - CrbTrade,          Eq. 218
GovMt, = GovMt, - CrbFeeTot,          Eq. 219
GovMt, = GovMt, - (CrbFeeRcyPct2 + CrbFeeRcyPct3)« CrbFeeTot,   Eq. 220
                    /v
                     yvi,j=26=gv,gvjj.
                                                        Eq. 221
                gv)j=l
GC;
              GC
                  i,j=26=gv,t-l
    i,j=26=gv,t   T"
              Factor, J=26=gv,
                   25
        (unitless) Eq. 222


         '.EVit     i,j~26=gv,gyjiv=t /
              gvjj=l
GEgvJJ=GovMtt» —
                          i=26=capitaLj=2fcgv,gyij
                                       • Pi
                      i=2fccapitaij=26=gv,gyij  -1 1i=ETEJ=2fcgv,gyij>v=t
                                         sig
                            j=26=gvgvjj      J=26=gv,gvjj
                                        GF5ig
                                        VJr=26
                                                                   Eq. 223
                              Eq. 224
                    gvjj=l
                gvju=l
ED;
    i=26=capilal,j=26=gv
                        Eq. 225


j=26=gv,gvjj * GCi=capiulj=26=gv,,gvjj * "^-'j=26=gv,gvij) +
                                 "  2w ^  ^j=26=gv,gvjj
                                  gvjj=i
                                        Eq. 228

                                 j            Eq. 229

                          • ExchRat^i^         Eq.230
and/or    Trade, i=1:25 = Trade, i=,25 • ExchRatef(:gion       Eq. 231
                                                  Eq. 226
                                             Eq. 227
                                          147

-------
ExP Imt = £ [Tradeo,i=i:25 • Pi>t ]          Eq. 232

          25 r             i
Exp Im, = £ |Trade,]i=1:25 • Pi>t]          Eq. 233
         i=l
Explm, = Exp Im, - Trade, i=23 • Pi=231         Eq. 234

Tradeu=23 = Trade1>1:=23 / ExchRatereglonl         Eq. 235

       N     (       *    ^
GNP = y Pi.. • PRD, - y ED1:  = KTot. + Cons. + GovMt. + Ex Im.  Eq. 236
      ^^^  1,J  I     J   j^^   'J
       i=l     V       J='    )
       N /           N          A   N /           N*M         \
GNP = J] Pr^PRDi-J^Pi^-ED^ =£ 1X11^+^+ XPii.J*EDw   Eq. 237
Salesy=1:23=PRDJ=123=^
                     v=t-3
                                          (see Equation 106)  Eq. 238
Mrk Pr dm = SalesV; • PRconvrti         Eq. 239

                                               Eq. 240

Xvec-mewt = Log(MrkEdm + Mrk PrdJ - Log(Mark Pr dj      Eq. 241
           27                .
MrkEdffl = X(Edij * PRconvrti )- Mrk Prd
W,,=
       DemTmp - (MrkEdm+Mrk Pr dm)  SupTmp - Mrk Pr dm
            MrkEdm + Mrk Pr dm             Mrk Pr dm
  j-j                                                     7   delta
                                                          Pit- delta
    Eq. 242

TotDem1=1:22 - J]EDIpJ - ED, ^         Eq. 243
                      •GWP,_3 •
/                           -3                              g
(0.97«PRconvrtfam3 •TotDem,=3 - PRconvrtfn=9 • Trade, 1=9=refmedoll)

EmissionsCH4_Bas = EMC • GWP4 •
,         '  8                                      v    Eq.245
(PRconvrtfn=4 • TotDem1=4 - PRconvrt,-^,,, • Trade0 i=10=G,s_T&D j

EmissionsCj=5=coaj = EMC5 • GWPi=5 • (PRconvrtfn=5 • TotDem1=5 )    Eq. 246
         5
EmTot, = £ EmissionsC,           Eq. 247
         J-3
EmActjx= PRconvrt^-TotDem^          Eq. 248

                                   148

-------
Emissions: = EMQ • GWP, • (PRconvrti • TotDenij)      Eq. 249
                                  149

-------

-------
                                                   PNNL-14256
           Appendices A - D for
           Model Documentation for the SGM
O
           Antoinette L. Brenkert
           Ronald D. Sands
           Son H. Kim
           Hugh M. Pitcher
           October 2004
           Prepared for the United States Environmental Protection Agency under
           Contracts AGRDW89939464-01 and AGRDW89939645-01
           Joint Global Change Research Institute, College Park, MD
           Pacific Northwest National Laboratory
           Operated by Battelle for the US Department of Energy

-------
LEGAL NOTICE
This report was prepared by Battelle Memorial Institute (Battelle) as an account of sponsored
research activities. Neither Client nor Battelle nor any person acting on behalf of either:

MAKES ANY WARRANTY OR REPRESENTATION, EXPRESS OR IMPLIED, with respect
to the accuracy, completeness, or usefulness of the information contained in this report, or that the
use of any information, apparatus, process, or composition disclosed in this report may not
infringe privately owned rights; or

Assumes any liabilities with respect to the use of, or for damages resulting from the use of, any
information, apparatus, process, or composition disclosed in this report.

Reference herein to any specific commercial product, process, or service by trade name,
trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement,
recommendation, or favoring by  Battelle. The views and opinions of authors expressed herein do
not necessarily state or reflect those of Battelle.
                             Printed in the United States or America

-------
Table of Contents
LEGAL NOTICE	2

  Table of Contents	3
  List of Tables	4

APPENDIX A: DATA TABLES FOR THE SGM	6

  Input-Output Tables	6
  Markup of Prices	16
  Conversion Tables	20
  Technical Change Tables	21
  Data Tables for the Operation of Vintaged Capital	25
  Carbon Policies and Emissions	26
  Demand Sectors	32
   Investment Demands	32
   Households	37
   Government	41
   Trade	42

APPENDIX B: DESCRIPTION OF THE SOLUTION ALGORITHMS	44

  Bisection Routine	44
  Newton-Raphson Routine	45

APPENDIX C: DESCRIPTION OF THE SOLUTION ALGORITHMS	46

  Input-Output Table Conversions	46

APPENDIX D: COMPARISONS BETWEEN THE SGM AND MINICAM	48

-------
List of Tables


Table 1 An example of input as a commodity-by-commodity hybrid input-output table (first 12 columns)	6
Table 2 Summations of total inputs in the commodity-by-commodity input-output table based on industry technologies,^^,, for all 14
       regions of SGM, indicating which parts of the input-output tables are active	9
Table 3 An example of a commodity-by-commodity hybrid input-output table with gross production as diagonal elements at time r=7
       (first 12 columns)	11
Table 4 An example of a commodity-by-commodity hybrid input-output table with demand minus gross production as diagonal
       elements at time (- 7 (first 12 columns) with carbon-equivalent emission limits imposed	13
Table 5 Variable values at the end of the last iteration of the market solving algorithms when carbon policies are based on carbon
       emission limits	16
Table 6 Initial and future market prices	17
Table 7 Price overrides (IPfix)	17
Table 8 Production-sector-specific indirect business taxes	18
Table 9 Transportation cost changes for each supply sector	18
Table 10 Additive taxes, proportional tax rates and transportation-export-import cost multipliers	19
Table 11 Adjustments to prices	19
Table 12 Emission coefficients and GWP	20
Table 13 Energy conversion factors (exajoules per million 1990 dollars)	20
Table 14 Exchange rates	21
Table 15 Technical change parameters for production sector 2, the Everything Else sector, for inputs of capital KA, labor L, energy
       production E, industry A/(manufacturing), land land, oil refining, gas processing, coal and electricity	21
Table 16 Technical change parameters for household fuel use	22
Table 17 Technical change parameters for government fuel use	22
Table 18 Elasticities of substitution for the production sectors	22
Table 19 Example output of the vintaged alpha transformations, a^j-,,  over time (for supply sector I and production sector 1)	23
Table 20 Example output of capita) stock technical coefficient transformations for all production sectors for one region and one point
       in time	24
Table 21 Example output of the Leontief coefficients for the fixed factor production subsectors of electricity production and the
       refined oil production sectors for one region at one point in lime for the first supply sector (agriculture; /=/)and for the 26*
       supply sector (capital; i-26)	24
Table 22 Initial values of prior capital stock	25
Table 23 Technology characteristics	26
Table 24 Global wanning potential of different gases	26
Table 25 Greenhouse gas emission coefficients and related parameters	27
Table 26 Cost curves for calculations of the carbon-equivalent emissions in relation to carbon prices	21!
Table 27 Mitigation data	29
Table 28 Descriptions of switches and variables partaking in carbon policy	30
Table 29 Policy options, carbon prices and emission limits	30
Table 30 Impacts of carbon policy options	31
Table 31 Initial values of annual investments and expected profit rate	32
Table 32 Investment accelerator equation parameters	33
Table 33 Production multiplier	33
Table 34 Production sector-specific investment elasticities and exogenous investment demands	33
Table 35 Investment switches for electricity in nuclear and hydro power over time	34
Table 36 Resource characteristics: oil, gas and coal are depletable resources	34
Table 37 Data on oil, gas, and coal resources	34
Table 38 Data on investments in oil, gas, and coal resources	35
Table 39 Example of the capital  cost scale factor transformations for oil, gas and coal production	35
Table 40 Capital demands and share calculation results at the  end of the base year calculations (f=0)	35
Table 41 Investment shares vector	36
Table 42 Projected male population	37
Table 43 Projected female population	37
Table 44 Male and female working age population	38
Table 45 Number of households in the base year 1990	38
Table 46 Household labor supply fraction in base year	38
Table 47 Demand for household labor supply in the base year	39
                                                            4

-------
Table 48 Total land area over time	
Table 49 Land supply function coefficient	
Table 50 Demand for land in base year	
Table 51 Personal income tax rate	
Table 52 Corporate income tax rates in base year	
Table 53 Investment tax credit rates	
Table 54 Retained earnings fraction in the base year	
Table 55 Total regional household retained earnings	
Table 56 Social security tax rate	
Table 57 Government transfers in the base year	
Table 58 Household savings in base year	
Table 59 Household savings function coefficient in base year...
Table 60 Household income and price elasticities in base year.
Table 61 Government preference function coefficients	
Table 62 Government deficit over time	
Table 63 Trade data	
..39
..39
..39
..39
..40
..40
..40
..40
..40
..40
..41
..41
..41
..41
..42
..42

-------
Appendix A: Data Tables for the SGM

Input-Output Tables

The basic structure on which the SGM is built is a regional hybrid commodity-by-commodity
input-output table. Table 1 shows a commodity-by-commodity hybrid input-output table. This
table shows input for the base year for the USA (XtJ values for t~0 for the year 1990).

Table 2 shows the summations, XSirV, over all inputs for each of the regions for which the SGM is
implemented, to illustrate the different regions' input breakdowns.

Table 3 shows for time f=7 a table similar to Table 1 to be solved for excess demand and related
prices. The matrix cells contain the demand values (Edtj which for the base year are denoted by
XtJ) with diagonal elements (bolded) equaling values of demand (Edjj) minus gross production
(PRDiJ). The point in time for which Table 3 is an illustration shows results in the form of carbon
emissions.

A similar table is shown as Table 4 for t=7 when a carbon policy is implemented consisting of
carbon-equivalent emission limits and inputs are given in Table 27 below. When Tables 3 and 4
are carefully compared, one can observe the shifts in values attributable to the carbon policy
implemented.

When the market solves for market prices as described in the "The solution procedure" (see
Chapter ten of the documentation), the values at time t=7 are as in Table 5 below.  Table 5
contains the results of a model run implementing a carbon policy consisting of carbon-equivalent
emission limits for which the full input-output table at /= 7 is given in Table 4.  The carbon price
value at r=7 (year 2025) can be found in this table.
Table 1 An example of input as a commodity-by-commodity hybrid input-output table (first 12
columns)

Region =
USA
Other AK.
ETE
C.OilPrd.
N.GasPrd.
CoalPrd.
Coke Prd.

Elec Gen.
RefOil
GasT&D
t=0

1
2
3
4
5
6
7
8
9
10
I
Agricult
UK
8341
8938
0
0
0
0
0
548
1012
744
2
ETE
13334
1137360
0
0
144
0
0
46167
2368
10980
3
Cnide
Oil
4
9551
0
0
0
0
0
0
0
0
4
Nat.
Gas
4
10000
0
0
0
0
0
0
0
0
5
Coal
10
2524
0
0
0
0
0
0
0
0
6
Coke
Prod.
0
100
0
0
838
0
0
0
0
0
7

0
0
0
0
0
0
0
0
0
0
8
Electricity
25
13,939
0
0
16,659
0
0
16,215
5,559
14,531
9
Oil
refining
16
14188
70929
0
0
0
0
0
9171
0
10
GasT&D
13
6214
0
43865
0
0
0
0
62
6439
11
Paper,
Pulp
94
23341
0
0
307
0
0
5668
845
2969
12
Chem
icals
445
41715
0
0
810
0
0
9516
7066
11227

-------
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrphtTran
Grains and
Oil Seeds
Animal
Products
Forestry
Food
Processing
Carbon
Land rental
Labor
income
OVA (other
value added)
!BT (indirect
business
taxes)
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
1330
4405
75
7
1
2607
624
1040
91
1050
35
129
0
0
17885
22000
1177
29157
31028
5681
635
783
310184
32293
30291
55
652
86
65638
0
0
2179060
1143280
360702
9
686
270
635
L2
1096
189
333
0
0
0
1
0
0
9789
15436
2058
9
719
283
665
2
1148
198
349
0
0
0
1
0
0
10249
16162
2155
77
217
106
60
14
2540
297
1018
0
0
0
0
0
0
8412
5060
2277
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2000
500
too
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
93
477
18
1
132
15,848
1,929
5,738
0
0
0
1
0
0
26,285
78,043
11,218
284
2955
565
90
2
2828
432
6626
1
I
1
105
0
0
9046
9251
6837
43
96
21
55
1
4577
333
594
0
1
0
58
0
0
9740
16356
4495
56484
9785
X05
272
207
13908
1477
7106
1
7
6496
513
0
0
43107
30415
2067
4612
65850
1123
384
164
18188
1837
8083
156
186
103
1498
0
0
50293
58979
3722
Table 1 Extension (next 13 columns)

Region =
USA
Other Ag.
ETE
C.Oil Prd.
N.GasPrd.
Coal Prd.
Coke Prd.

Elec Gen.
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
KFMetals
Othlnd
PassTran
FrghtTran
Grains and
Oil Seeds
Animal
Products
Forestry
t=0

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
13
Cement
,etc.
24
6798
0
0
311
0
0
7201
129
1916
1823
2551
7139
369
92
5728
522
4165
0
0
4
14
Iron
and
Steel
18
12698
0
0
0
3563
0
3589
169
2158
217
1321
1193
12346
1584
7467
661
2887
0
0
0
15
NF
Metals
19
11025
0
0
13
0
0
2271
40
1301
302
1568
400
716
19542
6445
387
2408
0
0
7
16
Other
Industry
8832
354937
0
0
193
0
0
24674
11989
10893
77694
62172
44128
64350
42771
518492
13351
35871
564
368
849
17
Passeng
er
Transpo
it
23
26392
0
0
0
0
0
1212
69830
0
100
130
61
43
20
6531
12357
3707
0
1
0
18
Freight
Transpo
it
35
46233
0
0
0
0
0
0
22137
0
375
297
42
230
94
14257
6260
35514
13
5
0
18
Grains
and Oil
Seeds
3094
12340
0
0
0
0
0
425
1093
1383
18
5335
79
9
0
2673
98
1144
2089
671
0
20
Animal
Product
s
4014
11037
0
0
0
0
0
1768
477
0
217
628
8
12
0
2050
290
3040
22876
13990
0
21
Forestry
1951
883
0
0
0
0
0
26
48
26
12
187
2
0
0
290
47
56
32
111
215
22
Food
Processi
ng
12116
46575
0
0
0
0
0
3655
218
2581
11813
3981
4522
7
32
21774
2179
8964
19601
69394
83
23
Carbon






















-------
Food
Processing
Carbon
Land rental
Labor
income
OVA (other
value
added)
IBT
(indirect
business
taxes)
22
23
24
25
26
27
22
0
0
17473
10576
769
3
0
0
17071
5231
859
6
0
0
11220
3931
676
1761
0
0
680626
300289
25806
303
0
0
40371
11847
5595
152
0
0
75956
36366
6024
0
0
0
1561
23083
2220
14039
0
0
3928
9885
1183
322
0
0
1183
1794
332
61555
0
0
51466
55597
9077






Table I Extension (demand sector columns)

Region = USA

Other Ag.
ETE
C.Oil Prd.
N.GasPrd.
CoalPrd.
Coke Prd.

Elec Gen.
RefOil
GasTiD
WoodPrd.
Chemicals
Cement
Steel
NFMetals
OtHnd
PassTran
Fr^htTran
Grains and Oil Seeds
Animal Products
Forestry
Food Process ing
Carbon
Land rental
Labor income
OVA (other value added)
IBT (indirect business taxes)
1=0


1
2
3
4
5
6
7
8
9
10
11
12
13
14
IS
16
17
18
19
20
21
22
23
24
25
26
27
24
Net Exports

-2911
66545
-30870
-1923
3336
-25
0
-145
-6186
0
-2587
6117
-4132
-8146
-3846
-119489
20012
28057
10963
-674
-571
-3165
0




25
Investments

0
57739
0
0
0
0
0
0
0
0
2935
1261
0
10
230
896796
1684
3180
0
0
0
2
0




26
General
Government
Consumption

1980
670812
0
0
0
0
0
15735
1667
3034
3754
12348
804
258
377
119290
11874
7374
563
141
-1802
8535
0




27
Household
Consumption

20560
2807997
0
0
0
0
0
68185
5635
22780
17104
71841
4416
27
75
425387
69193
46444
310
3539
2011
233708
0




Table 1 Extension (Electricity production sector columns)


Other Ag.
ETE
Elec Gen.
SUMMED
25
13,939
Oil
S.I
1
582
Gas
8.2
2
1,314
Coal
8.3
14
7,761
Biomass
8.4
0
0
Nuclear
8.5
5
2,871
Hydro
8.6
3
1,410

-------
COilPrd,
N.Gas Prd.
Coal Prd,
Coke Prd.
Elec Gen.
RefOil
G»» T&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains and Oil Seeds
Animal Products
Forestry
Food Processing
Carbon
Land Rental
Labor Income
Capital
R1BT
0
0
16,659
0
16,215
5,559
14,531
93
477
18
1
132
15,848
1,929
5,738
0
0
0
1
0
0
26,285
78,043
11,218
0
0
0
0
677
5,559
0
4
20
1
0
6
662
81
240
0
0
0
0
0
0
1,098
3,260
700
0
0
0
0
1,529
0
14,531
9
45
2
0
12
1,494
182
541
0
0
0
0
0
0
2,478
7,359
1,693
0
0
16,659
0
9,029
0
0
52
265
10
1
74
8,824
1,074
3,195
0
0
0
0
0
0
14,636
43,455
6,028
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3,340
0
0
19
98
4
0
27
3,264
397
1,182
0
0
0
0
0
0
5,414
16,074
1,876
0
0
0
0
1,641
0
0
9
48
2
0
13
1,603
195
581
0
0
0
0
0
0
2,659
7,896
922
4»
                 Table 2 Summations of total inputs in the commodity-by-commodity input-output table based on
                 industry technologies, XSj,v, for all 14 regions of SGM, indicating which parts of the input-output
                 tables are active
Regions
Other Ag.
ETE
C.OilPrd.
N.Gas Prd.
Coal Prd.
Coke Prd.
[ empty)
Elec Gen.
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains and
Oil Seeds
1
Australia
&New
Zealand
27,061
528,182
2,778
2,007
6,287
0
0
14,143
12,714
2,292
0
0
0
0
0
0
0
0
0
2
Canada
40,322
950,743
26,991
12,400
2,083
0
0
26,080
37,722
13,041
0
0
0
0
0
0
0
0
0
3
China
969,989
831,846
49,602
1,307
54,823
11,791
0
85,104
65,801
0
106,803
326,911
145^988
245,076
0
1,438,143
31,570
119.862
0
4
FSU
349,553
1,477,124
15,786
8,853
20,423
0
0
45,711
20,190
15,173
0
0
0
0
0
0
0
0
0
5
[ndia
2,100,342
6,120,061
50,462
26,556
64,969
0
0
248,677
169,702
43,368
0
0
0
0
0
0
0
0
0
6
Japan
19,554,283
377,778,588
10,507
87,918
1 12,976
2,286,462
0
16,9X1,103
8,338,786
2,096,483
6,424,761
27,299,221
5,557,366
29,693,833
7,868,568
348,222,337
16,882,083
16,911,496
0
7
South Korea
10,814,696
276,149,065
0
0
1,274,446
0
0
6,827,980
6,649,080
332,084
8,509,984
27,002,174
7,942j621
19,921,814
3,223,319
0
7,876,579
5,760,163
7,222,013
8
Mexico
91,546
1,002,115
26,282
4,051
1,419
0
0
17,176
19,971
0
0
0
0
0
0
0
0
0
0
9
MDE
60,561
809,433
128,747
16,825
64
0
0
29,612
68,909
0
0
0
0
0
0
0
0
0
0
10
ROW
222,910
2,548,301
124,946
28,250
11,660
0
0
106,927
157,349
0
0
0
0
0
0
0
0
0
0
11
USA
72,060
5,399,562
40,075
41,960
22,481
3,759

228,578
133,433
93,113
205±S62
286J02
67,535
74,478
62,300
2,282,075
179,026
244,213
57,366
12
WEU
1,671,002
10,292,799
63,598
36,976
67,440
0
0
313,931
327,922
100,933
0
0
0
0
0
0
0
0
0
13
EEU
27,227
378,347
3,751
6,250
16,269
0
0
60,467
35,968
20,443
0
0
0
0
0
0
0
0
0

-------
Animal
Products
Forestry
Food
Processing
Caibon
Land
Labor
OVA
IBT
0
0
0

4,222
183,272
113,934
16,316
0
0
0

2,093
357,083
222,038
81,595
0
0
0

54,142
799,554
679,664
220,007
0
0
0

4,458
520,069
571,881
26,761
0
0
0

127,206
3,060,807
1,104,168
576,065
0
0
11

0
249,831,202
172,910,645
23,415,106
3,138,767
659,449
29,467,801

0
79,690,214
81,997,961
16,629,256
0
0
0

43,216
211,910
414,768
69,004
0
0
0
0
2,032
399,324
249,913
68,500
0
0
0

7,003
1,077,713
612,276
155,569
89,463
7,539
385,457


3,266,745
1,854,112
449,375
0
0
0

66,169
4,658,161
2,332,359
454,525
0
0
0

641
155,245
86,871
21,577
Regions
Other Ag.
ETE
COilPrd.
N.GasPrd.
Coal Prd.
CokePrd.
[empty]
Elec Gen.
RefOil
Gas TAD
Wood Prd.
Chemicals
Cement
Steel
NFMctsls
OtWnd
PassTran
FrahtTran
Grains and
Oil Seeds
Animal
Products
Forestry
Food
Processing
Carbon
Land
Labor
OVA
IBT
3
Germany-
1995
86,640
3,457,558
634
4,516
20,287
3,213
0
101,439
44,963
34,813
139,166
199,421
82,241
101,350
243,140
1,708,312
35,783
214,599
0
0
0
0
0
14,206
1,942,820
1,228,755
81,880
8
Brazil
3,572,435
25,173.102
374.67U
79,282
27,335
1)
Q
1,297,676
1,806,015
165,801)
1,473,065
^_ 3,848,308
541,750
4,217,840
5,475,553
15,578,483
1,900,413
1,160,931
0
0
0
735,687
0
87,912
16,609,161
10,251,541
4,810,571
Over different value of/ this matrix shows all model aspects in summary, e.g., for time t=7 with
carbon fees imposed of $100 per ton carbon with the demands (Edy element) in the matrix cells
and the gross output produced (PRDj) values on the diagonal.
                                         10

-------
Table 3 An example of a commodity-by-commodity hybrid input-output table with gross
production as diagonal elements at time /= 7 (first 12 columns)
T=7
Region =
USA
Other Ag.
ETC
C.OilPrd.
N.Gas Prd.
Coal Prd.
Coke Prd.

Elec Gen.
RefOil
Gas T&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains and
Oil Seeds
Animal
Products
Forestry
Food
Processing
Carbon
Land rental
Labor
income
OVA
(other
value
added)
IBT
(indirect
business
taxes)
1
Agricultu
re
-136664
14926
0
0
0
0
0
921
1395
970
235!
7698
129
13
2
4545
1057
1774
161
1959
62
237
0
0
774
0
0
2
ETE
30703
1163290
0
0
0
164
0
0
98130
4202
186S7
69451
72774
13040
1462
1906
725313
72744
68802
130
1669
204
163816
0
0
118864
0
0
3
Crude
Oil
4
9339
47747
0
0
0
0
0
0
0
9
700
271
639
2
1115
187
332
0
0
0
1
803
0
253
0
0
4
Nat.
Gas
4
9778
0
-49992
0
0
0
0
0
0
10
733
284
669
2
1168
196
348
0
0
0
1
503
0
265
0
0
5
Coal
10
2237
0
0
-24772
0
0
0
0
0
72
200
97
54
13
2344
267
920
0
0
0
0
529
0
194
0
0
6
Coke
Prod.
0
142
0
0
1367
-6162
0
0
0
0
0
Q
0
0
0
0
0
0
0
0
0
0
0
0
79
0
0
7

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
Electricity
35
19293
0
0
18263
0
0
-394965
4057
62672
130
666
25
1
186
22124
2676
7978
0
0
0
1
0
0
1067
0
0
9
Oil
refining
17
153SO
92927
0
0
0
0
0
-166718
0
313
3244
617
99
2
3101
470
7220
1
1
1
117
0
0
280
0
0
10
GasT&D
20
9753
0
84584
0
0
0
0
121
-169295
68
153
33
88
2
7301
526
940
0
I
0
93
0
0
432
0
0
11
Paper,
Pulp
162
39010
0
0
299
0
0
9624
1174
3884
-344164
17056
1381
468
370
24193
2503
12108
1
13
11443
934
0
0
1890
0
0
12
Chemical
s
780
71095
0
0
803
0
0
16498
10017
14971
8283
-506413
1966
674
299
32266
3176
14045
279
352
185
2781
0
0
2241
0
0
Table 3 Extension (next 13 columns)

Region =
USA
Other Ag.
ETE
t=7

1
2
13
Cement,
elc.
41
11480
14
Iron and
Steel
30
20540
15
NF
Metals
30
16862
16
Other
Industry
18409
718420
17
Passeng
er
Transpo
it
34
37944
18
Freight
Transpo
it
50
63958
18
Grains
and Oil
Seeds
4402
17053
20
Animal
Product
s
6869
18346
21
Forestry
2164
951
22
Food
Processi
ng
25689
95919
23
Carbon


                                         11

-------
COil Prd.
N.Gas
Prd.
Coal Prd.
Coke Prd.

Elee Gen.
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains
and Oil
Seeds
Animal
Products
Forestry
Food
Processing
Carbon
Land
rental
Labor
income
OVA
(other
value
added)
mi
(indirect
business
taxes)
3
4
J
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
0
0
304
0
0
12397
182
2530
3246
4494
-132010
642
167
10069
894
7172
0
0
7
41
0
0
767
0
0
0
0
0
6187
0
6019
231
2717
370
2232
1988
-134011
2762
12595
1088
4759
0
0
0
5
0
0
685
0
0
0
0
11
0
0
3601
52
1548
488
2506
630
1133
-97752
10279
603
3753
1
1
11
10
0
0
426
0
0
0
0
223
0
0
51354
20359
17204
166054
131376
91928
134495
93059
490775
0
27452
74027
1203
830
1810
3896
0
0
34983
0
0
0
0
0
0
0
1806
84861
0
152
196
91
64
31
9792
-312487
5432
0
1
0
477
0
0
1440
0
0
0
0
0
0
0
0
25618
0
547
429
60
328
140
20536
8792
-376893
19
7
0
230
0
0
2694
0
0
0
0
0
0
0
596
1253
1497
26
7688
113
13
0
3844
137
1612
-98651
1027
0
0
0
0
57
0
0
0
0
0
0
0
2984
658
0
380
1089
13
21
0
3546
490
5152
39990
-175752
0
25403
0
0
17]
0
0
0
0
0
0
0
29
43
22
13
210
2
0
0
325
51
62
36
133
-10205
377
0
0
33
0
0
0
0
0
0
0
7662
374
4159
25639
8553
9568
15
70
46679
4551
18821
42472
158508
179
-922953
0
0
2767
0
0

























Table 3 Extension (demand columns)

Region = USA

Other Ag.
ETE
COil Prd.
N.Gas Prd.
Coal Prd.
Coke Prd.

Elec Gen.
t=7


1
2
3
4
5
6
7
8
24
Net Exports

-2911
91406
-45180
-34592
3336
-25
0
-145
25
Investments

0
160303
0
0
0
0
0
0
26
General
Government
Consumption

9143
3098190
0
0
0
0
0
61033
27
Household
Consumption

40979
7090590
0
0
0
0
0
122458
                                        12

-------
RefOil
Gas T&.D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains and Oil Seeds
Animal Products
Forestry
Food Processing
Carbon
Land rental
Labor income
OVA (other value added)
IBT (indirect business taxes)
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
0
0
-2587
6117
-4132
-8146
-3846
-119489
20012
28057
10963
-674
-571
-3165
0
0
0
-49639
0
0
0
8148
3501
0
27
640
2489800
4676
8828
0
0
0
5
0
0
0
2300210
0
5435
9229
17339
57028
3712
1192
1744
550948
54841
34058
2601
653
-8322
39418
0
0
0
0
0
6695
29207
43671
177774
10282
64
208
1045500
105119
70685
793
11270
5195
688275
0
0
-170365
-2250600
0
Table 4 An example of a commodity-by-commodity hybrid input-output table with demand
minus gross production as diagonal elements at time t=7 (first 12 columns) with carbon-
equivalent emission limits imposed
t=7
Region =
USA
Other Ag.
ETE
C.Oil Prd.
N.Gas Prd.
Coal Prd.
Coke Prd,

Elec Gen.
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Olhlnd
PassTran
FrghlTran
1
Agricu
Iture
12625
7
13759
0
0
0
0
0
862
1315
904
2168
7120
120
12
2
4194
983
163S
2
ETE
28791
11654
400
0
0
184
0
0
10059
7
4343
19003
69575
73220
13110
1470
1913
72740
1
73660
69065
3
Crude
Oil
4
9339
47778
0
0
0
0
0
0
0
9
702
272
641
2
1117
189
333
4
Nat.
Gas
4
9779
0
50025
0
0
0
0
0
0
10
735
285
671
2
1169
198
348
5
Coal
10
2419
0
0
27122
0
0
0
0
0
78
217
105
59
14
2536
290
997
6
Coke
Prod.
0
142
0
0
1287
-5933
0
0
0
0
0
0
0
0
0
0
0
0
7

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
Electricit
y
35
19527
0
0
20618
0
0
-396061
4102
59283
132
675
25
1
188
22400
2723
8085
9
Oil
refining
17
14979
92430
0
0
0
0
0
-164565
0
306
3173
604
97
2
3028
462
7060
10
Gas
T&D
19
9635
0
81394
0
0
0
0
117
-164136
67
151
33
86
2
7211
517
927
11
Paper,
Pulp
153
38612
0
0
312
0
0
9660
1180
3862
-340782
16928
1370
464
367
23974
2491
11999
12
Chemical
s
734
70246
0
0
835
0
0
16511
10035
14849
8184
-500882
1946
667
295
31913
3153
13893
                                         13

-------
Grains and
Oil Seeds
Animal
Products
Forestry
Food
Processing
Carbon
Land rental
Labor
income
OVA(olher
value
added)
raj
(indirect
business
taxes)
149
1803
57
218
244
0
719
0
0
130
166!)
204
16414
3
286
0
11921
4
0
0
0
0
0
1
729
0
25?
0
0
0
0
0
1
486
0
265
0
0
0
0
0
0
622
0
212
0
0
0
0
0
0
0
0
80
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
12
0
1084
0
0
1
1
1
115
0
0
277
0
0
0
1
0
92
63
0
429
0
0
1
13
11287
925
0
0
1872
0
0
276
347
182
2748
0
0
2221
0
0
Table 4 Extension (next 13 columns) for time t=7 with carbon-equivalent emission limits
imposed
1=7
Region -
USA
Other Ag.
E-ra
C-OilPrd.
N.Gas
Prd.
CoalPrd.
Coke Prd.

Elec Gen.
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains
and Oil
Seeds
Animal
Products
Forestry
Food
Processing
13
Cement,
etc.
39
11417
0
0
320
0
0
12464
183
2528
3226
4480
-130812
639
167
10024
893
7141
0
0
7
41
14
Iron and
Steel
28
20427
0
0
0
S959
0
5968
224
2617
367
2217
1971
-132727
2745
12531
1069
4720
0
0
0
5
15
NF
Metals
28
16745
0
0
10
0
0
3565
50
1490
483
2486
623
1121
-96985
10211
591
3717
1
1
10
10
16
Other
Industry
17221
711806
0
0
220
0
0
51211
20101
16855
164319
130298
91066
133175
92245
-4864610
27146
73333
1190
821
1786
3859
17
Passen
g=r
Transp
ort
32
38172
0
0
0
0
0
1811
82974
0
152
197
91
64
31
9854
31054
2
5449
0
1
0
479
18
Freight
Transport
47
63669
0
0
0
0
0
0
25581
0
544
427
60
327
139
20461
8758
-375374
19
7
0
229
18
Grains
and
Oil
Seeds
4138
16790
0
0
0
0
0
595
1258
1487
25
7593
111
13
0
3789
135
1589
96981
1010
0
I)
20
Animal
Products
6407
17951
0
0
0
0
0
2962
655
0
372
1069
13
20
0
3474
482
5049
39132
-171678
0
24864
21
Forestry
1907
878
0
0
0
0
0
27
41
20
12
195
2
0 "1
0
300
48
57
33
122
-9330
348
22
Food
Processing
23965
94013
0
0
0
0
0
7604
371
4090
25127
8403
9396
!5
68
45796
4482
18468
41615
155094
175
-903224
23
Carbon
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
                                         14

-------
Carbon
Land
rental
Labor
income
OVA
(other
value
added)
1BT
(indirect
business
taxes)
0
0
770


0


0

0
0
684


0


0

0
0
424


0


0

0
0
34747


0


0

0
0
1453


0


0

0
0
2686


0


0

0
0
56


0


0

0
0
168


0


0

0
0
31


0


0

0
0
2721


0


0

-2441
0
0


0


0

Table 4 Extension (demand columns) for time f=7 with carbon-equivalent emission limits
imposed
t=7
Region <= USA

Other Ag.
ETE
C.Oil Prd.
N.Gas Prd.
Coal Prd.
Coke Prd.

Elec Gen.
RefOil
Gas TAD
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains and Oil Seeds
Animal Products
Fores try
Food Processing
Carbon
Land rental
Labor income
OVA (other value added)
IBT (indirect business taxes)
24
Net Exports

-2911
173518
-44653
-31369
3336
-25
0
-145
0
0
-2587
6117
-4132
-8146
-3846
-119489
20012
28057
10963
-674
-571
-3165
0
0
0
1171
0
25
Investments

0
157406
0
0
0
0
0
0
0
0
8000
3438
0
27
628
2444790
4592
8669
0
0
0
5
0
0
0
2268460
0
26
General
Government
Consumption

9540
3232620
0
0
0
0
0
63681
5671
9629
18091
59503
3873
1244
1819
574853
57220
35536
2714
682
-8683
4U28
0
0
0
0
0
27
Household
Consumption

36050
6910570
0
0
0
0
0
118690
6366
27519
42120
171538
9869
61
202
1023080
100450
69249
757
10780
4873
667171
0
0
-170365
-2269520
0
                                         15

-------
Table 5 Variable values at the end of the last iteration of the market solving algorithms when
carbon policies are based on carbon emission limits
For t=7 when carbon
policies are based on
carbon equivalent
emissions and carbon
fees of $100 ton C
Region = USA
Other Ag.
COilPrd.
K.Gas Prd.
Coal Prd.
Coke Prd.
[empty 1
Elec Gen.
RefOil
Gas TAD
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains and Oil Seeds
Animal Products
Forestry
Food Processing
Carbon market for fixed
carbon fee of J 100 per
ton carbon

Land rental
Labor income
OVA (other value
added)
Mrk
(m)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
19
16
17
18
19
20
21
22
23
24
25
26
(J)
1
3
4
5
6
7
8
9
10
11
12
13
14
IS
16
17
18
19
20
21
22
23
24
25
26
2
MrkEd
=
Excess
Demand
0.02328
0.00000
0.00000
0.00000
0.00000
0.00000
0.00003
0.00000
0.00001
0.14703
0.29714
0.01484
0.02649
0.03776
6.44723
0.92306
0.55866
0.05353
-0.04671
-0.21275
-2.90778
0.00081
0.00000
-0.00001
71.01880
0.00000
MrkPrd
(note
energy in
ExaJoulcs)
138868.0
20.8
21.8
27.8
1.2
0.0
20.7
41.9
36.9
439236.0
616838.0
143155.0
153190.0
128960.0
5948400.0
328508.0
425260.0
99969.7
196859.0
9553.9
1038580.0
2440.6
0.0
170365.0
2269550.0
14169100.0
P,
0.91327
1.00000
1.00000
0.89636
2.17083
1.00000
1.38707
1.72712
1.59899
0.83425
0.85995
0.91768
0.90411
0.76174
0.85386
1.00436 1
0.95212
0.84195
0.67687
0.84770
0.72144
165.66
0.00000
60,62
0.08938
1.00000
SalesV
(note
energy in
monetary
values)
138868.0
47777.9
50024.8
27122.8
5933.4
0.0
425025.0
176722.0
176302.0
439236.0
616838.0
143155.0
153190.0
128960.0
5948400.0
328508.0
425260.0
99969.7
196859.0
9553.9
1038580.0
2440.6
0.0
170365.0
2269550.0
14169100.0
Markup of Prices

After solving for market prices, as described in "The solution process" (see Chapter ten of the
documentation) and illustrated in Table 5, the market prices are "marked up," for prices paid
(Equation 9) and prices received (Equation 13). The marked-up prices are part of the calculations
of expected prices paid and received (Equations 15 and 16). The marked-up prices are also part
of the calculations of the technical change coefficients when imposing changes in elasticity
(Equations 34 and 36), the Leontief technical change coefficients (Equations 39, 41,44-45), the
expected profit rates (Equations 55-57), profits (Equations 58 and 59 for old vintages; Equations
                                           16


-------
74 and 75 for new vintages), demands1 (Equation 61 for old vintages; Equations 76 for new
vintages) and gross production (Equation 63 for old vintages; Equation 76 for new vintages). In
addition, marked-up prices are used in the calculations of additional costs upon demands (e.g.,
Equations 82 and 83). The necessary information for the markup of prices is listed below and
described in " Prices and expected prices" (see Chapter four of the documentation).

Table 6 Initial and future market prices
Supply
sectors
(i)
1
2
3
4-22
23
24
25
26
Region = USA
Period
Ag
ETE
CrudeOil
Etc.
Carbon
Land
Labor
Capital
0
1
1
1
1
1
0
?^%
0.06
1





0
25.96
0.06
2
1
1
1
1
1
0
25.96
0.06
3





0
25.96
0.06
4
1
1
1
1
1
0
25.96
0.06
5





0
25.96
0.06
6
1
1
1
1
1
0
25.96
0.06
7
1
1
1
1
1
0
25.96
0.06
8
1
1
1
1
I
0
25.96
0.06
9
1
1
1
1
1
0
7596
006
10
1
1
1
I
1
0
25.96
0.06
11





0
25.96
0.06
12
1
1
1
1
1
0
?S%
0.06
Extended through
additional periods
if necessary








Alternatively, crude oil prices are set exogenously:
3 fcradeOil
1 J0.7068 |0.7682 |0.8118 |o.8367 |0.8636 |0.8974 |0.9325 |0.9691 |l.007 |l.0464 |l.0874 |l.!3
Table 7 Price overrides (IPfix)
Region =
USA
Start Period
Ag
ETE
CrudeOil
NatGas
Coal
Coke
Steel
Elect
RefOit
GasTD
Indll
Indl2
bid 13
Indl4
IndlS
Indl6
Indl7
IndlS
Ind)9
T:
Exogenous
F:
Endogenous
1
F
T
T
T
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
1 Demands and gross production based on the Leontief production function are price-independent, except
throught the Leontief technical scale coefficients (see Equations 64 and 78 for demands and Equations 65
and 79 for gross production).
                                             17

-------
Ind20
Ind21
Ind22
Carbon
Land
Labor
Capital
F
F
F
F
T
F
F
Table 8 Production-sector-specific indirect business taxes
Tax Rates on Production (Indirect Business Taxes) Region = USA
Production Sectors
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
MSTART (t=0)
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
TXH3T(IS,L)
0.016604
0.071580
0.054166
0054166
0.112005
0.029087
0
0.057385
0.054049
0.050808
0.010144
0.013186
0.011498
0.011895
0.010967
0.011445
0.032355
0.025316
0.040286
0.013398
0.046201
0.024134
Table 9 Transportation cost changes for each supply sector
Region =
USA


Sector
Subsector
Ag
ETE
CrudeOil
NatGas
Coal
Etc.
Ind22
Carbon
Land
Labor
For each supply sector
Transportation Costs
TRI
equals 0 for
all
0
0
0
0
0
0
0
0
0
0
0
0
TRZ
equals 0 for all
0
0
0
0
0
0
0
0
0
0
0
0
TTRZ
equals 20 for all
20
20
20
20
20
20
20

20
20
20
20
                                             18

-------
[ Capitol    | 0
JJL
20
 Table  10 Additive taxes, proportional tax rates and transportation-export-import cost multipliers
Region = USA

Region






Input
1
2
3
etc
26

Start Period
0
0
0
0
0
For each supply sector
Proportional Tax Rates
equals one for all
For each supply
rxpROjjH





Transportation Cost
Multiplier
For each supply sector,
nit also used for each
>roduction sector
feXIMPORTi
1
1
1
1
1
Additive Taxes equals 0 foi
all
For each supply
rXADDu.B
0
0
0
0
0
 Table 11 Adjustments to prices
Production (sub)
sectors (j jj)



1
2
3
4
5
6
7
8.1
8.2
8.3
8.4
8.5
8.6
9
10
11
12
13
14
15
16
17
18

Region =
USA
Supply
Sectors >
Other Ag.
ETE
C.Oil Prd.
N.Gas Prd.
Coal Prd.
Coke Prd.
empty
ElecOil
ElecGas
ElecCoal
ElecBio
ElecNuc
ElecHydro
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Olhlnd
PassTran
FrghtTran
Adjustment on Prices for
supply sectors 1:22
AD

1
1






1
1
1
1
1
1
1
1
1
1
1
1
1
1
I
1
ADJZ










1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
TADJZ


20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
Etc 2:22


























Adjustment on Prices for
supply sector 23
AD

23
1
1
1
1
1
1
1
1
1
1













ADJZ

























FADJZ


20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
For
land:
labor


























Adjustment on Price: for IR
Interest rates
(see Equation 13}
(see also below for alternative
values)
AD

26
0.184440
0.013406
-0.037437
0,036857
0.104267
0.246819
0.000000
1.326267
0.265579
0.034936
0
0.066597
0.089439
0.056189
0.027453
0.069210
0.152835
0.161308
0.012773
-0.005411
0.20443 1
0.203327
0.009212
ADJZ


0.184
0.060
-0.037
0.037
0.104
0.247
0.000
15.000
0.204
0.100
0.000
0.064
0.064
0.056
0.027
0.069
0.153
0.161
0.013
-0.010
0.204
0.203
0.009
TADJZ


20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
GO
20
20
Adjustment on Prices for IR
Retrofit
AD

27
0
0
0
0
0
0
0
0
0
0
P
0
0
0
0
0
0
0
0
0
0
0
0
ADJZ


0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
TADJZ


20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
                                              19

-------
19
20
21
22

26
27
Grains and
Oil Seeds
Animal
Products
Forestry
Pood
Processing

Capital
interest
rates
TxIBT
1
1
1
1

I
1
1
1
1
1

1
1
20
20
20
20

20
20







1
1
1
1

1
1
1
1
1
1

1
1
20
20
20
20

20
20







0.088871
-0.009659
0.072629
0.322878

0
0
0.089
-0.010
0.073
0.323

0
0
20
20
20
20

20
20
0
0
0
0

0
0
0
0
0
0

0
0
20
20
20
20

20
20
Conversion Tables
Information in the next three tables (12-14) are necessary for the conversion of energy units to
monetary units.

Table 12 Emission coefficients and GWP

Fn

Oil combined
Gas combined
Coal combined
EMC
(millions ton
C/EJ)
20.43
13.65
24.08

GWP

1
1
t
Table 13 Energy conversion factors (exajoules per million 1990 dollars)
ENERGY
Region
Ag
ETE
C.Oil Prd.
N.Gas Prd.
Coal Prd.
Coke Prd.
Empty
Electricity
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMclals
Othlnd
PassTran
FrghtTran
Grains and Oil Seeds
Animal Products

Sector
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
PRCONVRTr.i

1
1
0.00043592
0.00043592
0.00102535
0.00020574
1
0.00004878
0.00023709
0.00020927
1
1
1
1
1
1
1
1
1
1
                                          20

-------
Forestry
Food Processing
21
22
1
1
Table 14 Exchange rates
Exchange rate
Region
11
3
national currency per US dollar
EXCHRATE (National currency/US dollar)
1
4.783
Technical Change Tables

For each region, technical change parameters for each sector/, each subsector;;, and each time
period t determine the efficiency improvements in energy production, energy transformation (e.g.,
oil refining, gas processing, coal and electricity generation), industry, transportation and
agriculture.

An example of technical change parameters for one production sector is listed in Table 15. The
parameters are used as the base value for a multiplier (which changes over time; see Equations
19-21,29, 43, 187 and 222) of the base year's technical scale coefficients («y) extracted from an
input-output table (Table 1 is the input-output table from which the «//s are extracted). Thus,
technical change parameters are inputs for modifications over time of the technical scale
coefficients for inputs to production (that is, to capital (KA), labor (L), energy (E), industry (M)
(manufacturing), land (land), oil refining, gas production and processing, coal production, and
electricity towards the production processes,/ and//, for each region / and each time period /.

Technical change parameters also determine the efficiency of labor productivity, land
productivity, and capital (see Table 15).

Tables 16 and 17 show technical change parameters for household and government fuel
consumption.

Table 15 Technical change parameters for production sector 2, the Everything Else sector, for
inputs of capital KA, labor L, energy production E, industry M (manufacturing), land land, oil
refining, gas processing, coal and electricity
Region = USA
1
Period t
Sector, e.g.:
Subsector, e.g.:
Parmname
TECHNN (KA):
capital
TECHNN (L):
labor
TECHNN (E):



1
2
3
0
2
1

0
0
0
1
2
1

0
0.03
0
2
2
1

0
0.025
0
3
2
1

0
0.005
0
4
2
1

0
0.015
0
5
2
1

0
0.02
0
6
2
1

0
0.02
0
7
2
1

0
0.02
0
g
2
1

0
0.015
0
9
2
1

0
0.015
0
10
2
1

0
0.015
0
11
2
1

0
0.015
0
12
2
1

0
0.015
0
                                           21

-------
energy
TECHNN (M);
manufacturing
TECHNN
(land)
TECHNN
(RefOil)
TECHNN
(RefGas)
TECHNN
(Coal)
TECHNN
(Electricity)

4
5
6
7
8
9

0
0
0
0
0
0

0.01
0.01
0.03
0.02
0.02
0.005

0.01
0.01
0.025
0.02
0.02
0.005

0.01
0.01
0.01
0.02
0.02
(1.005

0.01
0.01
0.005
0.02
0.02
0.005

0.01
0.01
0.005
0.012
0.02
0.005

0.01
0.01
0.005
0.012
0.02
0.005

0.01
0.01
0.005
0.012
0.02
0.005

0.01
0.01
0.005
0.012
0.02
0.005

0.01
0.0 1
0.005
0.012
0.02
0.005

0.01
0.01
0.005
0.012
0.02
0.005

0.01
0.01
0.005
0.012
0.02
0.005

0.01
0.01
0.005
0.012
0.02
0.005
Table 16 Technical change parameters for household fuel use
Household
AEE1 by fuel
HHAEEI
Region^ 1 1
Period
RefOil
Gas
Coal
Elec
Period
0
0
0
0
0
1
0.01
0.012
0
0.005
2
0.01
0.012
0
0.005
3
0.01
0.012
0
0.005
4
0.01
0.012
0
0.005
5
0.01
0.012
0
0.005
6
0.01
0.012
0
0.005
7
0.01
0.012
0
0.005
8
0.01
0.012
0
0.005
9
0.01
0.012
0
0.005
10
0.01
0.012
0
0.005
11
0.01
0.012
0
0.005
12
0.01
0.012
0
0.005
Table 17 Technical change parameters for government fuel use
Government
AEEIbyfuel
GVAEE1
Regkm=ll
Period
RefOil
Gas
Coal
Elec
Period
0
0
0
0
0
1
0.01
0.012
0
0.005
2
0.01
0.012
0
0.005
3
0.01
0.012
0
0.005
4
0.01
0.012
0
0.005
5
0.01
0.012
0
0.005
6
0.01
0.012
0
0.005
7
0.01
0.012
0
0.005
8
0.01
0.012
0
0.005
9
0.01
0.012
0
0.005
10
0.0 1
0.012
0
0.005
11
0.01
0.012
0
0.005
12
0.01
0.012
0
0.005
Table 18 lists the elasticities of substitution for the reference case. In the headings of Tables 19
and 20 references are made to the equations describing the technical scale coefficient
calculations. Tables 19, 20, and 21 show example outputs of the technical scale transformation
processes captured. These transformations are dependent on the elasticities of substitution in the
CES production function.

Table 18 Elasticities of substitution for the production sectors
Region = USA
Column headings of the
production sectors
I
Agriculture
ETE
Crude Oil
Nat Gas
Coal
Coke Prod.
1
2
3
4
5
6
sigma 1,
Long-run
elasticities
0.3
0.4
0.276
0.276
0.276
0.1
sigma2,
Short-run
elasticities
0.
0.
0.
0.
0.
0.
dtol, pi is
based on
sigma 1
p = {a-l)/o
-2.333
-1.5
-2.623
-2.623
-2.623
-9
mul.fii is
based on
sigma 1
H=p/(l-p)
-0.7
-0.6
-0.724
-0.724
-0.724
-0.9
rho2, p2 is
based on
sigma2
-9
-9
-9
-9
-9
-9
mu2, (i2 is
based on
sigma2
0.111
0.111
0.111
0.111
0.111
0.111
                                            22

-------
Empty
ElecOil
ElecGas
ElccCoa!
[ElecBio]
ElecNuc
ElecHydro
Oil refining
GasT&D
Paper, Pulp
Chemicals
Cement, etc.
Iron and Steel
NFMeUls
Other
Industry
Passenger
Transport
Freight
Transport
Grains and
Oil Seeds
Animal
Products
Forestry
Food
Processing
7
8.1
8.2
8.3
8.4
8.5
8.6
9
10
11
12
13
14
15
16
17
18
19
20
21
22
0.276
0.051
0.051
0.051
0.3
0.1
0.1
0.1
0.1
0.276
0.276
0.276
0.276
0.276
0.276
0.276
0.276
0.276
0.276
0.276
0.276
0.1
0
0
0
0.3
0
0
0
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
-2.623
-9
-9
-9
-2.333
-9
-9
-9
-9
-2.623
-2.623
-2.623
-2.623
-2.623
-2.623
-2.623
-2.623
-2.623
-2.623
-2.623
-2.623
-0.724
-0.9
-0.9
-0.9
-0.7
-0.9
-0.9
-0.9
-0.9
-0.724
-0.724
-0.724
-0.724
-0.724
-0.724
-0.724
-0.724
-0.724
-0.724
-0.724
-0.724
-9



-2.333



-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
0.111
0
0
0
0.429
0
0
0
0.1 11
0.1 11
0.111
0.111
0.111
0.111
0.111
0.111
0.111
0.111
0.111
0.111
0.111
Table 19 Example output of the vintaged alpha transformations,
sector 1 and production sector 1)
                    i, over time (for supply
l-
0:1
2
4.
0
i
2
3
4
5
6
7
8
9
10
11
12
Equation
28 results
0.000769
0.000685
0.000610
0.000543
0.000483
0.000430
0.000383
0.000341
0.000304
0.000271
0.000241
0.000215
0.000191
Equation 3 1 results; used in
operating new capital, I- 1 : 1 2, in
the Z equation (see Equations 72,
74, 76 and 77) and in the
expected profit rate calculations
in the Z equation (see Equation
55 and 57) and consequently in
the new investment Z part of the
equation (see Equation 133)
at t=0forv=0
at t=lforv=l
at t=2forv=2
at t=3 for v=3
at t=4 for v=4
at t=5 for v=5
at =6 for v=6
at =7forv=7
at =8forv=8
at =9forv=9
at = 10forv=10
at =llforv=ll
at =12forv=12
0.116363
0.112380
0.108533
0.104819
0.101231
0.097766
0.094420
0.091188
0.088067
0.085053
0.082142
0.079331
0.076615
Equation 37 results; used in Z in demand function; for vintages (v=t-3:t-
1 ) short-run elasticities override long-run elasticities when operating old
vintages (see Equations 55, 58, 61 and 63)
at t=Oforv=-3:-l
at t= 1 for v—2:0; at t=2 for v=-l :0; at t=3 for v=0
at t=2 forv=l; at 1=3 for v=l; att=4 forv=l
at t=3 for v=2; at [=4 for v=2; at t=5 for v=2
at t=4 for v=3; at t=5 for v=3; at (=6 for v=3
at 1=5 for v=4; at t=6 for v=4; at t=7 for v=4
at 1=6 forv=5; att=7forv=5;att=8 forv=5
at t=7 for v=6; at t=8 for v=6; at t=9 for v=6
at t=8 for v=7; at t=9 for v=7; at t= 10 for v=7
at t=9 for v=8; at t= 10 for v=8; at t= 1 1 for v=8
at t=10forv=9; att=ll forv=9; at t=12forv=9
at t= 1 1 for v= 10; at 1= 12 for v= 10;
at t=12forv=ll
0.116363
0.112010
0.108177
0.104474
0.100898
0.097445
0.0941 10
0.090889
0.087778
0.084774
0.081872
0.079070
0.076364
23

-------
Table 20 Example output of capital stock technical coefficient transformations for all production
sectors for one region and one point in time

Other Ag.
ETE
C.Oil Prd.
N.Gas Prd.
Coal Prd,
Coke Prd.

ElecGen





RefOil
GssT&D
Wood Prd.
Chemicals
Cement
Steel
NFMeUU
Othlnd
PassTran
FrghtTran
Grains and Oil Seeds
Animal Products
Forestry
Food Process ins

1
2
3
4
5
6
7
8.1=8
8.2-9
8.3=10
8.4=11
8.5=12
8.6=13
9 = 14
10=15
11=16
12=17
13=1S
14=19
15 =20
16=21
17=22
18=23
19=24
20=25
21 =26
22=27
cir capital co»t,jjj,y
= o-t-jsji/aO"
Results from
Equation 30
0.6534
0.4903
48.9650
10.9379
0.5958
0.0002
0
95
119
2834
0
11704
11704
0.0004
22.2536
0.1954
0.2340
0.0792
0.0339
0.0329
0.0283
0.0024
0.5602
5.7653
0.2745
1.0939
0.0174

Results from Equation
31
0.8804
0.9020
2.9279
1.9359
0.8689
0.4610
0.0000
1.7814
2.1224
2.6925
0.0000
2.8337
2.6010
0.4575
1.3659
0.6372
0.6700
0.4960
0.4008
0.3899
0.3742
0.1901
0.8529
1.6227
0.6999
1.0253
0.3270
ar capital eort.m.,
Results from
Equation 34
0.653953
0.772669
49.024200
10.951200
0601115
0.000434
82546
2559520
271993000
33388
14171
0.000402
22.596700
0.195348
0.234395
0.078838
0.036424
0.032947
0.028394
0.002444
0.561938
5.777320
0,274525
1.094720
0.017428
0.653953
0.772669
exesti=capitalcostjjlj,v=
a^-costs^'*"
Results from
Equation 37
1.1858
1.7985
4.7324
2.8297
1.1776
0.4610
0.0000
1.7849
2.1271
2.6979
0.0000
3.1234
2.8532
0.5066
1.3659
0.9068
0.8894
0.6548
0.6074
0.6053
0.4810
0.2437
1.2955
2.2552
1.0927
1.4453
0.3967
Table 21 Example output of the Leontief coefficients for the fixed factor production subsectors of
electricity production and the refined oil production sectors for one region at one point in time for
the first supply sector (agriculture; /=/) and for the 26th supply sector (capital; /=2<5)
Production (subsectors
;
8.
1=8
8.2=9
8.3 =10
8.4=11
8.5 =12
8.6=13
9=14
ElecOil
ElecGas
ElecCoal
ElecBio
ElecNuc
ElecHydro
RefOil
^ijji.y
Equation 40
1






Vljjj.y
Results from Equation
41 for supply sector 1
0.00008063
0.00007521
0.00012472

0.00014823
0.00014823
0.00011989
>*-14-<^,ilJoji,v
Results from Equation
42 for capital
1.9725
2.3812
2.9777

3.4426
3.1299
0.5609
                                            24

-------
                 Data Tables for the Operation of Vintaged Capital

                 Each capital stock has a specified lifetime of 4 time periods or 20 years, the so-called nameplate
                 lifetime of a technology in the reference case for the USA. At the end of the capital stock lifetime,
                 the capital is retired and no longer used. Capital stocks are operated across their lifetime with no
                 decrease in technical efficiency (the alpha scale or technical scale parameters are constant over
                 the life (vintages) of the producing sector). Four vintages are operating simultaneously at each
                 point in time representing three operating old vintage technologies and one new technology.
                 Initial capital stock is input (see Table 22 for the reference case). Table 23 shows the technology
                 characteristics of vintaged capital for the reference case.

                 Table 22 Initial values of prior capital stock
Column
headings
of the
production
sectors
Production
Sectors
Other Ag.
ETE
C.Oil Prd.
N.Gas
Prd
Coal Prd.
Coke Prd.
Empty
ElecOil
ElecGas
ElecCoal
ElecBio
ElecNuc
ElecHydro
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMetab
Othlnd
PassTran
FrghtTran
Grains and
Oil Seeds
Animal
Products
Forestry
Food
Processing
Production
sectors
1
(Sub)
sector
I
2
3
4
5
6
7
8.1
8.2
8.3
8.4
8.5
8.6
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Prior Capital Stocks
KAPRIOR:
IVIN (-3)
22966
2831665
57692
34113
7332
430
0
5890
17206
76623
0
27571
12314
17325
36734
52849
69209
12010
13016
11214
293112.20
1 1605.32
92856.04
36102.39
29163.57
3058.80
39498.18
KAPRIOR:
IVIN (-2)
24138
2976109
60635
35853
7706
451
0
6190
18084
80531
0
28978
12942
18209
38608
55545
72739
12623
13680
11786
308063.90
12197.31
97592.63
37943.97
30651.20
3214.83
41512.98
KAPRIOR:
IVIN(-l)
25369
3127920
63728
37682
8099
474
0
6506
19006
84639
0
30456
13602
19138
40577
58378
76450
13267
14378
12387
323778.30
12819.50
102570.80
39879.50
32214.72
3378.82
43630.56
KAPRIOR:
IVIN (0)
26663
3287476
66979
39604
8512
499
0
6838
19976
88956
0
32009
14296
20114
42647
61356
80349
13943
15111
13019
340294.20
13473.42
107803.00
41913.75
33858.00
3551.17
45856.16
                                                            25
o

-------
Table 23 Technology characteristics
NTECHCHAR
Region












Sector
1
2
3
4
5
Etc
g
Etc
19
20
21
22
Subsector
1
1
1
1
1

5

1
1
1
1
NTECH1
nameplate
lifetime of the
technology
4
4
4
4
4

4

4
4
4
4
NTECH2
number of
periods
between initial
investment
and first
operation
0
0
0
0
0

0

0
0
0
0
NTECH3
maximum
allowable
lifetime (np)
4
4
4
4
4

4

4
4
4
4
NTECH4
lifetime of the
technology
renovation
2
2
2
2
2

2

2
2
2
2
NTECH5
number of
periods until
initial
investment
0
0
a
[1
0

0

0
0
0
0
NTECH6
period in
which
investment is
no longer
allowed
50
50
50
50
50

50

50
50
50
50
Carbon Policies and Emissions
Essential information for carbon emission calculations can be found in Table 24, which is an
extension of Table 12. Table 25 lists which gases EMC3 may be emitted in the different
production sectors processes (emission activities), the accompanying sector index EMC4, the
values for the conversion of energy units to monetary units PRconvrt (as in Table 13), and policy
switches (EMC2 and EMCS).

Table 24 Global warming potential of different gases

Region
11
11
11
11
11
11
Gas
1
2
3
4
5
6

CO2
CH,
NjO
MFCs
PFCs
SF4

Carbon dioxide
Methane
Nitrous oxide
Hydrofluorocarbons
Perfluoro carbons
Sulfurhexafluoride
GWP
1990
1
5.727273
84.54545
1982.668
1864.123
6518.182
                                         26

-------
Table 25 Greenhouse gas emission coefficients and related parameters
Region
11
11
11
11
11
11
11
11
11
li
11
11
li
11
11
11
It
11
11
11
11
11
11
Production
sector
index (j)
(EMC4)
indicator
3
4
5
5
1
10
3
2
1
1
2
2
2
2
2
1
2
1
2
2
2
8
2
PRconvrtj
0.00043592
0.00043592
0.00102535
0.00102535
1
0.00020927
0.00043592
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0.0004970
1
Emission activity
sector
Crude oil production
Natural gas
production
Coal production
Coal production
Agriculture
Distributed gas
production
Crude oil production
Everything Else
Agriculture
Agriculture
Everything Else
Everything Else
Everything Else
Everything Else
Everything Else
Agriculture
Everything Else
Agriculture
Everything Else
Everything Else
Everything Else
Electricity
generation/distribution
Everything Else
Index (ix)
(Nsource)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
Emission activity
process
Oil comb
Gas comb
Coalcomb
CoalPr
Enteric
NatGasSys
OilSys
Landfills
Manure
OlhAgMeth
OthNonAgMeth
Wastewater
HFC23
ODSSnb
IndProcaN
ManurcN
MobileN
SoilN
SlalionaryN
Aluminum
Semiconductor
ElecDist
Mg
EMCi,
(EMC1)
16.26676
13.53174
24.24744
4.18
5.71
5.77
1.29
10.2
2.61
0.444
0.707
0.15
0.004988
0.000157
0.117
0.04
0.163
0.891
0.044
0.002897
0.000429
0.000859
0.000261
Gas logic
(EMC2)
0
0
0
1


















1
Gas type
(EMC3)
1
1
1
2
2
2
2
2
2
2
2
2
4
4
3
3
3
3
3
5
5
6
6
Switch
(EMCS)
if--l then
not a GHG;
if =1 then
include in
GHG
calculations
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Cost curves can be defined for a variable number of points in each curve. The carbon price (level)
relates to a corresponding percent reduction in emissions. The model finds the percentage
reduction in emissions through linear interpolations based on the carbon fee. Note that all
nitrogen sources share a common curve, as do all high GWP sources2. Additional carbon policy
switches are listed in Table 26. Table 27 lists the data used in the carbon policy cases for which
results are illustrated.
2 See DeAngelo et al. (2004); Delhotal et al. (2004); Schaefer et al. (2004); Scheele and Kruger (2004); references can be found in the
documentation
                                             27

-------
Table 26 Cost curves for calculations of the carbon-equivalent emissions in relation to carbon
prices
Emission activity sector
Coal production

Agriculture/
Enteric Fermentation

Distributed gas production

Crude oil production

Everything Else/
Land fills

Agriculture/
Manure

Agriculture/
Other Ag Methane

Everything Else/
Other non-Ac Methane

Everything Else/
Waste water

Everything Else/
HFC23

Everything Else/
ODSSub

Everything Else/
Industrial N

Agriculture/
Manure N

Everything Else/
Mobile N

Agriculture/
SoilN

Everything Else/
Stationary N
Index
tixj
4

5

6

7

it

9

10

11

12

13

14

15

16

17

IS

19
Region
level
cc
level
cc
level
cc
leve!
cc
level
cc
level
cc
level
cc
leve)
cc
level
cc
level
cc
level
cc
level
cc
level
cc
level
cc
level
cc
level
level 1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
level 2
5
0.36786
5
0.2
5
0.3
5
0.2
1
0.2
5
0.14
5
0.2
5
0.2
5
0.2
5
0.19096
5
0.19096
5
0.00948
5
0.00948
5
0.00948
5
0.00948
5
level 3
10
0.42857
20
0.25
25
0.35
20
0.25
10
0.3
20
0.2
20
0.25
20
0.25
20
0.25
20
0.36765
20
0.36765
20
0.21124
20
0.21124
20
0.21124
20
0.21 124
20
level 4
20
0.46786
40
0.32
65
0.4
40
0.32
20
0.38
40
0.38
40
0.32
40
0.32
40
0.32
40
0.52553
40
0.52553
40
0.21134
40
0.21134
40
0.21134
40
0.21134
40
level 5
30
0.71429
100
0.38
140
0.5
100
0.38
40
0.42
75
0.61
100
0.38
100
0.38
100
0.38
80
0.52563
80
0.52563
80
0.21592
80
0.21592
80
0.21592
80
0.21592
80
level 6


200
0.4
220
0.55
200
0.4


150
0.69
200
0.4
200
0.4
200
0.4
150
0.56674
150
0.56674
ISO
0.21602
150
0.21602
150
0.21602
150
0.21602
ISO
level 7


















200
0.56684
200
0.56684
200
0.22489
200
0.22489
200
0.22489
200
0.22489
200
                                            28

-------

Everything Else/
Aluminum

Everything Else/
Semiconductor

Electricity
generation/distribution

Everything Else/
Magnesium


20

21

22

23

cc
level
cc
level
cc
level
cc
level
cc
0
0
0
0
0
0
0
0
0
0.00948
5
0.19096
5
0.19096
5
0.19096
5
0.19096
0.21124
20
0.36765
20
0.36765
20
0.3676S
20
0.36765
0.21134
40
0.52553
40
0.52553
40
0.52553
40
0.52553
0.21592
80
0.52563
80
0.52563
80
0.52563
80
0.52563
0.21602
150
0.56674
150
0.56674
150
0.56674
150
0.56674
0.22489
200
0.56684
200
0.56684
200
0.56684
200
0.56684
Table 27 Mitigation data
SGM Emissions mitigating technologies input tables
N GAS PROD AND PROC
Em Driver
7






Level
1
2
3
4
5
6
7
Mil. Pet.
0.0350012
0.1389745
0.2359669
0.3107168
0.4023341
0.4399916
0.4433727

Capital
0.0000797
0.0008593
0.0027236
0.0056303
0.0125880
0.0139066
0.0144586
N GAS TRANSMISSION AND DIST
Em Driver
26






COAL
Em Driver
8






Level
1
2
3
4
5
6
7

Level
1
2
3
4
5
6
7
Mil. Pet.
0.2348281
0.3540385
0.4241136
0.4838602
0.5533318
0.5557796
0.5568887

Mil. Pet.
0.1009039
0.2072688
0.3045475
0.4017072
0.4806272
0.5121412
0.5230969
Capital
0.0001607
0.0004834
0.0013729
0.0030017
0.0060539
0.0061375
0.0061892

Capital
0.0005048
0.0011051
0.0023189
0.0033485
0.0048686
0.0062200
^0.0070969

O andM cons
Cost
0.0000054
0.0000084
0.0001607
0.0004339
0.0006406
0.0013849
0.0014050
Cost
0
0
0
0
0
0
0
O andM costs
Cost
0.0000729
0.0002228
0.0003638
0.0005423
0.0006181
0.0006468
0.0006654
Cost
0
0
0
0
0
0
0
O andM costs
Cost
0.0005250
0.0011844
0.0019252
0.0035550
0.0056830
0.0077929
0.0092047
Cost
0.0000281
0.0000891
0.0001596
0.0003475
0.0005496
0.0007098
0.0008499
Tables 28 - 30 summarize the carbon policy option impacts through the recycling of revenues
obtained from the carbon fees and, if active, from carbon permit trade. The details of revenue
recycling are described in the household and government sections in this document.
                                           29

-------
Table 28 Descriptions of switches and variables partaking in carbon policy

CarbFeePi


CarbFeeP2






CsibFceP3







CaAFeeP,








CarbFeePj

CarbFeePj

Carbon policy options
Activate carbon policy:
0 for no policy: no carbon price
1 for policy: some kind of carbon pricing
Activate carbon pricing:
0 for a fixed carbon price
enter "0" under policy (PolType),
enter atari period, and
enter carbon prices by period
1 for a variable carbon price to be set to reach emissions goal
internal target (enter year for reference period: CarbFeePj)
Determine emission limits bated on COj or Carbon equivalent basis:
For user-defined target, enter"!" under Policy,
0 only CO2 emissions wed to compute limit
enter start period (CarbFee<) and
enter targets (CaibFeeO by period
1 all Carbon-equivalent emissions used to compute limit
enter start period (CarbFeej) and
enter targets (CaibFee,) by period
Set details of the emission limits:
0 external carbon emissions limit
enter carbon emission limits by period
enter under policy a CarbFeePj value of 0 or 1 : CO2 or Ce,
1 internal caibon emissions limit
enter reference year for target (e.g., "1990")
enter under policy a CarbFeeP3 value of 0 or 1 : CO2 or Ce,
enter start period (CarbFee() and
enter fraction of reference period emissions allowed in each period (eg, "0.95" for 5% reduction from
reference period)
Reference period for internal target for carbon emission limit (e.g., 2005 for year => year-1990yS = n)
Start period for policy
enter initial period for carbon fee to apply (must be after reference period; e.g., 3 for 2005)
Table 29 Policy options, carbon prices and emission limits











PolType (for explanation see descriptions above
and Table 28)
CarbFeePj = Carbon dioxide or carbon-
equivalent emissions
CarbFeePs = START PERIOD
Alternative 1
Reference
case








0

Q

0
Alternative 2
constant-
carbon-price
of$100/ton
C-C02






o

Q

4
Alternative 3
Emission
limits








1

o

3
Alternative 4
Emission
limits
million tons
Casa
fraction of
the
emissions in
the third
period
(C02)
2000

0

5
Alternative 5
Emission
limits
million tons
Casa
fraction of
the
emissions in
the third
period (CE)

2000

1

5
                                            30

-------
1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
CartVafM)
CaAVarH
CarbVar«
Cari>Var,-3
CarbVar^
CarbVarrt
CarbVar«
CaH>Var,-7
CarbVarMi
CaAVarM
CaibVarWo
CarbVarWi
CarbVar^u
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
100
100
100
100
100
100
100
100
100
1261
1329
1429
1345
1261
1248
1236
1224
1211
1199
1187
1175
1164
0
0
0
0
0
1.3
1.3
1.3
1.3
1.3
1.3
1.3
1.4
0
0
0
0
0
.3
.3
.3
.3
.3
.3
1.3
1.4
Table 30 Impacts of carbon policy options
Revenue Recycling Options: Select
case ^icrbfeeopt)
Cased: ICRBfeeOPT = 0
No carbon fees
Casel: ICRBfeeOPT=l
Carbon fee to general revenues
Case 2: ICRBfeeOPT = 2
Deficit reduction
Case 3: ICRBfeeOPT = 3
Carbon fee to consumers
Case 4: ICRBfeeOPT = 4
40% Households, 60% Industry
Case 5: ICRBfeeOPT = 5 Domestic to
consumers, permits to Deficit
Case 6: ICRBfeeOPT = 6
Revenue Recycling Options;
ICRBfeeOP 0 - no tax
ICRBfeeOP 1 = general revenue
ICRBfeeOP 2 = deficit reduction


Government tax revenues include a carbon fee option.
All carbon fees (CrbFeeTott) are retrieved from government resources
(Equation 214) and used for deficit reduction (Equation 215). Note that the
deficit is treated as a positive number, the fee has therefore to be
subtracted.
All carbon fees (CrbFeeTotO are retrieved from government resources
(Equation 216) and returned to household income (Equation 171).
All carbon fees (CrbFeeTott) are retrieved from government resources
(Equation 2 16);
40% of carbon fees (CrbFeeTott) are returned to households (Equation
172);
60% of carbon fees and increases in ibt taxes (CrbFeeTot, and ExIBTt
(Equation 2 1 7)) are returned to corporate earnings (TREte) (Equation
163).
For this option carbon permit trading (CrbTrade,) is kept separate from
domestic carbon permit fees (CrbFeeTot,) and there are two paths:
(a) if carbon trading (CrbTrade,) is not occurring at a loss it will reduce
government deficits (Equation 218), and it will be generated from personal
income (Equation 173), while, at the same time, the domestic carbon fee
(CrbFeeTott) is returned to households (Equation 173) and provided for by
government resources (Equation 217);
(b) If carbon trading provides for a net loss government resources provide
for the carbon fees (CrbFeeTot,) (Equation 219) and household income
(Pine) receives the fees (Equation 174).


CrbFeeRcyPct ,,: Revenue (CrbFeeTot,) and increases in IBT taxes (ExIBT,
(Equation 21 7) are recycled to corporate earnings (TREte) (Equation 1 72).
CrbFeeRcvPct j. Revenue is recycled to household income (Pine)
                                          31

-------

ICRBfeeOP 3 = consumption
(Equation 175).
CrbFeeRcyPct t Revenue is recvcled to government resources (Equation
219).
Demand Sectors

Investment Demands
Initial annual investments KAflow for the base year (v=t=0) and old vintages (v=-/) are input
parameters, as are initial expected profit rates (see Table 31).

Table 31 Initial values of annual investments and expected profit rate
Column heading) of the
production sectors
Other Ag.
ETE
C.Oil Prd.
N.GasPrd.
Coal Prd.
ColcePrd.
Empty
ElecOil
ElecGas
ElecCoal
ElecBio
ElecNuc
ElecHydro
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains and Oil Seeds
Animal Products
Forestry
Food Processing
Production
(sub>ectors
i
1
2
3
4
5
6
7
8.1
8.2
8.3
8.4
^8.5
8.6
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Annual Investment
KAFLOW
(-1)
4620
569663
11606
6863
1475
86
0
1185
3461
15415
0
5547
2477
3485
7390
10632
13923
2416
2618
2256
58967
2335
18680
7263
5867
615
7946
KAFLOW
(0)
5808
716050
14589
8626
1854
109
0
1489
4351
19376
0
6972
3114
4381
9289
13364
17501
3037
3291
2836
74120
2935
23481
9129
7375
773
9988
EXPPROF
(-1)
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
I
1
1
1
1
1
1
1
1
EXPPROF
(0)
1
1
1

1
0
1
1
1
1
0
1












1
1
1
Table 32 lists the three parameters that are used in the investment equations: rinv is the expected
profit rate function exponential, which equals one in the reference case; sealer — an investment
accelerator — is a scale coefficient with a value of 1.15  in the reference case; and accinv is the
working age population ratio exponential, which equals one in the reference case.
                                          32

-------
Table 32 Investment accelerator equation parameters
Parameters for Investment Equation
Region

sealer (accl)
1.2
accuw
I
Rinv
1
Anticipated increases in investments for all production sectors in this formulation are determined
by an exogenous parameter Qproj, in SGM 2000 (see Table 33).

Table 33 Production multiplier
PROJECTED OUTPUT MULTIPLIER (used for investment)
QPROJ
Region
Period
Multiplier

0
1

1
1.15

2
1.15

3
1.15

4
1.15

5
1.15

6
1.15

7
1.15

8
1.15

9
1.15

10
1.15

11
1.15

12
1.15
Some sectors or subsectors may have investment set exogenously (see last column in Table 34;
note that when Exolnvstj equals one or less, no exogenous investment takes place). Before 2040
hydropower and nuclear power-generated electricity generated is determined by exogenously
determined investments (see Table 34). The rhoinv parameter shown in Table 34 is the expected
profit rate exponential, which equals one in the example run.

Table 34 Production sector-specific investment elasticities and exogenous investment demands

Region
Ag
ETE
CradeOil
NatGas
Coal
Coke
Steel
Elect
RefOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Otiilnd
PassTran
FrghtTran
Grains and Oil Seeds
Animal Products
Forestry
Food Processing
Logit Exponential for
Subsector Investment
RHOINV
1
1
1




.2














Exogenous
Investment Demand
Start period 0
EXOINVST
0
0
1458X.7306
8626.26942
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
                                          33

-------
Table 35 Investment switches for electricity in nuclear and hydropower over time
EXOELEC

8
8
8
8
8
8
g
8
8
g

t
0
1
2
3
4
5
6
7
8
9

Exogenous Investment for
Nuclear Power
EXOELEC
6972.02379
9063.63093
9063.63093
8157.26784
8157.26784
8157.26784
8157.26784
8157.26784
8157.267g4
8157.26784

Exogenous Investment for
Hydro Power EXOELEC
3113.89224
3736.67069
4110.33776
41 10.33776
4110.33776
4110.33776
4110.33776
4110.33776
4110.33776
4110.33776

A set of triggers function as indicators of implementation of resource-related investment
functions in the oil, gas and coal production sector (Table 36).

Table 36 Resource characteristics: oil, gas and coal are depletable resources
Resource Characteristics
NRSCHAR
Region- 11













Product
1
2
Oil production 3
Gas production 4
Coal production 5
6
7
8
Etc
19
20
21
22
Ichar
0
0
2
2
2
0
0
0
0
0
0
0
0
Table 37 and 38 list the initial values of uninvested depletable resource Drsce^ or DrsCtrnp^,
and the vintage specific resource that is invested into and available for consumption Drsve^t or
         j. No subsectors are active, which implies jj is always one. Units are exajoules.
Table 37 Data on oil, gas, and coal resources

Sector
Grade 1 (Grade 2 iGrade 3
Quantity of Uninvested Depletable Resources: DRSCE
|3=oil 120000 |0 |0
Grade 4

0
Grade 5

0
                                           34

-------


4=gas
5=coa!
20000
50000
0
0
0
0
Initial: Annual Growth Rate in Resource Base: RESGRO



3=oil
4=gas
5=coal
0
0
0
0
0
0
0
0
0
Terminal: Annual Growth Rate in Resource Base: RESGRZ



3=oil
4=gas
5=coal
0
0
0
0
0
0
Time to Terminal Resource Growth Rite: TRESGRZ



3=oil
4= gas
5=coal
115
115
115
115
115
115
0
0
0

115
115
115
0
0

0
0
0

0
0
0

115
115
115
0
0

0
0
0

0
0
0

115
115
115
Table 38 Data on investments in oil, gas, and coal resources
Sector [Subsector |lVIN(-3)
Invested Capital in Depletable Resources: DRSVE
l3=oil

1 |42.64
Invested Capital in Depletable Resources: DRSVE
|4=gas

1 |44.65
Invested Capital in Depletable Resources: DRSVE
|5=coal jl

59.73
IVIN(-2)

89.64

93.86

125.55
IVIN(-l)

141.32

147.96

197.92
IVIN(O)

198.04

207.35

277.36
Investments into available energy reserves are calculated with the CES production function with
long-run elasticities ol. Thus, the values of a^fijjj.v used in calculating the reserves are as in
Table 39. Also note that jj=l in the reference case.

Table 39 Example of the capital cost scale factor transformations for oil, gas and coal production
Production sectors
i
C.Oil Pfd.
N.Gas Prd.
CoalPrd.
3
4
5
aMt^Ujjjiv- art»aop
(Results from Equation 30)
48.9650
10.9379
0.5958
OUWVw^MjjyseiMyji., W1*'
(Results from Equation 3 1)
2.9269
1.9353
0.8668
Table 40 shows intermediate results of the shares calculated by means of the sequence of
equations and the resulting annual investments into the production sectors in the base year.
Table 40 Capital demands and share calculation results at the end of the base year calculations
(t=0)




m



J
.1


J



V



capital



Sharey.ui
Results after
execution of
Equation 110
Sharejjj^-o
Results after
execution of
Equation 1 16
Kaflowjjj.v
Results after
execution of
Equation 1 1 7
                                            35

-------








ElecOil
ElecGas
ElecCoal
ElecBio
ElecKuc
ElecHydro















0
0
0
0
0
0
0






0
0
0
0
0
0
0
0
0
0
0
0
0
0








1
2
3
4
5
6















1
2
3
4
5
6
7
8
8
8
8
8
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22

()
0
0
(1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
I)
0
0
0
0

26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26
26







0
0.027
0.08
0.357
0
0.268
0.268
1
1











1
and
resharing







0.0591
0.1725
0.7684
0
0
0














through 130
5808
528683
14589
8626
1854
109
0
1489
4351
19376
0
6972
3114
43X1
92K9
13364
17501
3037
3291
2836
74120
2935
23481
9129
7375
773
9988
Table 39 shows the investment share information that is input for sharing the production of
capital in the SGM. The sharing of investment input is implemented as a vector of values, given
that the full matrix CapMat^ only consists of the row values i in the reference case.

Table 41 Investment shares vector
Investment Shares Vector
Region=ll
















AgRriculture
ETE
C.OilPrd.
N.Gas Prd.
CoalPrd
Coke Prd.
Empty
Electricity
RcfOil
GasT&D
Wood Prd.
Chemicals
Cement
Steel
NFMetals
Input Sectors
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
SHAREINV
0
0.05990578
0
0
0
0
0
0
0
0
0.00304478
0.00130845
0
0.00001024
0.00023904
                                          36

-------







Othlnd
PassTran
FrshtTran
Grains and Oil Seeds
Animal Products
Forestry
Food Processing
16
17
18
19
20
21
22
0.93044316
0.00174750
0.00329912
0
0
0
0.00000194
Households
The SGM keeps track of population within each region by gender and 5-year age cohort.
Population data may be read in directly, using projections from either the World Bank or the
United Nations for the model base year and for all future SGM time steps. Data for the reference
case are listed in Tables 42 and 43.
Table 42 Projected male population
Projected Male Population
Region
Period
Age 0-4
Age 5-9
Age 10-14
Age 15-19
Age 20-24
Age 25-29
Age 30-34
Age 35-39
Age 40-44
Age 45-49
Age 50-54
Age 55-59
Age 60-64
Age 65-69
ARC 70-74
A*e 75+

0
9647
9244
8806
9146
9901
10767
10978
9955
8804
6785
5523
5005
4948
4512
3423
4628

1
9993
9772
9632
9365
9311
9572
10941
11141
10039
8582
6638
5322
4727
4505
3835
5369


2
9712
10198
10273
10169
9347
8902
9744
11078
11155
9722
8375
6393
5040
4321
3859
6166


3
9786
9899
10655
10776
10209
9055
9070
9852
11091
10817
9492
8085
6081
4654
3755
6779


4
10243
9981
10359
11176
10812
9882
9219
9177
9868
10759
10572
9190
7732
5659
4094
7135


5
10844
10446
10455
10875
11188
10454
10049
9329
9201
9592
10532
10262
8816
7239
5034
7706


6
11259
11045
10933
10965
10893
10820
10610
10157
9360
8952
9401
10244
9876
8296
6495
8986


7
11525
11459
11547
11448
10978
10542
10974
10717
10183
9105
8779
9158
9890
9334
7492
11261


8
11813
11730
11979
12078
11453
10627
10698
11083
10744
9910
8950
8568
8873
9387
8491
13840


9
12243
12027
12269
12526
12070
11080
10788
10816
11116
10463
9751
8755
8333
8470
8601
16574


10
12788
12468
12587
12828
12510
11673
11245
10914
10861
10836
10308
9557
8536
7983
7814
18625


11
13348
13018
13047
13155
12805
12097
11839
11376
10965
10596
10683
10117
9342
8232
7399
19326


12
13877
13582
13617
13625
13123
12381
12263
11974
11430
10701
10454
10498
9906
9028
7671
19377
Table 43 Projected female population
Projected Female Population
Region
Period
Age 0-4
Age 5-9
Age 10-14
Age 15-19
Age 20-24
Age 25-29
Age 30-34
Age 35-39

0
9204
8814
8385
8654
9409
10591
11016
10081

1
9533
9311
9166
8800
8825
9444
10951
11190

2
9274
9722
9784
9667
9013
8889
9826
11143


3
9341
9439
10154
10237
9853
9071
9237
9991


4
9768
9508
9872
10623
10424
9896
9421
9400


5
10330
9941
9953
10335
10790
10451
10256
9585


6
10719
10503
10401
10414
10507
10818
10813
10418


7
10973
10897
10984
10872
10590
10546
11185
10978


8
11253
11159
11398
11474
11051
10632
10914
11354


9
11670
11447
11680
11905
11650
11085
11006
11088


10
12192
11871
11987
12198
12077
11674
11467
11182


11
12727
12394
12426
12509
12363
12092
12061
11642


12
13229
12929
12965
12954
12668
12370
12479
12234
                                          37

-------
Age 40-44
Age 45-49
Age 50-54
Age 55-59
Age 60-64
Age 65-69
Age 70-74
Age 75+
9015
7045
5848
5470
5671
5564
4599
8510
10234
8887
7010
5770
5323
5417
4991
9443
11342
10089
8850
6914
5614
5089
4867
10408
11289
11176
10027
8714
6726
5383
4578
11019
10134
11131
11109
9879
8483
6453
4852
11216
9542
10007
11071
10951
9622
8142
5828
11618
9735
9430
9963
10921
10674
9234
7361
12849
10572
9617
9394
9836
10658
10248
8350
15267
11140
10447
9597
9284
9623
10246
9283
18132
11524
11013
10428
9501
9102
9273
9300
21215
11260
1139S
10997
10327
9319
8776
8440
23595
11354
11135
11378
10896
10134
9015
7996
24553
11814
11225
11119
11271
10694
9801
8232
24750
Table 44 lists the male and female population summed between ages 16 and 65, representing age
groups 4 through 13. It also lists income for time periods before the base year.

Table 44 Male and female working age population
Male and Female Working Age Population (15-65)
Region







WoifcingAGE'
80
1
1
1
1

2
2
WorkingAGE'
85
1
2
1
2

4
4

77984.75
79165.50
81811.31
82799.92

5199.63
6146.42
Working_Age_pop
Male working age population att-1 (Wage(2,L,-l))
Female working age population att-1 (Wage(2,L,-l))
Number of working-age males at t=0 (Wage{ 1,L,0))
Number of working-age females at 1=0 (Wage(2,L,0»
Wage(3,L,M) is the workforce
Income (GNP/workforce) at t=-2 W»ge(4,L,-2)
Income (GNP/workforce) att=-l Wage(4,L,-l)
The number of households Nhh in a regional population is either a regional input parameter
(Table 45) or calculated based on the average number of people per household.

Table 45 Number of households in the base year 1990
Number of households in base year
Region

NHH
100000
The labor force for the base year (LBo,ng) is either fixed by an exogenous parameter (see Table 46:
Fix labor switch) or calculated from data.

Table 46 Household labor supply fraction in base year

Regional







ng
Gender
I
2





Household Labor
Supply
LB(0)=LB0j»
0.8
0.8






Period
0
1
2
3
4
5

FIX LABOR SWITCH
Rate
0.764468
0.768885
0.777627
0.785602
0.795574
0.809890
Identical to period 5 thereafter
                                          38

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The demand for labor by households is set exogenously for the base year (see Table 47).
Table 47 Demand for household labor supply in the base year

Region

Number employed in base year
ED(NIN-l)=Edi-Mt|-27
125840
Table 48 lists the total land area used as parameters in the reference case. Table 49 lists the
maximum potential share of land supplied to the market for the base year/?o, and Table SO lists the
demand for land supply in the base year.

Table 48 Total land area over time
Total Land Area
Region










Period
0
1
2
3
4
5
6
7
8
9

TLA
1000
1000
1000
1000
1000
1000
1000
1000
1000
1000
Table 49 Land supply function coefficient
Base year Land Supply Function Coefficient
Region

R(0)=R«
1
Table 50 Demand for land in base year
Land used in base year
Region
11
ED(NIN-
2)=Ed«4.|lWT-M,
500
Personal income equals the sum of retained income, labor income, and land rental income, minus
personal income tax to which government transfers are added and from which personal savings
are subtracted. Data required for the calculations are listed in Tables 51 through 60.

Table 51 Personal income tax rate
Personal Income Tax Rate
Region

SUrt Period
0
P1TR
0.1628223
                                           39

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 Table 52 Corporate income tax rates in base year
Corporate Income Tax Rate
Region

Start Period
0
CITR
0.07577859
Table 53 Investment tax credit rates
Investment Tax Credit Rates
Region





Production (sub)Sector
t
2
etc
21
22
XITCR=XITCratei
0
0
0
0
0

Initial Period for Investment Tax Credit Policy
PERIOD
Region



100



Table 54 Retained earnings fraction in the base year
Retained Earnings
Region









Sector
1
2
Etc
g
9
Etc
20
21
22

RE(0)
0.8
0.8

0.8
0.8

0.8
0.8
0.8
Table 55 Total regional household retained earnings
Total retained earning in base year
Region

TRETE(L)
624493.6
Table 56 Social security tax rate
Social Security Tax Rale
Region

Start Period
0
SSTR
0.15872188
Table 57 Government transfers in the base year
[Government transfers in base year           I
                                             40

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Region

GOVTR
808000
Table 58 Household savings in base year
Savings in base year
Region

Edwti-26
221300
Table 59 Household savings function coefficient in base year
Household Savings Function
Coefficient in base year
Region
11
S(0)=S0
0.4
Table 60 Household income and price elasticities in base year
Household Demand Function Coefficients; Region= 1 1
Supply sectors 
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Government Preference Function Coefficients
GF
Region


Sector
26

Index
4

Start Period
0

Coefficients
-0.5
Government deficits are input data with negative values (see Table 62).
Table 62 Government deficit over time
Government Deficit
GOVDEF
Region= 1 1














Period
0
1
2
3
4
5
6
7
8
9
10
11
12


Deficit (listed as +)
-68404.69
-54723.75
-41042.81
-27361.88
-13680.94
0
0
0
0
0
0
0
0



1990
1995
2000
2005
2010
2015
2020
2025
2030
2035
2040
2045
2050
Trade
If trade is fixed, trade quantities can be input values (Trade0^23'- e.g., Table 63) and trade demand
can be set equal to these initial trade values. Note that the SGM has the option to read in carbon
trade (into either Trade0.^23 or into an additional trade vector Trade/>#).

Table 63 Trade data
Region

Other AR.
ETE
C.0il Prd.
N.Gas Prd.
Coal Prd.
Coke Prd.

Elec Gen.
RefOil
GasT&D
Wood Prd.
Chemicals
Input
1
2
3
4
5
6
7
8
9
10
11
12
Net Trade in Base Year
Start Period
1-0
0
0
0
0
0
0
0
0
0
0
0
0
Trade0.i
-2911.44
66544.70
-30870.17
-1922.75
3336.18
-25.47
0.00
-144.75
-6185.95
0.00
-2587.47
6117.04
Net Trade when t=l
t=l
1
1
1
1
1
1
1
1
1
1
1
1
Trade,,.;
-2911.44
66544.70
-30870.17
-1922.75
3336.18
-25.47
0.00
-144.75
0.00
0.00
-2587.47
61 17.04
                                           42

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Cement
Steel
NFMetals
Othlnd
PassTran
FrghtTran
Grains and Oil Seeds
Animal Products
Forestry
Food Processing
(carbon market]
Land rental
Labor income
OVA (other value added)
13
14
15
16
17
18
19
20
21
22
23
24
25
26
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-4131.90
-8145.91
-3845.95
-119488,65
20012.44
28057.27
10962.S3
-674.20
-570.53
-3164.53
0.00
0.00
0.00
-49639.22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
-4131.90
-8145.91
-3845.95
-1 19488.65
20012.44
28057.27
10962.83
-674.20
-570.53
-3164.53
0.00
0.00
0.00
-49639.22
43

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Appendix B: Description  of the Solution  Algorithms

Bisection Routine

The bisection routine is a simple but robust approach to finding roots. To begin the bisection
routine, the solution or the root must be bracketed. Bracketing is achieved when the price of a
good is adjusted up or down until the excess demand (demand minus supply) changes sign. The
two prices at which the sign change occurs represent the initial bracketing interval. Bracketing
price intervals are found for all markets.

Once the bracketing price intervals are found, the midpoints of the price intervals are used to
determine the sign of the new excess demands. The midpoint price is used to replace the initial
bracketing price that has the same sign in excess demand. Each successive iteration reduces the
bracketed price  intervals by a factor of 2. After n iterations, if the solution is bound by an interval
of size sn, then after the next iteration it will be bracketed by an interval of size

8n+1 = en/2                                                                     Eq.AS.l

From the initial  bracketed interval, s0, to the desired tolerance, E, the number of iterations to
achieve the tolerance is given by

n = Iog2 (EO/E)                                                                  Eq. A3.2
Because there are multiple markets, however, the actual number of iterations to achieve the
tolerance for all the markets is determined by the largest initial bracketed interval.

In certain situations, a market must be bracketed again and the bisection routine reapplied. Supply
and demand for one market is dependent on the market prices of other goods. Thus, the solution
may shift and no longer lie in the initial bracketing intervals. New bracketing intervals must be
determined in such a case, hi other situations, bracketing may not be possible at all, e.g., when
resources are exhausted and there are no longer any supplies. In such a case, the bisection routine
cannot be applied.

Although the advantages of the bisection routine is its robustness and sureness in finding the
solution price, its disadvantage is that it is slow. To improve the speed of finding solution prices,
the bisection routine is combined with the Newton-Raphson routine, which relies on the use of
derivative.
                                          44

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Newton-Raphson  Routine

The Newton-Raphson routine is a numerical derivative approach to finding the solution. The
advantage of this routine  over the bracketing and bisection routine is that it converges
quadratically near a solution as opposed to linearly and approaches the solution very quickly
(Ref. Numerical Recipes). In the vicinity of the solution, each iteration of the routine
approximately doubles the number of significant digits in the trial solution. The Newton-Raphson
routine requires the evaluation of the function and its derivative at arbitrary points. The Newton-
Raphson formula is given by
    = x, + f(x,)/f(xi)
Eq. A3.3
where x, is the trial solution, x;+i is the next trial solution, and F(XJ) is the derivative of the
function evaluated at x,.

Graphically, the routine extends the tangent line of the function at a point until it crosses zero and
sets the next trial solution to the abscissa of that zero-crossing. This is repeated until the solution
is found.

The disadvantage of the Newton-Raphson routine is that it is unstable where there are
discontinuities and therefore, the routine's global convergence properties are poor. For instance,
at local discontinuities or extreme values, the tangent line of the trial point can move the next trial
point hopelessly far away from the real solution.

An effective strategy for creating a solution algorithm that is both fast and robust it to utilize both
the bracketing and bisection and the Newton-Raphson methods. This hybrid algorithm relies on
bisection whenever Newton-Raphson takes the solution out of bounds, or whenever Newton-
Raphson is not reducing the size of the brackets rapidly  enough.

The bracketing and bisection routine is applied first to find the initial bracketing intervals and to
come near the vicinity of the solution for all markets. The Newton-Raphson routine is then
applied to quickly come to the solution. If the Newton-Raphson routine takes the solution out of
bounds or does not find the solution within a set number of iterations, the bisection routine is
called. This procedure is repeated until the solution is found.
                                            45

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Appendix C: Description  of the  Solution Algorithms

Input-Output Table Conversions

For detail on conversion from use tables, make tables, and energy balance tables to hybrid
commodity by commodity tables see Fisher-Vanden 1993:4.

Let U be a commodity -by -industry use matrix3 with the same number of columns as industries.
Let g be a vector of production values by industry. V is an industry-by-commodity make matrix4.
An input-output table based on industry technology5 is created using the matrix equation
 T = Ug'V

where g is a diagonal matrix with the elements of g on the diagonal and zeros everywhere else.
Some notation will be set up to show why this works. Let silf be the value share of input i in the
output of industry k ,  which is equal to the element in the i-th row and k-th column of a
normalized use matrix Ug~l . Let v^ be an element of the industry -by -commodity make matrix
V. i is an index that runs through all inputs, including value added, k is an index for industries and
j is an index for outputs. Individual elements of the input-output table are given by
where t^ is the amount of input i used in the production of output j. Let k be any industry that
produces some of output j. Then v^ is the amount of output j produced by that industry. The
amount of input i required by industry k is given by s^v^ .
3 The use table has the commodities that industry uses as rows, and industries that use these commodities as column
headings.
4 The make table has the industries that make commodities as rows and the produced commodities as column headings.
5 http://www.beagov/bea/industry/iotables/prod'tablejist.cfm?anon=336: The input-output (I-O) accounts show how
industries interact; specifically, they show how industries provide input to, and use output from, each other to produce
Gross Domestic Product (GDP). These accounts provide detailed information on the flows of the goods and services
that make up the production process of industries. The I-O accounts are presented in a set of tables: Use, Make, Direct
Requirements and Total Requirements. The Use table shows the inputs to industry production and the commodities that
are consumed by final users. The Make table .shows the commodities that are produced by each industry. The three
Requirements tables are derived from the Use and Make tables. The Direct Requirements table shows the amount of a
commodity that is required by an industry to produce a dollar of the industry's output. The two Total Requirements
tables show the production that is required, directly and indirectly, from each industry' and each commodity to deliver a
dollar of a commodity to final users. The Use table is the most frequently requested table because of its applications to
the estimates of GDP.

                                            46

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Repeat this procedure for all industries that produce (re Make) any of output j and sum to get the
total amount of input i used in the production of output j.

Final-demand vectors remain unchanged by these calculations, and can be appended to the
derived input-output table. Note that this procedure will work even if there are more industries
than commodities,

Postmultiplying by a normalized make table is a way to convert information categorizied by
industry to a commodity categorization. This can be applied to all input rows of the use table as
well as energy consumption data where the rows are fuels and the columns are industries.
                                           47

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Appendix D: Comparisons between the SGM and
MiniCAM

The major characteristics of the two Integrated Assessment Models, the Second Generation
Model (SGM) and the Mini-Climate Assessment Model (MiniCAM) developed and maintained
by the PNNL Joint Global Change Research Institute (JGCRI) are listed below.

General versus partial equilibrium
   •   The MiniCAM is a partial equilibrium model; the energy sectors are tracked in
       MiniCAM's evolving Edmonds-Reilly-Barnes module (ERB)
   •   The SGM is a general equilibrium model, with an ' Everything Else' sector that
       encompasses all those sectors that are not explicitly simulated such that a general balance
       of supply and demand can be achieved.

The scope of the models
   •   The MiniCAM estimates the supply and demand of energy (in the ERB module),
       agricultural production and land use (using the Agriculture and Land Use model, AgLU),
       linking greenhouse gas and sulfur dioxide emissions with climate change and sea level
       rise (using the Model for the Assessment of Greenhouse-gas Induced Climate Change
       MAGICC) and determines the regional patterns of climate change (using the Regional
       Climate Change Scenario Generator SCENGEN).
   •   The SGM estimates a complete, albeit condensed set of economic accounts.

The time horizons of projections
   •   MiniCAM's time steps are 15 years. Parameters and variables are point estimates, e.g.,
       point estimates are found on the resource cost curves for the model solution.
   •   SGM's time steps are five years. Transfers or flows (profit rates, capital flows,
       investment rates, production rates, prices, technological change) are based on
       representative annual values of parameters or variables representative of 5-year time-
       period. Costs, stocks, resource values, etc. are integrated values over a 5-year period. The
       initial commodity-by-commodity hybrid input-output table is representative of the base
       year (1990); equilibrium solutions after each 5-year time step are representative of the
       number of time steps after the base year. Available energy resources are calculated based
       on investment, which, in turn are based on expected profit rates. Total resources
       consumed are subtracted from a raw resource stock that may grow independently.

Final demands versus providing energy services
   •   The MiniCAM simulates demands in the form of 'energy services' to three end-use
       sectors: transportation, industry and buildings.
   •   The SGM simulates the traditional economic concepts of factor markets in the form of
       'value added' (land, labor, and capital); these factor markets supply factor services to the
                                         48

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       production sectors and four components that play a role in SGM's final demand:
       households, government, investment and net exports.

Functional representation of demand
    •  In the MiniCAM demand functions are constant elasticity functions that are combined
       with logit share equations to calculate fuel and agricultural product demands. The
       demand functions have elasticities for general economic activity and the prices of the
       specific products demanded.
    »  In the SGM, demand is determined as the sum of intermediate and final demand sectors.
       Intermediate demands are determined by cost functions; final demands, in the form of
       investment-, household-, government-, and net exports-demand are each estimated
       separately, e.g., household demand is formulated as a constant elasticity function.

Functional representation of production
    •  In the MiniCAM all goods are produced with a fixed-coefficient (Leontief) production
       function. These functions are combined with logit share equations to provide a means for
       competition, e.g., implementation of the logit share equation results in different fuel
       modes competing in obtaining the lowest total cost of energy services to an end-sector
       (e.g., the share of oil and gas for heating buildings).
    •  In the SGM all goods are produced with either a Constant-Elasticity-of-Substitution
       (CES) production function with vintaging, or a fixed-coefficient (Leontief) production
       function in combination with logit share equations (e.g., for electricity). The CES
       equations allow for maximum output, to any given  vector of inputs. Moreover, as the
       SGM searches for equilibrium prices, technical coefficients remain invariant with respect
       to price while input-output coefficients will respond to changes  in price. This response,
       governed by the elasticity of substitution, is important for climate policy since production
       process intensity ought to respond to changes in the price of fossil fuels.

Capital, investment, profit
    •  MiniCAM simulates neither capital investment nor profit.
    •  SGM simulates vintaged capital investment and profit.
Units
       MiniCAM's supplies are based on prices (costs) of supplies: $/J for energy; $/cal for
       agricultural products; $/m3 wood for wood products. MiniCAM's energy demands are
       based on energy units (Joules); agricultural demands on calories and wood demands on
       m3 wood.
       The SGM calculates production in units that depend on the product unit demanded (e.g.,
       paper in tons, agricultural products in calories, energy in exajoules), and cost of
       production in monetary value (regional currency). Prices of supplies and of commodities
       produced are relative to the price of the numeraire sector, whose price equal unity (one).
                                           49

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-------