&EPA
United States
Environmental Protection
Agency
Environmental Research
Laboratory
Corvallis OR 97330
EPA-600 5-78-018
August 1978
Research and Development
Methodologies for
Valuation of
Agricultural Crop
Yield Changes
A Review
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the SOCIOECONOMIC ENVIRONMENTAL
STUDIES series. This series includes research on environmental management,
economic analysis, ecological impacts, comprehensive planning and fore-
casting, and analysis methodologies. Included are tools for determining varying
impacts of alternative policies; analyses of environmental planning techniques
at the regional, state, and local levels; and approaches to measuring environ-
mental quality perceptions, as well as analysis of ecological and economic im-
pacts of environmental protection measures. Such topics as urban form, industrial
mix, growth policies, control, and organizational structure are discussed in terms
of optimal environmental performance. These interdisciplinary studies and sys-
tems analyses are presented in forms varying from quantitative relational analyses
to management and policy-oriented reports.
the Nallonal Technical lnforma-
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EPA-600/5-78-018
August 1978
METHODOLOGIES FOR VALUATION OF
AGRICULTURAL CROP YIELD CHANGES: A REVIEW
by
Steve Leung and Waifred Reed
Eureka Laboratories, Inc.
1»01 N. 16th Street
Sacramento, California 9581A
Scott Cauchois and Richard Howitt
University of California
Davis, California 95616
Grant No. R80A957-010
Project Officer
John Jaksch
Criteria and Assessment Branch
CorvalHs Environmental Research Laboratory
Corvallis, Oregon 97330
CORVALLIS ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U. S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330
For Salt by the Superintendent of Documents, U.S. Government Printing Office
Waihington, D.C. 20402 Stock No. 05S-003-00092-1
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DISCLAIMER
ReSearhLahnratn™ rfvi?wed b* the Corvallis Environmental
Research Laboratory, U.S. Environmental Protection Aaencv and
approved for publication. Approval does not signify t£t the
contents necessarily reflect the views and policies of the US
Environmental Protection Agency, nor does mention of tradl names or
commercial products constitute endorsement or rSoSeSdSloHSr Sse.
ii
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FOREWORD
Effective regulatory and enforcement actions by the Environmental
Protection Agency would be virtually impossible without sound scientific
data on pollutants and their impact on environmental stability and human
health. Responsibility for building this data base has been assigned to
EPA's Office of Research and Development and its 15 major field installa-
tions, one of which is the Corvallis Environmental Research Laboratory
(CERL).
The primary mission of the CERL is research on the effects of environ-
mental pollutants on terrestrial, freshwater and marine ecosystem; the
behavior, effects and control of pollutants in lake systems; and the
development of predictive models on the movement of pollutant in the bio-
sphere.
This project was initiated on November 1, 1976 and work was completed
as of March 31, 1978.
A. F. Bartsch
Director, CERL
iii
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ABSTRACT
This research effort was initiated with the objective to complete a
review and evaluation, within the constraints in time and resources of
this project, of the methodological and analytical techniques used to
assess and quantify the economic impact of changes in agricultural crop
yields.
The review focused on two major areas: (1) physical effects of man-
made and natural factors on agricultural crop yield, and (2) methodolo-
gies and models used to evaluate and quantify the economic impacts of
crop yield changes on the farm, the agricultural industry and finally the
consumers.
Investigation of the first area involved extensive literature review
on the effects of the natural and man-made environmental factors, and
their combinations on agricultural crop yields. The major natural en-
vironmental factors included in this report are climate and weather, soil
and biological conditions. Air pollution is the main consideration under
the man-made factors. Production functions in relation to individual or
in combination with environmental factors are identified, when data are
available. This area is presented in Section V of the report.
Methodologies and models for assessing economic impacts due to crop
yield changes are considered in Sections VI, VII and VIII. Three alter-
native models are identified in Section VI for the evaluation of the cost
to an individual farm due to changes in crop yield. These models are
(a) mathematical optimization model, (b) simulation model, and (c) econ-
ometric model. Section VII outlines the regional input-output model and
the regional spatial programming model as two feasible approaches in
evaluating the secondary economic impacts. Finally, the market supply
and demand theories are identified in Section VIII as relevant concepts
in analyzing the overall impacts on consumers due to crop yield changes.
This report was submitted by the Eureka Laboratories, Inc. in the
fulfillment of Grant No. R804957-010, under the sponsorship of the
Environmental Protection Agency.
IV
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CONTENTS
Foreword 111
Abstract 1v
List of Figures and Tables v11
Abbreviations , v111
Acknowledgment 1x
I. Executive Summary 1
A. Introduction 1
B. Physical Effects of Man-Made and Natural
Factors on Agricultural Crop Yield . . 1
C. Methodologies and Techniques for Quantifying
Economic Impacts of Crop Yield Changes 2
II. Conclusions , 6
III. Recommendations 7
IV. Introduction . 9
V. Physical Effects of Man-Made and Natural Factors
on Agricultural Crop Yield 11
A. Environment . 11
1. Climate and Weather 11
2. Soil Factors 25
3. Biological Factors 27
4. Summary 28
B. A1r Pollution 30
1. Symptoms of Injury ...... 31
2. Factors Affecting the Expression of
Pollutant Damage to Plants 35
3. Summary 41
C. Production Estimates 43
1. General Problems 43
2. Field Surveys 44
3. Production Functions 45
4. Discussion 53
5. Summary ......... 59
VI. Farm Structure Profitability and Risk Changes due to
Agricultural Crop Yield Changes 61
A. Mathematical Optimization Modelled by
Representative Farm and Aggregated Region .... 62
1. Linear Programming (LP) in General 62
2. LP Model of a Farm: An Example 63
3. Aggregate Supply Response Modelled by
"Representative" Farm 64
4. Methods of Accounting for Risk Aversion
1n Farmers' Decisions 66
5. Incorporating A1r Pollution Effects
into the Programming Model 69
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B. Simulation Model with Production Function 72
1. Features of Mathematical
Models of Economic Systems 73
2. Simulation Compared to LP 74
3. Applications 75
C. Econometric Modelling of the Production System ... 79
1. Biological Production Functions -
Single Equation 80
2. "Whole Farm" Production Functions -
Single Equation 81
3. Simultaneous Systems 86
4. Summary 93
VII. Secondary Economic Impacts due to Agricultural
Crop Yield Changes 94
A. Regional Input-Output Models 94
1. Applications of 1-0 Analysis 95
2. Methodological Appendix 100
B. Regional Spatial Programming Models 107
1. Nonlinear Spatial Programming Model:
An Example 109
2. Applications Ill
3. Summary 117
VIII. Overall Impacts on Consumers due to Crop Yield Changes ... 118
A. Supply 119
B. Demand 121
1. Mathematics of Demand Theory 121
2. Price Elasticity of Demand 122
3. Cross-Price Elasticity 123
4. Income Elasticity of Demand 124
C. Stability Benefits 127
References 135
VI
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FIGURES
Number Page
1 Price Change Attributable to Shift in Market Supply .... 128
2 Price Change Attributable to Shift in
Consumer Demand ..,.,,,.,.... 128
3 Effects of Price Stabilization on Consumer Surplus .... 130
4 Effects of Price Stabilization on Producer Surplus .... 130
5 Welfare Effects of a Shift in Market Supply 133
TABLES
1 Constants and Multiple Regression Coefficients for
Years and Weather Variables and Their Relation to
Corn Yields in Five States 48
2 Variables used in Economic Damage Functions 54
3 Economic Damage Functions on Vegetation with
Pollution Relative Severity Indices 55
vn
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ABBREVIATIONS
Abbreviations Definition
ANOC analysis of covariance
CES constant elasticity of substitution
CS consumer surpluses
ET evapotranspiration
EV expected value-variance
1-0 input-output
LAR leaf area ratio
LP linear programming
Ly Langleys, (cal cnr2)
MLP multiperiod linear programming
NAR net assimilation rate
NSP net social payoff
PET potential evapotranspiration
PS producers' surplus
QP quadratic programming
RGR relative growth rate
RP recursive programming
viii
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ACKNOWLEDGMENTS
This study was funded under Grant No. R804957-010 from the U. S.
Environmental Protection Agency, Assistance in planning program ob-
jectives and direction was given by John A, Jaksch, of the Environmental
Protection Agency's Corvallis Environmental Research Laboratory, Criteria
and Assessment Branch.
Ronald Oshima of the California Department of Food and Agriculture
has spent many hours in reviewing Section V of this report on "Physical
Effects of Man-Made and Natural Factors." His invaluable input to this
report is gratefully acknowledged by the authors.
Special appreciation is extended to Ruby Reed for both her techni-
cal Input to the agriculture crop yield section and her effort in manu-
script preparation.
ix
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SECTION I
EXECUTIVE SUMMARY
This research effort is primarily concerned with the state-of-the-art
review and evaluation of the methodologies and analytical techniques used
in quantifying the economic impact of agricultural crop yield changes.
In achieving this objective, the review centered on two main areas.
The first area is concerned with the physical effects of man-made and natur-
al factors on agricultural crop yield, and the second on the methodologies
and models for quantifying the economic impacts of crop yield changes on
the farm, the agricultural industry and finally the consumers.
The entire report comprises eight sections, while the main body of the
report is found in Section IV through VIII. A brief summary of the high-
lights of these five sections follows:
A. INTRODUCTION
The purpose of this project is to provide a literature review and
evaluation of the methodologies and techniques available for the quantifi-
cation of the economic impacts due to agricultural crop yield changes. The
project was conducted in three phases: (1) information and data gathering;
(2) review relevant information and data; and (3) information evaluation.
B. PHYSICAL EFFECTS OF MAN-MADE AND NATURAL FACTORS ON AGRICULTURAL
CROP YIELD
The effects of physical factors, both natural and man-made, on crop
yield were reviewed. These factors include light, temperature, water, wind,
soil, biological factors and air pollution. Methods of estimating crop
yield in relation to these environmental factors were also discussed.
The growth rate and dry matter production of whole plants is propor-
tional to the light received or to the log of light intensity. Variations
in crop yield have been observed to result from variations in the amount
of light received. The growth rate of some crops is more sensitive to
light deficiency at certain developmental stages than others.
The rate of growth increases approximately linearly with temperature
between 5° to 30°C for temperate season crops. Growth stops at about 5°C,
and the rate usually decreases rapidly after an optimum at 25° to 35°C.
Variations occur with plant species, age and influence of other environmen-
tal factors.
Plant growth and crop yield are controlled by the available water
supply. The yield is approximately proportional to the amount of water used
by the crop, although excessive water or periods of drought can cause tem-
porary disruptions.
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Plant growth is promoted by low velocity air movements. High velocity
causes deleterious effects. The effects of wind have not been studied very
extensively except in relation to windbreaks.
Soil influences plant growth by limiting the availability of nutrient
ions because of the location of the ions in the soil complex, the relative
amounts of the different ions adsorbed, the soil ion exchange capacity, the
diffusional ion flux and the mass flow of ions in the soil matrix.
Crop losses from biological factors such as plant diseases, parasitic
plants and insects, were estimated to equal about 10% of the crop. The
estimates were based on surveys of various workers in the field.
Plant growth responses and visible leaf injury have been associated
with different air pollutants. Ambient oxidants in some areas of the United
States do clearly cause growth and yield reductions in some agricultural
crops. Reported yields in nonfiltered field chambers were reduced compared
with those in filtered chambers by up to 50% for citrus, potato, tobacco
and soybean, up to 60% for grape and up to 29% for cotton.
Plant responses to air pollutant are subject to variations from environ-
mental and genetic factors, distribution of exposure to pollutant and pre-
sence of pollutant mixtures. There is a distinct variation in susceptibility
to air pollution among plant species, varieties and individuals.
Field survey and production function are the two methods widely used
in estimating crop yield in relation to different environmental factors.
The field survey has been used to estimate crop losses resulting from air
pollution. Production functions are usually derived from multiple regre-
ssion analysis which relates crop yield to different environmental vari-
ables such as weather or air pollution. Oshima (1976) has recently deve-
loped a method to produce crop loss-ozone dose functions under field con-
ditions using ambient ozone variations at different sites in California.
There are difficulties with these methods for determining environmental
variable-yield relationships. There are a number of factors influencing
yield in the field which cannot be individually controlled. In various
controlled facilities the reverse is true, where ambient conditions cannot
be duplicated. For statistical analysis, the problems may include factor
interactions, correlation between factors, limitations in the range of
variables of regression analysis and uncertainties where quantitative mea-
surements of factors is difficult.
C. METHODOLOGIES AND TECHNIQUES FOR QUANTIFYING ECONOMIC IMPACTS OF
CROP YIELD CHANGES
In Sections VI - VIII an overview of methodologies is provided that
may be pertinent to measuring the primary and secondary effects of physical
factors in agriculture. The discussion in Section VI addressed the impact
of crop yield changes on the farm level. Section VII is concerned with
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broader primary and secondary effects on the agricultural sector, inter-
sectoral and interindustry effects, and regional effects of yield changes.
Section VIII focuses specifically on how the externalities of yield changes
in agriculture affect the consumer. A comprehensive assessment includes
all of these aspects and their measurement may be thought of as an essential
initial step in addressing the broader question of internalizing crop yield
externalities through appropriate public policy. In addition to various
quantitative techniques may be utilized to model the crop yield problem
under consideration.
Section VI focuses on farm structure, profitability and risk changes
due to crop yield changes induced by physical factors. We specifically
concentrate on the following areas: (A) mathematical optimization modelled
by representative farm and aggregated region, (B) simulation models, and
(c) econometric models.
In VI, A, the linear programming (LP) model of the firm is a point of
departure. Among the benefits of using LP are that it can solve complex,
large optimization problems with relative speed. Additionally, the alter-
native impacts of varying parameters (such as air pollution levels, for
example) can be readily derived.
On the other hand, LP is basically a comparative static, conditional
normative tool. Multi-period models can adequately overcome the first
problem, while recursive programming and risk inclusion help alleviate the
second. The incorporation of risk is particularly important. It helps to
reduce the discrepancy between the actual and predicted behavior of entre-
preneurs. Thus, in aggregate studies it reduces the typical overestimation
of supply that occurs due to the lack of specification of risk averse beha-
vior. Risk inclusion also prevents unrealistic over-specialization in
cropping activities.
Among alternative methods of including risk in a representative farm
study, the direct derivation of E-V frontiers with quadratic programming
is probably the most appropriate, assuming that a QP algorithm is available.
In VI, B, simulation models were considered to be an alternative
approach to modelling the air pollution-agricultural sector system. Simu-
lation is particularly flexible in the sense that it can manage large,
complex stochastic systems, multiple objectives, interdisciplinary theore-
tical problems, and is by its very nature, dynamic. However, simulation
models are non-optimizing and the conclusion was that in general, if data
are available and an analytic optimizing model can be constructed, the latter
is to be preferred.
Section VI, C gives a thorough treatment of econometric approaches.
The econometric approach is positive, that is, focuses on existing rela-
tionships and not on what should be. Single equation "whole farm" produc-
tion functions are a particularly good tool in diagnosing conditions of
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serious disequilibria. On the other hand, as the system under consideration
becomes larger, with more producing units, perhaps the best use of "whole
farm" functions are as inputs into aggregate regional linear or quadratic
programming models.
Single equation functions are often subject to simultaneous equation
bias which can be overcome by specifying one or more production relationships
as equations in a structural system in which inputs, outputs, and other
variables are simultaneously determined. A simultaneous system is not only
logically superior to the single equation approach, but in the reduced form,
allows for the derivation of dynamic impact multipliers, i.e., the effects
of changes in exogenous variables sustained for a period of time on endo-
genous variables.
In Section VII the secondary impacts of physical factors damage on crop
yields in a general equilibrium framework is considered. The methods
discussed in VII are equally applicable to communities, regions, multi-
regional units, or nations. We extend the analysis beyond producers of
agricultural commodities to consumers of such commodities - households and
other industries in VII, A. In VII, B, consumer demand is incorporated in
such a way that one can seek a social welfare optimum and measure the wel-
fare effects of physical factors such as air pollution and pollution stand-
ards on producers and consumers.
Input-output analysis is a multi-market analytical technique that deter-
mines the interdependence of various sectors of the economy. It is a posi-
tive tool and differs from the approaches in Section VI in that the indus-
try rather than the firm is the unit of production. It has been the most
widely used tool in the study of regional and interregional independence.
The producing unit shifts to the region in VII, B. in which spatial
programming models are reviewed. Among other things, such models are charac-
terized by discrete producing and consuming regions. They also may incor-
porate many commodities related in supply and demand, multiple time periods,
and storage activities. Spatial programming models, particularly the
activity analysis version, have long been used in agricultural economics
to derive efficient regional and interregional production, shipping patterns
and resource allocation.
Of major interest to the externality problem under consideration is
the nonlinear spatial programming model in which prices and quantities
demanded are endogenous, that is, determined simultaneously within the model
along with supply. In contrast, in the programming models discussed in
VI, A demand is given. With normal negatively sloping demand functions and
under the assumption of perfect competition, the appropriate maximand is
net social payoff, or the sum producers' and consumers' surplus. In the
absence of better measures, producers' and consumers' surplus measure the
dollar values of producers' and consumers' welfare. These concepts may be
used to identify gainers and losers due to alternative policy actions.
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In recent years the net social payoff objective function has been
modified to incorporate risk averse behavior. This is important to deter-
mining the effects of physical factors such as air pollution because they
will alter the risk patterns of crops in different ways.
In Section VIII some basic concepts in demand theory are reviewed and
the relevance of price and supply stability analysis to the measurement of
the welfare effects of crop yield changes due to physical factors is indi-
cated. Conceptually, we want to direct attention to the fact that when a
given'encironmental policy action such as that of air pollution is taken,
the impact reverberates throughout the economic system.
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SECTION II
CONCLUSIONS
The following conclusions are based on the literature review and
evaluation conducted in this study.
(1) The growth rate and yield of plants are affected by physical factors
such as light, temperature, water, wind, soil and biological factors.
Quantitative data identifying the environmental variables and yield
relationships are available in some areas while quite lacking in others,
(2) Considerable efforts have been extended to develop air pollution-crop
yield functions in agricultural crops. While some good experimental
data has been generated recently for several crops, much remains to
be done in order to provide reliable data for meaningful economic
impact assessment.
(3) Economic damage functions have been established in several studies.
There are, however, inherent weaknesses in the data base of which the
functions are derived, and other conceptual and empirical difficulties
associated with the damage functions estimation. Therefore these
functions should be used with proper understanding and caution.
(4) There are quite a number of econometric methodologies and techniques
available for assessing economic impacts due to agricultural crop
yield changes on the farm level, regional level, and the consumer
level. These methodologies and techniques vary in complexities. In
selecting from these techniques for one's use the choice will depend
upon the project objectives and input data availability; criteria for
these selection are covered in the text.
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SECTION III
RECOMMENDATIONS
The quantitative relationship between agricultural crop yield and phy-
sical factors such as light, temperature, water, wind, soil and air pollu-
tion should continue to be investigated in order to provide more reliable
functions. Priority should be given to the investigation of the effects of
physical factor interactions on proudction. Major consideration should
also be given to the consistency of techniques for evaluating changes in
crop yield so that sound comparisons can be made between studies.
Under the assumption that reliable yield response functions can be
estimated with either classical or Bayesian Techniques (the latter combines
a priori knowledge with specific experimental results), appropriate metho-
dologies are recommended with which the primary and secondary effects of
crop yield changes can be measured. Primary effects are those at the indi-
vidual farm level; secondary effects refer to impacts of yield changes on
both the agricultural and non-agricultural sectors at the regional level
and on the consumer.
In reality, one of the major problems in a California case study is
expected to be the quantity and quality of data available for estimating
yield response functions for the variety of crops found in typical California
regions. Given this limitation, the recommended methodological approach
at the farm level is to use yield response functions as inputs to an aggre-
gate farm linear programming model (LP). With such a model, one can readily
calculate changes in optimal cropping pattern (supply response), net returns,
resource allocation and resource demand that result from changing the levels
of given parameters. The level of air pollution is, of course, the para-
meter of major concern in this study. If we regard the estimation of yield
response functions as the first phase in a regional study, the LP model
may be regarded as the second phase in which one determines the primary
economic effects of air pollution at the farm level.
Alternatively, if all data limitations were overcome in estimating
yield response functions, such functions could be embedded in a simultaneous
regional farm level production system. Dynamic multiplier analysis could
then be used (with the system in its reduced form) to examine the impacts
of changes in exogenous variables (such as air pollution) on the endogenous
variables (for example, yields, output, profits) in the system.
An econometric model of a production system could also be used to
simulate alternative outcomes under varying environmental regimes. While
such a model is non-optimizing, it has advantages in that it can generate
the time paths of changes in endogenous variables or monitor outcomes under
alternative settings of decision variables.
In both the LP and econometric approaches, the risk and uncertainty
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inherent in farmers' can be incorporated into the models. The econometric
approach is superior to the LP approach in that jointly determined struc-
tural relationships are estimated rather than predetermined. On the other
hand, LP is an optimizing tool that can be made to be adequately predictive,
and essentially is less demanding in terms of response function requirements.
Third phase of research involves the determination of the secondary
regional effects of air pollution: on agricultural packers and processors,
the transportation sector, employment, consumers, and other sectors inter-
related with agriculture. Either the LP or econometric models of farm level
impacts can used as inputs into such regional models.
Our recommended regional modelling approach is input-output (1-0) ana-
lysis. This is the most widely used methodology that accounts for the
economic interdependence of sectors in a region. For given optimal farm
level adjustments to alternative air pollution levels (for example, as
ascertained in a farm level LP model), the 1-0 model may be used to deter-
mine existing and projected impacts in the entire regional economy. A
dynamic extension of the static 1-0 model may be made in order to make long-
run regional projections. The completely dynamic model is quite complex
and requires the addition of a matrix of capital coefficients. Alternatively *
judgemental assumptions about technological change can be used to make the
model "partially" dynamic.
Another distinct attribute of 1-0 analysis is that the data collection
process necessary to construct a regional transactions table is not as
cumbersome as it once was. A substantial number of regional 1-0 studies
have been completed in California. Consequently, there has been increased
awareness of the need to maintain viable data bases as well as where to
obtain regional data.
A regional spatial programming approach to measure the secondary effects
of air pollution is a viable alternative to 1-0 analysis. In fact, it has
several advantages: it is an optimizing technique; the objective function
may be defined so as to maximize net social payoff; it can account for risk
and uncertainty. These advantages are offset by a substantially greater
and more difficult data collection effort relative to an 1-0 study.
With respect to consumer effects, the indirect impact of physical
factors in agriculture will vary considerably according to the region sel-
ected for a case study. For instance, the effects of ozone on alfalfa
yield in the South Coast Basin are likely to have only minor effects on milk
prices faced by local consumers. On the other hand, physical factors damage
to the lettuce crop in the Salinas Valley would have more significant price
and quality effects - both on local consumers and on consumers in other
areas of the country whom, at times, are completely dependent upon Salinas
Valley lettuce. At the same time, since lettuce expenditures constitute
such a small proportion of the family food budget, there will not be sig-
nificant effects on overall consumer welfare.
8
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SECTION IV
INTRODUCTION
The main objectives of any air pollution control programs are
public health and safety protection and economic loss minimization,
Agricultural crop yield reduction is a main concern in economic loss due
to air pollution.
In assessing the economic impacts of air pollution on crop yield,
reliable yield data and appropriate econometric methodologies are required.
Agricultural crop yield data have mainly been generated by two methods,
field surveys and laboratory experimentation.
Field survey is the most direct way of measuring crop yield in either
a clean environment or in one impacted by physical factors such as air
pollution, weather, pests or poor cultivation. There is one drawback in
the field survey. The data accuracy depends very much on the experiences
of the inspectors. They may or may not be able to separate the effects
of different physical factors on crop yield.
There are difficulties involved with the laboratory approach also.
Differing conditions and extraneous conditions not present in the labora-
tory or poor laboratory work, can invalidate data developed with this
method Also, laboratory results at one concentration or condition are
often linearly extrapolated to other concentrations or conditions. This
induces error if dose-response is non-linear.
It becomes apparent, therefore, that in order to include reliable
crop yield data for economic impact assessment, one has to examine and
define those data in relation to specific conditions or physical factors
under which the data are developed.
The crop yield data are usually transformed statistically into re-
sponse functions. They are expressed in relation to different physical
factors such as weather, soil conditions, and air pollution. The value
of crop loss is then estimated by relating the functions to the total
crop losses associated with different variables.
This is one of the most widely used approaches in the economic assess-
ment of crop yield changes. This approach is direct and simplistic but
not realistic. It does not account for any indirect economic effects such
as labor forces, market behavior, etc. It considers only the economic
impact to the farmer, and ignores the effects on the agriculture industry
as a whole and the consumers.
This study was undertaken with those points discussed above in mind.
It is the intention of this research effort to complete a review and
evaluation of methodologies and techniques used for the quantification of
economic impacts of agricultural crop yield changes brought about by the
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physical effects^of natural and man-made factors, In achieving this ob-
jective, the project was conducted in three phases: (1) information and
data gathering; (2) review relevant information and data; and (3) infor-
mation evaluation. The main body of the report is presented in Sections
V to VII under four categories: (1) physical effects of man-made and
natural factors on agricultural crop yield; (2) farm structure, profit-
ability and risk changes due to agricultural crop yield changes; (3)
secondary economic impacts due to agricultural crop yield changes (4)
overall impacts on consumers. wionyca, \ ;
10
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SECTION V
PHYSICAL EFFECTS OF MAN-MADE AND NATURAL FACTORS
ON AGRICULTURAL CROP YIELD
A. ENVIRONMENT
Plant growth under natural ambient conditions is a complicated process
in which the input of radiant energy is used to convert carbon dioxide and
various elements from the soil into photosynthates. The growth process is
influenced by plant genotype, environmental variables and cultural or
other external parameters, The following section reviews research on the
major environmental factors as they are related to plant growth or yield.
Research carried out out under controlled laboratory conditions is con-
sidered first, and is followed by results from field studies.
"Yield", in agricultural production, is concerned with that part of
a plant or crop which can be marketed as food or otherwise utilized for
some economic gain. This marketable portion may involve almost any plant
part which may be harvested at various stages of maturity. Studies of the
relationship of environmental factors and to crop yield have been an area
of enormous interest (Thompson, 1962; Haun, 1973; Kuchl e£ al_, 1976), but
most investigations are not directly related to economic concerns. Most
experimental results were derived from studies investigated under con-
trolled conditions or artificial environments and in many cases yield was
measured over relatively short time intervals (Thome, 1970). Over the
short term yield may be measured as growth rate or more commonly as photo-
synthetic productivity (Setlik, 1970). Photosynthetic productivity is
determined by measurement of carbon dioxide uptake or by periodic measure-
ment of the dry weight increase of plant parts (Blcakman, 1961).
!• Climate and Weather
Climate represents the overall trend of weather in a region over a
long period of time, and weather refers to the daily fluctuations of
meteorological factors (Whyte, 1960; Evans, 1963). The types of crops
which may be grown in a particular area and the maximum yield attainable
are dependent on climate, but the yearly variation in yield for crops
which are grown frequently is determined primarily by weather variables
(Thompson, 1962; Warren Wilson, 1967; Haun, 1973).
a. Light
_2
Radiation. The radiant flux density averages about 1390 W m on the
irradiated side of the earth's atmosphere. About 75 percent of this ra-
diation may reach the earth's surface on a clear day, and about 25 percent
on a cloudy day. About half of the radiation reaching the earth's surface
is in the visible light, photosynthetically active (0.4-0.7 ym) wave-
length band (Milthorpe and Moorby, 1974). The radiation flux densities
vary with latitude and the time of year.
11
-------
Ph.otp.syn.thet.1c. processes . The primary influence of light (radiation)
on plant growth and yield is through photosynthesis, Photosynthesis
consists of at least three processes which are influenced by climatic
factors (Gaastra, 1962):
(1) a diffusion process in which CCL (carbon dioxide) is transferred from
the external air to the site of^the reaction in chloroplasts. In-
fluenced by temperature.
(2) a photochemical process by which light energy is converted into
chemical energy and the reduction of C00 into carbohydrate. Influ-
enced by light only. *
(3) biochemical processes in which the energy produced by light is used
for the reduction of C0?. Biochemical processes are strongly influ-
enced by temperature.
, Light intensity and photosynthesis. Assuming ample water supply and
nutritional level, photosynthetic rates may be limited by the COz concen-
tration. temperature or available light. Photosynthetic rates of most
plants increase linearly with light intensity until maximal rates are
achieved provided temperature and C0? concentration remains constant.
Further increases in light intensit/then fail to increase the photosyn-
thetic rate. In laboratory studies Bohning and Burnside (1956) found
light saturation intensities of about 2500 foot-candles for several field
3s* J0thers (listed by Chang, 1968) have reported values of 3000 to
4000 and even up to 6000 foot-candles (full sunlight at noon usually
exceeds 10,000 foot-candles) for sugar cane. Hesketh and Baker (1967)
did not find a saturation intensity for corn at irradiances up to 1400
c^l \ +2 lnieKS1t¥ 9reater than f"ll sunlight. Monteith (1965) has
stated that laboratory measurement of photosynthesis in relation to light
intensity, at fixed C02 concentration can be fitted to the curve:
P - U + ^ (0
where P is the rate of photosynthesis (grams carbohydrate per square
meter leaf area per hour), I is light intensity (Langleys/hour) , and a and
b are constants which vary for each plant variety.
h1Mn curve 1n terms of C02 uptake had been de-
by Hesketh (1963) as a rectangular hyperbola of the form:
'1
Ml + K I)' (2)
saturate™ i?nh$2.UPtakVn m9/dm2leaf area/hr, Qmax is the uptake
olant I? }ln iS f"51^' ' V'ntensity and K ifa constant for the
for q'.DPriL^^L n?iey|.iLyl per minute the response fits the curve
for 9 species tested. The fit where I < 0.25 Ly was poor apparently
at
the
12
-------
because of interference from respiratory COo. Qmax could be determined
more easily as the intercept with the equation in the linear form:
Carbon dioxide and photosynthesis. At high light intensities photo-
synthetic rates can be elevated two or three times by increasing the C02
content to about 0.13 percent compared to the normal atmospheric content
of 0.03 percent (Chapman and Loomis, 1953; Gaastra, 1959, 1962; Waggoner,
Moss and Hesketh, 1963).
Within plant communities there are variations in the ambient CO?
content, which depend on the consumption of C02 by the plants, and trie
input through diffusion or air movements (Lemon, I960*, Setlik, 1970),
Tanun and Krysch (1961) found the minimum C02 concentrations within a crop
canopy were between 0.025 and 0.029 percent, and a 0.02 percent minimum
was reported by Chapman et aj_ (1954). The local carbon dioxide deficit
may, therefore, cause a decrease of 10 to 20 percent in the rate of photo-
synthesis (Chang, 1968),
Temperature and photosynthesis. The photosynthatic rates of plants
increase with temperature until maximums are reached. The influence of
temperature on photosynthesis varies greatly with plant species or
variety. Molga (1962) showed there was linear increases in photosyn-
thesis of potato, tomato, and cucumber plants between 10° and 30°C, the
rate being about 5 times as great at the latter temperature. After op-
timal rates at 30°C there was a sharp drop with temperature above 37°C.
Temperature optima near 25° or 30°C are reported to be typical of tem-
perate and tropical plants (Milthorpe and Moorby, 1974), but for some
arctic and alpine plants the optimum may be as low as 15°C (Mooney and
Billings, 1961). In addition to differences among plant species, the
temperature optimum may be influenced by the previous environment of the
plants. For example, when measured at 30°C the photosynthesis of Panicum
coloratum plants grown previously at 20°C could be doubled by subjecting
them to 30°C overnight (Ludlow and Wilson, 1971).
Dry weight increase—Growth chambers. Growth or yield in terms of
dry weight increase have been measured in relation to light intensity
under controlled environment conditions. Such studies are valuable since
the effects of other factors, e.g. temperature, which may be correlated
with light under natural conditions (Warren Wilson, 1967) can be eliminated.
Most of these investigations have used a limited range of light intensities,
only 2 or 3 intensities in many cases (Hussey, 1965; Silsbury, 1971).
Hussey (1965) measured the dry weights of tomato plants grown at 400
and 800 foot-candles. The weights at the latter intensity were about
twice as great as the lower. There was a temperature optimum near 23°C
for both intensities. In barley plants, the log of dry weight was propor-
tional to light intensity up to 60 cal cm-2 (Aspinall and Paleg, 1964).
13
-------
°Utrde exce^ for a Period °f 16 days either 5
°f flower™9- During the 16 days in growth
, t0 light ^tensities of 374 or 740 J cm-2. and
at matur. f h higher lntensity yielded about 15 percent more grain
at maturity than those exposed to lower intensity,
lnht
for rntn
rankim S
co?n <
but
the Mahpc
fall
liaht
light
investigation of light intensity versus growth
'polled conditions was done by Rajan et al (1973).
! ^SL1'08 to,5'4 x ^ Lux "*™ combTned-wlth six
* H ™*? 3? C' NAR (net assimilation rate), LAR (leaf
!? (relative growth rate) response surfaces were shown
Sa nflower» be?n' and corn plants grown in each condition. The
ThaXima reln.^e growth rates (9 g^day-l) were sunflower <
The maximum RGR s were sunflower o!29, corn 0.25, cotton 0.23,
l^^ °f bean was almost ^affected by light intensity
? temperature. RGRs for sunflower and corn increased to
°f ^mperature and light intensity used, but began to
ra?S; .u0t?0n showed a near]y Tinear increase with
except at the lower temperatures.
fll
Black
increase-Field. Two methods have been used In
llght on growth and yield of plants in the field.
' 1S eCedby Sading to all°w ™"oul proportions of
, ng o a°w ™"ou proportons o
the Piant (Blackman and Wilson, 1951; Blackman and
k Se^^ more wide1y used method, an attempt is made
^served variations in growth with the naturally occurring
—a/change
Blackman and Black (1959a) found that when davlioht was reduced by
eSMfol?!TcL^e RGRS ?f sm?™r- alf^fa^latKrus maHt?.M and
e Trifom secie
fhyQO Tv-ifrti.;,,m ,.,, • , --"•'«™<=i, cuidiTa, Latnyrus marmrnum »..
e^tFiS r^n ^sss? sia^ dld'^T^ff^S^'
nsi 'sleJLTn^i±d,!^l 1*t«'' ""tip ""V
In every one of 22 species tested
f ; »-"-- a nspons
Wilson 1954? ?hP«? P^vious history of the plants (Blackman and
those such as ' arl^ll 11^° a dlfferen" between isolated plants and
5 .
Were made at varioUS
the same g MuHipe een9-00"1^6 medsured in plantS
experiments to anaii;! n^ 9^u" lon techniques have also been used in
penments to analyze growth in plants started at frequent intervals
14
-------
Experiments of this type were carried out by Warren Wilson (1967)
with rape, sunflower, and corn grown in an arid climate. The analysis
accounted for 92 to 95 percent of the RGR variation in terms of mean
temperature and radiation. The variation for rape was not influenced by
changes in light level. Hodgson (1967) found 75 to 95 percent of the RGR
variance of sunflower and Vicia faba growing in Scotland could be accounted
for using the leaf area ratio in addition to the light and temperature
variables. Eze (1973) determined correlations in terms of light, temper-
ature and relative humidity for sunflower and bean in Sierra Leone of
West Africa. Fifty-one to 52 percent of variance of RGR was accounted for.
Voldeng e£ a_l_ (1973) included light, mean temperature and in some instan-
ces minimum temperature and accounted for 77 to 89 percent of RGR variation
of corn growing in southern England. Equation for estimating RGR under
the conditions used were included in each of these reports.
Warren Wilson (1967) has pointed out that difficulty may arise in
multiple regression analyses of this kind when the variables are not
independent. Light and temperature, for example, tend to be correlated,
and Brenchley (1920) found r values of about 0.3 to 0.7 for those two
variables. It was suggested that the influence of the correlated variables
should be checked separately in controlled environment studies.
Comparisons of total global radiation for the growing season and
yield have been made for a number of crops. Sibma (1970) determined cor-
relations between the total radiation and yields of potatoes, sugar beets,
peas, wheat, barley, flax and corn in a number of fields in the Netherlands.
The correlations were found for annual yield data obtained over periods of
10 to 22 years for the different crops. An average of 57 percent of
yield was accounted for in terms of the total global radiation in each
growing season. The forage corn dry matter in an experiment in Britain
(Phipps et al, 1975) was closely correlated with solar radiation, about 94
percent of variation being accounted for by the radiation changes.
There are some reports of yield reductions through shading where the
economically important yield is produced at a late stage of development
as with a grain crop. The degree of yield reduction by shading is depen-
dent on the developmental stage in which shading occurs as well as the
amount of light reduction (Evans and Wardlaw, 1976). Shading had least
effect on wheat grain yield when it was given during the vegetative phase
of growth (Fischer, 1975). In this stage, reducing the sunlight by 60
percent caused a yield reduction of less than 5 percent, while a similar
reduction during the reproductive stage caused a yield reduction of up to
35 percent and in the grain filling period about 16 percent. Very similar
effects of shading at different developmental stages of rice were reported
by Yoshida and Parao (Evans and Wardlaw, 1976). Vegetative growth of wheat
was reduced by shading whether or not there was an influence on grain
yteld (Fischer, 1975). Gifford et, al (1973) found grain yield reduction
of barley about equal with shading before or after anthesis. When the
growing season for sugar beets was divided into 3 equal periods, shading
in any one of them caused a reduction in root-size at final harvest
(Watson et, al_, 1972). The dry matter of the root and the sugar content
15
-------
was proportional to the total radiation during the season regardless of
the period in which it was received. Reduction of radiation by 56 percent
reduced the dry matter of roots by about 50 percent.
b. Temperature
General characteristics. Plants have minimum, pptimum, and maximum
temperatures for growth, and these points have been called the cardinal
temperatures. Cardinal temperatures are not precise values (Parker, 1946),
but approximate values have been determined for most crop plants. With
cool-season plants, the minimum is 0° to 5°C (Chang, 1968). It was estab-
lished by Sachs (Went and Sheps, 1969) that cardinal temperatures do not
remain constant during the life of the plant but are different for each
developmental stage. This concept has been studied further and discussed
by Went (1948, 1957) and others (Stanfield et al , 1966; Hartsema, 1961).
Many plants have higher optimal temperaturesTirTthe early stages of growth
as it has been found for peppers (Dorland and Went, 1947), peas (Went, 1957 J
beans (Viglierchio and Went, 1957), and tobacco (Camus and Went, 1952).
_ There is a variable relationship between temperature and growth which
is dependent on the plant species. The general shape of the temperature-
response curve shows a rapid increase in the lower range (0° to 15°C), a
iio??r 1"crease with temperature in the intermediate range (10° to 3QQ or
1957- Erik3 "^ ™^ fallin9 off at hi9he^ temperatures (Went, 1956,
Jne Deported rate of dry weight increase was about 80 percent greater
at 30 than at 20°C in tomato (Abd El Rahman and Bierhuizen, 1959), soy-
bean (Hofstra, 1972), and Tidetromla (Bjorkman et al , 1974). Each of
these was over a linear portion of the response~ciirve. In other instances,
the Qin for the 20° to 30° range was smaller (ca. 1.60) if the plants were
older (Hofstra, 1972) or (ca. 1.27) if 30° was close to the optimum temper-
ature (Bjorkman et al_, 1974). This indicates that the experimentally
determined temperature-growth-response curve may only apply to the plant
used and to similar experimental conditions.
nv**. ^vr P°^itive correlations between vegetative growth and temperature
?nJ n!» JSii r?S?? h?!e £een rec°rded under controlled chamber conditions
1948? AM ? p\19?2; Stanfield etai, 1966), tomato (Calvert, 1964; Went,
Raian £ 1} R?Sl? and /nerhuizen, 1959), cotton, sunflower/bean, corn
IKajan et_aj[, 1973), and other plants.
studi P^nn^u!01^0"/ 1 ?fll Yi Plf1 ' There are relatively few growth chamber
f leld arSnc f f °! ^f"^"™ on the final yields of such crops as
SUr beets ' For studies Wlthin the ^^ rane °f °ut"
side tPmnf ? SU?Ir beets ' For studies Wlthin the ^^ range °f °ut
w th hSK alures> !here may be little ^crease or a small yield decrease
with higher temperatures although this varies with the crop tested.
the vield ofeara?l3± were Put into growth rooms at the flowering stage
tne yield of grain was greater from plants maintained at 150C than at
16
-------
20°C (Thome et^ a]_, 1968). Although the rate of dry weight increase of
vegetative parts was higher at 20°C, the leaves died sooner. This reduced
the leaf area available for photosynthesis and growth of the grain. In
another experiment (Thome e£ al, 1968), grain yield of wheat was higher
in plants exposed during spikeTet initiation to 15°C in the light period
compared with those exposed to 20°C. In this instance, the higher yield
was evidently due to the larger number of grains per ear formed at the
lower temperature. A similar application of higher temperature for 16
days which started up to 3 weeks after anthesis also resulted in lower
yield (Ford and Thorne, 1975). The final yield from sugar beets was
increased by exposure to 6°C higher temperature during the period of
greatest leaf expansion (Thorne et, aj_, 1967).
Heat unit summations. Field studies of temperature effects on plant
growth have been almost entirely confined to the determination of correla-
tions based on the existing natural variations in temperature of the air
and soil. The first of the many attempts to relate plant development to
temperature in a quantitative way was done by Reaumur in the 18th century
(Wang, 1960; Robertson, 1973). He proposed that a plant of a given va-
riety required the same sum of daily mean temperature from planting to
maturity regardless of the temperature variations. Reaumur's scheme has
been modified in the development of the concept of a degree-day summation
rather than a simple temperature summation. As presently used, a degree-
day is the daily temperature in daylight hours above the minimum tempera-
ture needed for growth of the plant. It was later established that there
was closer relationships with the developmental stage of the plant if the
degree-day was multiplied by the average day length (Nuttonson, 1957).
This can be expressed in the form of the equation:
r z (Tm - a) = K
L P
where (Tm - a) = 0/Tm < a
(K) is the photothermal constant, (L) is the average day length during the
growth period, (P) is the date of planting and (M) maturity, (Tm) is daily
mean temperature, and (a) is the minimum temperature for growth of the
plant.
A modification of the degree-day calculation was proposed by Gilmore
and Rogers (1958) which takes into account temperatures above or below
the optimum temperature range for grov/th of corn. Corrections were made
for exposure to temperatures below 50° and above 86°F. The coefficient of
variation of heat units required for corn development was reduced from
3.65 with only a 50° minimum to 1.63 with a 50° minimum and 86° maximum.
The degree-days and heat unit concepts have been criticized as over-
simplifications because they do not consider the fact that (a) plants
respond differently to temperature during different stages of their life
cycles, (b) threshold temperatures may vary under different conditions,
17
-------
and M»Jhore ?«?Ct.S, °f 0^f environmental factors are omitted (Thornthwaite
Ssefuf^r'so'ur960^ " "" C°^^ 9CCUrate en°Ugh t0 be
r3nninn,nHn. has been used with some success in the
1973 Wane iQrn^9 JndUSt7 t°r Potion of crop maturity (Robertson,
to mituH?; }* +°me °f the crops which have b^n evaluated with regard
oeas whiLt f?,SWeS5 C0n\' fie]d corn» tomat°es, snap beans, lettuce,
curv^ r^Hnl and ?9?P]ant (Arno1d* 1959>- A Polynomial regression
davTof oJ™Jh9 dccumulaied temperature to dry weight of corn over 150
et in! 1975)? accounted f°r ^ Percent of the observed variation (Phipps
methodselndC?orm.!lti0f--' kc°;t1nuin9 efforts have been put forth to develop
clan? in tlrl° nf 1S °r 56tter estimating the developmental process of
houHv 3aJ?iE ? temPrature- Ferguson (1958) suggested a method using
tionshiD nf KptS?)eraturesDa!!d takin9 into account the non-linear rela-.
^na |5fL?Lp r.nn ?°nSe< .Robertson ("53) proposed a method for determin-
bJlance TH, ISh ?>peratures which incl^ed a factor for radiation
was,exPa"ded by Newman et al (1967). Haun et al. u
'^6 °'
emperature
estimates of arlthC-n1qU?S/hich are bein9 developed do give improved
providing scienJif^'MnH61'!10!^0 temP^ature. They may be suited to .
SsefulneL ?n £lt Ujd^standln9 to some degree but have little practical
temperStu?; o?hp? Sl!lhthe re
-------
Photosynthesis continues at an undiminished rate with leaf water
potentials of -4 to -8 bars. At lower water potentials, the shape of the
response curves varied with the species tested. Sunflower (Boyer, 1970),
tomato and loblolly pine (Brix, 1962) showed nearly linear decreases, The
slopes for corn and soybeans continued to increase as the water potential
approached -16 to -18 bars (Boyer, 1970). Plants exposed to these low
water potentials do not necessarily show visible symptoms of desiccation
although the photosynthetic rates are 15 percent or less of the rates in
well-watered plants.
Some degree of adaptation to water stress is possible. For example,
when water was withheld from corn plants throughout most of the grain-fill
period, plants which had been grown previously in dry air became desiccated
more slowly and produced a higher yield than plants previously in humid
air (Boyer and McPherson, 1975).
The water potential and appearance of plants may return to normal in
a very short time after they are re-watered following a period of drought.
The rate of photosynthesis, however, may remain depressed for some time
if the desiccation was sufficiently severe. Ashton (1956) reported 2 days
were required for photosynthesis of sugar cane to return to near normal
after drought. Similar effects were noted for apple trees (Schneider and
Childers, 1941) and sunflower (Boyer, 1971).
The growth of leaves can be inhibited by only small degrees of desicca-
tion compared with the amount which reduced photosynthesis (Hsiao, 1973;
Boyer, 1970). For example, the enlargement of leaves was found to be
greatest at -1.5 to -2.0 bars. Enlargement stopped at -4.0 bars in sun-
flower and at about -10 bars in corn (Boyer, 1971). Leaf water potentials,
which attain low values during the day, usually rise again at night to the
level of the soil water potential (Cowan, 1965). Leaf enlargement, there-
fore, may stop during the day in periods of low water supply but growth
may resume at night.
There is some evidence that the response to water stress of plants in
growth chambers may differ from that of plants growing in the field. In
growth chamber studies, the leaf expansion rate decreased from -2 to -4
bars and ceased at -7 to -9 bars (Boyer, 1970; Turner and Begg, 1973;
Watts, 1974). In field grown corn, however, Watts (1974) found moderate
leaf extension rates at -9 bars, although in the growth chamber, leaf
growth of corn stopped completely at -7 bars. Moreover, the data of
Watts (1974) and McCree and Davis (1974) indicated that in the field leaf
expansion rates continued at about the same rate day and night although
leaf water potentials varied from -1 to -7 or -9 bars. The evidence in-
dicates that caution must be used when extrapolating from controlled
environment data to field conditions.
The transpiration - yield relationship. Another way of expressing
the relationship between yield and water is to directly compare the amount
of water transpired with the yield in dry matter. Transpiration is the
19
-------
e??ec
like J or e
explained bv the fart
St°mata of the leav«- * cause-and
?1eld 1s thouSht to be un-
col"relation between the two can be
and trlnspU^were
ship was 1 near Se Si
areas of gh^diation-
fre?water
the formula changed t
and'lre
and other variables
1?63) haVe described studi^ 1" which yield
1n 10 C!i0ps' and in each case the relation-
Pr°P°Sed the f°llowin9 relationship for
M = b W / E
production, I
> a constant,
M = c W
"«ter transpired, E0 is
For areas of
r«l1a1on.
?' b and C are different for each
climatic conditions, nutrient levels,
"*
°btained
experiments with
^ Many field studies have
crease yields (Hscher and Saopn iQ^?P ^T^^3^ that irrigations 1n-
degree of yield rlductlJnJjh'*196?1 Salter and Goode. 1967). The
timing and'dSrat on °t e'd ictt^th ?^ dePends °" the severity,
factors and weather fartnrc T£
on what part o? ^h crop i 'con s
vested (Fischer and Hagen, 1965).
as
v,
sPecies and variety, soil
f ?n°mic ^ield a^so dependS
USeful material to be har-
a development, as with crops such
stress are sinn ao those on JT" ^e?bles. the effects of water
be greater than effects on c^Sp^where ^PiH°f th^ plant and are likely t0
stored in seeds. Hagen (1957) for 11™^ consists of the dry matter
of the soil which reduced green foTaS K ™ " that mo™ture depletion
percent increase in yield of seedf QAI «y S 5ercent resulted in a 10
Turner, 1976) had a 47 percent redictftn V?d!r;on and White (Be" and *
from lack of Irrigation? K?the v eld Of °np ^°tal yie]d °f green pea pla"J
, uut une yield of peas was reduced only 36 percent.
Effects of the timin o ect* Man» ~i ,. u
In their development wTTIchsJeDarlJcul a H ! c P ^S have Certa1n stageS
(Salter and Goode. 1967 in terSs of v ^iy ^"^tive to water deficiency
annual leafy crops such as lett PP J ?1 reduction. In the case of
deficits occur at any time durina ;h^H1d ?eems to be reduced If water
any time during the development of a useable crop (Sale
20
-------
1966; Schwalen and Wharton, 1930; Salter and Goode, 1967). However, this
was not found to be true in every investigation. Veihmeyer and Holland
(1949) felt that irrigation near to harvest was not necessary for lettuce,
and Schwalen and Wharton (1930) reported dry conditions early in the grow-
ing season greatly reduced head weight.
The yield of cereal grains is especially sensitive to water stress at
3 stages of crop development although some aspects of yield development
are not common to all cereals (Slatyer, 1969). The first stage is that of
floral initiation. The second is the stage of anthesis and fertilization,
and the third is the stage of grain filling.
The number of floral primordia of wheat was reduced by 35 percent in
barley plants when water was withheld for 42 days compared to those with
continuous watering (Husain and Aspinall, 1970), and a similar effect was
noted by Nicholls and May (1963) in water stressed barley. In wheat, the
stage found to be most sensitive to water stress is approximately the last
15 days before anthesis. Fischer (1973) found a short period of plant
water stress of -27 bars 10 days before ear emergence reduced grain yield
of wheat almost to zero but has almost no effect on yield 12 days after
ear emergence.
Sorghum is relatively insensitive to drought during floral initiation.
Whiteman and Wilson (1965) subjected sorghum to "severe" stress for one
week at various growth stages and found that inflorescence development
could be suspended during the water stress period but could resume on re-
watering.
Further examples of the influence of timing of water stress on grain
yield are show in a study by Downey (1971). When water stress was allowed
to develop for 20 days during male meiosis in corn, the total dry matter
was reduced by 29 percent, but the grain yield was unaffected. When the
drought was allowed to develop during grain filling, the reduction for
total dry matter was 30 percent, but the reduction of grain yield was 47
percent.
Relating water supply to yield. There have been numerous procedures
developed for the assessing the relationship between water supply and crop
yield Among these are correlations with measured rainfall, soil moisture,
and evapotranspiration (Stanhill, 1973). Usually, the yield response
correlations have not been related solely to water, but have been combined
with other climatic variables such as temperature and radiation.
Total seasonal rainfalls have been correlated with yield with some
success in arid zones, especially with the wheat crop. Cole (1938)
related wheat yield to seasonal precipitation at 19 sites in the Great
Plains area of the Unite States, the period covered was 1906-35 and pre-
cipitation accounted for 36 to 80 percent of the annual yield variation.
There was considerable variation in the constants of the regression equa-
tions for different sites. These ranged from 8.40 kg ha^mm-1 to 4.27,
21
-------
from '14U50 to -530 ^ ha-1, Pengra (1952) related
SUth dk°ta toa1nfa11 which accounted for 37
oerent of HP vi
tion nvpr l5 ^ f' ^l6 and Lehane (1954a> found a *™^*r correla-
t P":oduction in Saskatchewan. The degree of
matterSv?PlH ^^"1 a5proach' Walter <1963) determined that the dry
with rVinf^ii gras!lands ln south-west Africa was closely correlated
with rainfall in _ regions of varying aridity.
curvprn- have been comb^ed with rainfall in multiple
divided rain?aliefninnfm°de1S-. ?°?Son (l962^ used this technique and"
^
1ncluded'
in the^nadfan'nrl^l 1n^onthly periods was correlated with wheat yields
be oredirtpH !Jth ' ^°tal annual Production of the region could
be predicted with an average deviation of 13 percent (Williams, 1969).
'-
capacity to hold and to conduct water (Taylor, 1964).
when theeIate?1iSlntXi PlHnt Srowth is the root zone- A Problem arises
measured One m^t H^ H" ^u^ C0ntent of soil in tne ^ot zone are
or potential at llLt% ^C*!r^ is best« or measu^ water content
.eas'ureme t ma'y "e'nJ cessaV "to alTl 19K61)' °etailed laborato^
of a soil for a oarticu?^ rL N perly cnaracterize the moisture status
and Robertiw 1 68 e coTcluded'S l?61i ^9ley ^^ 1973)" Bal'6r
suitable for quantitative staf 3«??r»i * ^^-term records of soil moisture
relationships are not readily III n^ilTsJigations 1nto crop-soil moisture
developed to try to relate water ulfl Van.°^S ?ther methods have been
1973)/ Some of ^them are diseased L^? yi?ld (Baier' 1973; StanhUl ,
ship between the measured water wtSl «nSP°tranS?1Jat1on-" A relat1T
for some crops. Potential and crop yield has been reported
Canada S^Indtt devel°P*d ™
6 soil moisture zones of the so 1? nroflip Ca^Ulat"d water Callable in
zones was based on standard wMthJJnh' Jhe estlmate of water in these
of daily estimates of SotentlS? «S ob_servatlons and required calculation
knowledge of thr^litSr^ffi^ |^o requlred.some
-del gave better estimates o
22
-------
seasons in Canada than did direct use of correlations with climatic var-
iables (Baier and Robertson, 1968).
The yield of a number of crops (peas, potatoes* sugar beets, alfalfa)
was found by Taylor (1952) to be linearly related to the soil water poten-
tial though there was considerable variation in the data. Bierhuizen
(1961) showed that percentage fresh weight increases of lettuce, spinach,
and radish were very similarly related to soil water potential.
Evapotranspiration. Evaporation from the soil surface and transpira-
tion from leaves of the crop are the two sources of soil water losses
which occur after drainage. However, it is difficult to separate these two
processes in the field measurement, Therefore, the term evapotranspiration
(ET) has been used in studying soil water status to represent the total
water losses by evaporation and transpiration. The maximum ET, measured
when water supply is non-limiting, is called potential ET (PET) (Penman,
1948). Since ET is a function of soil water contents, wind speed, humid-
ity, air temperature and day length, there have been numerous attempts to
relate crop production to ET, with the hope that the process of future
crop yield estimation may be simplified by using ET measurement rather
than by various climatic factors independently.
The relationship between ET and yield in the field may or may not be
linear. Allison et al, (1958) showed a linear relationship between ET
and yield of a number of crops grown in a lysimeter. Staple and Lehane
(1954b) found that the yield was a linear function of ET with spring wheat
grown in the tanks, and a curvilinear function to ET with wheat in the
field plots. The effect on crop yield of changes in ET due to water
moisture contents in the soil varies with various stages of plant growth,
as illustrated by Chang ejt aj[ (1963) in the study of sugar cane yield in
Hawaii. Most crops have critical periods, during which a decrease of ET
reduces economic yield much more than at other periods. Chang (1968,
Table 19) lists moisture sensitive stages for 21 crops.
Methods for estimating PET can be classified into 5 categories: (1)
direct measurement, (2) empirical methods, (3) energy balance calculation,
(4) aerodynamic approach, and (5) use of evaporimeters. A brief discussion
of the usefulness of these methods will be presented.
(1) Direct measurement. Lysimeters are soil tanks designed for grow-
ing crops under field condition, in which water loss can be directly
measured by periodical weighing of the apparatus (Arnon, 1972). Meeting
specific requirements (Chang, 1968), lysimeters are the most dependable
means for direct PET measurement. A specially designed circular tent was
introduced by Decker et_ aj_ (1962) to measure ET from undisturbed plots of
natural vegetation through determination of quantities of water vapor
produced.
(2) Empirical methods. Many empirical formulas relating ET to
meteorological measurements have been developed. The principle assumption
for this method is that there is a direct correlation between crop water
23
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requirements and the meteorological factors. Also, in attempting to
establish a relatively simple formulation for practical use, a minimum
number of factors are used.
The most popular and well-known formulas are: (a) Thornthwaite
formula (Thornthwaite, 1948) expressing PET as an exponential function of
mean monthly air temperature and day length; (b) Blaney-Criddle formula
(Blaney and Griddle, 1962), the most widely used procedure for semi arid
lands of western U.S., in which a crop factor showing seasonal variation
is added to the ET estimation formulation, in addition to air temperature
and day length factors; and (c) Makkink formula (Makkink, 1957), based on
solar radiation measurements weighted according to air temperature, that
is, a greater proportion of the solar radiation is used for ET at higher
air temperature.
The reliability of the empirical methods for PET estimation is greatly
improved when the formulas are calibrated for each specific crop in a
given region (Tanner, 1967).
(3) Energy balance calculation. The energy balance method of cal-
culating PETTsTaled~^nntnTirsTLinipti on that transpiration and evaporation
are both controlled by the same physical factors, and therefore, ET is
considered essentially a physical phenomenon which requires energy supply
(Penman, 1948), A complete energy balance equation may be given as follows:
Qn+H=S+A+ET+C+PS
where Qn = net radiation; H = horizontal divergence of sensible and latent
heat; S = heat flux to the soil; A = heat flux to the air; ET = evapo-
transpiration; C = heat storage in the crop; PS = photosynthesis. This
equation was further simplified to:
Qn = A + ET
by omitting factors S, C, PS because they are minor and negligible, and
by dropping the H for there is no simple way to evaluate this factor.
Penman (1948), based on physical principles, derived a formula com-
bining the energy balance approach and aerodynamic approach. This basic
equation and its further modifications have been tested in various regions
with various crops; such as: alfalfa-brome at Hancock, Wisconsin (Tanner
and Pelton, 1960), perennial ryegrass at Davis, California (Pruitt, 1963),
alfalfa at Gilat, Isreal (Stanhill, 1961). The testings clearly indicated
the widest applicability of this method.
(4) Aerodynamic approach. This approach utilizes various aerodynamic
methods to estimate the rate of water vapor diffusion related to ET
(Thornthwaite and Holzman, 1939). A portable machine analyzer called
"evapotron" was developed (Dyer, 1961) by CSIRO Division of Meteorological
Physics. This approach is found less satisfying by various workers, in-
24
-------
eluding a study conducted in Davis, California (Pruitt, 1963).
(5) Use of evaporimeters. Two types of evaporimeters are being used:
(a) open water evaporation pans, and (b) porous surface type atmometers.
The use of a evaporimeter to estimate ET is based on the similarity between
evaporation and ET. The advantages of using evaporimeters are that they
incorporate the effects of all meteorological factors, therefore, giving
better estimates of short-term ET changes. Also, they can be used to
estimate the ET throughout the life cycle of a crop (since ET rates vary
with the age of a crop) (Chang, 1968). The most commonly used evaporation
pan throughout the U.S. is the U.S. Weather Bureau Class A pan.
In evaluating the practical usefulness of each method mentioned above,
one has to take into account, not only the accuracy of these methods, but
also the convenience in field operation and the cost. Stanhill (1961;
made a comparison of eight methods in Isreal, using a lysimeter as a
standard. The simplest and least expensive method for obtaining a reason-
able accuracy was the evaporating pans.
d. Wind
Plant growth is influenced by wind (Chang, 1968, Yoshino, 1974) in at
least three ways. It may increase transpiration, change C02 intake and
cause mechanical breakage of leaves and branches.
Water loss through transpiration increases up to a certain windspeed
and then levels off (Stafelt, 1932) or decreases slightly (Hesse, 1954;
Fibras, 1931).
The uptake of C02 and photosynthesis may be promoted somewhat by in-
creasing windspeed (Limon, 1963). Deneke (1931) found an increase in
photosynthetic rates with windspeed to 167 cm/sec (3.7 mph) but there was
no further increase with speed.
High velocity winds tend to be harmful to growth and yield (Wilson and
Wadsworth, 1958; Pelton, 1967), but there are variations in response.
Whitehead (1957) gave examples of (1) exposure evaders (flat or low stature),
(2) exposure resistant (barley for example), and (3) exposure sensitive.
Growth, as dry weight increase, in the first two categories was almost un-
affected by high wind speed. In the sensitive plants, growth was inversely
proportional to wind speed and approached zero at 60 m/sec. Wadsworth
(1959) found growth of young rape (Brassica napus) plants was optimal at
winds of 0.3 m/sec. and decreased at higher speeds. Changes in relative
growth rate were small.
2. Soil Factors
The soil is the source of the mineral nutrients required by plants.
The mineral ions occur in the soil in a variety of forms. Some are free
in the soil solution; some are more or less tightly bound to the soil
25
-------
particles, and others are incorporated into the crystalline structure of
some soil minerals.
It was originally suggested by Liebig (Russel, 1950) that the nutrient
ions adsorbed by the colloidal fraction of the soil sere in some way uti-
lized by plants, and the measured contents of ions in the soil complex is
considered an index of the availability of these nutrients to crops (Millar,
1955). Nevertheless, there frequently is only a poor correlation between
the growth of plants and the total content of a particular ion in the soil.
This is because all of the ions in the soil are not readily available to
plants. The degree to which ions are available depends to a great extent
on the soil type. Some of the factors in the soil which affect availabil-
ity are the ease of an ion's being replaced by other ions, the location of
ions in the soil complex, the relative amounts of the different ions ad-
sorbed, the ion exchange capacity, the diffusional ion flux for root ab-
sorption and the mass flow of ions through the soil matrix (Mil thorp and
Moorby, 1974).
The ion exchange capacity of a soil is a characteristic of particular
significance in relation to the influence of soil type on nutrient avail-
ability. Except for saline and highly weathered soils, over 99 percent of
the cations are absorbed and less than 1 percent are in soil solution
(Thompson and Troeh, 1973). This ion exchange capacity of a soil also
represents ion storage capacity which is a significant factor determining
the response of crops to applied fertilizer. In addition, soils with a
high exchange capacity are, in general, fertile and have a long lasting
quality for crop production (Millar et_ al_, 1966).
Phosphate has probably been studied more than other ions in relation
to soil exchange capacities and availability to plants, An example of
some differences which may be found is shown by an experiment of Biddiscombe
% al. U969) in which they applied phosphorous to three Austrailian soils
of different exchange capacities. The amount of phosphorus remaining in
S5iUV°nu ter ec^1lbnu(n r™ged from 0.008 to 2.4 percent of the amount
added However, the soil with the smaller percent phosphorus in solution
had at least a 100 times greater exchange capacity for phosphorus.
i«am „« fT2V\phS-ph°If ab*orbed by barley plants in a medium heavy
loam was found to be directly related to the amount of exchangeable phos-
phorus in the soil (Russel et al, 1961). A similar linear relationship
K±e!; *?' !o7n?hOS?hate ^ Up-take was found for ei^t Plant speclesby
Keay et a]_ (1970). In another instance, the uptake of phosphate by kales
1969) depending on the scnl ^ the* were grown in (Russell and Newbould,
Other characteristics of soil such as particle size, porosity, soil
structure, pH, and organic matter content have importance in determining
yield and suitability for the type of crop which may be grown in an are!
(Arnon, 1972; Thompson and Troeh, 1973).
Soil surveys have been made in many areas of the United States and
26
-------
other parts of the world (U.S. Department of Agriculture, 1957; Dewan and
Famouri, 1964). The data from soil surveys can be used to estimate the
yield potential of a soil (Steele, 1967). If an estimate of the influence
of soil types on the variation in yield of one crop is desired over a
wider area, such as a county, it would be necessary to determine the soil
type under each planting. In addition, one must realize that the actual
yield will also be determined by the combination of interactions among
several different factors of soil, water, and crop management (Raeside,
1962).
3. Biological Factors
Disease and pest injury caused by viruses, bacteria, fungi, nematodes,
parasitic seed plants and insects have long been recognized as important
factors responsible for crop losses (Webster, 1972, Stapley and Gayner,
1969). The entire area of plant pathology is devoted to the study of plant
diseases. Therefore, it is not the intent of this review to cover details
in this area. A brief description of symptoms observed in the host plants,
the extent of crop yield reduction caused by plant pests and diseases, and
principles of pest and disease control will be presented here.
Diseased plants usually undergo various stages of morphological and
physiological changes following the entrance of the disease-causing agents
(Kenaga, 1970). The morphological changes that can easily be observed are:
(1) abnormal host coloration, e.g., chlorosis, mottling, lesions; (2)
wilting; (3) abnormal growth, e.g., overgrowth, dwarfing, replacement of
host tissues by the parasites; (4) abscission of forliage and fruits; and
(5) death, e.gi., pre- and post-emergence damping off, rots.
There are two most commonly used expressions for estimating crop
losses. One is expressed as percentage of potential crop yield, the other
is in terms of monetary value. A survey on the world-wide crop loss an-
nually due to plant diseases was summarized by Cramer (1967). The esti-
mated total yield loss of cereal crops was 506.4 million tons, or 34.1
billion U.S. dollars. Crop losses, due to insect damage, was estimated at
5 to 10 percent of total crop values (4 billion dollars per year) (U.S.
Dept. of Agric.-ARS, 1965). Plant diseases also cause estimated 10 per-
cent (over 3 billion dollars) loss of foodstuff. At about the same time,
crop losses in California, resulting from diseases, were estimated to be
247 million dollars (about 9.6%} with an acreage equivalent loss of about
9,4 percent (California Agric. Expt. Sta., 1965). The estimates of crop
losses, such as those noted above, are not, for the most part, based on
investigation and measurement. Most of them are based on surveys of
opinions of persons working in the various crop areas (California Agric.
Expt. Sta., 1965). It would, therefore, be difficult to assess the ac-
curacy of this kind of report or to use the data in conjunction with
estimates of losses from other sources.
Extensive research in the area of plant pests and disease control
have greatly reduced both quantitative and qualitative losses. Methods
of controlling pests and diseases can be categorized into two groups'
27
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(1) cultural practices and biological control. Sons control methods that
are included in this group are: use of resistant varieties, eradication of
diseased plants, clean culture, crop rotation, use of pest predators for
pest control; (2) legal control. This includes quarantine and chemical
control (Hughes and Metcalfe, 1972; Pfadt, 1971; Webster, 1972, Kenaga,
1970).
4. Summary
The plant growth and yield modifying effects of the following factors
were reviewed: (1) light, (2) temperature, (3) water, and (4) wind. Some
consideration was given to the effects of the soil and biological factors.
Visible light from the sun is used in photosynthesis and is the source
of all the energy used by plants for growth and agricultural production.
Many of the basic relationships between light and plant growth have been
found in controlled environment studies where light is independently
varied and other factors are held constant (Thorne, 1970). Photosynthesis
of single leaves generally increases linearly with low light intensity
but falls off and becomes constant at high intensity. The rate of growth
and dry matter production of whole plants is more or less proportional to
the light received (Phipps et_ al_, 1975; Watson et al, 1972) or to the log
of light intensity (Backman and Wilson, 1951).
Decreases in the intensity of light, reaching crops in the field, are
mediated primarily by the degree of cloud cover. Variations in crop yield
have been observed to result from variations in the amount of light re-
ceived (Sibma, 1970; Watson et al . 1972). In some crops, certain stages
?Fischer°P1975)are m<>re Sens1t1ve to deficiencies in light intensity
h** The.rate °f 9rowth increases approximately linearly with temperature
between temperatures of about 5° to 30°C for temperate season crops. Growth
nf°?loa! ao?nr 5°!; a?d the rate usually decreases rapidly above an optimum
of oLer^nviLm"" "™ Pl*nt ^™> ^ ™* 1nflueflCe
ment inVhf ^if-^5 !nS *he f fect of temperature growth or develop-
ment in the field is related to the sum of degree-days. A degree-day is
the temperature above the minimum and below the optimum for growth in any
t1?i vietd (tnIiHe9iQrQda^.may be closely related to maturity or vegeta-
arowth alri IP™ ! J ^l' Phlpps &&> 1975>« The second method relates
other variablT HUnhiby r.**r***i™ analysis usually in conjunction with
/Ph?n« «f9 y ^?lficant Delations have been found in some
(Phipps et^al_, 1975; Haun, 1973).
suDOea «Tpo f 6 controlled by the available water
Sescr thi, Jpil^ ner».197/)' Some success has been had in attempts to
able waLr l\ rl}^l^^T yield Prediction by measuring the avail-
Robertson ?U\ f H (Williams, 1969), estimated soil moisture (Bair and
Robertson, 1968) and evapotranspi ration (Staple and Lehane, 1954b . Water
28
-------
potential has been used to estimate water availability in the laboratory
(Boyer and McPherson, 1975), but is not useful for yield estimation,
The yield of crops is approximately proportional to the amount of
water used by the crop (Arkley, 1963; Staple and Lehane, 1954b), although
excessive water or periods of drought (Ashton, 1956) can cause temporary
disruptions.
Individual crops have different water needs, and many crops have one
or more developmental stages with particular sensitivity to water deficit,
e.g., 14 days before flowering in wheat (Fischer, 1973; Salter and Goode,
1967). In crops where the economic yield consists of seed or grain, there
is often greater resistance to water shortage than in crops where the pro-
duction of leaves is important (Begg and Turner, 1976).
Plant growth is promoted by low velocity air movements (Wadsv/orth,
1959), but high velocity causes deleterious effects (Whitehead, 1957).
The effects of wind have been little studied except in relation to wind-
breaks (Pelton, 1967).
Soils influence plant growth by limiting the availability of nutrient
ions because of the location of the ions in the soil complex, the relative
amounts of the different ions adsorbed, the soil ion exchange capacity,
the diffusional ion flux and the mass flow of ions in the soil matrix
(Milthorpe and Moorby, 1974).
Crop losses from biological factors, i.e., plant diseases, parasitic
plants and insects, were recently estimated to equal about 10 percent of
the crop (U.S. Dept. Agric. ARS, 1965). The estimates were based on
surveys of various workers in the field.
29
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B, AIR POLLUTION
The effects of the air pollutants on living systems have long been
known as an important threat to the natural ecosystem. Much of the con-
cern about pollutants stems from the resulting injuries to vegetation,
especially to agricultural crops. Unlike the meteorological, soil, and
biologicalfactors, air pollution is almost exclusively generated by men
and their activities. The recognition of the sources of pollutants and
their influences on the biosystem should therefore lead to the active pur-
suit of control standards and measures.
Although various definitions for air pollution exist, pollutants are
generally considered as substances which, added in sufficient concentra-
tions, produce a measurable effect on man, other animals, vegetation, or
materials. Therefore, air pollutants may include almost any natural or
artificial composition of matter capable of being airborne (Chambers,
1968).
Field surveys of air pollution injury on California agricultural
crops have given an indication of the extent of the problem. Surveys
suffer from the lack of a quantitative method of assessing losses. Most
rely on subjective estimates from surveyors. The success of such surveys
are therefore directly related to the competence of the surveyor. The
first statewide survey (Middleton and Paulus, 1956; Middleton, 1961)
estimated an 8 million dollar loss from smog damage. Another survey was
taken in 1970 (Mill lean, 1971). Millican listed six pollutants, each with
its percentage of the total observed plant injury: ozone (03) 50%,
peroxyacyl nitrates (PANs) 18%, fluorides 15%, ethylene 14%, sulfur dioxide
(S02) 2%, and particulates 1%. 03 and PANs were most prevelent in the
South Coast Air Basin. Fluoride is normally localized since it is normally
emitted from stationary industrial sources. The amount of agricultural
acreage located near fluoride producing industries is small. Ethylene
injury is mainly associated with the cut-flower trade since it is generated
from ventless or rusted heaters in heated glasshouses. S09 is also local-
ized as it is normally emitted from stationary sources. Its emissions
can be reduced through corrective measures of SOo-discharging industrial
plants. There has been only a single reported case (at El Dorado Co.) of
lime parti cul ate damage in this survey.
,«™ T!le most recent California survey on air pollution crop losses from
1970 through 1974 (Millican, 1976) shows an upward trend in economic losses
(from 16.1 million dollars in 1970 to 55.1 million dollars in 1974). This
trend is not necessarily correlated with increases in air pollution levels
(for example, increases in planted acreage and crop value contribute to
the increased loss estimate in 1973), but are more closely related to in-
flated market prices, an increasing inventory of susceptible crops and
better methods of evaluating the effects of air pollution.
0nw-in,u of plants to a1r Pollutants and their interacting
environmental factors have been extensively covered in recent reviews
30
-------
and Kozlowski, ed. 1975; Naegele, ed. 1973; Jacobson and Hill, eds.
1970; Taylor, 1974; Heck. 1968), only a general discussion is presented
here.
1. Symptoms of Injury
Plant responses to air pollutants can be generally classified into
three types: (1) visible injury symptoms, which are observed most dis-
tinctively on leaves. Normally these symptoms are observed as tissue
collapse with necrotic patterns, chlorosis or other color changes, pre-
mature abscission; (2) growth responses, such as reductions in biomass,
quantity of the crop yield; and (3) quality changes, such as, changes in
nutritional content, color, texture, flavor, etc. of the product.
One of the most complete descriptions of visible air pollution symp-
tomology can be found in a pictorial atlas by Jacobson and Hill (1970).
The visible symptoms of acute foliar injury are somewhat specific for a
given pollutant. The severity of injury varies from species to species,
and depends on physiological leaf age, water status, and other interact-
ing factors. Chronic injuries, associated with long-term or intermittent
exposure to lower concentrations of pollutant, are less specific and often
resemble symptoms of other environmental stress, senescence, insect and
disease problems or nutritional imbalance. Visible symptoms of acute
injury have been the principle means of identifying the effect of air pol-
lutants on plants and in estimating pollutant effects on crop yield
(Millican, 1971). However, pollutants may cause quantitative and/or
qualitative changes in crop growth and eventual yield without any visible
foliar injury (Heck, 1976).
a. Ozone
Ozone injury was first observed as stippling on grape leaves (Richards
et al, 1958) and flecking on tobacco leaves (Heggestad and Middleton,
1959J. Necrotic lesions were visible on the upper leaf surface as either
red-brown pigmented stiple or bleached flecking. This pigmentation occurs
in the mesophyll layers beneath the upper epidermis as a result of plas-
molysis and eventual disintegration of palisade cells. Prolonged exposure
or exposure to high concentrations of ozone extend the injury from pali-
sade to spongy cells, producing bifacial necrosis. Chlorosis (Taylor ie_t
al, 1960) and pre-mature senescence (Engle and Gabelman, 1967) are commonly
observed chronic injury symptoms. Small -lesions may also coalese to form
necrotic blotches (Heggestad and Middleton, 1959; Jacobson and Hill, 1970).
Injury to conifers appears as tip burn (brown necrotic tips) with no clear
separation between brown and green tissue. Chronic Oo exposure causes
chlorotic mottle, terminal die-back and abscission (cnlorotic decline)
(Miller jtjil, 1963).
The tip of the youngest leaves and the whole of the oldest leaves
tend to be more susceptible to 03. Reports have indicated that leaves
ranging from about 65 to 95$ of their matured size are most sensitive to
31
-------
03 (Ting and Dugger, 1968). Mature plants in general are more resistant
than young plants (Jacobson and Hill, 1970),
Reduced growth of some forest tree seedlings was reported after
prolonged exposure to low concentrations of 03 (Jensen, 1973). Growth
and subsequent yield associated with 0s damage are reported to signif-
icantly reduced in sweet corn (Heagle et_ a]_, 1972; Oshima, 1972), radish
(Tingey et_ aj_, 1971) and tomato (Oshima et_ al_, 1975). A yield reduction
of as much as 50 percent was reported for citrus (Thompson and Taylor,
1969) and for potato (Heggestad, 1973). Crop composition was also reported
to be altered by ozone (Pippen et_ al_, 1975),
b. Peroxyacyl Nitrates and Nitrogen Oxides
Peroxyacyl nitrates are the best known of a group of compounds which
result from photochemical reaction between nitrogen oxides and reactive
hydrocarbons in the atmosphere. Peroxyacetyl nitrate (PAN) is the most
abundant of this group and is responsible for serious plant injury in
many polluted areas (Taylor, 1969). Another two members of the PANs
group are peroxypropionyl nitrate (PPN) and peroxybutyryl nitrate (PBN).
Although PPN and PBN are only found in trace amounts in heavily polluted
they are several times more Phytotoxic than PAN (Jacobson and Hill,
The injury induced by PAN varies with plant species, from a glistening
appearance of the leaf under-surf ace to complete necrosis, In dicotyledon
leaves, silvering", "bronzing", "brown-black motting" may be found. In-
jury in monocotyledon leaves generally appears as transverse banding. The
™ ^entiation and maturity
sublectedorMnn ™ tomato ™* b**n Plants
Hill! 1970)? Pr°longed exP°su^ of low concentrations of PAN (Jacobson and
rCessesnai of co"^stion and certain indus-
C. Fluorides
uonde are the main forms
32
-------
cause plant injury because they are readily absorbed by plants. Fluoride
accumulation over a long period of exposure also results in visual injury
(Jacobson and Hill, 1970),
Acute fluoride injury in broad-leaved plants usually appears along
the margins and tips of leaves as reddish-brown dying necrotic tissue
(DeOng, 1946). In some leaves, the necrotic tissue may fall off, leaving
a chewed appearance to the leaves. Occasionally streaking or spotting may
occur. In monocotyledons, the necrotic area is at or near the blade tip,
with clear darker banding separating tissue killed in succeeding exposure.
Some may have intercostal streaking (Hitchcock et al, 1962). Fluoride
accumulation in conifers results in brown or redUisF-brown necrosis, be-
ginning at the tips of needles and progressing toward the base. Chronic
fluoride injury in general appears as loss of chlorophyll, resulting in a
chlorotic or mottled pattern on the affected leaves (McCune, 1969).
It is interesting to note that the more resistant species or variety
usually accumulates the most fluoride (McCune, 1969). In maize, plants
that have past the elongation stage of development are most susceptible
to injury and the degree of injury increases with the age of.the leaves
(Hitchcock ejt £l_» 1963).
Significant growth and yield reduction was reported in injured plants
(Hitchcock et_aj_i 1963). At very low HF concentration, the growth and
vigor of young navel orange trees were greatly reduced even though easily
distinguishable visible symptoms were absent (Brewer e£ _al_, 1960).
d. Sulfur Dioxide
Injury induced by S02 is the consequence of the conversion of S02 to
sulfite and sulfate upon entry. The severity of injury depends on the
rate of their accumulation and species tolerance. Sulfite is much more
toxic than sulfate because of its reducing potential.
The leaf injury usually is initiated in the spongy mesophyll cells.
Palisade cells are then affected. Acute injury in broad-leaved plants is
characterized by initial dark-green, water soaked discoloration and, upon
drying, bleached or pigmented marginal and intercostal necrosis (Linzon,
1965). The necrotic areas may fall out after a period of time. In mono-
cotyledon species, necrotic streaks developed from near the tips and ex-
tended towards the base of the blades. Injury at the bend of the long
leaf blade is most severe. The injury in conifers appears as brown necro-
tic tips of the needle, sometimes with a banded appearance as a result of
a series of injurious exposures. Chronic injury in general resembles
senescence (Jacobson and Hill, 1970; Taylor, 1973).
Fully expanded young leaves are first to show injury, while less
mature expanding leaves are least affected (Jacobson and Hill, 1970).
Plant growth suppression by SOg has been reported. In alfalfa,
Thomas and Hill (1937) demonstrated a reduction in carbon dioxide assim-
33
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llatlon induced by S02. Cotton yield in terms of number of bolls was aUn
shown to be reduced by SO? (Brislev et al IQRcn r™,,L 5 Ol s was also
tlon by S02 «as also
e- Ethyl ene and other Phytotoxic Pollutants
dental spillage. Heavy metals and industrial
very;arelrause extensive injury
o
similar collapsed type injury in cottSn f Sn .1^6?^ al * 1956)» and
lily (Rhoads et al / 1973) were r^porteS PhL^-'-1957 and in easter
portance, andTsThe consequence^? thp'n^ K ° V* 1s of more im-
ethylene. This takes ?he ?orm " retardat?! r9Ulat!n9 act1on of
^ marginal and inter-
tip necrosis of the needles Is thpSiSnh leaf plants< In conifers,
and Lacasse, 1969). he °"ly obse^ed symptom of injury (Means
tissue Old and middle-aged leaves
Abscission of leavls
dPd
of the leaf
appearance and may stay
concentrations of ammonia
6aVSS my Show a cooked green
«S.1"SSatArer-t,l^..^nganese, zinc, nickel
roads> has ' s °?a^ ffi
° "-"t-kllntot. on
.
e
of
34
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the high pH of the dust-water mixture (Lerman and Darley, 1975).
2. Factors Affecting the Expression of Pollutant Damage to Plants
Plant sensitivity and the severity of injury produced by a pollutant
is determined not only by concentration and duration of exposure, but also
by environmental variables and biological factors.
a. Time - Concentration. Air pollution injury is a function of both
pollutant concentration and time (Heck, 1968). However, the time-concen-
tration (dose) parameter must be carefully utilized in describing exposures
since equal doses may not produce an equal plant response. Plants normally
have a greater response to higher concentrations and short exposure than
to an equal dose of low concentration and long exposure periods. A time-
concentration ozone reponse surface (Heck et_ a]_, 1966) and a model (Heck
and Tingey, 1971) to predict acute foliar injury have been developed for
some plant species. In a recent review, Heck (1976) lists time, concen-
tration, injury-response equations calculated from this model for 19 types
of plants which are divided according to 03 susceptibility into sensitive,
intermediate and resistant groups.
Multiple exposure is another area in which equal doses may not give
equal responses. Studies on 63 injuries have reported that, for a given
dose, a greater plant response was el cited in a single continuous expo-
sure than to two or more separated exposures of equal exposure time (Heck,
1968). Greater injury was found in pinto bean and tobacco subjected to
continuous exposure than when the exposure was split into two time periods
(Heck and Dunning, 1967).
b. Environmental Factors
Light. Three aspects of light: photoperiod, light quality and light
intensity will be considered in this section.
Photoperiod. Plant sensitivity to photochemical air pollutants has
been reported to be influenced by photoperiod. Reports indicate that
plants were more sensitive to ambient oxidants and 03 when grown under an
8-hour photoperiod than either a 12-hour or a 16-hour regime (Heck and
Dunning, 1967; Juhren et al, 1957; Macdowal, 1965). The effect of photo-
period is particularly striking in relationship to PAN. Light is required
before, during and after exposure for the development of PAN injury
(Taylor et al, 1961). This photo-dependent relationship of bean and PAN
injury was described in detail by Taylor (1969). Light affects 03 plant
sensitivity to a lesser degree. Ting and Dugger (1968) reported that
cotton plants were no longer sensitive to 03 after a 24 hours dark treat-
ment. Longer pre-dark period (48 hours) was needed for 0$ protection in
pinto bean and petunia (Taylor et al.» 1961). With Virginia pine, however,
24 hours in the light prior to 03 exposure protected seedling trees from
injury while plants that were kept in darkness for up to 95 hours suffered
injury (Davis and Wood, 1973). Pots exposure light was also found to
affect the 03 sensitivity. Extended dark periods following 03 exposure
35
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delayed the development of symptoms in Virginia pine, until plants were
placed in the light (Davis and Wood, 1973).
Light period-pollutant relationships appear to be sepcies specific.
The mechanism of this relationship has not been identified and it remains
an area requiring further study. Carbohydrate level within the leaves has
been correlated with sensitivity (Dugger et_ al_, 1962). Other possibili-
ties such as stomatal interference have been discussed but no conclusion
is yet available.
Light intensity. Taylor ejt aj_ (1961) found in the pinto bean and
petunia that sensitivity to PAN was increased by high light intensity
(21.5 Klux) before PAN exposure, while the sensitivity to 03 was increased
by low light intensity (8.5 Klux) before 03 exposure. Generally, plants
are more sensitive to 63 when grown at lower light intensities (Ting and
Dugger, 1968; Dunning and Heck, 1973; Shinohara et al_, 1974; Heck and
Dunning, 1967). An exception was Bel-W tobacco "(Heck, 1976).
Sensitivity to 63, as light intensity changes during exposure, gen-
erally increases with increasing intensity. This was reported for tobacco
(Heck, 1976) and pinto bean (Dunning and Heck, 1973) but the effect of
light intensity (prior to and during exposure) on 03 sensitivity was com-
plicated by the interaction of relative humidity.
Light quality. The action spectrum of PAN injury to bean plants was
studied by Dugger et al_ (1963). Maximal injury was observed at 420 nm and
480 nm, and less thTn half that at 640 nm. The sensitive spectral ranges
closely resemble absorption spectrum of carotenoid. Shinohara et_ al_ (1974),
working with tobacco, found that the 03 injury was at its maximum under red
light, followed by green, blue and far-red lights in decreasing order of
sensitivity.
Temperature. The temperatures in which plants are grown, exposed and
kept after exposure, are closely related to plant susceptibility to pol-
lutant injury.
The plant susceptibility is influenced by day/night growth tempera-
tures but appears to be species dependent. Macdowall (1965) reported that
tobacco grown under a low day (210C) and high night (32°C) temperature was
more susceptible to 03. Ozone susceptibility in Poa annua was greatest
with 26°C day/17oc night temperature (Juhren ejt aT7~19S7). Again, no
general trend exists as pollutant susceptibility varies with species
(Heck, 1976).
Using three tobacco cultivars in Japan, Shinohara et al (1973) re-
ported interactions between 03 sensitivity, growth temperature, and post-
exposure temperature. Plants grown at 23°C were more sensitive than at
13bC. Night temperatures had a greater effect on sensitivity than day
temperatures. High post-exposure temperatures accelerated symptom develop-
ment but low post-exposure temperatures rendered more severe injury. While
low post-exposure temperatures caused increased sensitivity in tobacco and
radish, the reverse is true for Virginia pine (Davis and Wood, 1973) and
36
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white ash (Heck, 1976).
The relationship between sensitivity and exposure temperature has
been the subject of many studies. This relationship also seems to be
variety or species dependent (Taylor, 1973; Heck, 1976). Contradictory
data cloud a clear defination of this relationship. For example, in pinto
beans, Heck et al_ (1965) found that increasing exposure temperature causes
decreased foTTar injury. Dunning et_ aj_ (1974), on the other hand, indi-
cated that increasing exposure temperature decreased foliar injury.
Relative humidity. Many of the studies on interactions of growth,
humidity, exposure humidity and post-exposure humidity are summarized in
a recent review by Heck (1976). In general, there appears to be a posi-
tive correlation between susceptibility to 03 and increasing relative
humidity. Tobacco and pinto bean plants were always more sensitive to 03
when grown at 75% relative humidity (Heck, 1976).
Exposure humidity appears to have a similar relationship. This is
illustrated with Virginia pine (Davis and Wood, 1973), pinto bean and
Bel-W3 tobacco (Otto and Daines, 1969). The exposure humidity also inter-
acted with pre-exposure humidity (Dunning and Heck, 1973; Heck, 1976).
Many of the studies involving relative humidity have utilized values
at extreme ranges. The definition of relative humidity-dose responses in
plants has not been worked out within the realistic ranges normally en-
countered in ambient situations. Moreover, these studies were short-term
in duration without adequate statistical designs.
There is no conclusive experimental evidence that relative humidity
significantly affects susceptibility of plants to PAN, according to
Taylor (1974) as long as conditions are such that the stomata remain open.
However, little work has been done in this area.
Soil factors
Soil moisture. Soil moisture status prior to exposure is probably
the leaYt" controversial factor that affects the susceptibility of plants
to pollutants. Adequate soil moisture is essential to maintain maximum
susceptibility. Tomato (Khatami an et a]_, 1973), pinto bean and tobacco
(Seidman et al. 1965; Macdowall, 1965) subjected to water stress prior to
exposure w?rF~found to be protected from 03 injury. Similar findings were
reported for beans and tobacco in response to 03 and PAN. Observations of
stomatal function showed that 03 induced rapid stomatal c osure in water
stressed plants, while the closure in plants under optimal water availa-
bility was slow (Rich and Turner, 1972). Excessive soil moisture for an
extended period of time may reduce susceptibility to 03 due to impared
root function under oxygen deficiency (Stolzy et aj_» 1961J-
Soil type Plants grown in heavy clay soils were less susceptible to
0? than plants grown in vermiculite; similarly, plants grown in clay
loam were less susceptible than plants in peat-perlite mix (Seidman et. aj_,
37
-------
1965; Heck and Dunning, 1967). Low oxygen tension was suggested to be
one of the reasons for reduced sensitivity. Stolzy et al (1961) reported
that the supply of oxygen to plant roots influenced tKe susceptibility of
plants to oxidants. Plants growing in soils with an oxygen diffusion rate
of 16 to 24 x 10-yg.cm-2.min-l were completely protected from PAN and 03
injuries, whereas at 34 to 90 x 10-8g.cm-2.min-l, plants were moderately
to severely injured by both PAN and 03. This and a later study by Stolzy
et al_, (1964) on the root zone oxygen reduction in relation to apparent
photosvnthetic rate, carbohydrate concentration and susceptibility to 03,
indicate that for plants subjected to low root oxygen supply, the resulting
accumulation of leaf carbohydrates rendered the plant protection from CU
injury. °
Nutrition
. Sa1inity_. Salinity (use of multiple strength of macronutrients) and
moisture stress (by application of vacuum) were found to increase the
resistance of sunflower plants to oxidant injury (Oertli, 1959). Yield
reduction caused by 03 was reported. It was found, that under high sa-
linity, there was a smaller loss of bean pod yield from Oo than with no
salinity (Hoffmann et al_, 1973). However, high salinity itself greatly
HnfSfSS P°? Pi°dl/fnISx *hether or not °3 was present, 'in a recent report,
Hoffmann et al.. (1975) found that -200 R>a (kilopascals) gave alfalfa
protection from 03 with no effect of salinity on biomass production. There
ipaf'rinn866"18 possibl* that salinity might increase production of some
leaf crops grown in polluted areas.
to Do,,chi+. that were studied 1n their relation
et al nS rS i Jl1^? "l^™ has rece1ved most attention. Leone
etai_ J1966J reported that in tobacco, nitrogen concentration that is
s'e sit v ?; Ttlo-^T 2?° and 5'° ^ni^eTm im fo
Ormrod et l\ Aw\*}*™\* nutritional nitrogen (ca. 60 and 300 ing/D
StuE%(d?J ip?lh! 3emonstra^d that higher nitrogen caused greater
tud ph cuse
reported nfemna Trll^ i^f ^te^°3 treatment. Similar results were
Sowall (IS n M : lml Conflicting results were reported by
by both def ciencv (0 i N} eHshowed ^at ^3 susceptibility was enhanced
was l-emed> °f so11 nutr1ents other than nitrogen
S""- 1.ntet-act1ons bet«en these nutrients.
-.v,,,.^ v'-iaiser, la/jj. In these, po-
phosphorus concentrations while at high
et_ a]_, 1972). Increasing zinc v/as
38
-------
found to correlate with increased 03 injury in pinto bean (Mcllveen et_ a_l_,
1975). Lemna plants growing on a nutrient medium lacking copper had sig-
nificantly less 03 injury than plants grown on a complete nutrient media
(Craker, 1971). In this same study, Craker found no difference in Oo
response with plants grown in nutrient solution varying from one-tenth to
half strength. This suggested that with balanced nutrient supply, plants
may respond fairly uniformly to oxidant.
Modification of fluorine toxicity in tomato plants by altering nitro-
gen, calcium and phosphorus nutrition was reported by Brennan et al (1950).
A deficient supply of these nutrients aided in preventing the aFsorption
of a toxic amount of fluoride through roots or from fumigation.
Deficiency in either nitrogen or sulfur nutrition was found to de-
crease S02 susceptibility in tobacco and tomato (Leone and Brennan, 1972).
An overabundance of nitrogen and sulfur tend to decrease and increase
susceptibility, respectively.
Genetic factors. Air pollution susceptibility is known to vary among
species, varieties and individuals. Breeding new air-pollutant resistant
varieties has been carried out on a limited scale to reduce adverse
effects of air pollutants.
A list of crop, ornamental, and forest species, in which variation
in sensitivity to various pollutants has been observed, was given by Ryder
(1973). Lists of species susceptibilities to 0? and of cultivars responses
to oxidants, 03 and PAN were given by Heck (1976).
Pathogen interaction. A summarized review by Manning (1975) on the
interaction between the effects of air pollutants and plant associated
fungi, bacteria, and viruses provided information in this sphere of re-
search. Plants that are injured by 03 appear to be more susceptible to
invasion by facultative parasitic and saprophytic fungi, while the 03-
injured host tissues tend to retard obligate parasitium by fungi. Ozone-
injured leaves of potato (Manning et a]_, 1969) and geranium (Manning et aj[,
1970) were reported as more susceptible to Botrytis infection than non-
injured leaves. Experiments with obligate parasites showed fewer infec-
tions by urediospores, decreased hyphal growth, and uridiospore production
by wheat stem rust fungus, when plants were exposed to 03 (Heagle and Key,
1973a).
Plant responses to oxidants in the presence of pathogens were also
studied. Yarwood and Middleton (1954) first observed that rust-infected
bean and sunflower leaves were less injured by Los Angeles Basin smog than
were healthy leaves. Generally, pathogen invaded leaves are less suscep-
tible to 0/injury. This was illustrated in rust-infected wheat (Heagle
and Key 1973b) and in Botrytis infected broad bean (Magdycz and Manning,
1973). It was suggested that the apparent protection may be due to some
diffusible substance emanating from the point of infection Pinto bean
leaves infected by common mosaic virus were also reported less sensitive
to 03 injury (Davis and Smith, 1974). Kerr and Reinert (1968) found that
39
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red kidney bean leaf areas infected by Pseudomonas are protected from 03 in-
jury.
In connection to the above discussion, it is interesting to note that
fungicide benomyl was shown to reduce Oo injury in bean cultivars (Manning
et.al_, 1974).
Field observations showed that leaf and needle diseases decrease in
incidence near the source of sulfur dioxide. Sulfur dioxide was reported
to decrease the incidence and severity of bean rust and also affect the
size and percentage germination of uridospores (Weinstein et al , 1975). Ac-
cumulations of hydrogen fluoride above the field level were"~foUhd to decrease
disease in bean and tomato (Manning, 1975).
Pollutant combinations. Combinations of two or more pollutants are
commonly monitored in a polluted atmosphere. Menser and Heggestad (1966)
first reported the synergistic response of tobacco plants to combination of
S02 and 03. To date, a great portion of studies on plant responses to mix-
tures of pollutants is of S02 and 03 combinations.
SQ2 and (h. Menser and Heggestad (1966) first noted that mixtures of
ih and S&2 caused foliar injury to tobacco at concentrations which were non-
phytotoxic when fumigated singlely. Ozone and SO? synergism was also reported
^iNeas^ern whit? pine
-------
In field studies on native desert vegetation, Hill et al (1974) did
not find synergism of plant injury in plants treated with NOy and S02 com-
binations. Studies by Skelly et al_ (1972) of eastern white pine located
near a source of oxides of nitrogen and SOg were also non-conclusive of
the interaction of pollutant combination,
Fluoride and S02. Studying the influence of a sulfur dioxide and
hydrogen fluoride combination on the growth and development of citrus,
Matsuchima and Brewer (1972) reported an additive effect of HF and S02 in
Keothen sweet orange and no significant difference in linear growth in
HF and SO? applied singlely or combined. Mandl et. a^ (1975) found that
growth of barley, corn, and bean shoots were also not affected by HF and/
or SO? treatments. However, they reported that at low S02,concentrations
(0.06 to 0.08 ppm), foliar response of barley and corn was accentuated by
the combination of S02 and HF.
Cultural practices. The severity of air pollution injury and damage
to agricultural crops can be reduced by proper cultural practices. The
understanding of the various factors discussed in this section of pollutant
interaction (Section B.2.), namely meteorological, edaphic, genetic and
other factors can be applied in practices which change the susceptibility
of crops A review by Ormrod and Adidipe (1974) presented suggestions in
this regard. Cultural practices that can change pollutant susceptibility
are- application of fertilizer, pesticide, herbicide and other chemicals,
irrigation, selection of resistant cultivars as well as resistant crops,
and planting schedules.
3. Summary.
Plant injury has been attributed to a number of different air pollu-
tants, most notably ozone, peroxyacyl nitrates (PANs). fluoride, ethylene,
sulfur dioxide, and particulates. The photochemical oxidants (ozone and
PANs) are more widespread. The other pollutants are usually from industrial
sources and effects are more localized.
Plant responses to air pollutants may be: (1) visible injury systems,
(2) growth responses, and (3) metabolic changes, with resultant differences
in nutrition, flavor, etc. The symptoms of aSute.1"Ju^h2y be character-
istic for a specific pollutant but may be produced by other agents. In
acute injury, necrotic patterns on leaves result from collapse and death
of cells. Chronic injury is associated with chlorosis or other color
changes which may eventually result in leaf necrosis or abscission and is
less characteristic for the toxic agent.
Ambient oxidants in some areas of the United States do clearly cause
growth and yield reductions in some agricultural crops Reported yields
in nonfiltered field chambers were reduced compared with those in filtered
chambers by up to 50 percent for citrus, potato, tobacco and soybean, up
to 60 percent for grape and up to 29 percent for cotton.
Plant responses to air pollutants are subject to variations from
41
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environmental and genetic factors, distribution of exposure to pollutant
and presence of pollutant mixtures. There is a distinct variation in
susceptibility to air pollution among plant species, varieties, and indi-
viduals.
Plant injury responses are a function of pollutant concentration and
time, but the response to a given dose is frequently greater if presented
in a shorter exposure time. Plants generally are more sensitive when
grown under a short photoperiod, medium temperature, and adequate soil
moisture. Low light intensity increases sensitivity to ozone and decreases
sensitivity to PAN. Plants grown at low temperature prior to exposure or
under dry conditions are more resistant. Usually high humidity increases
susceptibility to ozone. Low root oxygen and high salinity may reduce
plant growth and ozone sensitivity. Ozone and sulfur dioxide are most
studied in pollutant mixtures, but in some, NOg or fluorides were added.
Plant responses have been varied. Additive, less than additive and greater
than additive effects have been reported.
42
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C. PRODUCTION ESTIMATES
1. General Problems,
a. Economic Yield Criteria
For the purposes considered in this review, it would be desirable to
have crop production expressed in terms of the economically valuable yield
of the crop. Unfortunately there is no uniform criterion for deciding
what constitutes yield among the workers, in various fields, who attempt
to find functional relationships between crop production and environment.
Of course this non-uniformity results largely from the fact that there are
different aspects of the crop-environment response being studied, l-or
example, those investigating basic relationships in photosynthetic_pro-
duction often report production as net assimilation rate (g f-^day J,
relative growth rate (g g-lday-1) or as C02 uptake (g m-2hr-l). It would
not usually be advisable to use factors obtained in such studies to cal-
culate assessments of environmental effects on annual crop yields. Never-
theless, such a procedure might be necessary when no other data are avail-
able.
If economic gain or loss is taken as the desirable criterion on which
to base production estimates, it is obvious that it is not easily applied
uniformly in experimental studies. In determining air Pollution damage,
leaf injury estimates are the most common means of assessing the degree of
•iniurv hut as has been pointed out more than once, economic loss is not
always'closely related to eaf damage (Brandt and Heck, 1968; Westman and
Conn 1976) Bronzing of leaves or other superficial injury to some leaves
could result in a complete economic loss of a crop such as lettuce without
causing measurable changes in leaf weight. In other cases, the assessment
of loss Sn the basis of visible leaf injury may, on the contrary, over-
estimate the economic loss, since photosynthetic production from the total
leS surface of the plant is sometimes not required for full yie d n a
study of defoliation effects on yield, for example, Jones |t al (1955)
removed 50 percent of sugar beet leaves (at the 4th and 8th leaf stage) and
found no reduction in yield of roots or of sugar content.
b. Estimations
The effects of environmental factors on crop yield may be defined by
correlating yield variations with variations in environmental factors. This
approach canyaiso be utilized in defining the relationship with diseases.
pests, and air pollutants,
Crop yield is normally reported in terms of yield per unit land area,
Estimates of the effect of an environmental variable on yield may be ex-
pressed in terms of the amount of yield per unit change in the variable
Sr as the percentage yield increase or loss per unit change of the variable.
It would be preferable to determine the effects of various environ-
mental variables on crop yield by the use of properly constructed controlled
43
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environment chambers that keep all non-experimental variables uniform. Un
Hnnc !nS ^n • I ewojments are not representative of ambient condi-
tions and experimental results from growth chambers cannot be presumed to
be valid for field conditions.
Se W-Sn the atempt 1s made to determine the relationship
,
is toT«asirerexilt?no^h^ tC exPertata"y varying environmental factors
impact on y eld res o^nse J*"^":!?""" «nd..t.t1st1c.ll, test their
few of these are lined below: ° 1S n0t Wlthout Problems- A
^"ch is'hiuh'raTatio^and^in.': the f1eld' some ^nations of factors
especially If measurem^T^ ? temperature often occur at the same time
for example, i would not be DOSS bTJ*? ^5 alm°St C0ntinual Sunsh1ne»
radiation variations nSt included in thP ? 5T26 the effeCts °n yield
then, of unusually cloudy weather iSulH 5SJed data Set> The effects ,
equations. Robertson (1974) indica?Pd th^ be P[edicted from the developed
were changing in recent years makinan^- Wiat^er Patte™s in Canada
functions inadequate 9 Previ°usly developed yield predictive
are hard 't^measure q-ullfllHV;iv$hnfhfa(?^rs which can Influence yield
selves and also the influence on viP?H ^ re?ard to the factors them'
Pests are examples. If thev a^ i« ^ ^ Plant diseases a"d insect
and this is subject to all the uncer?^n?J U mUSt be done by field surveyS
(Anonymous, 1965). uncertainties associated with that method
2. Field Surveys
Field surveys for estimating air po,lution-re,ated crop damage are
44
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normally conducted by well trained crop survey reporters. This method is
by its nature strongly dependent on the judgment of these survey reporters.
as they make on-the-spot investigations of each air pollution episode,
usually based on visible symptoms (Waddell, 1974; Mill-Jean, 1971). The
range of information in such reports, normally include: county, location,
suspected pollutant, crop variety, acreage affected, data of incidence,
average percentage of each plant affected, average percentage of plants
affected, loss in quantity or quality, and estimated crop loss (Laccasse
and Moroz, 1969).
Economic losses to an agricultural crop were extropolated from an
estimated yield loss, often using the "rule-of-thumb" (Milllean, 1971).
In this, the observed visible injuries are related to yield loss by various
indices, i.e., 1 to 5 percent leaf injury resulted in 1 percent dollar
loss, 6 to 10 percent leaf injury in 2 percent dollar loss, 11 to 15 per-
cent injury in 4 percent dollar loss, and so forth. In cases such as
citrus and grapes in California, where experimental data are available
concerning productivity reduction as a result of photochemical smog, the
assessment estimates were adjusted according to the degree of ambient smog
(Millican, 1971). In the event of total crop distruction, the loss was
sometimes calculated as the cost of replacement at the prevailing market
price (Pell and Brennan, 1975).
The first state wide survey was made on an experimental basis in
California (Middleton and Paulus, 1956). The survey covered four cate-
gories of crops (field, flower, fruit, and vegetable) and one of weeds.
Similar programs were established in Pennsylvania, New Jersey and New
England states. In total, air pollution losses In Pennsylvania for 1969
were estimated at approximately $11 million (Weidensaul and Lacasse, 1972).
In New Jersey, $1.2 million was estimated as the losses on agricultural
crops and ornamental plantings in 1971 (Feliciano, 1971). Similar loss
(ca, $1.1 million) was evaluated for New England between 1971 and 1972
(Naegele et al, 1972). It is interesting to note that great annual varia-
tions in estimated air pollution damage exist. For example, a 98/0 re-
durtlon was observed ^Pennsylvania between 1969 and 1970 (ca $ 1 million
and $225 thousand, respectively) (Weidensaul and Lacasse, 1972), a 8W re-
duction in New Jersey between 1971 and 1972 (ca. $1.2 million and $128
thousand, respectively) (Pell and Brennan, 1975). As discussed prev ously
in I, B.2., various factors are responsible for the sensitivity of plants
to air pollutants. Among the environmental factors, Pell and Brennan
(1975) attributed the reduction in yield loss mainly to the unusual rain-
fall pattern in 1972.
3. Production Functions
a. Environment-Yield Relationships
Crop production has been related to weather data on many occasions.
The objective in these studies is in some cases to produce an equation
which will estimate the yield effect of weather factors in any given year
(Thompson, 1962, 1963; Staple and Lehane, 1954a; Lomas, 1972). At other
time-studies have been designed for development of mathematical models
45
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marily to studies of the former type.
The field environment is generally characterized by complex variations
and interactions among the climatic factors. Therefore yields "nnot
usually be expressed in terms of functions with only one independent vari
able. Mo?e often a response function is obtained by multiple regression
of more than one variable.
Progress is being made in the analysis of the complex relationship
between weather and crop development and crop yield (Baier, 1973, Stann;i n.
1973; Shawcroft et al_, 1974). Most of the studies relating weather factor*
to crop yield can be divided into one of three groups depending on tne
approach used. One approach has been the straight forward statistical
analysis of the growth or yield in terms of weather data. A second appro*
uses the soil water status or soil moisture estimates calculated from tne
weather data and characteristics of the soil under consideration, in tne
third approach evapotranspiration estimates are related to yield, comoi-
nations of these approaches are also used at times.
Estimates from weather data. Crop yield has frequently been studied
in relation to a single climatic factor with varying degrees of success.
Dermine and Klinck (1966) attempted to relate yields of oats in eastern
Canada to precipitation or temperature. They found low and not signuica
correlations in the analysis. Lomas and Shashoua (1973) reported the
yield of wheat in three semiarid sampling areas of Israel was linearly
related to unusual rainfall according to the equation:
Y = -27.2 + 0.599X
with Y in KG/1000 M2 and X in mm of rainfall. The correlation coefficient
was small (0.154) but significant at the \% level.
The production of three varieties of corn grown for forage during on
season in Britain was separately related to accumulated temperature,
Ontario heat units or solar radiation by Phipps et_ al_ (1975). Cubic re-
gression equations were developed for temperature, heat units, and radia-
tion to predict continuing dry matter production of each variety during
150 days of growth. An average of 94.9 percent of yield variation was
accounted for by those variables.
Staple and Lehane (1954a) determined that the yield of wheat in f .
Canada over a number of years was fairly closely correlated with precipi-
tation. Simple linear regression accounted for 62 percent of annual yiel
One of the most widely used methods of statistical analysis of crop
weather relations was developed by Fisher (1924). Fisher analyzed wheat
yields obtained over 60 years at Tothamstad England by multiple regression
46
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techniques. The rainfall of each year was divided into 61 periods of 6
days and was fitted to a fifth-degree polynomial on time. A trend variable
was included for yield changes due to non-weather causes. Little correla-
tion was found between yield and rainfall. Buck (1961) used the same
techniques and data as Fisher, but in addition to rainfall and temperature,
a term for actual transpiration was calculated. There was still no signif-
icant correlation between wheat yield and rainfall and transpiration, but
when the method was applied to sugar beets, 73 percent of annual yield was
accounted for.
Some of the most successful analyses of yield and weather have been
done by Thompson (1962, 1963, 1964). Using annual crop yield data from a
number of states of the mid-west and Plains areas of the United States,
Thompson calculated equations by multiple curvilinear regression analysis
for weather effects on annual yield of wheat (Thompson, 1962), corn, soy-
beans (Thompson, 1963) and sorghum (Thompson, 1964). Standard weather
data were used to find averages in each state for monthly temperature and
rainfall during the growing season and preseason precipitation. A factor
for trend due to technologically related yield increases was included in
each analysis. In most of the calculations, correlation coefficients were
0.90 or greater.
An example, in Table 1 shows the multiple regression coefficients and
constants found for the relation of corn yields to weather in Illinois,
Indiana, Iowa, and Missouri (Thompson, 1963). It can be seen that regression
coefficients vary between states and only apply to the area for which they
are calculated.
Similar statistical analyses have been successful when they were
applied in semi-arid regions (Gangopadhyaya and Sarker, 1965; Lomas, wti
Lomas and Shashoua', 1973). In India, Das and Madnani (1971) used multiple
regression analysis and long-term records of weather and yields. The
equation derived for final yield (Y) of rice was:
Y = 430 + 33.7 X2 - 49.7 X3 + 9.65 X4
where X2 = the number of rainy days in July; X3 = the number of times of
drought in August and X4 = the number of rainy days during the last half
of September. The multiple correlation coefficient was nearly 0.90. Sim-
ilar techniques were used for other rice growing areasJ^J"^*' *^a*
found that other weather elements were important as predictors (Robertson,
1975).
Estimates from soil nunsture status. Since standard weather data and
multiple regression analyses sometimes have not adequately explained crop-
weather relationships, some workers have designed ways of using soi
moisture to estimate crop growth and production. Long-term soil moisture
records are not readily available, and therefore, methods have been devel-
oped ?orest?Lt"ng soil moisture'from standard weather data (Dale and Shaw,
1965; Baier and Robertson, 1966; Baier, 1967J.
Baier (1973) concluded that "a realistic crop-weather analysis model
47
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Table 1. Constants (a values) and multiple regression coefficients (b
values) for years and weather variables and their relation to corn
yields in five states (after Thompson, 1963).
Illinois
Indiana
Iowa
Constants (a val
xl
x2
X2
Xo
2
X4?
X4
X5
b2
X5
Xfi
D2
X6
X7
'2
X7
82
X8
Xg
Xg
x4x5
X6X7
X8Xg
Thn
-3072.84
.8069
1.0263
- .0134
-19.9559
-91.1648
.8194
3.4943
- .0562
17.2262
- .2354
3.6315
- .0316
107.0276
- .2296
92.6869
- .5818
1.1520
- .1665
-1.3963
-2454.18
Regression
.8605
.5248
- .0165
____
-39.9844
- .3249
8.5441
- .0781
52.7694
- .5343
12.5574
- .0786
104.2592
-1.6697
43.2209
- .2673
.5945
- .6065
-1,2351
-3223.10
Coefficients
.7045
3.7065
- .0773
« Bk_p.
-18.3570
.5067
48.0467
-.3464
-81.4565
1.6797
25.0782
- .1851
-8.7055
- .3593
22.7112
- .1697
.1597
.9431
.1598
Missouri
ues)
628.62
(b values)
.7012
- .6489
.0143
-12.0473
-79.6712
.5437
-24.1244
.1334
-40.1511
- .0247
16.4336
.0892
14.9916
.1427
41.4311
- .2680
.9905
.5496
- .2177
Ohio
-2269.80
.9472
3.1553
- .0637
w •* — —
-8.4442
.6745
16.3843
- .1186
-20.6316
-1.2751
-1.2856
- .0022
19.6940
- .5797
49.7832
- .3477
.0355
.4590
- .2021
Mi QQnuv' 9Q n -•'-'•'"••" ••" ••"• • «>'v-t. j. i i i uu ia o£. £. inaiana i/ .o. IOW3
Xi=year, X2=preseason precipitation, X3=May temperature, X4=June rain,
X5=June temperature, X6=July rain, X7=July temperature, X8=August rain,
Xg=August temperature.
°ne degree of freedom is "sined to each re-
«
48
-------
must account for the daily interacting effect of at least temperature, soil
moisture, and an energy term." For the "versatile soil moisture budget
of Baier and Robertson (1968), daily estimates of precipitation and evapo-
transpiration were required. To calculate the soil moisture using the VB,
it was necessary to know the moisture tension characteristics of the soil,
and this was obtained by analysis of the particular soil throughout the
root zone,
The soil -water balance method was found to provide a better estimate
of wheat yield than multiple regression on climatic data (Baier and Robertson,
1968).
Using wheat yields from three regions of differing rainfall in Israel,
Lewin and Lomas (1974) analyzed the data by (1) multip e !^rf s}?n' *>
principal components (Richard and Pochop, 1975; Kendall, 1957), (3) Fishers
method, and (4) by a soil moisture simulation technique. The moisture
simulation technique gave the best results under all rainfall conditions.
Both the simulation mSdel and the statistical methods gave good results ; in
the arid zone each accounting for more than 70 percent of yield variation.
The higher ?he rainfall amounts, the lower was the predictive accuracy for
all of the analysis methods.
Estimates from pvapotranspiration. Evapotranspiration (ET) is used
as an agroclLtic inde£ whilfec^ts for plant factors In addi ion to
weather variables, and it has been wide y used to assess the effects of
water and energy supply on growth and yield. ET has also been used to
estimate the consumptive water use of crops for determining when and how
much to irrigate (Haise and Hagen, 1967).
Annual wheat yields and annual evapotranspiration among two sets of
field plots in Canada were curvilinearly related in a study by Staple and
Lehane (1954a, b). The resulting curves corresponded to the equations.
Y = 0.26 M2 - 2.10 M + 8.7 and
Y = 0.40 M2 - 3.09 M + 5.63
tential ET. The average deviation of yield estimates wa s« percent in
the first case and only 7 percent with the potential ET included.
Penman (1962) used ET values computed from climatological data In
analysis™ of resell ^irrigation experiments in "^ernjngj.nd. Ac-
cumulated dry matter production of fa«w« linearly related to ET over a
period of six years. There were only small deviations trom tne si ope aue
to winter temperatures.
49
-------
A linear relationship was also found by Smith (1960) for the relation-
ship between ET and hay yields in England from 1939 to 1956. The equation
describing this relationship was:
Y = 7.05 + 1,56 T + 0.27 N
where Y is yield in hundreds of pounds per acre, T is inches of ET and N
is the number of years after 1946, The average annual deviation from the
predicted value was 2.1 percent.
Grain sorghum was grown in irrigated experimental plots at Davis,
California. Stewart et al_ (1975) found that the annual grain yield from
these plots was proportional to the seasonal total of ET. The regression
ot grain yield on total ET resulting from various irrigation programs gave
the equation: K
Y = 541 + 144.8 ET
Y was in KG/hectare and ET in cm of water.
b< Air Pollution Loss Functions
VpapJilnnS!CHi0-.iS conc!rned with Pollution-economic loss functions for
economic loss cr°P-loss functions which can be readily converted to
1t 1? "Si1 recognized that results from controlled chamber
nol 1 ,,nn n 5Ply dl!;ectly to field editions, nearly all of the air
env ronS^S fT tU"?H?ns have been derived f™m controlled chamber
197^ ?EL(e? H-— -• 1966; Heck and T1ngey» 1971' Westman and Conn«
HnniMn 5 ' es SU"est that the ^sults, at least as general rela-
u e2 inPviel5P }Ll° af1e?t f]Stt condit^^, and the functionShave been
used in yield loss estimates (Millican, 1976; Benedict et a].. 1973).
from acSte((?o68 h^fn" fr°! 7^ referenc« on percentage leaf injury
foTl9 kinds of n^nf ^ rSne fumi9at1ons and calculated response equations
Tingey (1971)? P hese Were based on the equation of Heck and
A2/T
In hSuCrS-Ca=ndCAnCTa^nfi0f °3 in Pphmi l is Percent response; T is time
that are'specif^c fir Irtti**? Constants (partial regression coefficients)
used. speciflc for Pollutant, plant species and environmental conditions
n thsndotnrudwnre ±7. t0 eC°n°TC yield remains obscure
^S^ -cs^tKTr
or varieties as recorded in several studies. The
50
-------
ratio of percent growth reduction to percent foliar injury average 1,17,
indicates a close correspondence. However, among the 12 plants, it would
not be possible to relate the vegetative growth response to the yield of a
salable crop with the possible exception of tobacco. The research with
ozone or other oxidants which would make it possible to assess economic
loss from leaf injury has not been done.
In some work using plants fumigated with sulfur dioxide in small field
plots, the relationship between destroyed leaf area and yield was inves-
tigated for some crops. The relationship was linear between the percent
of leaf area destroyed and yield as percent of control for alfalfa (Hill
and Thomas, 1933), wheat (Brisley and Jones, 1950) and cotton crop
(Brisley et, a]., 1959). The equation for alfalfa was:
Y = 98.6 - 0.263 X
following a single fumigation and
Y = 96.6 - 0.754 X
after 3 fumigations, where Y = percent of control yield and X "Percent
of leaf area destroyed. The amount of yield loss for one percent foliage
destroyed varied from 0.26 to 0.62 percent for wheat and was reported as
0.68 percent for cotton.
In what seems to be the only case in which an ozone dose-response
function has been made for a crop ^?er approximately ambient field con-
dition, Oshima (1975, Oshima et al., 1976) nas developed a method for pro-
ducing crop yield-loss functiSFsTn relation to seasonal ambient ozone
level? at a number of sites in southern California. The seasonal 03 doses
were calculaEeS fVom hourly averages obtained from Air Pollution Control
District monitoring stations.
Only one
-------
Oxidants
Sulfur dioxide
Emissions x ^t^factor" x area x e51»o = P°lluti°n potential
y (6 classes)
Fluorides
Emissions from various types
of large single sources = P°]]ution potentials
(4 classes)
The pollution potentials were used in these formulas for calculation of
dollar loss:
crop value x crop sensitivity x " = dollar loss
ornamental ornamental pollution . ,,
value x sensitivity x potential = d°11ar loss
The pollution potentials were divided into classes such that in de-
scending order each lower class was about one-half that above, i.e., class
1 was about half of class 8 and double that of class 6. The loss factors
were also arranged in a given sensitivity class so that the factor for
each lower class was half that above, e.g., the highest loss factor in
class 8 was 0.400 and in class 1 was 0.200.
m ^ A * -,"• approximations and subjective judgements were used in this
method of loss estimation. For example, the relative sensitivities of the
bb plant species used in the study were based on many sources of informa-
tion, and in some cases, the sensitivity was not known or represented sub-
jective opinion. The sensitivity indices were based largely on foliar in-
nattp™ nfW^ ^ij1! 1nput from y1eld data- The assumption that the
pattern of the pollutant dose-yield response curve is the same for each
the iprfirl?« nS JhlnS?urate' There is no way P^sently available to test
tinnc Sn Sy 4-u ! X1 loss estimates. With so many unverified assump-
accuracy. ValU6S obtained may not be presumed to have great
the M1d2SrRl«»t1XnTf0I.!sses51ng damage to vegetation was developed by
the Midwest Research Institute (Liu and Yu, 1976). Five meteorological
or oxides of nitrogen emitted per square kilometer
SollStSitlndlSniV; °f-the.tendency °f climatic conditions to concentrate
C\\ ?n,iiro nf ^unn3.an a^-stagnation period.
" °f thSMSA* a"um1n9 th^ a^a a^ circular.
ln
52
-------
variables to account for weather effects were included in the function.
This method used pollution potential indices and data for value of vegeta-
tion and vegetation loss from the SRI study. Coefficients were calculated
by step-wise linear multiple regression for 12 crop categories in 74
counties for which useable weather data were available.
The equation used and the key to variables are as follows:
CROPL. = a + b CROPV. + c TEMB + d TEMA + e SUN + f RHM + g DTS
+ f S02 + g OXID
where CROPL. denotes the economic loss (in $1000) of the ith type of crops
by county from the Benedict (SRI) study.
Table 2 lists the variables used in the economic damage functions.
The damage functions resulting from the regression analysis are shown in
Table 3 for 10 crop categories using pollution severity indices. The
numbers below the degression coefficients are standard errors with (*) in-
dicating that they are significant at the 1 percent level.
Estimated economic damages from pollution for all crops were shown by
Liu and Yu (1976) for the 74 counties where appropriate data were avail-
able throughout the United States.
It aooeared that the model worked well for oxidant damage to vegeta-
tion " Shi hly si gnlficant correlation coefficients were obtained
for some of the multiple regression varnables. Other variables appear to
be non-significant and have high variances. JhJ 9r"*e;* JffIuleJSicj!
the model is the lack of an objective standard against which the calcu-
lated estimates may be compared.
4. Discussion
a. Agricultural vipld Loss Function
The discussion emphasis will be directed to consideration of Jjethods
and data available for development of air pollutant dose-vegetation loss
functions.
Tho for,,.: of attention will be directed toward California, and par-
ti culInythTselreis of the"state where the greatest pollution losses
occur.
considered first is, what is the best method of
•{cultural yield resulting from air pollution?
P most widelv used method for making crop loss assessments has been
£S^
53
-------
Table 2. Variables used in economic damage functions (from Liu and Yu,
1976).
A. Dependent variables - vegetation loss (in $1,000)
CORNL
SOYBL
COTNL
OVGTL
NUSRL
FLORL
FRSTL
FCROL
FRNTL
VEGTL
TOCRL
TOORL
ALPLL
Corn grain loss
Soybean loss
Cotton loss
Other vegetable loss
Nursery loss
Floral loss
Forestry loss
Field crops loss
Fruit and nuts loss
Vegetable loss
Total crop loss
Total ornamentals loss
All plant loss
B, Explanatory variables
CROPV
TEMB
TEMA
SUN
RHM
DTS
SO 2
OXIDE
CSOo
The value of the vegetation in question (in $1,000)
Number of days with temperature 320F or below
Number of days with temperature 900F or above
Possible annual sunshine days
Relative humidity
Number of days with thunderstorm 3
Annual mean level for sulfur dioxide (ug/m ).
The relative plant-damaging oxidant pollution
potential index
The relative plant-damaging sulfur dioxide
pollution potential index.
54
-------
Table 3. Economic damage functions on vegetation with pollution
relative severity indices ($1,000) (from Liu and Yu, 1976).
in
en
(1) CORNL
(2) SOYBL
(3) COYNL
(4) OVGTL
(5) NUSRL
(6) FLORL
(7) FRSTL
(8) FCROL
(9) FRNTL
(10) VEGTL
a
4.4
(32.1)
-2.2
(0.3)
-5.8
(6.9)
133.6
(58.5)*
-113.1
(300.2)
-616.4
(485.2)
-616.4
(485,2)
CROPV
0.001
(0.001)
0.003
(0.001)*
0.0063
(0.0002)*
0.006
(0.001)*
0.11
(0.02)*
0.10
(0.01)*
0.071
(0.003)*
520.5 0.003
(222.3)* (0.002)
-90.9
(281.2)
-308.7
(168.4)
0.061
(0.006)*
0.011
(0.002)*
TEMB
0.02
(0.04)
0.01
(0.03)
0.0006
(0.0094)
-0.03
(0.08)
1.12
(0.42)*
0.93
(0.57)
1.93
(0.70)*
0.28
(0.32)
0.83
(0.43)*
-0.33
(0.23)
TEMA
0.09
(0.10)
0.04
(0.07)
-0.054
(0.028)
-0.44
(0.22)
-0.19
(1.03)
-0.30
(1.41)
-2.33
(1.63)
1.17
(0.82)
0.43
(1.00)
-1.66
(0.64)*
SUM
-0.13
(0.35)
-0.04
(0.28)
0.067
(0.077)
2.02
(0.63)*
0.35
(3.27)
-0.79
(4.37)
5.20
(5.34)
-5.61
(2.44)*
-2.28
(3.18)
4.92
(1.80)*
RHM
0.16
(0.34)
0.03
(0.07)
0.10
(0.65)
-2.95
(3.26)
-6.7
(4.4)
-1.88
(5.22)
-3.26
(2.44)
0.28
(3.09)
1.05
(1.85)
DTS CS02
-0.041 6.73
(0,10) (1.84)*
0.05 3.58
(0.74) (1.49)*
0.03 0.05
(0.02) (0.40)
0.06
(0.21)
2.34
(1.02)*
3.03
(1.37)*
4.77
(1.71)*
-1.20
(0.77)
1.74
(0.98)
0.08
(0.60)
OXID
-0.85
(2.18)
0.24
(1.65)
0.57
(0.48)
97.73
(3.71)*
191.51
(33.09)*
356.3
(30.8)*
370.52
(30.71)*
54.07
(14.20)*
121.3
(18.02)*
136.02
(10.69)*
R2
0.28
0.26
0.98
0.96
0.90
0.93
0.96
0.35
0.82
0.89
-------
accuracy of the final estimate of loss is hard to assess since there is a
subjective judgment in the initial estimate of percentage leaf damage and
another subjective judgment in relating leaf damage to yield loss. Surveys
which have been done also lack an organized geographical grid to be assessed
at uniform intervals. Observations were made randomly over a years period
without standardization.
The relationship between crop yield and leaf injury induced by oxi-
dants has not been adequately defined. There have some functions for yield
vs. leaf damage produced for crops fumigated with sulfur dioxide (Hill and
Thomas, 1933; Brisley and Jones, 1950; Brisley et aj_, 1959). Problems
arise when these are applied because of the mixture of oxidants and 502
present in affected areas. Only the western regions presently have a
single major pollutant (oxidant) acting without an interacting sulfur
pollutant.
The surveys would be placed on a much more objective basis if crop
yield-leaf damage functions were produced for the major crops even if short
duration exposures were used. The application of such functions would be
difficult since enormous man power requirements would be involved and the
expense of implementing such a program with qualified observers would be
prohibitive. The outlay necessary to effectively monitor a large produc-
tion region might not be worth the assessments.
The main drawback of Oshima's oxidant crop loss models is their spe-
cificity. Ozone dose-crop yield models must be developed for each crop
considered before any assessments can be made for that crop, This develop-
ment is time consuming and expensive, but alternative procedures require
the injection of more subjective judgment. Only one ozone dosage-crop
loss function for alfalfa is presently available from this method. There-
fore, the method may have good potential for the future, but the inventory
of such functions must be increased in order for it to become highly
useful.
The economic damage function developed by Liu and Yu (1976) for pre-
diction of vegetation losses from air pollution appears to be a step
towards the desirable goal of including more of the significant environ-
mental variables in the damage functions. However, the method has a
number of inadequacies which limit its usefulness.
incc fT9 th* 1naiequacies a™ the use of pollution potential and crop
loss figures from the SRI studies (Benedict et al , 1971. 1973). Therefore,
daLaSalf1ST^SnCiiri-d °Ut Using Va1ues obHi^d f™n a questionable
data base. The pollution potential and crop loss figures are only rough
SSflcfenS of"! mnlY leadMt0 r°Ugh est1mates in the analysis Also the
the croDftP,?LSOnin,i;anab^Suappear to be not significant for most of
more appropriate; ^ V3nableS °r Sh°rter «•» swmatlons might be
croDs^r'SlaPt^inn6,]1'"11'13110"5: est1mates °f vegetation loss for the 10
crops or vegetation classes may be calculated from the equations for
56
-------
counties where the appropriate weather and pollutant data are available.
Most of the functions from Liu and Yu (1976) were derived for aggregate
crop categories such as "other vegetables," "field crops," and "forestry."
If one attempts to apply the model, a crop can be readily fitted into one
of these categories, but in doing so one must take on the additional un-
certainty involved in the assumption that all crops in the category re-
spond in the same way to each environmental variable of the function.
One of the goals in this report is to devise a method, or methods,
to incorporate weather and other environmental influences into crop pro-
duction functions.
We have found essentially no data for crops in California which show
weather factor-yield relationships. Such equations may have to be devel-
oped as needed from the available crop yield and weather data.
It was noted previously in this report (V, C, 3, a) that yield may be
correlated with (1) direct weather data, (2) calculated soil moisture
status, or (3) evapotranspiration. The regression against direct weather
data would be the first choice of methods because it is the simplest
whether annual or shorter time averages are use. The use of curvilinear
regression seems desirable especially in an area where supraoptimal tem-
peratures are common as in many parts of California (Thompson, 1964).
The correlation of yield with soil moisture status has been more
successful than direct use of weather data under some conditions (Baier
and Robertson, 1968), but it requires a prior study of soil characteris-
tics in the area of interest and might lead to too much complexity. In
addition, the bulk of California crops are grown on irrigated land and the
soil moisture methods were not designed for that condition.
The use of evapotranspiration for correlation with yield might be
best to consider if weather data alone are insufficient.
If multiple regression analyses of crop yield in terms of weather
factors are done in an area where air pollution damage occurs, it would no
doubt be advisable to include the air pollution level as one variable.
This would be possible only in those areas where sufficient data on pol-
lutant levels is available. It may be feasible to take advantage of var-
iations in pollutant levels of different regions, as was done by Oshima
et. a]_, (1976), in order to obtain sufficient data to include pollution as
a variable in the analyses.
Research studies have provided an understanding of many of the basic
relationships between the most important environmental variables and the
growth and yield of crop plants. It must be concluded, however, that
there is almost no data base available which can be used for an objective
assessment of the influence of these environmental variables on yields of
a major portion of the crops and vegetation in one agricultural region
such as California. There are methods available which can be, and to some
extent, are being used to generate data for more objective assessments. It
57
-------
may be necessary or desirable to continue using the less objective models
for assessments and analyses until more objective methods are available.
b. Bayesian Approach to Incorporating Prior Information in Response.
Functions
Throughout this section, it has been stressed that the basis of any
analysis of pollution effects on agricultural production is an estimated
response (or production) function with the relevent pollution indices as
explanatory variables. However, a daunting range of problems in empirical
field experimental results have been raised, Thus the currently available
empirical results need additional information on the relationships before
they can be used in a comprehensive economic model. This additional in-
formation, or prior information, may take several forms: (a) Constraints
on the sign or range of coefficients to ensure "feasible" projections or
resolve multicol linearity problems, (b) Prior distributions on the value
of some or all parameters based on data from similar experiments, or (c)
Prior distributions on the value of some or all of the parameters based
on the subjective opinion of "experts" in the area.
While applied statisticians often subjectively influence the outcome
of their analysis based on their theoretical expectations, the Bayesian
!ii£!nn K J i ^ °f Prior J'ud9me"t explicit and formal as well as
allowing the formal inclusion of a wider range of prior information than
the traditional classical approach.
fe|Jheor^. Bayes theory utilizes the definition of conditional
probability to show the relation between:
Prior information on a parameter - P(Q)
Information on e -P(y/0)
The posterior distribution on 0 -P(0/y)
that is P(Q/y) . p(e) p(y/0)U)
loss fulctiof ovprethl°n *l °.can be obtained by minimizing an appropriate
terlor Is iiSt?1but2 nS±?i10r d1stributi°n. For example, if the pos-
same po nt estimate as S^ * qXaSr atic loss functi™ will lead to the
v ^ estimate as that obtained from a classical least squares approach.
Prior Probabilities Thp fioKat-c, i,, +u ,. ^- ~v
the merits of the feavp^l^ ^ ™*T!.ln *V? statistical literature over
corporation of subjective nnSI.. '!*ls,?i!l]^1ve!. since the.!°^al 1P"
as
those based on frwinenrw 3L* OTT^el"le' by an expert are as admirable as
terms, but frl the n rspect?^ S" S debatable in classical statistical
the ideal experimental rSle ka d!(rlsion maker who cannot wait for
is thus bestuser?n anTxD feu ^JHeft1Ve1informat1on has ^ be used, and
n exP'lclt and formal statistical manner.
(1) Where the symbol « means "proportional to"
58
-------
An empirical examination of alternative methods of obtaining priors
may be found in Winkler (1967).
Operational Problems. A significant problem in implementing a Bayes
approach to multiple variable response functions with n variables results
from the n dimensional integration implied by the formation of the poster-
ior distribution. This computational problem may be reduced if the prior
distributions belong to a class of "natural conjugates" that may be com-
bined analytically.
An example of the use of prior information in a Bayesian manner to
estimate a production function is in Zellner and Richard (1973). A com-
prehensive theoretical treatment of Bayesian estimation may be found in
Zellner (1971).
The review of the literature on physical factors and agricultural
production functions suggests that prior information will be needed to
derive meaningful relations and that the^Bayesian approach is the most
logical and rigorous way to incorporate it.
5. Summary
Methods of estimating crop production in relation to environmental
factors were discussed with regard to problems encountered, field survey
methods, and the use of statistically derived production functions.
General problems. Much research data pertaining to crop growth or
crop injury is of limited uses because it is not expressed in units which
are transformable to economic units. Frequently used growth measurements
such as relative growth rate (g g-lday-1) and net assimilation rate (g m *
day-1) are almost exclusively relevant to scientific interests In other
instances there are described effects of environmental vanab es on growth
or injury of one portion of a plant, such as leaves, which bear an unknown
relationship to the marketable products of the plant which may consist of
seeds or roots.
There are difficulties in determining environmental variable-yield
relationships because in the field there are a number of factors influ-
encing yield which cannot be individually controlled and in the various
controlled facilities, ambient conditions cannot be duplicated.
Existino outdoor variations of environmental factors can be analyzed
statistical?? ?o estimate their influences on jljld responses, but here
also, there are some problems. Some of these may arise beeau" of. (1
factor interactions, (2) correlations between f"tojf• J^ ^*«'°"s in
the range of variables of regression .ana yss,, or (4) un«^ainties where
quantitative measurement of factors is difficult, e.g., diseases.
Field surveys The field survey is a method which has been used for
estimatinq crosses resulting from air pollution. The estimates which
are Eased9on?he judgment of trained observers. A state-wide survey was
59
-------
first made in California (Middle-ton and Paulus, 1956} and surveys were
used later there and in other states.
Production functions. Crop yield has been related to weather variables
on many occasions by functions usually derived from multiple regression
analysis (Baier, 1973; Stanhlll, 1973). In a few instances, regression on
a single weather variable has been successful (Phipps e£ al_, 1975; Staple
and Lehane, 1954a). Most studies have related yield to direct weather
data, calculated soil moisture content or evapotranspiration, or have
used combined approaches. Nearly all reports have analyzed yield in areas
where the water supply was by natural rainfall. Field grains are the
crops most frequently studies. The reported amount of yield variation
accounted for in terms of weather factors has been variable, less than 1
percent to greater than 90 percent in many cases. There is some evidence
that the accuracy of the analyses is greater in regions of lower rainfall
(Lewin and Lomas, 1974).
Air pollution loss functions. There is little experimental data from
which objective air pollution loss functions can be made. A number of air
pollution-plant damage functions have been derived from controlled environ-
ment studies in which the percentage leaf damage was recorded following a
single exposure (Heck and Tingey, 1971; Heck, 1976). The relationship
between leaf damage and yield is little understood, but it has been studied
tor some crops exposed to sulfur dioxide (Brisley et_ aj[, 1959).
A method has been developed for producing crop loss-ozone dose functions
under field conditions using ambient ozone variations at different sites.
1976)r °Se C0nversion Sca1e for alfalfa has been published (Oshima et. al»
- °f Station due to air pollution in the United States were
in a study by Stanford Research Institute (SRI) (Benedict et aT.,
h^ Su ° cal^ulate losses used estimates of pollutant levels
K!Car5°n> SUlfur dioxide and fluoride emissions in the most
som, 5nS «;h Cr°P sensitivity factor was derived from visible
vo^ed S ?nd '^.sources With a number of subjective assumptions 1n-
wh ch uses th?Snl0n anal^-S m°del WaS devel°Ped by Liu and Yu (1976)
from the SRI ct H P 5Kei;s;tlV1ty fact°r and calculated pollutant levels
oroloSical variahiL Ut ha?«lculated regression coefficients for 5 tnete-
base was offered " WSl1' N° mod1fication of the questionable SRI data
60
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SECTION VI
FARM STRUCTURE, PROFITABILITY AND RISK CHANGES
DUE TO AGRICULTURAL CROP YIELD CHANGES
While we recognize that not all air pollution effects 1n agriculture
are adverse, 1n this and subsequent sections we are formulating a frame-
work in which we assume that air pollution adversely affects crop yields
and increases the marginal cost of production. Thus, we may expect
subsequent changes in production patterns and 1n farm firm profitability.
From a theoretical perspective the problem is one of how farmers adjust
to technological external diseconomies imposed by air pollution.
In modelling this adjustment problem we are confronted with three
general methodological alternatives: (A) programming models of mathema-
tical optimization by "representative" farm and aggregated region; (Bj
simulation model with production function; (C) regression estimation of an
aggregate farm production function or aggregate profit function. The
strengths and weaknesses of each general approach will be discussed as
well as specific modifications of each approach. Particular attention ^
will be focused upon extending the models to account for risk Inherent in
farmers' decisions due to factors such as air pollution, weather, changes
in consumer tastes, and combinations thereof.
Before proceeding, it should be understood that we are building upon
yield response functions derived from previous research or estimated in
Section V. What is required are sufficient functions that re ate the
incidence and magnitudes of air pollutants (and other physical factors,
including interaction effects) to crop yields. The importance of other
factors (fertilizer, water, pesticides, etc.) depends on the substituta-
bility of physical inputs. For example, if yields are reduced by air
pollution damage, fairs may respond by planting more acreage, hence
increasing use of the aforementioned inputs. The est1m^ed response
functions become the basis for forming input-output ^efficlentsd) relating
the use of each input to a unit of output of each farm activity.
11) This is not to be confused with input-output coefficients in "INPUT-
OUTPUT" analysis the subject of III,A. In 1-0 analysis, an Input-
oul I c SffS MloS the a^unt of o^put fro? one sector required
per unit output in a given using sector. (Converted to value terms,
It shows ?he value of output from one industry required to produce a
dollar's worth of product in another industry}.
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A. MATHEMATICAL OPTIMIZATION MODELLED BY REPRESENTATIVE FARM AND
AGGREGATED REGION.
The use to which we put our matrix (array) of input-output coefficients
depends upon the specific research questions we want to answer. In this
section we will consider programming models which are typically comparative
static and conditional normative. That is, they are usually concerned with
single time periods and tell the researcher what "should be* rather than
"what is" or "what will be". Extensions of the models to make them multi-
period and thus predictive will also be mentioned.
The structure of Section A will be as follows: (1) general description
of linear programming (LP); (2) outline of a simple LP model of "repre-
sentative" farms in Yolo county, California; (3) use of LP to derive
aggregate (regional, statewide, or national) agricultural supply; (4)
methods of accounting for risk in LP modles; (5) Incorporating air pollu-
tion effects into programming models.
1. LP in General(2)
LP is primarily an allocation model that can solve simple to very
complex problems of optimization. For example, 1t can solve a profit
maximizing problem for the individual farmer and a welfare maximizing
problem for a social system. It must have at least three quantitative
components: an objective function capable of being maximized or minimized,
alternate methods or processes for attaining the objective, and resource
and other restrictions.
The basic LP assumptions are (1) linear production relationships
™00"?*??* inPut-°^Put coefficients); (2) the linear relationships
nequalities (a productive activity can use less than or equal to,
°e +?n' the ™ounts of resources available); (3) a linear
hplnl0"' J4l ;tructuiral relationships must be specified (as
nri, « ? 9 !?t1.m!ted 1n an econometric model); (5) additivlty (total
Perfect dv^ihiUr 7^ equal the sum of individual activities);
A <£?t 5 +u ^visibility of inputs and outputs; (7) flniteness (there is
th I can be rnnHH.erHf a]*rnat1ve activities and resource restrictions
t can be rnnHH.H
1-0 cSffiHeS! nHrl; ^] 3^l^&^ exoectati ons (resource supplies,
i u coeTTicients, prices known with certainty). Obviouslv there are
'1 these «U*XiS1~'tS abstract.
References: Heady and Candler (1964), Baumol (1965).
62
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2. LP Model of a Farm; An Example
A good example of the use of LP 1n a static environment Is a study
^%^«te ffil?Ki.to^f .S^*1'
as to resource availability (particularly capital and ^or), nstitu-
tional arrangements (land tenure system and acreage ^^"^tlnn
yields and prices (normal, 1n this study), and efficient production
techniques. Given that Yolo County is a fairly homogeneous farming areaW.
four typical size (or "representative") farms were fleeted to represent a
reasonable array of alternatives. These were also defined on the basis or
soil type, machinery, operating capital, and rental contracts.
Among the data requirements for this study or any other farm planning
model using an LP format are prices of inputs (i.e, variable costs) and
outputs, yields, fixed land and machinery costs, and per acrfam^"inery
power requirements for each crop and time period (within a season).
(3) The basic LP model used by Dean and Carter 1n matrix notation:
maximize Z = P'X
subject to: A X <. b
X >.0
Where: P is an nxl vector of (discounted) net returns resulting
from a one unit Increase In the Jtn activity.
x i
-------
and*CS^5r apcounted for the possibility of pronounced yield
is -"
3' Aggre9ate Supply Response^) Modelled by "Representative" Farm
demand, or crooolna natt*™ 3, I objective), resource allocation, resource
standard^ Cr°Pplng pattern due to varying parameters such as air pollution
sgVe 1J natUr?' 1«e- the* take
several crops competing fo? iSn Si! Presents problems when there are
alternate lePve?nraS9r1c2ltu?a?'suSi !!!' «hl?rects On1consumers of
cannot be measured. aancuilural suPP'y as well as supply Instability
of supply^iSroStfmal SSlSSSl"? 1S S ;°f:mat1ve to01 • Programing models
poor predictive tools A si Shtli°U • Sh°Uld ^ Eut are 9e'erally h
1s that of aggregat on bias 9?hl? S in)P?rtant Problem with th1s approach
to represent the^upSly resoonlS of S "Iodell1n9 "representative" farfns
that differs from that which m nhJ h9 °^S,°f fams m* 91ve a solution
m n ,
separately. Nevertheless there aVh*!"6^ modell^9 every farm
bias. Day (l9G3a) propoed three suf??cS °f 3 J!m1z1n9 aggregation
aggregation (for referenced on nn+!*i 1ent Cond1tions for unbiased
input-output Mtrlcs (Ihe A SStriJf^fpf n f°0t:?te (2) ): ™ identical
net returns vector (the P vector!- '^ } Pr°P°rt1onal variation in the
vector of restraints (?he b^tor^ ( I hpr°P°rtl°nal variation in the
to criticism. Miller (1966) Ind Lee hSS? "nditions have been subject
(2) and (3) are unnece sari y restrict vf ifaV6DSh?Wn that Conditions
ny restrictive while Paris and Rausser (1973)
Can be found ^ Nerlove and
64
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have suggested a framework for dealing with nonproportlonallty in the net
revenue and resource vectors as well as the matrices of technical co-
efficients. If Paris' and Rausser's suggestions are correct, the researcher
can avoid the time consuming and costly collection and assembly of data
for a large number of individual farms.
The commonly used procedure for making programming models of supply
response more predictive is that of recursive programming (RP)(o). RP is
essentially a synthesis of regular LP (thus 1t has a linear objective
function and linear constraints) and regression analysis of time series
data. The predictive capabilities of RP are due to the use of flexibility
constraints which are usually estimated by regression techniques. Maximum
and minimum flexibility constraints represent upper and lower bounds on
allowable changes in the level of each enterprise in the programming
solution from one year to another. That 1s, these constraints relate
the production pattern of one year with that of the preceding year under
the assumption that a farmers' current production decisions are deviations
from the allocation pattern of the preceding year. There are many factors
that may cause a farmer to be unwilling to make large changes in his
established production patterns: risk and uncertainty due to demand factors,
weather, other physical factors such as pollution!/J, institutional
restrictions (acreage allotments, for example), or simply personal prefer-
ences related to firm goals. Flexibility constraints Indirectly measure
the Influences of these factors.
Since the predictive accuracy of RP models rests on the estimation
of the flexibility constraints, there has been appropriate_attention to
this matter In the literature. Alternative methods of estimation have
been proposed by Schaller and Dean (1965). More recently Sah1 and
Craddock (1974) have criticized previous studies for Ignoring the effects
on flexibility coefficients of year-to-year changes in specified economic
and noneconomlc variables. They proposed an alternative approach to
Incorporate such changes and found that the predictive performance of
RP models was enhanced.
Before proceeding to the problem of accounting for uncertainty, the
possibility of utilizing a multiperlod framework should be brief y mentioned.
At the firm level, multi-period LP models (MLP) attempt to describe the
(6) Day (1963a; is a good general reference for RP.
(7) The use of flexibility constraints with RP might b%•PP"6* *° *[«
air pollution problem. For example, suppose we want to predict the
consequences of alternative standards upon regional agricultural
supply. Furthermore, suppose we have abatement technologies that are
Improving over time. Aside from the question of the costs of alter-_
native abatement technologies (which can be modelled in a cost minimiz-
ing LP framework), we could use flexibility constraints to place bounds
on-allowable year to year changes in the magnitudes of particulate
pollution In a given air shed.
65
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wssr s'sa St3s.
and W^nnr™? ferat1cn was the w«tlands Water District
' '
4' Meth°dS of Accounting for m,i, fl.ors1on in Farmprg. npfHHftr>B
at farmers must make
that
air polio n cro
has a certain utility for
tlons of Savior
sive
major factor account
behavior o? Ind^Sa
farms, has led to both
in enterprise choices
"
reasons to 1^'^ r1«k aver-
r1sk 1n Lp "dels has been a
between ^ actual and Pred1cte5
a99re9at1on of "representative"
(Kennedy and
(9) In fact Lin, Dean and Moore (1974^ et,,H^H e4 ,
and found profit maximization to L f 5 e? s1x large California farms
maximization and lexlcowaihlc StJ?-J en?r to Bern°ullian utility
explaining the
r^ The specification
a profit maximizing goaf! g 1Uy 1s theoretically superior
to a profi
66
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In the first approach, quadratic programming^11' (that incorporates
a quadratic objective function) has been a popular technique for directly
deriving the expected Income-variance (E-V) frontierU^. The use of
the E-V criterion is equivalent to maximization of the expected value
of an exponential utility of income function if income is normally dis-
tributed (Freund, 1956). If a utility function is specified, the optimal
decision is specified by the point of tanqency between the E-V frontier and
the highest utility locus in E-V spaced3). In the absence of a utility
function, the decision maker himself must select a point on the frontier.
Applications of this approach Include W1ens (1976) in which the impact
of yield uncertainty in peasant agriculture is examined. Wiens is also
concerned with the uncertainty faced by peasant farmers regarding the
future impacts of new technology. Farmers in regions of heavy air pollution
may be facing an analogous situation. They are confronted, in current
time periods, with the adverse effects of pollution. In future time periods
they are facing uncertainty regarding abatement technology and the poli-
tical decisions necessary to Implement such technology and enforce
standards.
Hazell (1970), among others, has utilized a game theoretic approach
1n a risk programming framework In which the classical decision ru es of
game theory are applied. Basically, in this approach all competitive
forces and uncertainty facing farmers are specified components of nature ,
The farmer then is playing a game against nature.(he can win or lose;
when he decides on enterprise choices.
(11) The basic QP model:
suEjectVAVi b, I.e. same production system as 1n LP
and f'x » X, x >. 0
D6= vaHance-covarlance matrix of enterprise gross margins
f = a column vector of gross margin forecasts
of efficient E-V solutions is obtained;
the variance V 1s as small as possible.
(12) How and Hazell (1968) and Stovall (1966) have also suggested the QP
approach.
&" e«ed U op d io nSmally distributed) outcon« distributions
and when good quadratic algorithms are unavailable.
67
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OP has several advantages over the game theory approach among which
are: (1) QP can specify a series of farm plans whereas the game theoretic
approach is rigid for any given decision criterion; (2) QP takes explicit
consideration of the covariance relationships of gross margins; (3) QP is
able to incorporate any probability distribution for state outcomes.
The third approach assumes that the probability of some critically
low value or worse of expected net returns (total gross margin) is deter-
mined along with the expected value of net returns. This 1s usually termed
a safety-first approach. Boussard (1971) and Boussard and Petit (1967)
propose focus loss constrained programming (FLCP) as linear alternatives
to QP They conceive of farmers' behavior as maximizing expected income
?«5™ ?h* pPrDlf1ed Pr?b?b11ity of attaining some minimum level of
Income. The ^ FLCP approach 1s defended on the grounds that 1t produces
farm plans similar to those actually implemented. A more general defense
aLprlii.P5v^?\?r any I1nearu alternative is that LP algorithms are
£ h£w ^ K? -6 toMreSearchers whereas appropriate QP algorithms may
elpH^iv ?h! I!1?' Moreover« the QP approach has extensive data demands,
especially the variance-covariance matrices of income.
unnn0^!3?1' ?e ^Peclf ication of the admlssable loss constraints
of aaPS??nn J subjective local knowledge. Thus, as the level
for different locales.' *° ^ ^ °f °bta1n1ng ne<*SSary
and pSu^nnS?^""?^ i(1?75) ?uggest a modification of the Boussard
and petit approach. The latter 1s actually belna used in an aaarpaate
PtuW^e1as&
Petit SDecifvthP m5n?^ 1Cat ?? 1! technical 1n nature: Boussard and
»«5 5 spe^lfy t"!6 Animal possible Income level as a constant- Webster
-^L&-^
1ng -t «1ten"t1w m** of corpora-
Ing for r Sk MewloS^i™ /T T?dels w1th the Intention of account
model. aversl°n »mong Australian farmers In the aggregate
68
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empirically applied by Rae (1971). Without going Into excessive detail,
the discrete model may be valuable 1n the specification of utility functions
as objective functions and the Incorporation and evaluation of new Infor-
mation. This method sounds appealing in the sense that new Information
on both the effects of air pollution on crop yields, and farmers reactions
to it, will become available over time, thus necessitating the updating of
any economic model.
A regional model of this type could be developed based on "represen-
tative" farms, altnougn data collection (of decision dates, subjective
specification of probabilities for different states of nature in addition
to normal LP data requirements) would be time consuming and expensive
Also as the number of Individual "representative" farms needed to model
the region grows, the dimensions of the problem become vast. For example,
Input-output coefficient matrices would have to be constructed for each
state of nature in time period 1. Then, depending upon the actual out-
come in period 1, period 2 matrices would have to be constructed that were
conditional upon the outcome in period 1. This 1s the sequential nature
of the problem.
Incorporating Air Pollution Effects into the Programming Model
5.
In this section we will start with a simple example of how the effects
of S02 on wheat might be incorporated Into an LP model. ™!™!"L^' ts
we will mention the advantages of parameterizing the technical coefficients
that relate pollutants to yields and the use of such Parameter zat on to
derive efficiency frontiers relating expected Income to pollution levels.
u +j +• are snpcific 3s to SOT i type> This means tnat
problem.
A specific row 1n the A matrix (see footnote 3 for notation) appears
as follows:
(15) Or at least Information on plant growth that can be converted to a
yield per acre basis.
(16) Alt.rn.t1v.1y we can loo* at three geographic regions classified as
high, medium, and low pollution regions.
69
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allxl + 312X2 + ...... + alnxn ^ b°
For example, 1f b° 1s the total amount of land available for cultivation
on a farm in our particular region of Interest, and xi represents the
production of one unit of wheat, then aj} is the Input-output coefficient
relating the quantity of land that is required to produce one unit of
wheat. Similarly X2 might be sugar beets and ai2 is the amount of land
required to grow one unit of sugar beets. The Inequality means that the
farmer cannot use more land than is available to him.
Now suppose that the farm land 1n question is composed of two soil
types, A and B. In programming, wheat produced on type A soil, wheat
produced on type B soil, sugar beets produced on type A, and so on ----
must be specified as different activities (or processes). Thus, wheat
produced on soil type A with a high concentration of S02 would be speci-
fied as one activity or process. Each process 1s represented by a vector
of Input-output coefficients (or per unit resource requirements).
Thus, we might have six processes for wheat:
Type A soil, high S02 = xi
Type A soil, medium S02 = x2
Type A soil, low S02 = xs
Type B soil, high S02 = X4
Type B soil, medium S02 = X5
Type B soil, low S02 = X6
The dimensions of the problem grow rapidly, 1f we consider that wheat
might also be adversely affected by nitric oxides (6 x 2 = 12 whest
processes).
Suppose that yield response research has shown that the yields per
of Mah sn6 m«HtypeAareJ0' 30» and 40 bushels under conditions
£fr,h ?n 2£n *? Um 2 andJow S°2» ^actively. Furthermore, we define
high S02 pollution as emissions of 500 million pounds per year from all
r ^^
b11"on
For soil type A, part of the A matrix might appear as follows:
(high) (medium) (low)
20 xx + 30 x2 + 40 x3 < ^
uhDoneh1bstor1caierprnJLPr?dUCtl<0!; of wheat a11o*ed °" soil type A based
upon Historical records of cropping patterns, intuition, etc. Pollution
70
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concentrations might be represented as follows:
500 Xj_ + 250 x2 + 75 X3 <. b2
where: bo might be defined by some measure of S02 pollution potential
that depends upon recent historical Incidences. With pur simple model
we can then specify additional constraints to Incure that only one
pollution level could occur at a time.
Thus for any given discrete level of pollution, optimal output and
croDDlnq mix may be obtained. Discrete changes In output and cropping
patterns9 can Sen be derived so that one would have a linear approximation
of an efficient production-pollution frontier.
We are not aware of the use of such an approach *oa1r pollution-
aaricultural system modelling. Theoretically and empirically, it appears
to be ihe slmpllst me?hod ^obtaining optimal cropping patterns for given
alternative pollution regimes.
There are however, two problems. The first 1s that we can only
obtailharseries ^discrete solution points (though this may e due in
part, to the nature of our experimental results which are like y to be
discrete resoonse surfaces). Second, 1n a multiple crop, multiple air
?JllS2trSl!lJlJ soil type region, the dimensions of our model will
rapidly surpass our time and computer constraints.
We mav be able to partially mitigate these problems. By utilizing
nc'tioS] in°wR?ch we Le estimated^"^^ ^51°"
c.^^
ant he'coeTfiKfof InpSts affected by pollution JJ^J^ It
71
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B, SIMULATION MODEL WITH PRODUCTION FUNCTION
Naylor et, al_, (1968) have defined simulation as a numerical technique
for conducting experiments on a computer which involves a mathematical
model describing a system. More generally, 1t is an approach to the
study and use of models (Orcutt, 1960). It should be stressed that it 1s
only a technique - an alternative approach to conventional mathematical
analysis of economic systems. There is no theory of simulation.
Conventional mathematical techniques can be used to determine the way
in which a model implicitly relates endogenous variables to initial condi-
tions, parameters, and time paths of exogenous (given outside of the
system) variables. Given the initial conditions, parameters and exogenous
variables, simulation generates time paths of endogenous variables. A
single solution generated by a simulation run is highly specific so that
many runs are required to generate a more general solution.
In agricultural economics there are two general reasons why simulation
has been appealingU), First, agricultural economics have been problem
oriented (as opposed to theoretically oriented) with an interest in
providing a basis for informed decisions. Second, as agricultural econo-
mics have focused increasing attention on natural resources and the
environment, community and economic development, firm and market decisions
involving truly dynamic and stochastic elements, and large scale policy
questions of regional or national scope, systems analysis and simulation
nave been increasingly applied. The study of problems encompassed by
these categories typically involve unresolved theoretical considerations,
or interdisciplinary theoretical problems. Simulation offers the chance
to experiment with the predictive power of such models under alternative
oehavioral assumptions.
Simulation also presents an alternative when models are difficult
to solve by analytical methods (usually because of stochastic elements
and nonlinearities in functions). Simulation models can be solved numeri-
cally (and can approximate analytical solutions) to investigate the
response surfaces of endogenous variables or to monitor the output of a
model under alternative settings of decision (control) variables.
Finally, in terms of introductory remarks, simulation is a tool for
sh±n9f ±ar1C SyStfS !sP*c1ally' That 1s» the 1n?ertemporal relation-
snips of the components of the system are one of the key features of the
Discussion follows Johnson and Rausser (1972).
72
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techn1que(2). Simulation is also a particularly good tool for handling
complex systems with interacting stochastic and nonlinear elements, but
aside from these attributes it cannot do any better than a well-conceived
analytical model. Thus, where data are available and analytic-optimizing
models can be constructed to model a system, the latter are preferable to
simulation techniques.
1. Features of Mathematical Models of Economic Systems
Any mathematical model of an economic system consists of components
(firms in a production system), variables, parameters, and functional
relationships^). Variables can be classified as exogenous, state, or
endogenous.
Exogenous variables are predetermined and given from outside of the
system being modelled. They are controllable or noncontrollable vari-
ables^), in a production system firms might be able to control planting
dates, purchases of inputs, and numbers of workers employed. In a complete
economic system policy makers should be able to control the emissions of
certain kinds of pollutants into the atmosphere. To the farm firm, however,
air pollution is clearly noncontrollable. Additionally, weather is
certainly the key noncontrollable variable for farmers as it affects growth
rates, yields, and quantities harvested.
State variables describe the state of the system or one of its com-
ponents at a certain point in time. These variables may be functions of
both exogenous and endogenous variables and are particularly important
in viewing the dynamics of the system (or sequential nature of a decision).
For example, the state variables of a firm (cash on hand, inventory level,
harvestable acres, soil moisture content) would depend on production,
sales, cash on hand, etc., 1n previous time periods.
Endogenous variables are the dependent or output variables of the
system and are generated by the interaction of the system's exogenous and
state variables according to the systems operating characteristics
(Including functional relationships and identities), For example, a firm's
net revenues, output, crop mix, etc, may be endogenous. In simulation
experiments we are particularly interested in the effects of different
levels of the exogenous variables on the values of endogenous variables.
(2) Simulation models are Implicitly dynamic except when one is simulating
probability density functions.
(3) Descriptions generally follow Naylor (1968).
(4) And, exogenous variables can of course be stochastic or nonstochastic.
73
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Functional relationships describe the interactions among the variables
of the system. There are three types of relationships: behavioral, iden-
tities, and decision rules.
Behavioral relations must be empirically derived on the basis of statis-
tical inference or determined from technical relationships. For example,
the response function relates yield per acre to water, temperature, soil,
fertilizer, and air pollutants. The probability distributions of random
variables (temperature, water, air pollution) are also included in the
behavioral relationships.
Identities are definitional or tautological statements. For example,
profit equals total revenue minus total cost or the output of all indivi-
dual producers of wheat in a region equals total regional output of wheat.
Decision rules specify the manner in which the farmer assigns values
to the decision or control variables (in a regional systems model, we
would have decision rules by which the EPA sets air quality standards).
Decision rule values as well as other parameters (such as coefficients of
the behavioral relationships) would be varied among simulation runs in
order to observe their effects on the system.
2. Simulation Compared to LP
La Due and Vincent (1974) suggest specific areas of usefulness for
simulation: (1) when complex decision processes are present that involve
uncertainty and/or multiple goals; (2) where indivisibilities of inputs
and outputs exist; (3) we are interested in sequential planning decisions;
(4) nonlinear functions are involved; (5) we want to incorporate concepts
of behavioral theories of the firm.
1n Se(?tion A 1t would aPPear ^at there are
hpnum ^Porating uncertainty into programming models. As
the number of stochastic elements deemed necessary to represent) in a
T ^T Tl^ pr°bably be better to use^than LP. For
to y.-tOChaSt!S P*61 wh1ch can be used in Monte Carlo
W°Uld be tfanSndoSTJ expensivfrelative
aoal !ith IddUinnJ? mul?'ple ?oal!> |-p imP11es the maximization of a single
goal with additional goals having to be represented by constraints (for
example, focus-loss constraints), assuming that they are linearly related.
Simulation, on the other hand, is valuable in comapring outcomes under
alternative decision rules - each incorporating different sets of Soals
Note again that simulation cannot generate optimal outcomes 9
Indivisibilities of inputs and outputs can be handled by simulation
74
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(5)
models and also by interger programming with LPV '.
Simulation can handle sequential planning decisions, but in programming
there is still recourse to recursive programming for short-run optimiza-
tion or dynamic LP for long-run optimization. However, simulation does
provide an advantage in that it traces out the time paths of the endogenous
variables, not just optimum points over time.
Simulation models can incorporate any number of continuous or dis-
continuous linear or nonlinear functions, qualitative variables, and
conditional relationships in any combination. In LP we must assume that
linear approximations suffice to represent nonlinear functions. In QP
we can use quadratic objective functions.
Finally, for our air pollution problem it is not relevant to consider
outcomes generated under alternative behavioral theories of the firm.
3. Applications
Johnson and Rausser (1972) thoroughly review the use of simulation
models in agricultural economics. They classify simulation models of the
firm as to whether they are process, farm planning, or growth_models.
Within each category most of the models are stochastic, dynamic, and
involve some nonlinearities.
Process models objective functions such as minimizing costs, maximiz-
ing returns over costs, and maximizing E-V utility. They involve certain
types of producing and marketing activities over which the firm has
control. An example is the Glickstein et. aj_. (1962) model of a cheese plant.
Planning models usually incorporate numerous production activities
with many strategies for combining them. Some contain innovative methods
of handing risk. Examples include Eidman et. al_. (1967) and Halter and
Dean (1965) compare alternative price expectation models in a range-feed
lot operation.
Firm growth studies are similar to those mentioned in (A) except
that they use simulation techniques or a combination of techniques.
Patrick and Eisgruber (1968) formulate a simulation model to trace the
time path of firm growth. Armstrong et al_. (1970) combine simulation with
LP while Chi en and Bradford (1976) use a MLP, RP, and simulation combined
approach.
We will provide a more in-depth description of three models: one that
simulates an integrated physical (hydrologic) - economic system; a dynamic
firm growth model; and a micro-macro model in which optimal decision rules
are derived for administration of the Federal Feed Grain Program.
15) See Chou and Heady (1961) for applications of integer programming.
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Horner and English (1976) sequentially link an LP and hydrologic
model in order to simulate the agricultural production and environmental
adjustments that would occur as results of environmental policies. Speci-
fically the objective of the study is to analyze the impacts of two alter-
native policies of increasing the quality of irrigation return flows. The
policies (increasing the price of surface water or requiring certain water
use standards) (6) are two of those conceivable under the Federal Water
Pollution Control Act Amendments of 1972.
The LP model derives optimal cropping patterns, optimal use of ground
and project water and fertilizer for 40 subregions in a 700,000 acre area
in the San Joaquin Valley. The objective function maximizes returns to
land and management in the area subject to the usual physical, institu-
tional, and market restrictions including the total amount of surface
water available and crop rotation requirements.
The results of the LP model function as inputs to physical submodels
that analyze the hydrology, salinity balances, and nitrogen concentrations.
In the submodels, the effects are estimated of irrigation water and
fertilizer use on water table depths and the quantity and quality of
irrigation return flows. Costs of collection and disposal of return flows,
and employing tile drainage systems are calculated. Then production costs
are adjusted accordingly in the LP model for the following year. Solutions
from the models are derived on an annual basis and are iterated until they
simulate the adjustments due to water-use changes that result from alter-
native policies.
The models were used to project future crop acreage, nitrogen ferti-
lizer use, water use, and net returns to land and management under "no
policy", the pricing policy, and management policy alternatives.
This particular approach to evaluating alternative policies is limited
in one main respect: it is only a crude approximation of the hydrologic-
economic system in the study area. Among the limiting assumptions are
that current irrigation practices and the chemical composition of avail-
able water will hold in the future. Both are likely to change which
suggests that the single period optimal LP solution is also unlikely to
be representative of future time periods.
In the Horner-English model, pollution producing and pollution receiv-
ing firms are both in the agricultural sector. An analogous approach to the
air pollution problem would be much larger in scope since air pollution
externalities are produced by nonagri cultural firms and individuals' autos,
whereas the recipients of the pollutants are in agriculture (excluding the
major sufferers of pollutants - individuals in all sectors).
(6) ^policies are designed to improve the efficiency of water use:
i™,iHnJnroeJS • Pnce 1S an alternative to an effluent charge; (2)
Water
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Chi en and Bradford (1976) integrate multiperiod LP (MLP) and simula-
tion techniques into a recursive sequential model of the farm firm growth
process. Applying-the model to a beef enterprise, they are able to com-
pare alternative management strategies and how they affect alternative growth
processes. In considering the problem of air pollution effects at some
level of aggregation, a model of farm firm growth does not have specific
relevance. However, the techniques have relevance in that policy makers
might want to compare alternative abatement strategies in the nonfarm
sector (the source of air pollution) and then explain and predict alter-
native time paths of regional growth processes. In other words, if air
pollution is reduced there are going to be abatement costs in the nonfarm
sector and presumed benefits in the farm sector. The adjustments of the
two sectors taken together will certainly alter existing development trends.
Basically Chien and Bradford combine MLP, recursive LP (RLP), and
simulation techniques into a single sequential model. The authors wanted
the optimizing features of MLP, the behavioral (flexibility) constraints
of RLP, and the ability of simulation techniques to handle multiple goals,
indivisibilities, and sequential decisions^}.
Phase 1 of the model consists of a Nerlovian (Nerlove, 1958) submodel
that quantifies the farmer's price and yield expectations in accordance
with his objectives, resources, finances, and organization. This submodel
forms the basis of the MLP submodel employed in phase 2. The MLP submodel
is used to derive the farmer's approximate long run plan and provide an
optimal "first move". The current farm plan (from MLP), plus prices of
inputs and outputs, consumption expenditures, inventories, other data and
a stochastic price and yield generating scheme are inputs into the simula-
tion model.
The simulation model then executes alternative decision-operation
processes for the current plan. Since in reality the farmer probably
cannot carry out the optimal plan as specified in the MLP submodel (due to
uncertainty, lumpiness of inputs), flexibility constraints are constructed
to place boundaries on enterprise levels in each period. Thus, a modified
current plan is obtained.
Given the modified optimal current farm plan, the simulator then im-
plements operation of the plan and executes a number of decisions regard-
ing purchases of inputs, purchases or rentals of capital assets, borrowing,
paying off debts, and depreciation of assets.
Growth of the firm was measured according to the time paths of three
variables: total assets, net worth, and size of the enterprise. The simu-
lated values were relatively close to the actual values of the variables,
T7) Remember that all of these things can also be handled without simulation
techniques.
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the differences being attributed to difficulties in accounting for house-
hold consumption and the debt repayment schedule. The model was also used
to examine the effects of alternative management strategies upon growth
patterns for future periods.
While the integrated model did incorporate dynamic and stochastic
features of the growth process, it also required substantial amounts of
time and money for data collection and computer software and hardware.
Shechter and Heady (1970) use a simulation model to derive response
surfaces in the Feed Grain Program. The components of the model are micro
units (firms) and macro units (aggregate regional outputs and the govern-
ment). Allocation and production decisions for the firms (for which
behavioral relationships are specified) are derived in the micro-simulator.
Outputs of individual farms are aggregated and enter the aggregated market
system (plus government), i. e., the macrosimulator. The decision vari-
ables (the alternative effects of which are examined in different simu-
lation runs) are minimum acreage diversion, price supports, payment and
loan rates, and diversion payment rate. The response variables are net
farm revenue of participants, stock accumulation, and total treasury costs.
The main emphasis in the study is the derivation of efficient decision
rules via response surface analysis. In the context of a multi-response
surface a locus of efficient decision rules is provided. This is important
in the respect that for any government decision there are going to be
trade-offs: in this case, increasing farm income conflicts with the goal
of reducing government cost.
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C. ECONOMETRIC MODELLING OF THE PRODUCTION SYSTEM
A broad definition of econometrics is that it encompasses "every appli-
cation of mathematics or of statistical methods to the study of economic
phenomena" (Mai invalid, 1966). Mai invalid defines econometrics in a narrower
perspective as the use of numerical data to test the postulated relation-
ships of economics.
In this section we are interested in agricultural production at either
the firm, industry, or regional/national level and econometric analysis
of either single equation production functions or simultaneous systems.
For our purposes, the latter could be production systems, biological/
behavioral systems, or market systems in which supply and demand_simul-
taneously interact. To be more specific, we are focusing on positive
relationships, i.e., what is the relationship between air pollution and
yield? How does it affect output and profits? In the previous section, LP
gave us "normative" answers, e.e., what should the optimal cropping mix be
given air pollution externalities and additional behavioral assumptions?
Within the general category of supply response^) (see section VI, A)
econometric analysis can be applied to the derivation of supply functions
from data relating to production functions and individual behavior, or
aggregate supply functions can be estimated directly with time-series and/
or cross-section data. In the following two sections on the single equation
approach to estimating biological and "whole farm" production functions,
we are concerned with the positive impact of air pollution as derived
explicitly from production functions. In our later consideration of simu-
ltaneous systems we are interested in the effects of air pollution on the
endogenous variables (determined simultaneously within the system) in
either production or market systems.
The basis of our analysis is an implicit production function,
f(y-l , yn; XT, ..... xm) = 0
that relates all outputs (y's) to all variable inputs (x's). Air pollu-
tion can conceptually be regarded as a variable input. If we are inter-
ested in any one output, it can be expressed as an explicit function
y0 = g(x-|, xn)
Given production functions for the firm of either form, plus infor-
mation on the functional forms, we can derive functions express!ng out-
puts, costs, and derived demands for inputs in terms of prices of inputs
and outputs. For example, we can derive short or long-run cost functions,
the marginal products of inputs (labor, capital, fertilizer, etc.), the
marginal rates of substitution between inputs, or the demand function for
TO As in section VI, A., Nerlove and Bachman (1960) and King (1975) are
basic review articles for agricultural supply analysis.
79
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labor. Before proceeding to a discussion of "whole farm" (aggregates of
firms) production functions, we will briefly digress by looking at the
biological (or firm) production function.
1. Biological Production Functions - Single Equation
(2)
A typical biological production function for wheat might appear as
follows (a function for sugar beets would be specified analogously):
YW = f(N. PgO^/K^O, Labor, Management, Weather, Air Pollution / weather)
(a) (b) (c)
Variables in set (a) may be varied in experiments. Hopefully, air pollu-
tion can be in (a) if there are enough observations (cross-sectional) in
areas with different air pollution levels. Otherwise, it might be incor-
porated in set (b), variables which are fixed by the investigator. Set (c)
is composed of random variables.
One firm could be represented by several of these partial production
functions - depending upon the number of crops grown. Given output (final
product) and input prices (factor prices), the behavioral criterion of
profit maximization can be applied to a hypothetical two crop, wheat-sugar
beet farm firm:
total revenue factor costs
< ' v . 1 ,
max ~ (PWAWYW + PSBASBYSB^ " (PNN + P|_L +....)
where: PW = price of wheat, PSB = price of sugar beet,
AN = acreas planted in wheat, ASB = acres planted in sugar beet,
Yw = yield per acre of wheat, Y$B = yield per acre of sugar beet,
PN = price of N, p, = wage ratej
L = man-hours of hired labor.
Profit maximization is subject ot the following constraints:
identities —
N = Nw + NSB, i.e., total N applied equals the sum of that
applied to wheat and sugar beets.
(2) By single equation we mean that production functions are specified as
unilateral causal relationships in which output is a function of pre-
determined input variables. Furthermore, output is assumed to be produced
independently of all other outputs and the estimated error term is assumed
to be independently distributed. Typically a single equation production
function at any level of aggregation would be linear or intrinsically
linear in which case classical linear regression techniques could be
applied. ^
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production f YW = f( )
functions [ Y$B= f( )
The profit maximization problem could be solved using calculus with
Lagrangean terms for restrictions. Additional restrictions could be
added for particularly limiting factors of production. However, in reality
the researcher is usually not able to derive continuous functions for each
process. Also, the solution procedure becomes cumbersome as the number of
crops and restrictions grows. Thus the best use of such estimated functions
is as inputs to LP models.
For specialized problems biological functions may be of use, especially
when we consider the time dimension (response efficiency over time, inter-
nal rate of return) and uncertainly. For example, De Janvry (1972) used
corn and wheat fertilizer response data to determine conditions under
which fertilizer use would be economical in Argentina (where most farms do
not use fertilizer). He attempts to assess the risk attached to different
dosage levels and obtains internal rates of return for particular invest-
ments in fertilizer. From a policy point of view he obtained an estimate
of the social returns from alternative fertilizer price policies.
2. "Whole Farm" Production Functions - Single Equation
In this section we are specifically speaking of aggregates of firm
production functions. Our starting point might be the following relation-
ship:
Output = f(labor, land, machinery, variable expenses,
management, air pollution (say S02) )
If we are concerned with one crop, output is an aggregate of all firm out-
puts of that crop. If we are concerned with more than one crop the depen-
dent variable would be product value at constant prices. Inputs would of
course be aggregates also™'. The function is usually fitted to cross
section data, or sometimes, cross section and time series data combined.
Among the applications of such models are analysis of supply response
(see VI, A for policy questions that are pertinent) based on aggregation
of firm marginal cost functions. Or, once we derive the marginal pro-
ductivities of factors, they can be compared: among different regions, or
with actual marginal products within the same region. For exampie, one
might estimate the marginal product of labor and compare ^ to average
waae rates (the two are equal at equilibrium in accordance with economic
fhlory) tn a regioS. ?n any case, once marginal products are estimated,
(3) Two general rules for input aggregation (particularly when using the
} iobbSgUs function) a?e (ij the inputs Sm^"*?^,^ d
be as nearly perfect substitutes or perfect complements as possible,
(2) relative to each other, the categories should be neither perfect
substitutes nor perfect complements.
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policies can be recommended. For example, if the marginal product of labor
was greater than actual wage rates it suggests that workers are being
underpaid.
Generally speaking whole farm functions may be useful as a positive
diagnostic tool in policy analyses concerned with serious disequilibria.
For example, the policy question of labor migration might be examined
from the point of view that surplus labor in one region is depressing the
returns to labor (i.e., causing poverty). Meanwhile a shortage of labor in
another region is depressing farm returns (thereby hindering firm expan-
sion and raising consumer prices) by causing farmers to plant non-labor
intensive crops. A policy of inducing migration from the labor surplus to
the labor deficit area is implied.
For purposes of analyzing the effects of air pollution in a market
system where we are interested in producer, consumer, aggregate welfare
effects and associated policy implications, we might view aggregate regional
production functions (by crop) as inputs into a general equilibrium model.
Such models are capable of being solved with LP or QP techniques and will
be discussed under VII, B.
Problems in Production Function Analysis
The problems pointed out below pertain to production functions aggregated
at any level.
We will briefly examine the following problem areas: (1) algebraic
form, (2) simultaneous equation bias, (3) specification bias, (4) measure-
ment problems, (5) combining time series and cross section data, (6)
technological change.
Algebraic form. Whole farm functions have frequently been estimated
as polynomials because the data suggests response surfaces of this type.
The commonly used Cobb-Douglas function is simply a log transformation of
a first degree polynomial.
The Cobb-Douglas function requires a constant elasticity of produc-
tion, constant returns to scale throughout the region of production, and an
elasticity of substitution equal to one. There are many alternatives to
these restricting assumptions and many alternative algebraic forms. For
Af AcTt4 fi- ( ?61} Su99ested the CES function in which the elas-
of substitution (between capital and labor in a two factor work)
n0a t0 With resPect ot cons^nt returns to
ttt1lMte * ^-Douglas ^™ with
. . Simultaneous equation bias. The question of simultaneous equation
bias arises because single equation estimation procedures normally lead
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to biased^ estimators when the true system is better represented by a
system of simultaneous equations(5). Most production function research
has utilized the single equation approach because of computational sim-
plicity and because it allows for theoretically satisfactory predictions
of output. Nevertheless knowledge of the underlying economic structure
remains unknown. Hoch (1958) found that in production functions where
simultaneous equation bias exists there was a general tendency for the
least squares estimated sum of elasticities to equal one (implying const-
ant returns to scale) even though the true sum was not equal to one (im-
plying either decreasing (sum < 1) or increasing (sum > 1) returns to scale).
Specification bias. It is not possible to completely specify and fit
the true production function relevant to a given process. Usually the true
functional form and complete range of input variables are unknown. Even
when variables are known it may be too costly or too difficult to measure
them. Thus there are specification errors in the typical function which
in turn results in specification bias in the estimated coefficients.
Typical specification errors made in Cobb-Douglas studies are: (1)
omission of variables (for example, neither technology in time series
studies, nor management effects in cross-section studies can be explicitly
measured; or, if ozone concentration really decreases alfalfa yield by
15 percent, it would be important not to omit ozone as an in2ePfndent
variable); (2) aggregation within inputs (no matter how carefully we define
input categories there are likely to be quality differences in inputs; for
example, one unit of labor is not likely to be the same as any other unit);
(3) aggregation over inputs (specification bias will result if the rules
in footnote (3) are violated).
Griliches (1957) obtained some general results fromT!pecification
errors in Cobb-Douglas production function estimation. If an input is
excluded that vaHIs less than proportionately with the included inputs
(and vice versa), returns to scale will be underestimated The omission
of a managerial input variable biases the estimate of returns t.scale
downwards and the elasticity of output with respect to capital "P™*- .
The omission of quality differences in labor (due to education for example)
results in an upward bias in the estimated elasticity of capital, and a
downward bias in elasticity of labor and returns to scale.
Measurement problems. We have touched upon conditions for aggregation
of inputs and the biases that result from aggregation bias. In this
fectTn we will deal Sre explicitly with actual measurement problems in
variables.
(4) Specifically, simultaneous equation bias °f^.^^i
the production relation affect the observed values of al variables
(notPj2st the dependent variable), thus producing inconsistent estimates
(5) See later sections for more discussion of the simultaneous approach.
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(i) Output: If we have a single product, we can aggregate output in
physical terms. Since most farms produce more than one crop we are typi-
cally faced with the aggregation of multi-product firms. It might be pre-
ferable to estimate aggregate functions for each crop (with the restrictive
assumption that there are no interdependencies among crop choices) so that
something can be said about investment in individual enterprise choices,
but frequently individual enterprise data relating quantity of each input
to quantity of each output are unavailable. This is especially true for
cross section studies where a wide range of farms should be included. Thus,
the researcher usually turns to an aggregate measure of value output. For
example, if we have multiple products produced in constant proportions we
can use prices as weights to obtain a value index. However, if we have
multiple products in varying proportions it would be reasonable to use a
simultaneous approach.
(ii) Labor: Usually, the researcher aggregates operator, family, and
hired labor using wage rates as weights. But, there are problems in the
following areas: what is the proper wage rate for the operator's labor?
(or family labor?). Also, data are usually lacking for labor used so labor
available is measured. Finally how do we account for differences in labor
quality as influenced by age, education, etc. Griliches (1963) incorpo-
rated separate variables for labor and education in his aggregate agricul-
tural sector production function. Since there was no significant differ-
ence between the coefficients, he later included labor and education as an
interaction term so that labor could qualitatively improve over time
(Griliches, 1964).
(iii) Capital; As Heady and Dillon (1961) suggest: a finding (based
upon farm sample estimates) that capital inputs have a marginal return of
so many dollars tells nothing about the productivity of different forms of
capital inputs except for the sample firms. Thus, capital inputs must be
categorized (again following the rules in foot not (3) ). Among the
factors to be considered in specifying a production function, in addition
to land, labor, pollution, etc., are improvements, liquid assets, cash
operating expenses, maintenance and depreciation of fixed assets. Which
factors to include as capital inputs depends on the production process
being examined. For example, purchased feed, seed, and fertilizer might be
very important in some operations. Durables are usually very important and
can be measured by the maintenance and depreciation costs (plus the rate
of interest on the investment) associated with the use (as opposed to
measuring their value on an inventory basis). Thus, the service flow is
measured.
(iv) Land: The basic problem in measuring land is that of quality.
One could use price (or cash rent) to obtain the value, or land taxes.
The latter would present problems if the region were significantly urbanized,
Alternatively, a service flow concept analogous to that in the measurement
of capital could be employed. Land would be specified as real estate
(land, buildings, equipment tied to land) and would be measured by depre-
ciation on buildings and equipment, maintenance on buildings and equipment,
84
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plus interest on the investment^ '.
(v) Management: This is probably the most difficult variable to
measure in "whole farm" studies. Obviously, management ability will vary
among entrepreneurs and the consequences of omitting this variable were
mentioned in the section on specification bias. But what are our choices?
Management is usually considered to be part of the error term and not
specified at all. In this case the residuals between production levels
estimated from the fitted function and actual observed production levels
are attributed to management. Alternatively, one could measure management
with objective or subjective test scores. This approach has not been widely
used, but Heady and Dillon (1961) used a management index and found that
increasing returns to scale (as opposed to constant) "seemed to be due
to management. Doll (1974) has suggested representing management efficiency
by attaching efficiency level coefficients to each input as well as speci-
fying an overall general efficiency leveU".
(vi) Time series - Cross section data combined; Another way of handling
the management effect is by analysis ot covanance (ANOC) using time series
and cross section data. Hoch (1962) init ally introduced a constant term
to a Cobb-Douglas function to represent differences in tehcnical eff ciency
among farms. Realizing that simultaneous equation bias would occur if
either cross-section or time series data were used alone, he added a time
c'onsLnt to represent°changes in technical efficiency over time anc suggested
analysis of combined time series and cross section data. Among Hoch s
conclusions were that the firm effect could represent technical efficiency
or alternatively, entrepreneurial capacity (management). Thf *™%®"®"
measured weather differences (the significance of the time effect ndicates
that explicit consideration of weather would be useful) and changes in
productivity overtime.
Paris and Hoch (1966) advocate the use of the ANOC model to allow
production e?ast?c?ties to vary among firms and years Norma "yi "Pro-
duction function analysis all farms are assumed to be operating with the
(6) we are likely to have a multicol linearity problem (that is,
c^t^lM^
Bfe
slyThlt thY effeSte of urban encroachment on land values and pollu-
tion on production are col linear.
(7) C-D function to be fitted to cross section data:
Xi2B2ecp
With added symbols mi to represent level of management on 1th farm:
85
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same function. Attempts to avoid this problem by estimating individual
farm functions have generally been poor. Thus the Paris-Hoch approach
includes firm and time effects both as constant terms and as components
of input coefficients. The results of this approach include meaningful
estimates of firm elasticities (as well as some measure of management)
which makes the results much more applicable to individual farm deci-
(vii) Technological change: We have just seen that the inclusion of
firm and time effects in an ANOC model estimated with time series and cross-
section data provides indicators of technological change. Generally, the
problem of measuring technological change has arisen because of observed
shifts in firm production surfaces over time. These shifts may be due to
the use of new inputs (i.e., replacing old) or due to qualitative improve-
ments in inputs (for example, labor improved due to education). From a
cross-sectional viewpoint we may observe firms operating with different
arrays of inputs (i.e., old and new arrays).
With time series data, a time trend variable t can be added as an
independent variable to allow for technological change^). In the case of
neutral technological change (i.e., not biased toward capital or labor),
t would be incorporated as a shift variable (see Solow, 1957).
3. Simultaneous Systems
In the previous section we mentioned the implications of simultaneous
equation bias in production function analysis: that is, the consequences
of specifying and estimating a unilateral causal relationship when in fact
a system of mutually determined relationships exists. In other words, the
production relation may well be embedded in a system of equations in which
inputs, outputs, and other variables are mutually determined 00).
(8) Hoch has come out with two recent articles (1976a and 1976b) on this
subject. Suffice it to say that there is some disagreement over the
applicability of elasticity estimates to the firm level.
(9) In a Cobb-Douglas framework, technological change can be expressed by
shift variable (change in intercept) and/or by changes in the partial
elasticities of production.
(10) Except where relevant, we will not discussing estimating procedures
and other statistical problems. Generally, some of the problems involved
in estimating a structural system are similar to those in single equa-
tion models. That is, there are similar problems in choice of vari-
ables, algebraic form of the functions, validity of assumptions and
interpretation of results. Among the references for simultaneous equa-
n2^eCMn^UeS ia/?n!l?gle ecluation) are: Foote (1955), Goldberger
(1964), Malinvaud (1966), and Theil (1971)
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The variables in a simultaneous system can be divided into the
following categories:
(1) Endogenous: variables whose current values are determined simul
taneously in the system (note that in the single
equation models discussed earlier there was one
endogenous variable - the dependent variable).
(2) Predetermined: current values are treated as given.
(a) exogenous: values determined outside of the system.
(b) lagged endogenous.
The structural model may be written in matrix form as:
B Yt + rj Y(t-l) + T2 Xt = Ut 0)
where: B = matrix of coefficients of current endogenous variables
(G x G in system of G structural relations)
Y+ = vector of current endogenous variables
n = matrix of coefficients of lagged endogenous variables
Yt i = vector of lagged endogenous variables t
T2 = matrix of coefficients of current exogenous variables
Xt = vector of exogenous variables
Ut = vector of disturbance terms
In contrast to the structural form of the system the reduced form
of a complete (the number of endogenous variables equals the number of
equations) system expresses each endogenous variable as Actions of
only, predetermined variables and disturbances. That is, each equation
hiFbnly one endogenous variable and it is the dependent variable.
The reduced form of equation (1) is:
Yt = nl Y(t-l) + n2 Xt + vt (2)
where: ni = matrix of reduced form coefficients of lagged endogenous
I • i_ i
no = matrix of'reduced form coefficients of exogenous variables.
Vt = vector of reduced form disturbances.
and IT, = - B-lrls n2 = - B-lr2, Vt = B'lUt
The estimation of structural coefficients in (1) provides know-
ledae of the underlying economic structure under consideration. The
reduced fofm is usefTfor prediction, that is, predicting the impact
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of a change in an exogenous variable on the endogenous variables^11^. The
reduced form coefficients nj and 112 in (2) are referred to as impact multi-
pliers and specifically "show the effect of a unit change in any giveTTixo-
genous variable on the expected value of a contemporaneous endogenous vari-
able after all the simultaneous effects of the system have been worked
through" (Sarhan e_t al_., 1976).
The implications for analyzing pollution effects should be apparent.
Suppose that we have a market structure for crops adversely affected by
air polluiton. On the supply side we might have yield equations which
enable us to quantify the direct effects of air pollutants on yields. We
also might have production functions (from which supply functions can be
derived) embedded in the supply system. On the demand side we have the
price-demand structure representing the consumer and faced by the farmer.
Air pollution is obviously exogenous to this system. Aside from estimating
the coefficients of the structure in which air pollutants operate, we will
be particularly interested in the impacts of changing air pollution levels
(they may increase in the absence of standards or decrease with the imple-
mentation of standards) on the endogenous variables in our system: yields,
output, demand for inputs, profits, consumer prices, etc. We will also be
interested in the distributional impact on producers' and consumers'
surplus. The effects of sustained changes in air pollution are even more
important in which case we can obtain dynamic multipliers
(11) The relationship between the structural and reduced forms of the model
is known in econometric terms as the problem of identification. There
?SiraS i* order conditions for exact identification (see Theil,
971; Malinvaud 1966; Goldberger, 1964), but instead of citing these
in econometric terms we offer a verbal description.
lLt]"c° °r-m°^ t!;eories uare observational ly equivalent, then they
] cions about observable phenomena under all cir-
-
won K We attfP* to estimate the parameters of the theories,
nay to disnguish the parameter estimates of one
ssr
Reduced form parameters are always identified i e thev are
teob eV a' ions^ Th™ ^ 5*™^ °f the ^ dlliHbSSoSlf
if aSd onlv 5? JA nlh structure of the structural form is identifiable
othe? wS?ds I JJrnrJr ?tructure has the same reduced form, or, in
other words, a structural parameter is identified if and onlv if it
can be uniquely deduced from the reduced fSrm parameter! y
-------
Applications of the Simultaneous Equation Approach
In this section we describe three studies that employ a simultaneous
equation approach to answer alternative research questions. First, we
describe the work of Lau and Yotopoulos (1972) in which they jointly estimate
profit and labor demand functions for Indian agriculture. Second, we
examine a biologic/behavioral model of a mosquito abatement district.
Finally, we outline a dynamic econometric model of the market structure for
white dry edible beans.
The analysis of an aggregate profit function is advanced as an alter-
native to the analysis of production. Under the assumptions that (a) firms
follow the decision rule of maximizing profits, (b) firms are price takers
in output and input markets, and (c) the production function is concave in
the variable inputs, "there exists a one-to-one correspondence between the
set of concave production functions and the set of convex profit functions"
(p. 11). Among the advantages of working with a (unit-output-price) pro-
fit function instead of the typical production function are that the aggre-
gate supply function and factor demand functions can be derived without
the explicit specification of the production function^2'. Furthermore,
the profit function, supply function, and factor demand functions so
derived may be written as explicit functions of variables normally consi-
dered to be determined exogenously to the firm's behavior. Direct estima-
tion of these functions in the reduced form thus avoids the problem of
simultaneous equation bias.
In production function analysis with labor as a variable factor, the
farmer's decision variables would be output and labor input. These vari-
ables would be jointly dependent with the prices of output, wage rate, and
quantities of capital and land specified as predetermined variables.
However, the specification of a profit function leads to use of profits
and total labor costs as jointly dependent variables. Because the right
hand side of the two equations includes only predetermined variables the
application of ordinary least squares (a single equation technique) will
be consistent, but inefficient because of the appearance of H] in each
TT2) In this particular study, with labor as the variable factor and
capital and land fixed, the particular estimates of importance
are the labor demand and output supply elasticities with respect
to wage rate, price of output, and quantities of capital and land.
Also, the coefficients of the production function (Cobb-Douglas)
are obtained and the hypothesis of constant returns to scale is
tested.
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equationOS). Thus, the authors jointly estimate the equations with
Aitken's generalized least squares04) and in fact obtain the best results
by adding two constraints: a* = oq and e-| + ej? = 1. The 1atter constraint
spefifies constant returns to scale.
The reduced form elasticity of a change in output with respect to a
change in the quantity of land is derived because of its policy implica-
tions. For example, an increase in land will lead to an upward shift in
the marginal product of labor (hence, wage rate). This reduced form elas-
ticity, derived from output expressed in terms of the profit function, has
distinct advantages over the analogous production function elasticity (of
output with respect to land). In the latter, the effects of an exogenous
increase in land on output can be measured, but holding other factors
constant. In the profit function, other factors can be influenced by the
exogenous change in land.
Sarhan e_t a]_. (1976) use a simultaneous equation approach to model a
biologic/behavior system, specifically, a mosquito abatement district.
The objectives of the study are to first formulate an empirical model
(simultaneous system) of an abatement district in which mosquito popula-
tion variables, mosquito control methods, and control method effectiveness
are simultaneously determined. Second, unit cost data were applied to the
endogenous variable coefficients in the model in order to compare the
economic efficiency of alternative control methods(15). Third, given that
(13) Without going through the mechanics, this is true both theoretically
and empirically. The final empirical model is:
(1) In n = cu + En- D,- + ai In w + et In K + BO In T
,
where: n* = profit per farm
w1 = money wage rate per day
D-j = regional dummy variables
L = labor in days per year per farm
K = interest on fixed capital per farm
T = cultivatable/and in acres per farm
(14) Zellner (1962) proposes this approach to estimating a system of equa-
tions because of efficiency gains and minimization of aggregation
bias.
(15) The indirect effects of changes in the stock of past sumps, ponds, etc.
(or any other control method), on the light-trap index variables were
calculated from the reduced form of the model. The coefficients of the
exogenous variables in the reduced form are impact multipliers.
Of more interest, however, are the dynamic multipliers, i.e., the
effects of unit changes in exogenous variables sustained for a period
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a comparison of the physical efficiency versus economic efficiency of control
methods showed that the abatement district managers were making suboptimal
decisions (i.e., the application of pesticides was expensive and not as
efficient as other methods given the build-up in pesticide resistance), an
LP model is constructed that selects the minimum cost combination of con-
trol methods subject to appropriate physical, labor, and institutional
constraints. The model also assures that the mosquito population will
not exceed a specified level.
Among the direct policy implications of the study were that over-
reliance on chemical pesticides in the short-run would lead to more expensive
physical control methods in the future, given tolerance build-up and the
decreasing probability that replacement pesticides can be developed.
Vandenborre (1968) formulated a dynamic econometric model of the market
structure (i.e., it contained empirically estimated demand and supply rela-
tionships) for white dry edible beans in order to (1) evaluate the impact
of government price support programs, (2) study the impacts of changes in
exogenous variables on the system, and (3) estimate the effects of esta-
blishing support prices above free market prices.
The supply (or production) system contained a relationship for each of
four bean varieties. The relationships involved one acreage equation
(since acreage data was generally unavailable) and three equations speci-
fying production in terms of thousands of hundred-weights. Pre-determined
variables included lagged prices (own and competing crop prices) and time
trendsOS) to indicate yield fluctuations. Vandenborre justifies this
specification on the grounds that acreage data were unavailable for all
varieties. However, even this line of reasoning is insufficient to justify
(15) continued:
of time on the endogenous variables. For example, the direct and in-
direct effects of sumps, ponds, etc., constructed was compared to the
number of locations treated with pesticides over a time horizon of
eight years. Both methods were found to be beneficial in the short-
run, but in the long-run the indirect costs of pesticide use greatly
outweighed the short-term benefits due to tolerance build-up.
(16) The use of time trends or lagged production in supply equations can
account for yield fluctuations due to externalities such as air
pollution. Time trend variables also serve as proxies for many other
effects (weather, technology, management improvement), thus their
interpretation is difficult.
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the lack of use of more satisfactory alternative specifications^ '.
On the other hand, since the components of the price-demand structure
are determined simultaneously, a system of eight structural equations was
postulated. Structural coefficients were estimated by two-stage least
squares.
The supply and price-demand structures are integrated into one dynamic
model through various operations including the computation of the reduced
form of the price-demand structure. Just as in the Sarhan et_ al_. study,
dynamic impact multipliers are obtained. With respect to the structure of
the market for white dry beans the impacts of changes in the following
exogenous variables were deemed to be important: price of corn (because
corn competes with navy beans for acreage), disposable income (its impact
on quantities supplied and demanded and on prices in the absence of govern-
ment programs), and income from feedgrains.
(17) A more satisfactory approach would have been to use an adaptive
expectations or partial adjustment model on the supply side. The
former has been used extensively in the analysis of agricultural
supply and is expressed generally as:
Yt = A0 - ._. ,
k=0
where Yt = vector for which explanation is sought (supply or acreage)
Zt = vector of explanatory variables
A0 = parameter vector
A] = parameter matrix
0 = a seal or
E£ = disturbance terms
and * .
- e (l-e)k Z
where Z. = decision makers subjective expectations vector for prices
and yields on which the decisions Yt are based. Just
(1974) geometrically includes quadratic lag terms to
indicate the farmer's subjective evaluation of the
variances of prices and yields (i.e., risk accounted for).
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4. Summary
In II, C. we have progressed from single equation biological production
functions (conceptually regarded as inputs to firm LP modles) to whole
farm single equation production functions (which may conceptually be
thought of as inputs to a spatial programming or econometric model of a
regional market structure) to simultaneous equation models of a production
system, biological/behavioral system, and a market system. It is suffi-
cient to say that since economic models realistically involve many jointly
dependent variables whose values are determined simultaneously, the
simultaneous equation approach is preferred. Additionally, the reduced
form of structural models allows for the evaluaiion of impact multipliers,
i.e., the effects of changes in exogenous variables on the system can be
determined.
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SECTION VII
SECONDARY ECONOMIC IMPACTS DUE TO AGRICULTURAL CROP YIELD CHANGES
A. REGIONAL INPUT-OUTPUT MODELS
In put-output analysis as originally developed by Leontief (1951) is
an empirically oriented multimarket analytical technique^). Leontieff
used an input-output system to determine the interdependence of various
sector of the U.S. economy. 1-0 analysis is a simplification of the
general equilibrium framework referred to in VII, B. For example, utility
functions are omitted and consumer demands are usually specified as exo-
genous without regard to consumer market equilibrium. The production
function for each industry is a constant coefficient function. The major
function of 1-0 analysis is the determination of interdependence coeffi-
cients among the sectors which in turn may be used to predict output.and
employment in different sectors under varying conditions of demand^'.
In the following subsection on 1-0 applications, we describe two
1-0 models developed for local economies. Humboldt County, California
is richly endowed with timber resources and natural resource amenities
that appeal to residents and tourists. It is also an economically
depressed economy with high unemployment and sluggish economic growth.
One of the crucial issues facing decision-makers in the County is the
trade-off between preservation of natural resources and their exploitation
at higher rates which would stimulate economic growth and employment.
1-0 analysis is used as a tool to quantitatively interrelate the crucial
forest products sector with the rest of the economy. Similarly, 1-0
analysis is an appropriate tool to use in relating air pollution effects
at the farm level to secondary impacts at the agricultural processing
level and in nonagricultural sectors. Welfare effects can also be deter-
mined because of the inclusion of households as an exogenous or endogenous
sector. With an 1-0 model we can look at relationships under recent
normal levels of pollution as well as project changes in sector outputs,
regional income, and employment under pollution levels that are estimated
to occur if standards are set.
The second 1-0 model discussed is a more complex and conprehensive
economic-ecologic model of the Charleston, South Carolina economy. The
authors are particularly interested in aiding environmental planners in
issues concerning economic growth, resource utilization, and pollution
(1) Two general descriptive references are Isard (1960) and Heady and
Candler (1958 - see references under VI, A).
(2) There are, of course, many other problems that may be handled with
1-0 analysis.
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generation. Such a model pertains to the air pollution-agriculture system
in that the latter is also an ecologic-economic system. We might think of
nonagricultural sectors such as particular industries (responsible for
factory emissions) and households (auto emissions) as economic units
emitting elements that adversely affect the ecological system. In agri-
culture the damage is manifested by crop damage of specific forms mentioned
in Section V. This ecological damage is transmitted back into the economy
through its effects on yields and quality.
1-0 analysis is closely related to programming procedures discussed
in VI, A and VII, B, but differs in certain respects that we want to empha-
size: (1) 1-0 analysis is positive in nature as opposed to the normative
nature of programming; (2) the industry rather than the firm is the unit of
production*3'; (3) in 1-0 the initial set of activities (the product mix of
the various sectors and final demand are given and solution involves
determination of interdependence coefficients. In contrast, in programming
models the input-output coefficients (of the firm) are given and the
solution yields an optimal set of activities. On the other hand, there is
one major similarity - both 1-0 and programming involve linear relationships
and are easy to solve.
1-0 may have some shortcomings in terms of oversimplification, but
nevertheless has been the most widely used tool in the study of regional
and interregional interdependence. Its strength lies in the detailed
presentation of (1) the production and distribution characteristics of the
industries of different regions and (2) the nature of the interrelationships
of these industries among themselves and among these industries and other
economic sectors (Isard, 1960:310).
1. Applications of 1-0 Analysis
a. 1-0 Model of Humboldt County. California
The general objective of Dean et al_. (1973) in formulating an 1-0
model of Humboldt County was to provide an analytical framework that would
aid public and private decision-makers to make decisions crucial to the
economic development and environmental quality of Humboldt County. The
issue of economic growth versus environmental quality is particularly im-
portant in Humboldt County since it contains abundant natural resources
(timber, fisheries, wildlife) and because its economic vitality depends
heavily on natural resource-based industries: forest products (primarily)
and fisheries and recreation-tourism (secondarily). In addition, the
(3) Thus, an aij coefficient in 1-0 gives the amount from industry 1
necessary to produce one unit of commodity j while in LP the a^
coefficient is ?he quantity of the 1th input required to produce
one unit of output.
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depressed nature of the economy (leading to high average and seasonal un-
employment) increases the importance of current and future decisions.
Thus, the specific objectives of the study were to construct an inter-
industry model in which natural resource-based industries were emphasized,
and to make 1980 projections of the county economy under alternative out-
put specifications, or final demand for, those natural resource industries
most likely to be affected by environmental decisionsW.
The model was "partially" open in that the household sector was endo-
genous while exports and state and local governments were autonomous, thus
constituting "final demand".
The industry data used to construct the transactions table (which
ultimately contained 28 sectors) were primarily secondary, although a
personal survey of businesses was carried out (mainly in the natural resour-
ces sectors) to collect cost information from certain firms. Government
sector data came from both published sources and city budgets. Household
output ("output" since it was endogenous) was specified as being equal to
personal income, while the distribution of expenditures was based on
patterns found in similar areas in the Western U.S.
Output multipliers (from the interdependence table) are used to evalu-
ate the local output impact of increases in final demand (exports, includ-
ing tourist expenditures, and nonlocal government). Typically, low output
multipliers were found for industries that imported most of their inputs
thus creating few backward linkages (example, food processing).
Of more interest in the Humboldt County study was the derivation of
two types of income multipliers. The "Type I multiplier" was the ratio of
direct plus indirect to direct household income generated by a unit increase
in final demand. For example, in the Seafood Processing Industry a $1
increase in final demand (exports in this case) could lead directly to an
additional $.36 local income and indirectly (through strong linkages) to
an additional $.45 in local income. The Type I multiplier is equal to the
sum ($.36 plus $.45) divided by $.36, or 2.25.
The "Type II multiplier" shows the ratio of direct, indirect, plus,
induced income to direct income generated by a $1 increase in final demand.
This additional induced income is that proportion of direct and indirect
increases estimated to be spent within the County, thus creating additional
multiplier effects through demands on local industries.
(4) These alternative specifications included variations in the level of
cut in the lumber industry, size of catch in the fisheries industry,
level of recreation-tourism activity, and level of certain government
activities related to the environment.
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The use of the 1-0 model to make 1980 projections yielded results
with important policy implications for the County. It was found that
prospective output increases in nonlumber sectors of the economy would be
offset by decreases in lumber output because of the effects of technological
change(5j, employment would likely decrease from 1969 levels. This
suggests that, in the absence of new employment creating firms, large
amounts of nonlocal government expenditures will be required just to
maintain employment levels. The bleak employment picture also raises
questions about school financing (with a dwindling tax base) and suggests
a policy of encoruaging out-migration.
b. Laurent-Hite Economic - Ecologic Regional Model
Recognizing that economic development creates (exports) environmental
externalities and that the ecologic system in turn exports various products
to the economic system(6), Laurent and Hite (1971) formulate an economic-
ecologic model based on input-output analysis that incorporates both
environmental and pecuniary values. The model is given empirical content
by (V) developing a 31 sector 1-0 model for Charleston, S.C., a small
coastal economy; (2) identifying and quantifying some relevant economic-
environmental linkages; (3) developing environmental-income multipliers, i.e.
the environmental impact per dollar of income generated by the 31 sectors.
Finally, the use of the model in environmental planning (particularly
resource management and zoning decisions) is discussed.
The theoretical underpinnings of the model are as follows: using a
Leontief(') model as a base, a general equilibrium approach is conceived
in which materials move from the environment to the economy and then back
to the environment.
The ecologic system consists of a large number of interdependent acti-
vities involving inputs and outputs. Commodities (materials) are exported
from the ecologic system to the economic (processing sector) system, change
(5) Technological change was accounted for through labor productivity only.
Wage increases of workers were assumed to match increases in average
product per worker as projected using U.S. trends. The authors deemed
this approach to technological change to be superior to the best
practices" approach (assuming the average firm in the future will use
the technology currently employed by the most advanced firms) suggested
by Miernyk (1965).
(6) This conceptual framework parallels that of Ayres and Kneese (1970) in
which environmental pollution is conceived of as a materials balance
problem. That is, if man uses materials from the environment he must
return the residuals of these materials to the environment.
(7) The Leontief model, is, in effect, the generic name for the basic 1-0
model as developed in Leontief (1951, 1966) and refined by several other
authors.
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form, and are then exported back to the environment^ . By conceiving
of environmental resources in this way and by closing the household sector
into the endogenous part of the model (hence removing the labor constraint
on production), the only input constraint on production is the amount of
resources available. By varying the amount of resources available and
computing their effects on the economic-ecologic system, alternative resource
management shemes can be evaluated.
Operation of Model
The final version of the model closed the household and all government
sectors into the endogenous part of the 1-0 table. The actual 1-0 table
was constructed primarily on the basis of field survey data supplemented
in a few cases by secondary data.
The 1-0 table was used to obtain the table of interdependence coe-
fficients and the usual multipliers were obtained showing the income effects
of direct and indirect increases of export sales for given sectors.
A 17 x 28 environmental matrix (data obtained from secondary) sources
was formulated to represent 17 environmental goods and their use by 28
economic sectors. One limitation of the study is that environmental
emissions had to be placed in the sector to which they were most closely
linearly related. Thus, auto emissions are charged to service stations
rather than households^).
The next step in the empirical operation of the model is to derive the
R matrix of direct and indirect environmental impacts (see previous foot-
note). The direct effects come about because some sectors draw directly
(8) The actual linkage of the economic and ecologic models was performed by
post-multiplying the environmental linkages matrix (ecologic system) by
the inverse matrix of the input-output model:
(E) (1 - A)"1 = (R)
where: E = matrix of inflows to and outflows from the economy to the
environment;
(1 - A)"' = inverse matrix of 1-0 model;
R = matrix of direct and indirect environmental impacts of each
economic sector.
(9) There may be no way to avoid this. That is, auto emissions are not char-
ged to the sector most responsible for them. On the other hand, exhaust
emissions are more likely to increase linearly with gasoline sales than
with household income. The problem is that of the linearity assumption
of the 1-0 model. For example, it is necessary to assume that auto emi-
ssions per dollar of household income are the same for any level of
income in order to charge auto emissions to the household sector.
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on resources; the indirect effects because other sectors purchase inputs
from sectors that draw directly on resources. Thus, all sectors are in
some way responsible for resource utilization.
The economic-ecologic model is then used to derive environmental -
income multipliers, i.e., the direct and indirect environmental linkages
per dollar of pecuniary income generated in the various sectors. These
multipliers have significant planning implications'10). For example, a
policy making body intent on maintaining supplies of regional natural
resources will use the multipliers to determine which sectors can expand
with the least environmental usage per dollar of income generated. Simi-
larly, regional authorities can decide what types of industries should be
encouraged to locate in the Charleston area, given existing technology
and the trade-offs between income generation and resource utilization.
Resource utilization is only part of the environmental problem, the
other part being emissions. Thus, planners are faced with three variables
in their decisions: resource utilization, income generation, and pollution
generation. If the researcher can accept the underlying assumptions of
the model, it is a comprehensive tool to analyze the trade-offs between
these variables. The model extends 1-0 analysis beyond the consideration
of income and jobs as the only important development parameters^1'I.
The necessity of updating the environmental coefficients should be
kept in mind. As mentioned in footnote 10, the estimated environmental
coefficients are, at best approximations of the true coefficients. This
problem is further complicated by the assumption of static technology.
Thus, coefficients in the environmental matrix are based upon current
intakes and discharges and each column in the 1-0 table represents current
purchases, given the technology in place. Allowing for alternative treat-
ment levels (for example, waste treatment) would require additional environ-
mental matrices and the 1-0 model would require changes in purchasing
patterns for each level of treatment. The researcher would be faced with
combining the 1-0 table with different environmental matrices.
TlO) The implications must be considered in relation to the data used.
For example, the environmental coefficients are at best ballpark
estimates, having been generated in large part from engineering data.
However, there is always the possibility of updating the coefficients
as new knowledge becomes available.
(11) Laurent and Hite esentially ignore the job question. Unemployment
may be low in Charleston, but in other areas, notably California, the
trade-offs between environmental quality and employment creation are
extremely important. The Dow Chemical decision is a notable example.
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One alternative to the problems discussed above would be to include
various sets of 1-0 and environmental matrices into a comparative static
programming model in which one could analyze the effects of different levels
of economic activity and changing treatment levels. The major constraint
on this type of analysis would be the availability of the extensive data
required.
c. Summary: Application of 1-0 analysis
One shortcoming of the Humboldt County model was its exclusion of an
environmental matrix - especially given Humboldt County's rich endowment
of natural resources. This exclusion may be due in part to the focus of
the study on income and employment. The timber resource was viewed as
something to be exploited, not preserved. The authors do point out that
over the long run the "amenity resources" value of Humboldt County would
likely improve. If so, some methods of incorporating "amenity resources"
lost due to development (perhaps by means of an environmental matrix)
should have been included.
1-0 models are relevant to the problem of air pollution and its effects
on the agricultural sector. We are interested in the interrelationships of
agriculture and the non-agricultural economy, specifically in what effects
the polluting non-agricultural sector has on the non-polluting (in terms
of air quality) agricultural sector. From a positive viewpoint we are
interested in what effects air pollution damage in agriculture has on
agriculture-related sectors. We also wish to project the consequences of
alleviating air pollution damage on agriculture and related sectors.
What we are losing in 1-0 analysis and what might be gained by a
spatial equilibrium approach (see VII,B) is allowance for riskiness in
farmers' decisions given the prospect of pollution damage to crops, the
specification of alternative cropping activities (recognizing that pollu-
tion affects crops in different ways), and the possibility of observing
welfare gains and losses due to adjustments to air pollution and projected
gains and losses directly by calculating the model maximand for alterna-
tive air pollution abatement policies.
2. Methodological Appendix
a. Building an 1-0 Model
Regardless of whether the researcher is interested in a national,
interregional, regional, or community-based model, three general stages of
analysis are involved.
The first stage (and the major effort in building the model) is the
construction of a transactions table. This involves defining relevant
economic sectors and allocating the output of each sector to a purchasing
or using sector. Since the construction of a workable model will require
some aggregation of sectors, transactions (or flows) are converted to money
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units. The number of entries required in the transactions table is approxv
mately the square of the -number of sectors defined because of the double
entry accounting of the dollar flows of all goods and services.
1-0 models are referred to as open or closed depending upon whether
all sectors are endogenous (closed) or whether some sectors (notably,
household, government, exports) are autonomous or "outside the system.
The second stage in the analysis is to obtain a table of input-output
coefficients in which the elements relate the amount of inputs (in dollars)
required from each sector to produce a dollar's worth of output for any
given sector. The basic assumption made here is that the coefficient is
measured from a single (and current) observation of the ratio between the
transaction of one sector to another and the gross output of the receiving
sector.
The third stage of 1-0 model building is to develop a table of inter-
dependence coefficients. Each coefficient summarized both the direct and
indirect dependence of one sector on another. Although the interdependence
table may be summarized in several ways, the most common is to determine
output multipliers (by vertical summation of the columns). These give
thitFtal value of inputs generated from all sectors associated with a one
dollar sale to final using sectors. Other.types of multip Jers.^e income
and employment multipliers and will be defined in a later 'Applications of
1-0 Analysis" section.
b. Example of an Open Static 1-0 System
We will illustrate the basic model by means of an illustration found
in Gass (1969).
The following is an input-output table of a 3 industry economy (rail-
road, steel , coal ):
iTTii - sales - sales sales sales to Total
to RR to stlel to coal to other final demand sales
RR sales
steel
sales
Coal
sales
Other
sales
xn
X21
X31
x41
X12
X22
w
*32
X42
X]3 X]4
X43
The elements may be interpreted as follows (examples):
X12 = sales of rail road industry to steel industry
X32 = sales of coal industry to steel
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Y2 = sales to steel industry to final demand
All sales are in dollars. Final demand in this case includes foreign
trade, government operations, and households. The definition of final
demand may vary as one or more elements may be considered as endogenous
instead of autonomous. Also, such items as inventory accumulation and net
investment could be part of final demand or could be classified as producing
sectors. Actual classification depends upon objectives of the research.
X] = final bill of goods of railroad industry. Each row may be interpreted
as a sales row; each column as a purchases column.
By specifying: X-j > 0
Y]J>"O
we can summarize the table in a system of linear relationships for a base
period:
- xi2 - x13 -
X2 - X2] - X22 - X23 - X24 = Y2
X3 - X31 - X32 - X33 - X34 = Y3
X4 - X4i - X42 - X43 - X44 = Y4
The first eauation (for example) states that the total sales of the railroad
industry minus sales to individual industries equals what is left over for
final consumers.
Now let us define an input-output coefficient as:
X- •
0 < a,-- = —— = amount °f industry 1 necessary to produce
~ 1J Xj one unit of commodity
Since X^ = a^-Xj we can substitute for the Xjj's in our base period system:
xl - ail*] - ai2X2 - a]3X3 - ai4X4 = Y]
X2 - 32iXi - a22X2 - a23X3 - a24X4 = Y2
X3 - 331X1 - a32X2 - a33X3 - a34X4 = Y3
X4 - 341X1 - a42X2 - a43X3 - a44X4 = Y4
In matrix form this system can be written as:
(I - A) X = Y ^
where A = [aij]; X - ^ ; Y =
X4 Y4
and (I - A) is known as the Leontief matrix.
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With this linear structure of our simple economy we can determine a
production vector X which satisfies our final demand vector Y. That is
find X such that:
X 2 0
(I - A) X = Y
where: A = 1-0 coefficient matrix.
Solution of the system for the required levels of X to meet final demands
Y is given by:
X = (I - A}"1 Y
We can also formulate this as a programming problem by allowing pro-
duction to fall short of final demand requirements, i.e.,
(I - A) X < Y
Thus, we introduce a vector of slack variables W:
(I - A) X + W = Y
In addition, we introduce an objective function c'X. This function may
represent total profit or the output of one industry or some combination
of industries (or for a given regional problem we might want to maximize
total employment).
Additionally, we will specify that the production (activity) level of
each industry is constrained by known capacity levels L, i.e., X $ L.
Another vector U will represent unused capacity. Finally, allowing for
the stockpiling of finished goods available from production in previous
periods we introduce a vector S.
Thus, our entire problem can be stated in LP form as:
max c X
subject to: (I - A) X + W = Y - S
X + U = L
X ;> 0
c. LP Formulation of a Dynamic 1-0 System
Dynamic input-output theory is a natural extension of the static and
comes from consideration of intersectoral dependence involving time lags
or rates of change over time. The theoretical basis "Prided by the
relations between stocks and flows in a system of structural relations.
In a study concerning the effects of air pollution in agriculture the
researcher would want to know both the static and dynamic direct and in-
dirlct effects of crop yield changes due to air pollution (and subsequent
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changes in crop mix, total output, producers' and consumers' surplus) on_
such parameters as regional employment, gross regional product, and the
output and employment levels of industries interrelated to agriculture.
In other words, how will current decisions to limit air pollution
emissions affect agriculture and the emitting sectors directly and in
future time periods? Interrelated sectors (for example, agricultural
processors and suppliers to emitting firms) will be affected indirectly in
current and future time periods. Thus, current air pollution standards
have important implications for regional development.
We may extend the static model example above to multiple time periods
by making the following changesU2):
n = number of time periods considered
t = 1, 2, ..... n = particular time periods
xt = (xtl> Xt2 ...... Xtm) = production vector
Yt = (Ytl. Yt2 ..... , Ytm) = final demand vector
st = ( ) = storage vector
ut = ( ) = unused capacity vector
The major change is that we must provide for the expansion of capacity
to meet future final demand requirements. That is, we must allow for
population and economic growth.
Let: Vt = vector of additional available capacities
B = matrix of capital coefficients in which the jth column
represents the inputs from each industry necessary to build
Thon fho -sth v, an J Jltlonal uniJ of caPacity for the jth industry.
Then, the ith row of the product B Vt represents the amount of the 1th
t0 bUild additional "P^ity in time period t
We can summarize the new conditions as follows:
(I -*A) Xt + St-i = Yt + B Vt + St (1)
Xt+"t=L+V Vq
Equation 1 states that total output plus previous stocks equals the final
demand and capital expansion requirements for output plus the current period's
unused stocks. Equation 2 states that total used and unused production
(T2) Model given in Wagner (1954).
104
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equals initial production capacity plus previous increases in production
capacity.
Equations 1 and 2 may be rewritten in the format of typical LP
constraints:
(I - A) Xt - B Vt - St + St_! = Yt (3)
X, - V V + Ut = L (4)
t q=1 q t
d. Problem Areas in 1-0 Analysis
Some of the problem areas in 1-0 analysis will be mentioned in the
description and discussion of two regional 1-0 studies contained in sub-
sequent sections. In this section we mention two well known problems:
aggregation and the assumption of constant production coefficients.
The problem of aggregation is probably the most significant one faced
in a prospective 1-0 study. By aggregation, we mean the process of com-
bining industries into the economic sectors to be analyzed. If we aggregate
the economy into a fairly small number of sectors (that may be consistent
with time and funds available)!13', we may lose important details of
specific products and industries. On the other hand, an appropriately
disaggregated model for a given set of research objectives will be very
expensive with respect to clerical and computational needs, although the
researcher gains in predictive reliability.
There are several alternative bases for aggregation. One might aggre-
gate industries which have similar production functions, or similar rates
of technical change, or that feed into homogeneous consuming industries.
General procedures that may be followed are to define sectors_so as to
minimize intersector transactions and to maintain similarity in input
structures among the products of any sector. Unless some means is found
to break down aggregates into flows to industries, aggregation can be no
more refined than that allowed by available data sources.
The assumption of constant production coefficients is the most Citing
assumption of 1-0 analysis. Since production coefficients largely reflect
existing technological relations, the assumption of constant coefficients
means unchanging or constant technology. The use of constant coefficients
does not reflect real world conditions in the following areas.
'(13) As the nuniber Of sectors decreases the tremendous data collection
job necessary for 1-0 studies becomes less costly.and time consuming.
JS?mpsoeneandr^mS (1975) have shown how to "iS?1JJ1JxJ;S|grSS
the transactions or technical coefficients matrix of ex sting I 0
studies in order to determine output and income multipliers for
product lines.
105
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(1) Economies of scale (present in most industries);
(2) Localization external economies (i.e., similar plants agglomerate
in one place);
(3) Urbanization external economies (dissimilar plants agglomerate in
one place);
(4) Price changes (lack of relative price changes means that substi-
tutions among inputs cannot be induced);
(5) Technological change: where technological advance leads to a
regular pattern of change in input requirements for an industry,
coefficients may be reasonably extrapolated; where change is
unpredictable (including the introduction of new products), the
use of the model for projection is limited;
(6) Finally, projections made on the basis of constant coefficients
limits the use of the model for projection'14J;
(7) Finally, projections made on the basis of constant coefficients
abstract from the roles of expectations in the behavior of
entrepreneurs, governmental units, and consumers.
(14) Note that the introduction of pollution control policies, if they are
efficiently implemented, implies technological change
106
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B. REGIONAL SPATIAL PROGRAMING MODELS
Among spatial aspects of agriculture of traditional interest to agri-
cultural economists are land-use patterns, interregional competition and
supply potential. To these we can add topics of contemporary interest such
as the interregional effects of water quality and quantity changes, energy
supplies, and air quality.
Spatial models may be broadly defined as any theoretical construct
having space as one component (Bawden, 1964). Economic models that include
space as a component generally involve several commodities and describe
one or more of the following activities: regional location and level of
production (both primary (farm) and secondary (processing) stages); regional
level of consumption of final goods; relative and absolute prices. The
model formulations describing these activities include plant location models,
regional activity analysis models, transportation models, and spatial equi-
librium models. These formulations, in turn, provide several types of
information: efficient shipping patterns (implying efficient location
patterns), efficient production patterns and resource allocation, fore-
casts of shipping and production patterns, forecasts of regional storage,
consumption, and prices, and the effects of changes in exogenous variables
on the models.
Spatial models, as applied, have attempted to provide information on
the following areas0): , . ,
(1) Allocation of production and land-use under free market (compe-
titive equilibrium) conditions versus the allocation under land
retirement and/or marketing quota programs;
(2) The costs of alternative government programs;
(3) The effects on production, land-use, and cropping patterns of
techno!og1caT"change, changes in export and/or domestic demand,
and energy shortages;
(4) The impacts of alternative development projects;
(5) Optimal sizes, numbers, and location of processing plants.
A few general remarks are pertinent concerning the difference between
spatial models and the supply response models discussed in VI, A. Spatial
models typically use a region as a basic producing unit; supply response
models use the representative farm. Supply response models attempt to
predict market supply under a given set of market C0l?dltlons?nu^?'^me
ignoring interactions between farms in d fferent regions or in the same
region. Spatial models usually take explicit account of inte^gional
competition by including demand restraints and allowing for interregional
(1) Heady and Hall (1968) provide a brief review of spatial models used in
the 1958 - 1966 period. The basis of these models and post - 1966 to
present models was provided in Samuelson (1952), Beckmann and Marschak,
?1955) with later developments provided by Takayama and Judge (1964).
107
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shipment of commodities. Additional, and more specific differences in
spatial and supply response models will be discussed in the subsequent
sections.
There are also differences among spatial models that are pertinent to
analyzing air pollution effects on producers, processors, and consumers.
Following Bawden (1964) we may classify spatial models as standard equi-
librium °r activity analysis models. The standard equilibrium modeliT
characterized by:
(1) discrete producing and consuming regions;
(2) quantities supplied and demanded may be predetermined or endogenous
to the system; y
(3) unit transfer costs are specified between producing and consuming
points;
(4) given that production and consumption are endogenous, equilibrium
quantities of production, consumption, imports and exports, and
absolute prices are specified under the assumption of profit maxi-
mizing behavior; K
(5) the solution is consistent with regional and total profit (net
l Pr?duct) maximization and transfer cost minimization;
JH J xay ln<:orporate many commodities interrelated in supply
f°r
nr^p^n9H°nS' blf Can determin* market boundaries within model;
predetermined or endogenous demand;
(3) generates own supply relationships instead of relying on explicit
(41 rPnP?±IUnCtl°nS 'V" tdndard ^1™^ model!
5
id^ol S^InpH? ^V^ ^ are similar with the main dl'ffer
lS! ?K?nng7R^ 1S' " deriV6d ^ ll!S"Sii™ (LP)
aM?^^^^
108
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The research implications of these differences are as follows:
standard equilibrium models with econometrically estimated supply equa-
tions would be best for analyzing the short-run effects of changing govern-
ment programs (price supports, acreage allotment) or other exogenous vari-
ables such as pollution standards. However, the long run effects of such
exogenous changes would better be analyzed by either activity analysis or
standard equilibrium models with supply derived by LP or RP methods.
One further difference in spatial models should be noted: the linear
versus nonlinear model. In the linear version we assume that demand
(whether regional or national) is known. The appropriate objective function
is one of minimizing the production and transport costs of a final bill
of goods(2).
The nonlinear case occurs when prices and quantities demanded are not
given as a priori knowledge, but instead are variables whose values we
want to d?te7mThT simultaneously with supply. Demands are represented by
continuous linear functions.
1
Nonlinear Spatial Programming Model: An Example
Before outlining the basic model, we note that the same assumptions
and limitations apply to spatial programming models as applied to the
programming models discussed in VI, A. We are extending the firm and
aggregate supply response models in VI, A to the whole market, i.e., pro-
ducers and consumers. The thre« major differences between the f rm and
market models are that in the latter we have homogeneous P^uction
regions, endogenous demand, and a maximand of net social payoff (instead
of net revenues).
We will define the following symbols and equations according to those
in Hall et al_. (1968):
K consumption regions; H production regions
bhk = vector of primary resources for production region h in consumption
Xhk = vector" of output levels for production region h in consumption
Ahk . in&u'tput matrix relating bhk to a unit of xnk
pk = vector of prices for elements of dk (see below)
Chk = vector of costs associated with X"* ..
Uhk = victor of imputed values of primary resources, bhk
SJk = vector of shipments from market j to k
tJk = vector of unit shipping costs associated with S3*
12) Among the formulations of this model are Egbert and Heady (1961) and
Heady and Whittlesey (1965).
109
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Linear demand system: dk = dj< + Dk Pk
d|< = vector of quantities demanded
dg = vector of constants
DK = matrix of constants (negative semi definite)
The problem:
MAXIMIZE f(xhk, pk, uhk, Sjk) = jj { (dk + Dkpk).pk _ g chkxnk _ ? Uhkbhk}
k=l h=l h=l
- i i tJksJk n)
jVk ( ' '
subject to:
AhkXhk < bhk
Pk . (Ahk)'uhk ; Chk
z (sjk . Skj) . Xhk < . dk
PJ-Rk^tkj h=l - o
pk . pj ,. tjk = tkj
xhk nhk ^jk pk n
A » u » J » P > 0
Interpretation of equations:
(1) Quadratic objective function
(dk + Dkpk)tpk = Total
chkxhk = Production costs
Uhkbhk = imputed land rent, etc.
tJksJk = Transportation costs
Sn !uSlUli°?nf^l!%1mpK?d ValU6S Of scarce ^sources in the objective
1 *"" * ^^ ^^ in Which there is
that ?heeconc?ra{^ ^fc?ncave (since Dk 1s negative semidefinite) and
programming (QP)ln ^ 1S n°n6mpty' the problem is *°^ «1ng quadratic
(2) Resource use cannot exceed availability
(3) Marginal returns from an activity «st be less than or equal to marginal
°r e
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2. Applications
The basic aggregate programming model discussed in this section involves
the interface of a market demand structure with a supply model to obtain
simultaneous determination of the equilibrium levels of production and
prices. Under the assumption of a perfectly competitive environment
Samuelson (1952) showed that the appropriate objective function is the
maximization of net social payoff (NSP) or the sum of producer and consumer
surpluses (PS + CS)(3)
Takayama and Judge (1964) extended this objective function to obtain
a quadratic programming solution for multiproduct markets. They also
showed how the model could be modified to include multiple time periods.
Duloy and Norton (1973) showed how LP approximations of QP solutions could
be obtained in sector models. Hazel 1 and Scandizzo (1973, 1974) modify
the Duloy-Norton objective function to incorporate risk averse behavior,
i.e., assume that farmers behave according to an E-V decision criterion^;.
The NSP ( = PS + CS ) maximand specification ensures that the optimal
solution will be a competitive market equilibrium and allows for the
identification of gainers and losers due to policy actions. For example,
allowing air pollution to continue at current or increased levels (assuming
that standards will not be set immediately) may lead to adverse soical
effects, that is, on producers or consumers, or both. On the other hand,
air pollution abatement hypothetically may lead to a net social gain but
with consumers gaining (through increased production and lower prices) at
the expense of producers (expanded supply and inelastic demand leading
to lower prices and revenues). The possibility may then be raised of
compensation of the losers by the gainers.
Risk inclusion is important because in deterministic risk free models
the production of high risk crops is typically overestimated. Variations
in income associated with any crop are, of course, due to yield and/or
price variability. By specifying risk averse behavior, the solution will
'(3) Samuelson developed this welfare maximization problem in thecontext of
spatial equilibrium among spatially separated markets. In h s analysis
of interregional trade, back-to-back graphs (with a positively sloping
excess supply function in one region) are used in which social payoff
in any region is the area under the excess demand curve (which is equal
to the area under the excess supply curve but opposite in sign). In the
absence of better measures, PS and CS are measure the dollar values of
producers' and consumers' welfare.
(4) Hazell and Scandizzo (1974) develop the appropriate aggregate objective
function when farmers are assumed to maximize E-V utility (see VI, A
for further discussion of the E-V criterion). Hazell and Scandizzo
0973 show how the objective function may be modified to handle other
probabilistic decision criteria: notably the type in wh ch the risk
aversion coefficient is measured in standard deviation units.
Ill
-------
avoid high acreages of high risk crops. In addition, given that many high
risk crops are also high value crops, risk inclusion will prevent over-
statement of the returns to investment.
Again, there are implications pertaining to the air pollution problem.
Given levels of air pollution are going to alter the risk patterns of crops
in different ways since some crops will be more adversely affected than
others. By incorporating risk averse behavior we hope to account for these
differential risk patterns and derive realistic cropping patterns.
a. Duloy - Norton Model
The Duloy-Norton (1973) model (CHAC) is a comparative static risk-
free model of Mexican agriculture. Many of the attributes of this model
apply equally to the Adams (1975) model of California agriculture which is
discussed in section b.
The production system in the CHAC model is composed of 20 geographic
submodels. Each is solved to yield returns on fixed investments. For
example, in low income agriculture, investments in new machinery or new
seed (i.e., new technology) are particularly important. In the aggregate
sector model, the effects of interregional competition on estimated returns
are examined.
The sector model describes the production imports, domestic demand,
and exports of 33 short-cycle crops. The production of these crops in the
20 aceas is represented by 2300 different production techniques.
The demand structure is price dependent (i.e., price is a function of
quantity), hence market clearing prices are endogenous. With a few special
exceptions, demand functions are national. The general benefits of the
price endogenous demand structure are that it prevents overspecialization
in cropping activities (the negatively sloped demand curves serve as constra-
ints), thus enabling the model to more realistically portray actual con-
ditions, and it permits appraisal of the distribution of benefits between
consumers and producers accruing from increases in agricultural production.
nL -fi1? KreSt u° ? devel°P1n9 economy, this specification also
?i ll ruSr Su5s^ltution to occur through changes in domestic
X model such substitution can also occur through changes
Xn°r °!i9 C5an?6S 1n the commodity <"ix of exports. Finally,
Hr! product Price taxes> exP°rt sub-
n ™iiHp< nn nS ?J 9e i"*8' ™e effects of these alternative govern-
zedM Profits, employment and other variables may also be analy-
TsTThFperfectly competitive model can also be modified to represent a
will be substantially different.
112
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Note also that the demand structure is not completely interdependent.
That is, demand functions are defined by commodity groups and substitution
is allowed only within groups, not among groups (i.e., cross-price elasti-
cities equal zero).
The Duloy-Norton objective function (and the risk free Adams objective
function) are conceptually written as follows:
(1) Assuming linear demand functions and zero cross-price elasticities we
have the demand function:
P = a + B q
where P = price vectro
q = quantity vector
B = negative diagonal matrix of slope coefficients
(2) Assume the following vector of total cost functions:
c (q)
(3) Thus, under perfect competition the objective function is:
Z = q [a + ]5 B Q ] - c (q)
dZ
and the first order conditions are (obtained by setting -—- = 0):
P = a + Bq = c' (q)= marginal cost (MC)
(4) We can decompose Z into the sum of two things:
Consumer Surplus (CS) = .5 q1 [a - P] = .5 q1 B q
Producers' Surplus (PS) = q1 P - c (q) = q1 [a + B q] - c q
That is, the objective function is net social payoff or the sum of CS
and PS.
Operationally, the net social payoff maximand (NSP) in the Duloy-
Norton model may be verbally represented as: n™,^ mctd
maximize Z - [sum of CS and PS] + [export earnings] - [import costs]
- [total labor costs] - [total long term capital costs]
- [interest on short term debt] - [seed costs] - [chemical costs]
- [draft animal service costs] - [gravity water costs]
- [well water costs] - [increments in gravity water cost]
- [increments to well water cost] + [district crop price differ-
ences]
The farmers' total profit function serves as a contract to the NSP
function In5?s identical to the NSP function except for the following
differreces:
113
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(1) maximized profit instead of NSP;
(2) gross revenue from domestic sales replaces sum of CS and PS;
(3) interest on long term capital replaces total long term capital costs;
To obtain total farm income add the following term to the profit function:
(1) farmers wage income;
To obtain total sector income, do the following:
(1) delete total labor costs;
(2) remove labor cost element from interest on long term capital.
b. Adams Model
Adams (1975) formulated a short run comparative static OP model that
analyzes the effects of alternative commodity price levels, energy availa-
bility evels, and energy input levels on irrigated acreage, total output,
regional cropping patterns, the demand for land, water, fuel, and other
inputs, and the resulting changes in producer and consumer welfare. Since
the spatial allocation of production was not of concern to Adams, there
are no transportation costs included.
The model encompasses 19 crops (hence, 19 demand functions extended
fL? J0.1;01^6 appropriate seasonal effects) and 14 production regions
irrn^n 1° h "comodate 2 soil types). Each region is defined
according to homogenous climate, water, and soil types. For the air pollu-
nnnnHon ?!*? mi9ht.deJ1n? production regions according to homogenous
pollution levels or air basins as well.
Yield response functions were developed to permit evaluation of the
fr?SntI Mn °t r^ucl\on5 ^ fertilizer. The matrices of technical
icients (input-output) are formulated to reflect the lower yields due
to fertilizer reductions. Similarly, we propose the use of yield response
functions to evaluate the effects on yields of alternative pollution levels.
As in the Duloy-Norton model, the demand structure was orice endogenous
™" >
in gross domestic product or per capita income.
and teazellcanSf nnwnnS • ^thes1s <* the Duloy-Norton function
ana ine tiazeii-bcandizzo work on risk incorporation That i* X/^IH
variability coefficients (previously estimated In another slud/Tact as
proxies for the subjective risk faced by fanners The price d™and struc-
ture ,s assumed to be nonstochastlc. T^is approach undeTstates tte actual
PS be der1Ved under v^ --estrictive assumptions
n,ay Ke
114
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subjective risk faced by fanners, but such data may be obtained only by
interview which would be very time consuming and costly in a statewide
study. On the other hand, in a regional sutdy based on representative
farms, interview procedures would be feasible.
Adams' risk free objective function which maximizes NSP may be written
as:
r
- £ C, X,jk + 1 d, X.k - T V C1jk
where: C,- = intercept of demand function for crop i
= slope coefficient of demand function for crop i
= production of crop i in region j by process k
= total variable cost (exclusive of land and management) of
producing a unit of crop i in region j by process k.
r, s, t, are upper limits on commodities, regions and processes.
The objective function with risk included may be written in matrix
notation as:
Max Z = C X + .5 X'DX - TVC - * JVC
Thus, it is the same as the risk-free function except for the appearance
of a vector of risk coefficients ( ) as an additional cost element.
Risk in this case may be interpreted as the additional expected return
demanded by farmers in return for assuming risk. The risk cost for each
crop is the product of variable cost and yield variability.
The constraints in the Adams model are soil acreage by type, aPPjjed
irrigation water, several purchased inputs (gasoline, diesel fuel, nitrogen
fertilizer, pesticides), institutional (total production and regional
processing capacity), and the usual non-negativity conditions.
The procedures for obtaining a solution differ .between the Adams and
Duloy-Norton models. Adams uses quadratic ProgrammingjQP) *° °™roxima-
competitive equilibrium solution while.Du oy and Norton use LPapproxima
tion procedures. Their technique is similar to the grid linearization method
of s^aTable programming. Hazel 1 and Scandizzo also propose methods < of
linearizing quadratic terms to ease computional Problems.
nn i ... ._ ____ -i-ui- 1-,^,-t/-, c/~aia nuaHrat.ir; nroDiems
However, if a
nearzng quaraic erms .
QP algorithm^ available, large scale ^^fatjcuPr°bl^saSnrox?ma? ons
fairly easily, thus precluding the necessity of using LP approximations.
Some of Adams' results and their implications will be briefly mentioned
to illustrate the benefits of using the NSP objective function. .By incor-
porliing Hsk into the model, Adams found that consumer surplus CS was
reduced (from the non-risk case) by 22 percent while producers surplus (PS)
115
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was reduced only 1.5 percent <7). These relative changes were due to farmers'
decisions to increase the production of less risky (and price elastic)
field crops while cutting back on high risk (but price inelastic) vegetable
crops. 3
°tuse!!er? energy shortages varied in their distributional
s r?«IP °H K I 11! fertlllzer availability significantly reduced
PS, but CS stayed about the same. This has environmental policy implica-
tions. For example, the cost of a policy to reduce ground and surface
innut H h c°ncentriat1orV by reducing the amount of nitrogen fertilizer
input would be borne by producers. This raises the question of compensa-
1 1 on •
are 11°tedTar1Ze *"' StUdy the fo11ow1n9 essential elements of the model
(1) specification of 28 production regions;
9veaban6fa1n.Pl-Ce-f0l-eCaSt1^
^5r1!!?!ion °.f nitr»3en fertilizer response functions-
a'°1CUU -
.
ilT roisa'°?nc^H^1CUU^0n °T non-land costs production for
all crops — including yield variations;
'10^
6 deEer^nationT'Inn^10^ ?hySiCa1' ener^' institutional (estimated);
b determination of input requirements for each crop-
7 determination of regional cropping patterns and y elds-
8 derivation of input-output coefficients by cropping activity •
(9) development of future projections for all of the aboJe!
The main attributes of the model are-
(1 ) risk inclusion;
III
Among the limitations of the model are-
(1) limited to California, excludes rest of U S
' cCJsiveeUmodels(o?Uth!r^;9 t0 err°rS 1n P™^ctions; however, re-
(3) Uck of cross orUl^t! a^ currently unfeasible computationally);
are d°ff1cClt t'o StSIta • ' "' "" be handled c™P"tationally but
(4> '' "' ^^ 'e"er' 1'e- b* Us1"9 • Duloy-Norton kinked
total value
116
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3. Summary
In VII, B we have seen that spatial programming modles can be applied
to a wide variety of regional research topics. The general form of the
models discussed in "Applications" involves the interface of a market
demand structure with a supply model to obtain simultaneous determination
of the equilibrium levels of production and prices. The appropriate
objective function was the maximization of net social payoff (sum of produ-
cers' and consumers' surplus) which facilitates measuring welfare gains
and losses due to alternative policy actions. With the additional feature
of risk incorporation, such models are capable of providing information of
use to decision makers. We can readily derive alternative regional out-
comes due to varying such parameters as cost coefficients, ™Put-°";;P"J
relationships, and resource and institutional constraints. Changing air
pollution levels, whether by natural occurrence or policy action, may be
indicated by the investigator by altering these parameters, Subsequent
changes in output, cropping pattern, profits, and consumer surplus may then
be generated by the model.
117
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SECTION VIII
OVERALL IMPACTS ON CONSUMERS DUE TO CROP YIELD CHANGES
In this section we will review some basic concepts in suoolv and
demand theory w th the objective of elucidating the theoretical underpinn-
ings of the empirical techniques discussed in Section Vllnd Secti'on VI^ )
" 1" ^ the -IsSsiloSlnSoVv i
sulied;
is
SsfuctJSn^nf^0!!-!;156? *-Pply func«°ns as derived from the
cost functions of individual firms. In subsection R W
'
demands Spvprai HQm=,nH „« 1 -••<- -syicyauiuri UT inaiviauai consumer
aemanas. beveral demand concepts are discussed: direct and cross-price
^r£s;iliuSS
sr^SbK^A.'iSssj:!-air -"*«s "ss^ix 'lissss
Section V
2 In W!11*a5 a99re9ate Production/profit relationships In Section VII
SSSffi^S^1
a:»H£=~Ssr.'.1¥."2S!,rs.i?s5it'£u
several attHhiitocV"s«" bpatlal Programming models were found to have
anowance £r risk'mav S^hn?!^- °f Q1]do^n^ demand relationships,
speci??caeJon o'thHo 1 " K?,^^!11 *^°nS *"* ^
or thP sum nf rnnc,,mo^. llj "^,ppr°Priate Hiaximand was net
surplus (CS + PS).
j_ I . "wijr UT ine Tirm
118
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under study. Given the objective function of maximizing CS + PS and the
additional assumption that these concepts can measure consumer and producer
welfare, Adams examined the distributional effects of alternative energy
prices and policies.
A. SUPPLY
Thus far in this review we have spoken of supply functions in the
following contexts: supply function of the firm as derived from a program-
ming model or from a production function; aggregate supply function as
derived from an aggregate programming model or aggregate production function;
statistically estimated aggregate supply function.
For purposes of defining the elasticity of supply, we set forth the
economic rationale underlying the empirically derived supply functions
mentioned abovet2). Specifically, the short-run marginal cost curve of the
firm may be derived from its marginal product curve under the assumption of
constant input prices. That portion of the firm's short-run margina cost
curve lying above the average cost curve constitutes the firm s supply curve.
Although the industry's short-run supply curve is only on approximation ot
the horizontal summation of the marginal cost curves of firm s in the
industry (approximate, because even under perfect competition, the simul-
taneous expansion of output by all firms will bid up input prices), it
is positively sloped, meaning that quantity supplied varies directly with
pri ce.
The elasticity of SUBB]£ may then be defined as the relative respon-
siveness of quanta-supplied to changes,™ price. To expand upon this
concept we may say that Inelastic, sufipj^^ means that for a given change
(2) Empirically, the general supply response relationship may be expressed
as follows:
qt = f(pt> pct> At)
where: qt = amount of commodity supplied in time t
Pt = price of given commodity
pr* = nrices of competing commodities
At = technological change and/or institutional influences
In the long run, the dynamic supply relationship may be expressed as:
qt = f(pt » At)
d
sear
dicers SfteUneTsUffikand for, their price expects.
ly)>
elastic supply means e > 1-
119
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in price, supply responds less than proportionally. Unitary supply elasti
city occurs when supply responds exactly proportionally to a given change
in price. Elastic supply means that for a given change in price, supply
responds more than proportionally.
120
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B. DEMAND
The principle assumption upon which the theory of consumer behavior
is constructed is that a consumer attempts to allocate his limited income
among available goods and services so as to maximize satisfaction lor
utility). Given this assumption and the properties of indifference curves^,
individual demand curves may be derived. For almost all goods individual
demand curves are negatively sloped -- that is, quantity demanded varies
inversely with price.
There are four basic determinants of individual demand: (1) the price
of the commodity determines quantity demanded given, the level of demand;
(2) money income is one of three determinants of the level of .demand;
(3) tastes (determines level); (4) prices of related commodities (deter-
mine level). These four factors jointly determine quantity demanded and
the level of demand, and market demand for a specific conmodity equals the
horizontal summation of thiThTividual demands of each consume r. Given
this negatively sloped market demand function and following a brief mathe-
matical digression we can proceed to define the fol owing concepts, price
elasticity and cross-price elasticities of demand, income and substitution
effects, and income elasticity of demand.
1. Mathematics of Demand Theory
Mathematically, the following function represents utility maximization
subject to a budget constraint for an individual consumer.
U = f(qi, ..... qn) + *(Y - I P^i)
where: (qls ..... qn) = commodities
Y = consumer's fixed income
Pi = commodity prices
x = Lagrange multiplier
By setting the first order partial derivatives of U ( ) with respect to
substitution and price ratios for any pair of
Assuming the second order conditions hold, the individual demand func
tions can be expressed as:
, • • • • » pn> Y>» 1 = 1' ..... "
erence curve forms a locus of .11
which a consumer derives the same level of
121
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By aggregating these n equations over all consumers the market demand
S"?^.!! dHVHd;- " Sh<"?ld be clear that th1s Wt- of equations
s that all commodities are interrelated.
even analon. *ntBre** f°CUSes on Particular cormodities (or
eauation 9 UnSpr^hl^c6 ar^alter.nat1ves *> estimating the whole set of
tion for i Oivpn r™ ^^P*10" of ™± independence W . the demand func-
tion tor a given commodity can be expressed as: -
, Pf, Y)
where P^ = price of ith commodity
oc
Pi = prices of other commodities affecting i'th commodity
Y = income
The corresponding market demand function is
Ql =f(Pi> Pf, Y, A)
where Q.J = z q^
Y = zy over all consumers
2- Price Elasticity of Demand
- s
P
-u_
q
change 1n quantity demanded. If - i n
tlclty and a given change In price wi i
equal change 1n quantity. If e > 1
"111 ^ 3SSOClat
1S ![!elast1i: and a 91ven
r™ "^ J° be °f Un1tary
Panid by a
relationships. °J 50 estlmate a alrge system of demand
(6) in mathematical terms; given the demand function for co«odity i:
£»•••• »Pfrj,Y)
The direct price elasticity is: P - 3CH pi
XY ~ ~ —
X 3Pi qi
122
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Two basic factors determine the direct price elasticity of demand:
the availability of substitute goods and the number of uses to which the
goods may be applied. As the number of substitute goods and the uses to
which a given commodity may be put increase, so does the value of the
elasticity coefficient.
Generally farm products have low elasticities, that is, less than one.
Among farm products a commodity such as wheat (with few substitutes) would
have a lower elasticity than a commodity such as wool which has many subs-
titutes.
The values of the elasticities have significant policy implications.
For example, for a highly price elastic commodity, an increase in price
would result in a proportionately greater reduction in quantity demanded
and farm revenues would decrease, A more realistic case for agricultural
products would be the case of a price inelastic commodity. A given reduc-
tion in price (brought on, for example, by a shift in the supply function)
would be accompanied by a proportionately lower increase in quantity de-
manded and total revenues would decrease.
3. Cross-Price Elasticity
When we speak of the demand schedule for commodity X as we did in the
previous section, we are implicitly assuming that money income, tastes, and
the nominal prices of related goods remain constant. In certain cases,
however, the prices of related goods are interrelated with the price of
commodity X. That is, if prices of related goods are allowed to vary,
there will be a definite impact on the quantity demanded of commodity X.
Thus, our market demand function in this case is:
qx = f(Px» Py)
where y is a related commodity. By defining the cross-price elasticity
of demand we can characterize goods as either substitutes or complements.
The cross-price elasticity of demand exy is defined as^ '•
AP,, AqY Pv
/ y. = • y
py
(7) Mathematically:
» P2
3P
123
-------
It may be interpreted as the proportional change in the quantity of x
demanded in response to a given change in the price of y. Commodities may
be classified as substitutes if exy > 0 and complements if exy < 0.
Most empirical work has focused upon the substitutability of related
commodities with substitutability (or relatedness) increasing as the
cross-price elasticity increases. For example, George and King (1971)
found the cross-elasticity of lettuce with respect to the price of carrots
to be .000814 indicating that they are not closely related commodities.
Wold (1953) found the cross-price elasticity coefficient of pork with
respect to beef to be .14 and the coefficient of margarine with respect to
butter to be .81. Thus, beef is a poor substitute for pork, while mar-
garine and butter, as one might expect, are closely related and substitu-
table. As the price of butter rises we may expect consumers to purchase
less butter and more margarine.
Substitution and Income Effects. Most empirical work focusing upon
market demand uses the cross-elasticity approach to commodity classification
in which the total effect of a price change is the criterion used to
classify goods. Underlying this total effect are the substitution and
income effects of price changes as they apply to individuals' preference
functions. That is, a change in the nominal price of a commodity exerts two
influences. The first is that a relative price change occurs, i.e., the
terms at which a consumer exchanges one good for another. Second, a change
in nominal price (nominal income remaining constant) means that relative
income has changed, i.e., a consumer can buy a greater or smaller bundle of
goods compared to before the price change. For example, a fall in the price
of one good in the bundle effectively increases real income and we may
expect that the consumer will buy either more of the good whose price
decreased and/or more of other goods.
Translated into market terms, suppose we have two goods, wheat and
corn. A decrease in the price of wheat (nominal money income and all
other prices remaining constant) will augment the quantity demanded of
wheat as consumers substitute it for corn. Simultaneously, the increase
in real income may augment both wheat and corn purchases. In fact if
the income effect was greater than the substitution effect it would appear
that wheat and corn are complementary goods. An estimated cross-elasticity
coefficient might even be negative -- indicating complementarity when in
fact this is not the real case. Wheat and corn may well be weak substitu-
tes, but the income effect outweighed the substitution effect. The total
change can go either way. Generally, however, in the case of strong subs-
titutes, the substitution effect will dominate. In the case of strong
complements, the income effect will obviously dominate.
4. Income Elasticity of Demand
In the previous section we relaxed the assumption that the nominal
prices of commodities related to X were constant. Analogously, in this
124
-------
section, we are relaxing the assumption of constant money income and
allowing income to vary, since for many commodities a change in income will
influence quantities purchased.
Assuming that our simplified market demand function is
qx = f(Px, Y)
(8)
we can define the income elasticity of demand e as v ':
y qx Y AY q
It may be interpreted as the proportional change in the quantity demand of
X in response to a given change in real money income. Generally, if income
elasticity is low (usually less than one), quantity demanded is not very
responsive to income changes while if ey > 1 quantity demanded is more
responsive.
Empirically, Wold (1953) found the estimated income elasticity of meat
to be .35 indicating that for a given increase in income there is a less
than proportional increase in meat purchases. On the other hand, tobacco
pruchases were very responsive to income changes.
The existence of inferior goods has been documented by estimated income
elasticities. Wold (1953) found the income elasticities of flour and mar-
garine to be -.36 and -.20 respectively indicating that as income rises
the purchases of these two commodities actually decrease. George and King
(1971) also found negative income elasticities for both commodities.
George and King found an income elasticity for all food items of .176
confirming that food is a necessity and that food purchases on the whole
are relatively unresponssive to income changes.
We can summarize our description of the three types of elasticities by
noting their interrelationship as follows:
For a given market demand function for one commodity,
q] = f(P], Pg» . • • • » Pn> Y)
We can write the direct price elasticity of demand as the sum of cross-
price elasticities and its income elasticity^/.
Mathematically: ^ = f(P], ?2 py) aq- Y
and the income elasticity for the ith commodity is eiy = _L •
(9) See Ferguson (1969), p. 45-46.
125
-------
That is,
611 =
or
for 1
126
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C. STABILITY BENEFITS
Let us refer back to the discussion of Adams' QP model of California
agruculture in VII, B. The maximand of the Adams' model constituted a
quantitative measure of toal revenue to two groups: producers, who maxi-
mize returns to land and management (producers' surplus (PS) ) and consumers,
(defined as total value of the objective function minus net returns to
producers, or consumers' surplus (CS) ). The maximand, net social payoff
(or net social benefit) equaled the sum of PS and CS.
This maximand turned out to be particularly useful in analyzing the^
policy implications of energy constraints. Both theoretically and impin-
cally, the impact of energy shortages was not shared equal iy> by producers
and consumers. That is, any given shortage would produce gainers and losers,
irrespective of the change in net social welfare. Thus, Adams found that
a significant shortage of fertilizer would reduce net social welfare,
although the burden was distributed such that CS was relatively unchanged
and PS was reduced. On the other hand, the impact of total energy short-
ages was to reduce CS and increase PS.
In this section we will look in more detail at fir
PS, keeping in mind the application of these terms to the problem of air
pollution damage in agriculture. The first assumption we must make is
that the sum of CS and PS is an adequate measure of socia welfare. This
assumption has been the subject of extensive controversy in economic litera
ture, but the fact remains that we have no better measures.
Before proceeding we can also clarify what ge mean by stability bene-
fits and further elucidate the terms CS and PS(IU>. First, given a typical
negatively sloping market demand curve and a positively sloping market
supply curve, it is clear that either shifts in supply (because of the
influences of changes in factor costs, technology, weather air Pollution.
water pollution, etc.) or demand (due to changes ly.""!^^!?^^ In
example) will cause price fluctuations. The situation is -l""!*^6? ™
Figures 1 and 2 In Figure 1 an outward shift in supply from i>i to *? wu
reduce pri from P to9P2. Alternatively, ^ reduction insupp y woutd
*™
.
Increas^ price. In Figure 2 a shift in *™^^ Td^and shifted
n a change in equilibrium price (P^ to ™"" '"•
and Subotnik and Houck (1976)
127
-------
Price
Quantity
Figure 1. Price change attributable to shift in supply.
Quantity
Figure 2, Price change attributable to shift in consumer demand.
128
-------
Now, following the Massell (1969, p. 285-287) synthesis of the work
of Waugh (1944) and Oi (1961) on CS and PS respectively, we present Figures
3 and 4 in which Pi and P? are equally likely prices faced by consumers
and P3 is an alternative (stable) price that obtains with certainty.
In Figure 3, CS may be defined as follows^ ':
r a + b + c + d + f if P = PI
CS = L f if p = P2
The expected value of CS is given by:
E (CS) = f + .5 (a + b + c + d)
Under the stable price regime (?$), expected CS is:
E (CS) = a + b + f
At the stabilized price, P = PS, consumers lose an amount equal to c + d
compared to the prestabilization price P = P]. Conversely, when P = PS,
consumers gain an amount equal to a + b compared to the prestabilization
price P = P2. Since c + d > a + b, stabilization leads to a net loss in
consumers' surplus (™).
Figure 4 represnets the situation under demand Instability, Producers
are confronted with two equally likely prices, PI and P2, and a third price
PS that obtains with certainty. Thus,
r a + b + c + d + f if P = P2
PS = [ $ if P = Pf
The expected value of PS is:
E (PS) = f + ,5 (a + b + c + d)
and at the stable price P3,
E (PS) = a + b + f
For any combination (Pi, qi)
CS = /51 f (q) dq "
Note
that the demand curve ._ ...^ - . ^Ua,,-QC
money is constant with respect to price changes.
129
-------
Price
P3
Quantity
Figure 3. Effects of price stabilization on consumer surplus,
Price
S
Figure 4. Effects of price stabilization
Quantity
on producer surplus
130
-------
Compared to the prestabilization price, P = P?, producers lose an amount
equal to c + d when P = P$. However, compared to the prestabilization
price P = Pi , producers gain an amount equal to a + b when P = P3- Since
c + d > a + b, producers' surplus is reduced under price stabilization with
the amount of loss being equal to 1/2 (c + d - a - b)UJh
The discussion thus far provides a framework within which the generali-
zations that follow may be understood. Masse! 1 (1969) has shown that: _
(1) Producers gain from price stability if the source of instability is in
supply; consumers, in contrast, lose from price stability if the source is
supply; (2) Consumers gain from price stability if, the source of instability
is shifts in demand; producers lose in this case^'; (3) When demand and
supply are random variables (as in the real world), the gains to each group
depend upon the relative sizes of the variances of demand and supply and
the slopes of the demand and supply functions. From the producers perspec-
tive, both the likelihood and magnitude of gain from price stability are
increasing functions of variance of supply and the steepness of the supply
curve.
The Waugh-Oi-Massell work is based upon certain knowledge of prices.
Turnovsky (1974) introduces two alternative models of price expectations
for producers. That is, producers are assumed to make decisions based
upon their expectations of prices. He concludes that producers gain from
stabilization of supply regardless of how they form their expectations.
If risk averse behavior is specified, the desirability of stabilization
will be even greater (15).
Extending this analysis to the distributional effects of price stabi-
lization (given supply side instability) among producers, a single producer
will gain more from stability the steeper his supply curve Dative to
industry supply and the greater his variance in supply relative to industry
supply.
(13) In Figure 4, the source of instability is demand Furthermore, it
must be assumed that the supply curve is positively sloped and the
marginal utility of money remains constant.
(14) We are iqnoring the basic welfare question of whether the gainers
(proSuce?s in (1) and consumers in (2) ) can compensate the losers,
leaving both parties better off.
entes market supply n a multiplicative way, social welfare may be
increased by havi Kg an pj>tin!§l Saxket distortion involving a higher
average price and Iwer o^eTlupply as compared to a competitive
market equilibrium price. The policy mechanisms necessary to obtain
the distortion wouldP probably include a combination quota and price
stabilization scheme.
131
-------
Conceptualization of the Impact of Air Pollution. Using the concepts
discussed in C and assuming a constant technology, we might envision the
scenario that follows^;. Suppose that in a given region, air pollution
damage has reduced crop yields by some significant percentage. Further-
more, the region is subject ot increasing urbanization so that farmers have
only had limited possibilities of expanding acreage to offset yield defi-
ciencies. Thus, in general we might expect that market supplies are sig-
nificantly below what they would be in the absence of pollution. Further-
e ™C dand f°r a9r1cultural commodities {see earlier
M°?ce1vable that pollution damage has actually
anv nhPr nnnii • * ^ llmiting ^PP1*' Th1s would be analogous to
Such nrnnr^P y }™t*t™n P™9™ri designed to increase prices and returns.
Such programs include "green drop", acreage limitation, amrketing quotas,
bv local' 'or'rpninn^-1'6"??6 °f ai> Polll*ion standards set by the EPA or
increased cnS??? air Po1 ^lon districts, yields increase leading to
™ft^ Siven inelastic demand, wl would
tn 't n ^ Stfp1y sl°Ped demlnd cur'v nPt e f gure,
tne total revenue rectangle under the new price-quantity combination
(d Pz 0 q^is clearly smaller than the^oll^1^^
octoh air Poll"tant concentrations in agri-
(producers This SaSSSfth" Pr?dUCed ga1ners (Consumers) and lose?s
welfare economic 5S? I application of a very important concept in
ex sts of hlvTna \l nli °f ^omPensatio.n-- In this case the possibility
1n th
Ano. •
ing research are estimated. the SOClal returns to rice breed
°7) t0 technological improve
abatement equipment and pollution-
resistant plants
132
-------
Price
Quantity
Figure 5. Welfare effects of a shift in market supply.
133
-------
and the amount of compensation are political decisions, but theoretically
it can be shown that the gainers could compensate the losers leaving both
parties better off and leaving social benefit unchanged.
The same principle would apply if pollution control measures reduced
the variation in supply schedule faced by the consumer.
134
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153
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163
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REFERENCES - SECTION VII-A
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167
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1 REPORT NO.
EPA-600/5-78-018
4. TITLE AND SUBTITLE
Methodologies for Valuation of Agricultural
Crop Yield Changes
3. RECIPIENT'S ACCESSI ON- NO.
5. REPORT DATE
August 1978
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Steven Leung, Walfred Reed, Scott Couchins,
et. al .
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Eureka Laboratories, Inc.
kQ] N. 16th Street
Sacramento, CA 9
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
Grant #
12. SPONSORING AGENCY NAME AND ADDRESS
Corvallis Environmental Research Laboratory
Environmental Protection Agency
200 S.W. 35th Street
Corvallis, Oregon 97330
13. TYPE OF REPORT AND PERIOD COVERED
Final H/l/76 - 3/31/78
14. SPONSORING AGENCY CODE
EPA/600/02
This research effort was initiated with the objective to complete a review
and evaluation of the methodological and analytical techniques used to
assess and quantify the economic impact of changes in agricultural crop
The review focused on two major areas: (!) physical effects of man-made
and natural factors on agricultural crop yield, and (2) methodologies and
models used to evaluate and quantify the economic impacts of crop yield
changes on the farm, the agricultural industry and finally the consumers.
KEY WORDS AND DOCUMENT ANALYSIS
Air Pollution
Economic Effects, Air Pollution
Air Pollution Effects, Crops
Environmental Economics
Agricultural Economics
13. DISTRIBUTION STATEMENT
b.lDENTIFIERS/OPEN ENDEDTERMS
Air Pollution Economics
Air Pollution Effects
(Agricultural Crops)
Economic Evaluation
19. SECURITY CLASS (This Report)
Unclassified
20. SECURITY CLASS (This pagoT
Unclassi fied
cos AT I Field/Group
02/B
05/C
13/B
21. NO. OF PAGES
176
22. PRICE
168
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