Allocating Land for an Ecosystem Service A Simple Model of Nutrient Retention with an Application to the Chesapeake Bay Watershed


NCEE0

NATIONAL CENTER FOR
ENVIRONMENTAL ECONOMICS

Allocating Land for an Ecosystem Service: A Simple
Model of Nutrient Retention with an Application to the
Chesapeake Bay Watershed

R. David Simpson

Working Paper Series

Working Paper # 10-04
April, 2010



stA}.^ U.S. Environmental Protection Agency

National Center for Environmental Economics
1200 Pennsylvania Avenue, NW(MC 1809)

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Allocating Land for an Ecosystem Service: A Simple Model
of Nutrient Retention with an Application to the
Chesapeake Bay Watershed

R. David Simpson

NCEE Working Paper Series
Working Paper # 10-04
April, 2010

DISCLAIMER

The views expressed in this paper are those of the author(s) and do not necessarily represent
those of the U.S. Environmental Protection Agency. In addition, although the research described
in this paper may have been funded entirely or in part by the U.S. Environmental Protection
Agency, it has not been subjected to the Agency's required peer and policy review. No official
Agency endorsement should be inferred.

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Allocating Land for an Ecosystem Service:

A Simple Model of Nutrient Retention with an Application to the

Chesapeake Bay Watershed

R. David Simpson*

National Center for Environmental Economics
United States Environmental Protection Agency

March 2010

* All opinions expressed herein are those of the author alone, and do
not necessarily reflect those of the United States Environmental
Protection Agency.

1

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Allocating Land for an Ecosystem Service:

A Simple Model of Nutrient Retention with an Application to the

Chesapeake Bay Watershed

Abstract: There has been great interest in recent decades in "ecosystem services". One
of the services most often mentioned is the retention of nutrients. I construct a simple
model of agricultural land use under a regulatory requirement that nutrient loading cannot
exceed a fixed ceiling develop three propositions. First, when the regulatory constraint is
relatively weak there will be a corner solution in which no land is set aside to provide the
service of nutrient retention. Second, for any given regulatory constraint there is in
general a minimum amount of land that would be set aside to provide ecosystem services,
regardless of the efficiency with which preserved land provides the nutrient retention
function. Third, there is sort of paradox of value: the more valuable it is to set some land
aside for nutrient retention, the less land in total would optimally be preserved for this
purpose. I illustrate the implications of this model with an application to the Chesapeake
Bay watershed. Estimates reported in the literature suggest that land retained in natural
cover could prove very effective in retaining reactive nitrogen and other nutrients. If so,
there is a sort of "good news/bad news" scenario for conservation advocates touting the
importance of ecosystem services. The good news is that the ecosystem service of
nitrogen retention is, in fact, likely to be very valuable. The bad news is that "a little may
go a long way": setting aside small areas of land may be sufficient.

Key words: reactive nitrogen; diamonds and water paradox; ecosystem services;
constrained optimization; land use regulation; corner solution.

Subject Areas: Costs of Pollution Control, Land Use (in agriculture)

JEL classification: Q24; Q53; Q58

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Introduction

The term "ecosystem services" is in vogue (see, e. g., MA 2005; Daily and Matson 2006;
Daily and Turner 2008; Fisher et al. 2009; and the papers introduced by Kareiva and
Ruffo 2009). The basic idea is that preserved or restored "natural"1 ecosystems
sustainably provide a suite of goods and services whose aggregate net present value
exceeds that which would arise from managing the land more intensively. A large and
growing literature promotes the vision that a society that recognizes the importance of
ecosystem services will devote larger fractions of the landscape it manages to the
preservation of natural areas.

Yet despite the burgeoning literature2 on the topic, there are relatively few contributions
that document a rigorous empirical case for the economic value generated by ecosystem
services. Since "ecosystem services" can comprise an extraordinarily broad spectrum of
goods and services (see, e. g., Daily 1997 and MA 2005 for representative lists),3 it
would be difficult, if not impossible, to conduct a point-by-point assessment of each and
every component element. While some very trenchant criticisms have been offered of
seminal work on water purification (see Sagoff 2002, who comments on Chichilnisky and
Heal 1998, and Plummer 2009, who comments on Breaux et al. 1995), and pollination
(see MccCauley 2006, who comments on Ricketts el al. 2004), there are whole topic
areas awaiting both initial empirical estimates and careful peer review.4

While it is frustrating to be reduced to a piecemeal approach to such a wide topic area,
there appears to be little alternative. Yet in considering specific ecosystem services, we
may yet uncover, or, perhaps put more accurately, confirm, the importance of economic
principles that will apply more broadly. This is my objective

One ecosystem service that is often mentioned is the capacity of natural ecosystems to
retain and neutralize pollution, especially nutrients that would otherwise eutrophy (that is,
over-fertilize) and disrupt aquatic ecosystems (see, e. g., Daily 1997; MA 2005; Breaux,
et al. 2005; Plummer 2009). Such services could be of great value in many policy
settings. Ribaudo et al. (2001) consider the economic implications of setting aside
cropland for the retention of nitrogen and other nutrients.

This subject is also very topical. A recent Presidential Executive Order requires U. S.
federal agencies to take more active steps to protect and restore the Chesapeake Bay.5 A
recent interagency report responding to the Executive Order concludes that "There is no
more cost-effective strategy [for meeting environmental and other goals], . . than
conserving existing farms, forests, natural areas, habitat, and other vital resources" (FLC
2009). It is natural to ask, then, both how cost-effective such a strategy is, and, if it is
cost-effective, how it might best be implemented.

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The Chesapeake Bay example is very useful, as regulators have suggested a quantitative
nutrient loading reduction goal: nitrogen loading to the Chesapeake Bay is to be reduced
by 30% (EPA 2009). Thus I can largely sidestep the vexing issue of the valuation of
natural habitats for their contribution to ecosystem services. Because nonmarket
valuation methods are often imprecise and in some instances very controversial, estimates
of value are unavoidably suspect. If, instead of needing to determine what level of
nutrient loading would result in the greatest social value, I can ask what costs would be
incurred to meet a particular standard, the analytical task is far simpler. I can, however,
still talk about the "value" of natural ecosystems as the reduction in opportunity costs
their preservation affords relative to alternative methods of complying with the regulatory
requirement.

This perspective is useful, although the main message that emerges from employing it is
that concentrating on the "value" afforded by natural ecosystems in their provision of the
ecosystem service of nutrient retention may be misleading. I use a very simple but, I
argue, canonical, model to demonstrate three key results. As much of the concern with
nutrient reduction arises from the fertilizers employed in, and animal excrement that is a
by-product of, agriculture, I employ the terminology of "farmland cultivated" and "farm
earnings" in the model, although similar principles might also be applied to other sources
of nutrient loading. The three results are:

1. When required nutrient reductions are modest, the optimal policy response is a
corner solution in which nutrient inputs are reduced but all available land is
cultivated.

2. When nutrient reduction targets are more aggressive, it will often be cost-effective
to meet them by reserving some areas of natural habitat, but the areas whose
preservation may be justified by their provision of the nutrient retention service
may prove to be surprisingly small.

3. There is an inverse relationship between initial value on the margin - that is, the
benefit realized from setting aside the first hectare of habitat to provide ecosystem
services - and the extent of habitat whose preservation can be justified by its
provision of the nutrient retention service. The least preservation of natural
habitats may be justified when the nutrient retention service provided by the first
hectare preserved is most valuable.

These results can be explained by two principles. Both underscore the crucial economic
role of scarcity. First, land is, in general, scarce. Farmers incur substantial opportunity
costs if they forgo the cultivation of available land, or give up the option to employ it in
uses that would not be compatible with conservation. In contrast, it is reasonable to
suppose that, in the status quo, farmers employ polluting inputs until the marginal profit
they can realize from further application vanishes. Under such circumstances, it is easy
to see what a farmer would do in order to meet a requirement to slightly reduce the
pollution her activities cause: reduce the employment of polluting inputs rather than
setting aside more land to retain them.

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I might characterize the other important principle as "the diamonds and water paradox on
steroids". The diamonds and water paradox is the principle that things that may be
immensely valuable in aggregate may be of negligible value on the margin. The
"diamonds and water paradox on steroids" holds when marginal values are necessarily
negligible as quantities increase. The ecosystem service with which we are concerned
here is the retention of nutrients. Suppose that preserved areas of natural ecosystems are
very effective in performing this function. If this proves to be the case, then "a little goes
a long way". If the first hectare of land retains the lion's share of pollution, there will be
little left for the second hectare of land to retain, and hence, little reason to preserve it.
Conversely, if preserved land is not very effective in retaining nutrients, it will prove
more cost-effective to forgo its preservation and reduce the application of nutrients.

Most of this paper will be devoted to establishing the results above and demonstrating the
intuitions just outlined. The heart of the paper consists of formal, if schematic, modeling.
Before launching into that venture, however, I present in the next section a description of
an area in which the nutrient retention ecosystem service may prove to be very important:
the Chesapeake Bay watershed. Following that I introduce a simple model, solve it, and
demonstrate the first three results above. The fourth section of the paper calibrates the
model to the circumstances of the Chesapeake Bay watershed. The fifth section
considers the robustness of the results. The final section concludes with some
conjectures regarding the application of similar methods to the allocation of land for the
provision of other ecosystem services.

2. A motivating example: the Chesapeake Bay watershed

Several contributors to the literature on ecosystem services have included among the
most important services treatment of pollution. Natural ecosystems filter and trap
materials that would otherwise enter more sensitive receiving areas and cause greater
damage. In some instances the ecosystem merely slows the transmission of pollutants,
but in others pollutants may be detoxified or neutralized.

One interesting and, at this point, very topical, application of this pollution treatment
function is found in the Chesapeake Bay watershed. Chesapeake Bay is the largest
estuary6 in the United States. Its watershed spans about 64,000 square miles in the states
of Maryland, Delaware, Virginia, West Virginia, Pennsylvania, and New York, and the
District of Columbia. While about 17 million people live within the watershed, some
25% of the land in the watershed is devoted to agriculture (FLC 2009).

The Chesapeake Bay is in poor condition. One of the largest problems is eutrophication.
Eutrophication results when excessive nutrients are introduced into a water body. The
nutrients stimulate the growth of organisms such as algae. When the algae die they sink
to the bottom, and oxygen is depleted from the water in the process of their

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decomposition. This leads to hypoxic (low dissolved oxygen) or anoxic (no dissolved
oxygen) conditions under which fish and other animals cannot survive.

The two most important nutrients in the Chesapeake Bay are reactive nitrogen and
phosphorus.7 I will concentrate on the former here. Reactive nitrogen can come from a
variety of sources. Natural sources include lightning, fixation by microorganisms, and
recycling via excretion of pre-existing reactive nitrogen. Man-made sources include
combustion, sewage treatment plants, rural septic systems, storm runoff from urban areas,
and agriculture. Some 284 million pounds of reactive nitrogen are now introduced into
the Bay per year. Experts estimate that this will need to be reduced by about 30%, to 200
million pounds per year, if the Bay is to recover (EPA 2009).

About 46% of reactive nitrogen entering Chesapeake Bay comes from agriculture. Of the
nitrogen of agricultural origin, about half results from the application of fertilizer to
crops, the other half from farm animal excretion. While some of the reactive nitrogen
employed in agriculture becomes airborne and reaches the Bay through deposition, the
great majority runs off in surface or groundwater (EPA 2009).

It has proved particularly difficult to reduce reactive nitrogen loading to the Bay because
most of it comes from "nonpoint sources": relatively small-scale operations whose use
and emissions are difficult to monitor. However, many commentators hope that loading
from agriculture can be reduced considerably. There are a number of ways in which this
might be accomplished, other than by simply reducing the scale of agriculture. Farmers
can adopt different tillage practices, target fertilizer applications, plant "cover crops" to
reduce runoff when other crops are not present, modify animal feed, better manage
manure, and/or better manage runoff water from their lands. Moreover, farmers (and
other landowners) can preserve or restore elements of the natural landscape to intercept,
retain, and, ideally, "denitrify" runoff.

Less intensively managed landscapes can reduce reactive nitrogen loading for a couple of
reasons over and above the simple fact that no further nitrogen is applied to them. One
factor is that water flows more slowly through such landscapes. Taller, denser vegetation
forms a physical barrier to water flow. Root networks create channels into the soil into
which water can percolate. More of the reactive nitrogen is then likely to be incorporated
into plant growth. Of course, in steady state, this might lead only to a slower speed of
transit from farm to Bay, rather than an actual reduction in flows.8' 9 There are, however,
natural processes by which reactive nitrogen is "denitrified"; this means that the various
molecular forms of reactive nitrogen are broken down into other elements and N2, the
molecular form of the inert, "nonreactive" nitrogen that comprises nearly four-fifths of
the atmosphere.10

The facts as I have laid them out can be used to structure a constrained optimization
problem. Suppose that total reactive nitrogen loading is restricted to a set limit. What
fraction of the landscape should be devoted to natural ecosystems so as to meet the
loading constraint with the least sacrifice of other social benefits? I turn to the
characteristics of a solution to such a problem next.

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3. A Simple Model and its Implications

In this section I present a very simple model. This model is not intended to represent
real-world circumstance with any precision; rather, it is intended to illustrate possibilities.
It can, however, be argued that model is relatively general.

Consider a production process. Let me call it "agriculture" for concreteness, although it
could apply in other contexts, or to some aggregation of activities. Agriculture involves
the combination of "inputs," which I will denote by a vector x, with "land," A, to produce
output, Q. Suppose also that this production process gives rise to a residual, which I will
denote by R.11 Now if/(x, A, R) is the production function describing the amount of
output that can be produced using variable inputs x and some fixed amount of land, A,
while generating a polluting residual of no more than R, we can say that profits are

n(i?, a) = max Pf(x, A, r) - w'x s. t. r < R,	(1)

x

where P is the price of output and w the price vector of the inputs.

While the first and second results I derive below can be demonstrated to be reasonably
general, it is difficult, and not always very revealing, to work at a very high level of
generality. Let us, then, consider what functional form might be adopted as a laboratory,
as it were, in which to experiment with the properties of the function II (R, A).

Reasonable desiderata for such a specification are, first, that profits be increasing over a
range of values of R and A, second, that for a fixed area of land available, profits are a
single-peaked function of R — that is, there is a point at which farmers reach diminishing
returns in residual pollution; and third, that the profit function exhibits diminishing
returns in R and A separately. It is also helpful to suppose that the profit function exhibits
constant returns to scale in R and A : if we scaled up both land area available and the
residuals permitted proportionately, profits would increase in the same proportion.

The reader may find this last assumption problematic, so I will digress momentarily to
defend it on two bases. First, I will argue in more detail below that this assumption is
conservative, and my results would hold a fortiori if I supposed - admittedly more
realistically - that the existence of other fixed factors prevents perfect replication.

Second, my intention here is to sketch a rather simple argument: that the amount of
valuable land whose preservation can be justified to provide the ecosystem service of
nutrient retention may be limited. This is not to say, of course, that the preservation of a
lot of cheap land would not be a good idea. If copious quantities of cheap land were still
lying about, however, there would be far less controversy about conservation policy. It
is, then, useful to go through the exercise of seeing what happens in a homogeneous
benchmark model in which all land is of equal potential value before thinking about
special cases.

7

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Finally, it seems reasonable to suppose that the release of some residual nitrogen would
be essential: nothing can be produced without some pollution. In the case of nitrogen
this is literally true. Even if one did not apply fertilizer, the very act of breaking ground
results in the oxidization of some of the nitrogen trapped beneath it. Similarly, it is
impossible to raise farm animals in numbers greater than the land's natural carrying
capacity without feeding them from some outside source and, consequently, releasing
nitrogen in their excretions.

A function satisfying these requirements is

n(R,A) = aR-p?j,	(2)

where a and (3 are constants that could be calculated by calibrating the model to real-
world data. Expression (2) has been chosen because of the strikingly simple form of the
results that emerge from it. However, it is worth noting that expression (2) is a second-
order approximation to any constant-returns to scale profit function in R and A in which R
is essential. 12 While there could be infinite variations on the theme, I would argue that
any results that arise from the use of expression (2) merit at least a rebuttal presumption
of generality.13

Normalize the land area to one. Then setting A0= 1 (the subscript zero will relate to
quantities that obtain in the absence of regulatory restrictions), profit is maximized in the
absence of regulatory constraints when the derivative of (2) with respect to R is equal to
zero, i.e., when

Ro = — ¦	(3)

It will be convenient to note for later reference that earnings in the absence of any
regulatory constraint (or, equivalently, the rent to land) are given by

a2

n0 = —•	(4)

0 4/?	W

The ecosystem service of nutrient retention is provided when some portion of the
landscape is preserved to provide ecosystem services rather than cultivated to produce
more output. Suppose that a fraction D of the residual is "passed through" and deposited
in a sensitive receiving area — in the motivating example, Chesapeake Bay — while the
complementary fraction, 1 -D, is retained so it cannot harm the receiving area. It seems
natural to suppose that the fraction neutralized would increase in the amount of land
retained for the provision of ecosystem services, but that the relationship would be
concave: adding more land would result in a less-than-proportional overall reduction in

8

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the neutralization of residual pollution (this diminishing returns assumption is not crucial
to the results; see section 5). Moreover, it is also reasonable to require that if no habitat
were retained for this purpose, 100 percent of residual pollution would be passed directly
from the agricultural sector into the receiving environment.

A function having these properties is

"M = itWay	<5)

where ^ is also a constant. I will refer to this as the "deposition" function.

Note that

lim D{y) = 0;	(6)

y-»°°

if it were possible to put aside an arbitrarily large area to retain nutrients, all nutrients
would be retained. Since the area available can be no greater than one by our choice of
normalization, however,

°(o) -	(7)

and

£>(l) = 1.	(8)

Moreover,

D\A) = 		7^ = ~^A\.	(9)

MM)]2 i + 4i-a)

Note that the deposition function is approximately exponential for values of A near one.
Expression (9), like expression (2), was chosen for analytical tractability rather than
verisimilitude. However, its "quasi-exponential" form means it comports reasonably
closely with the description often encountered in the empirical literature on the nutrient-
retention potential of natural ecosystems; that is, that a certain area of natural ecosystem
will retain a certain fraction of incident nutrients (see, e. g., Mayers el a12007).

9

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The parameter (f> can be regarded as a measure of the efficacy of preserved habitat in
neutralizing pollution: fixing A, the larger is o£ + /?2Ml + ^(|-^)]+ MM)? 77- > 0. (13)

The first-order condition is expressed as an inequality because, as we will see
momentarily, corner solutions in which all land is cultivated obtain under some
circumstances.

Assuming equality for now, simplifying and rearranging,

PL\l+f -2A2\ (14)

a =

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there would be no reason not to expand agriculture to the full area available for
cultivation, A0= 1 in the absence of regulation. Thus the pollution load received in the
sensitive area would also be L0 = a/2|3. I will now express the loading constraint, L , as a
fraction, p, of the unregulated loading, L0. That is,

L = pL0 = (16)

0 2 P

Substituting this expression in (16), a and (3 cancel, leaving

= pML (17)

(p(l + pcf)

While it is an artifact of the approximation by which (2) was derived, expression (17) is
conveniently compact. The area of land cultivated depends only on one parameter
measuring regulatory stringency, p, and another indexing the effectiveness of preserved
land in retaining nutrients, (p.

I can now demonstrate the three results summarized in the introduction.

Proposition 1: When the regulatory loading constraint is not very strict, there must be a
corner solution in which all land is cultivated.

The area of land cultivated, A, will be less than one when

p(l+)2 < (2+ p) (18)

p < (19)

1 + 2^

The fraction on the right-hand side of (19) is strictly less than one. For any finite
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Expression (19) demonstrates that if ^ were small enough, A would be one for any
positive value of p. Intuitively, it makes little sense to set aside land for retaining
nutrients if the land being set aside is not very effective for this purpose. It is also
intuitive, though, that if (f> where large enough, the area preserved to retain nutrients
would be vanishingly small. This intuition is easily confirmed by applying L'hospital's
Rule twice to expression (17):

lim

^—>00

P(l + Y
A2 + pf)

= lim

^—>oo

2/?(l + ^)

2(l + p00

2 p

(20)

If vast quantities of nutrients could be neutralized by setting aside only a very small area
of land, there would be no reason to forgo the cultivation of any more land than
necessary.

So, if

Thus dA/d(j) = 0 when the term in square brackets is zero:

p > 0 and, as I will now show that it
leads to a value of A that is not greater than one, it must identify a unique minimum.
Substituting from (22) into (17),

A* = Vl"(l~Pf ¦ (23)

The minimum amount of land area cultivated varies from none, when nutrient loadings
are to be totally eliminated, to one, when the status quo is preserved. In between,
however, land cultivated is a convex function of the regulatory constraint, p, with A
greater than p for all values of the latter between zero and one.

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The optimal reduction in land area is often much less than proportionate to the reduction
in loading required. For example, the maximum reduction in land area cultivated that
would be required to meet a 28% reduction in loading would be 4%.

Proposition 3: The more preserved land is "worth " ab initio, the less land should be
preserved.

Much of the literature on ecosystem services has focused on the question of whether land
would be worth more preserved in, or restored to, natural habitat, as opposed to in more
intensive managed use. The goal of such exercises is to determine whether some land, or
a particular parcel of land, should be devoted to providing ecosystem services. It is also
important to know, however, how much land should be devoted to providing ecosystem
services. It may seem natural to suppose that if some land could be shown to be
extremely valuable in the provision of an ecosystem service, then a lot of land out to be
set aside for that purpose. That is not generally correct, however.

Note first that when there is an interior solution - that is, when the area of land cultivated
is strictly less than the total area of land available for cultivation - the marginal value of
land preserved for nutrient retention would be exactly equal to the marginal value of
cultivated land.

Let us, then, conduct a thought experiment. Suppose that the regulatory constraint, (10),
must be met without reducing the amount of land cultivated below its normalized ex ante
value, 1. It would then follow from (10) that

where I denote by R the residual permitted while meeting the loading constraint. This, in
turn, implies that

where the second equality follows from (4) and (16), and ;zo is land rent in the absence of
regulation.

Now let's ask by how much would overall earnings from agriculture increase if one
hectare of land were removed from production and restored to provide the nutrient
retention ecosystem service?

To answer this question, we need to return to the first-order condition, (13), and evaluate
it at ^4 = 1. It will be useful to rearrange (13) as

R = L,

(24)

(25)

(26)

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The second term on the right-hand side of equation (26) is the direct effect of cultivating
more land - it is the marginal increase in profit resulting from employing more land. The
first term on the right-hand side of (26) is the indirect effect induced by affording the
possibility of producing more residuals since such residuals can be partially offset by the
ecosystem services provided by preserved habitats. Differentiating the regulatory
constraint, (11), with respect to A,

^ = -f, (27)

Substituting (27) into (26) and evaluating (26) at ^4 = 1

— = -(pL[a-2pR\ + PR2. (28)

Since L = R = pR0 when evaluated at A = 1, and combining (3) and (4) to note that 7io =
|3i?o2, we have

-j7 = -2^(1-/jVo+A (29)

Note that dx/dA < 0 when evaluated at A = 1, so the optimal solution requires A < 1, only
if condition (19) is met. When the optimal solution requires A < 1, we might refer to the
negative of the first term of (29), which I earlier characterized as the indirect effect of
cultivating the marginal hectare of land, as the value of the first hectare of land preserved
in terms of increased profit afforded by more intensive application of other inputs (and
gross of the opportunity cost of leaving such land idle, as represented by the second term
in (29)). Note that this value is increasing in grows large, I have established Proposition 3 for this case: the value of the
first hectare of land preserved is greatest when the overall amount of land preserved
would be least.

This derivation has been somewhat convoluted, so let me provide some further context.
Much of the literature on ecosystem services has asked "When is land more valuable for
providing ecosystem services than it would be if employed in production directly?" It
seems entirely appropriate to conclude that preserving land for the provision of
ecosystem services would make sense in many circumstances. My point, however, is that
a demonstration that some land could be extremely valuable for the provision of
ecosystem services says nothing about how much land should be devoted to this purpose.
I am suggesting that the demonstration that preserving some land to provide ecosystem
services makes sense may, in fact, set up a sort of good news/bad news scenario for those

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who appeal to ecosystem services to motivate conservation more generally. The good
news is that the argument to set some land aside may be logically impeccable. The bad
news is that demonstrating very high values associated with setting some land aside may
necessarily imply that very little land in total should be preserved for that purpose.

4. A Calibration Exercise

In this section I calibrate the model presented above to data from the Chesapeake Bay
watershed. As I have suggested above, and will document further in the next section, a
multitude of caveats should accompany any such exercise. I will not repeat them here,
but say only that it is useful to perform an exercise under the benchmark assumptions of a
homogeneous landscape in order to develop a rough idea as to likely real-world
outcomes.

With no further ado, then, let us begin with the facts that the current annual loading of
reactive nitrogen received in the Bay is about 284 million pounds. It is felt that this
loading must be reduced to 200 million pounds per year if the Bay is to be restored. This
represents a reduction of about 30%. Of the total nitrogen loading, nearly half - 131
million pounds per year - is attributed to agriculture. Draft plans call for a reduction of
loading from this sector by some 44%, to 73 million pounds per year (EPA 2009).

The scientific literature on the effectiveness of riparian buffers for nutrient removal
reports a range of estimates of the relationship between the area of land set aside and their
effectiveness (Rupprecht, el al., 2009). It seems, however, that buffers are often very
effective in removing nitrogen. A recent meta-analysis of 88 studies finds that four meter
(13 feet) wide buffers remove half of incoming nitrogen, effectiveness climbs to 75% as
width expands to 49 meters (160 feet), and at a width of 149 meters (485 feet) 90% of
nitrogen is removed (Mayer, et al., 2007). While individual studies do, of course, vary
widely, it seems safe to conclude that the general finding of such studies is that relatively
small areas can remove substantial fractions of nitrogen, but that, beyond a certain size,
little nitrogen remains to be retained (see, e. g., Dillaha et al. 1989; Palone and Todd
1997; Mayer etal. 2005).14

The Chesapeake Bay Watershed encompasses an area of 64,000 square miles (FLC
2009). About 115,000 miles of streams run through the watershed (GFIS 2001). Let us
suppose, then, that the density of streams in the watershed is 115,000 miles/64,000 square
miles =1.8 miles of stream per square mile. Let us suppose, in what seems a somewhat
conservative interpretation of the data as summarized in the Mayer, et al. (2007) and
Rupprecht et al. (2009) reviews, that a riparian buffer extending 50 feet from each bank
of a stream is sufficient to remove 50% of the nitrogen that would otherwise flow into it.
This corresponds to a total area of 1.8 miles of stream per square mile of area x (2 sides
of each stream x 50 feet of buffer on each side)/(5,280 feet per mile) = 0.034 of the area
available for cultivation. From the deposition function, (8), we have

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1 + 0.034^'

(33)

(p =

0.034

= 29.4.

(34)

Using this figure and the regulatory objective of p= 0.56 in (17),the cost-effective
strategy would call for the cultivation of

= 036(1 + 294)' =

\ 29.4(2 + 0.56-29.4) ^

of land available, with the preservation of only 2.4%. This figure would correspond to
buffers of about 35, rather than 50, feet on each side of streams.

It is, on a moment's reflection, obvious why relatively little land should be devoted to the
provision of the nutrient retention ecosystem service. The policy objective only requires
that nitrogen loading be reduced by 44%. If buffers extending 50 feet on either side of
streams would reduce loading by 50%, the objective could obviously be met with
narrower buffers.

In fact, it would appear that the objective could be met largely by requiring modest
buffers with little need to modify other practices. It is easily shown that the ratio of
residual nitrogen under the cost-effective solution to that in the status quo is, from (10)
and (16),

— = \[ +
-------
dx

= - 2(f>p{v - p)n{) + p2n{)

Using the values (fi = 29.4 and p = 0.56, the first term in expression is some 14.5 times
profits in the absence of regulation, while the second term is only about a third of profits
in the absence of regulation. These relative magnitudes confirm that it would be a very,
very good idea to set aside some land to provide an ecosystem service, nutrient retention.

However, such land quickly becomes superfluous. Recall from expression (22) that the
area of land preserved would be maximized if the effectiveness parameter were

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hybrid specifications of the deposition function have yielded more, rather than less,
dramatic results than emerge from the analytically tractable model I have employed
above.15 This has also been the case with the third result. Substitution of alternative
functional forms makes the analytical derivation of results more complex, but does not
eliminate the ostensibly paradoxical result that less land would be preserved when the
effectiveness of nutrient retention renders the value afforded by the first hectare
preserved greater.

In short, then, numerical results support the contention that the results outlined above are
robust.

The next question to ask, then, is whether the ways in which I have structured the general
problem are unduly restrictive and, if so, if they bias results. Is it unreasonable to
suppose there are constant returns to scale in production, and hence that the profit
function if homogenous of degree one in R and A? Yes, it probably is. "Land" is not
homogeneous, and consequently, agricultural operations cannot be replicated perfectly on
less-advantaged land. However, the clear implication of this observation is that the
opportunity cost of withdrawing land from production is increasing in the area of land
preserved. Thus my results should be strengthened under alternative assumptions.

It may also be unreasonable to suppose that the perfectly competitive conditions required
to derive the reduced-form profit function of expression (1) obtain over large landscapes.
As land is withdrawn from production and residual nutrients decreased agricultural
production would decline. This, in combination with less-than-perfectly elastic demand
for output would mean, again, that the opportunity cost of withdrawing land from
production would change as the amount of land withdrawn increases. At the same time,
however, the prices of less-than-perfectly-elastically supplied inputs would fall. It seems
reasonable to conclude, however, that the net effect of such offsetting factors could be
regarded as close to neutral (for a study that carefully considers the general equilibrium
effects of land preservation policies designed to address nutrient retention, see Ribaudo et
al. 2001).

Another concern that might be raised with the modeling assumptions I have adopted is
that it is unreasonable to suppose that land available for farming is strictly fixed. Several
justifications might be offered for the simplifying assumption that it is, however. First,
the total amount of land available for all purposes in a particular region is, of course,
fixed. Land not devoted to farming or preserved in natural areas would likely be devoted
to some combination of activities that would themselves involve the laying down of
impermeable surfaces, combustion, occupation by people who produce more sewage, and
other activities that also increase reactive nitrogen residuals. Second, inasmuch as the
supply of land to agriculture is determined by the demand for residential and commercial
purposes, that supply may be relatively inelastic. Finally, and apropos of the subject of
the next paragraph, while agriculture might well expand into the still-plentiful forested
upland areas of the watershed, the more relevant question for our purposes concerns the
division of land use between cultivation and preservation in the often-more-valuable
downstream areas.

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The largest problem with the modeling approach I have adopted is that it presumes all
land is homogeneous. The simple model I have developed would be of little, if any, use
in determining exactly which parcels of land would best be devoted to the retention of
nutrients. Such micro level, on-the-ground planning will remain the province of more
careful modelers who will compensate for the idiosyncrasies of topography, soil
chemistry, hydrology, native vegetation, and the like in making their determinations of
which specific areas should be farmed and which preserved to provide ecosystem
services such as nutrient retention.

It is, however, worth emphasizing that if it were widely accepted that a fortuitous but
strong inverse correlation existed between a parcel's value in agriculture and its
effectiveness in retaining nutrients, the problems of excess nitrogen loading in water
bodies like Chesapeake Bay would have been solved long ago. Over half of the land in
the Chesapeake watershed is currently in forests (FLC 2009). If these forests are
effective in retaining nutrients and they were in the "right places" for that purpose, there
might well be no problem with excessive nutrient loading. If there is a problem, it must
be because the opportunity cost of setting aside natural areas to retain nutrients in the
areas in which they would do the most good are considerable. The question I have been
asking, then, is whether appeal to the ecosystem service of nutrient retention would
motivate the preservation (or, more likely, restoration) of a great deal of additional
natural habitat. The principles illustrated by my simple model suggest that it might not.

6. Conclusion: Implications for the Ecosystem Services Framework

Let me return in closing to the "good news/bad news" message of this paper. The good
news, from an ecosystem conservation perspective, is that the preservation of natural
ecosystems is likely to comprise a critical part of a cost-effective strategy for nutrient
management. My modeling effort, simple and schematic though it may be, would appear
to confirm the conclusion noted above: "There is no more cost-effective strategy . . . than
conserving existing farms, forests, natural areas, habitat, and other vital resources" (FLC
2009).

The "bad news", however, may be that the provision of this ecosystem service does not
necessarily create a compelling argument for larger-scale conservation. Precisely
because preserved natural ecosystems perform their functions so cost-effectively, "a little
may go a long way".

Natural ecosystems provide a host of services, however, and economic theory suggests
that they should be preserved so long as the sum of the values of the incremental benefits
their preservation generates exceeds the opportunity costs of preservation. The
incremental benefits of the full suite of services remain to be established. Many of the
benefits of ecosystem services may be of a similar character to those of nutrient retention,
however. Many of the services of natural ecosystems are valuable precisely because they

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protect or augment the value, or mitigate the impact, of the decidedly unnatural systems
of homes, agriculture, and industry of the areas they adjoin. There will, then, generally
be an interior solution to the land allocation problem characterized by a tradeoff between
the benefits of expanding areas preserved and the opportunity cost of forgoing intensive
use of such areas. The "diamonds and water paradox on steroids" that motivates my
results could prove to be general. If natural ecosystems are not sufficiently productive in
generating ecosystem services, they may not provide enough value to justify the
opportunity costs of their preservation. If, however, they prove too effective in providing
ecosystem services, we may conclude that a little goes a long way, and not decide to save
much of them.16

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References

Breaux A, Farber S, and Day J. 1995. Using natural coastal wetlands systems for waste-
water treatment - an economic benefit analysis. Journal of Environmental Management
44 285-91.

Chichilnisky, Graciela, and Geoffrey Heal. 1998. Economic returns from the biosphere:
Commentary. Nature 391 (6668). 629-630.

Daily, Gretchen. 1998. Nature's Services: Societal Dependence on Natural Ecosystems.
Washington: Island Press.

Daily, Grechen, and Pamela Matson. Ecosystem services: from theory to
implementation. Proceedings of the National Academy of Sciences 105 (28). 9455-
9456.

Daily, Gretchen, and V. Kerry Turner. 2008. The ecosystem services framework and
natural capital conservation. Environmental and Resource Economics 39, 1. 25 -35.

Dill aha T.A., Reneau R.B., Mostaghimi S„ Lee D.. 1989. Vegetative filter strips for
agricultural nonpoint source pollution control. Transactions of the ASAE 32, 2. 5 13-5 19.

Fisher, Brendan, R. Kerry Turner and Paul Morling. 2009. Defining and classifying
ecosystem services for decision-making. Ecological Economics 68 (3). 643 - 653.

Federal Leadership Committee for the Chesapeake Bay (FLC). 2009. Executive Order
13508 Draft Strategy for Protecting and Restoring the Chesapeake Bay. Online at
http://executiveorder.chesapeakebav.net/file.axd?file=2009%2fl !%2fChesapeake+Bav+
Executive+Order+Draft+ Strategy.pdf. Accessed 7 January 2010.

Kareiva, Peter, and Susan Ruffo. 2009. Using science to assign values to nature.
Frontiers in Ecology 7 (1). 3.

Madison et al. 1992

Mann, Charles. 2005. 1491: New Revelations of the Americas Before Columbus. New
York: Alfred A. Knopf.

Mayer P.M., Reynolds S.K., Jr., Canfield T.J., McCutchen M.D.. 2005. Riparian Buffer
Width, Vegetative Cover, and Nitrogen Removal Effectiveness: A Review of Current
Science and Regulations. EPA/600/R-05/118. Cincinnati, OH: US Environmental
Protection Agency.

Mayer, Paul M., Stephen K. Reynolds, Jr., Marshall D. McCutcheon, and Timothy J.
Canfield. 2007. Meta-analysis of Nitrogen Removal in Riparian Buffers. Journal of
Environmental Quality 36 (July - August). 1172 -1180.

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McCauley, Douglas. 2006. Selling out nature. Nature 443. 227-228.

National Consortium for Rural Geospatial Innovations (RGIS). 2001. Taking Stock of
Riparian Forest Cover: GIS Streamlines Inventory of Riparian Forest Buffers in
Chesapeake Bay Watershed. Pennsylvania State University. Online at
http://www.lic.wisc.edu/pubs/Penn2.pdf. Accessed 7 January 2010.

Pal one R.S., Todd A.H., ed. 1997. Chesapeake Bay Riparian Handbook: A Guide for
Establishing and Maintaining Riparian Forest Buffers. NA-TP-02-97. Radnor, PA:
USD A Forest Service.

Plummer, Mark L. 2009. Assessing benefit transfer for the valuation of ecosystem
services. Frontiers in Ecology 1 {I). 38-45.

Ribaudo, M; Heimlich, R.; Claassen, R.; Peters, M. 2 001. Least-cost Management of
Nonpoint Source Pollution: Source Reduction vs. Interception Strategies for Controlling
Nitrogen Loss in the Mississippi Basin. Ecological Economics 37. 183-197.

Ricketts, Taylor H., Gretchen C. Daily, Paul R. Ehrlich, and Charles D. Michener. 2004.
Economic value of tropical forest to coffee production. Proceedings of the National
Academy of Sciences 101 (34). 12579 - 12582.

Rupprecht, Ryan, Chris Kilgore, and Roger Gunther. 2009. Riparian and Wetland
Buffers for Water Quality Protection. A Review of Current Literature. Stormwater: The
Journal for Surface Water Quality Professionals 10, 8 (November - December)

Sagoff, Mark. 2002. On the value of natural ecosystems: the Catskills parable. Politics
and the Life Sciences 21 (1). 19 - 25.

United States Environmental Protection Agency (EPA). 2009. The Next Generation of
Tools and Actions to Restore Water Quality in the Chesapeake Bay: A Revised Report
Fulfilling Section 202a of Executive Order 13508. Online at

http://executiveorder.chesapeakebav.net/file.axd?file=2009%2fll%2f202a+Water+Quali
tv+Report.pdf. Accessed 7 January 2010.

End notes

1 The quotation marks around "natural" are intended to suggest the difficulty of defining what comprises a
"natural" as opposed to an "artificial" or "managed" system. See, e. g., Charles Mann's fascinating book
1491 (2007) for examples of how ostensibly "natural" systems may reveal hints of long and careful
management. For the purposes of this paper, it may be better to distinguish "more intensively managed"

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from "less intensively managed" systems, and consider the assertion that the latter are more effective than
the former in supplying certain socially valuable goods and services.

2 Fisher and Turner document exponential growth in the number of publications dealing with "ecosystem
services," beginning from essentially none in the early 1980's to more than 250 in 2007, the last year for
which they had data.

3 It should also be noted that the term "ecosystem services" is used in different ways by different authors.
For example, the nutrient recycling function performed by microorganisms in the soil is certainly an
"ecosystem service," but its provision does not depend on the preservation of large areas of pristine habitat
(I am grateful to Andy Manale for providing this example and emphasizing its importance).

4 I might also add to this list the work of Simpson el al. 1996, which suggested that the value of
biodiversity in new product research had been overstated, although that work, and the earlier papers to
which it responded, was completed before the term "ecosystem services" came into vogue. New-product
sourcing continues to be listed in compendia of ecosystem services, however (see, e. g., MA 2005).

5 Executive Order 13508, Issued 12 May 2009. http://www.gpoaccess.gov/presdocs/20Q9/DCPD-
200900352.pdf.

6 An estuary is a body of water in which fresh and saltwater mix.

7 I will not consider phosphorus or sediments, which are also major problems in Chesapeake Bay, further
here. However, reactive nitrogen, phosphorus, and sediments tend to arise from similar activities, and to be
retained in roughly proportionate quantities by preserved or restored natural ecosystems.

8 We should not, however, completely dismiss timing-of-load issues. If reactive nitrogen is greatly
slowed in its transmission to the Bay, it could arrive in a Bay less stressed by other nitrogen sources and
perhaps better situated to deal with more nitrogen. In particular, it is hoped that native oysters might be
reestablished in the Bay. The current oyster population of the Chesapeake is believed to be less than one
percent of its historical level. Widely cited figures claim that, when oysters were healthy, they could filter
the entire water mass of the Bay in a period of three or four days. Doing so now would take over a year
(FLC 2009).

9 The processes of nitrogen retention may become very complex. Plants also bind nitrogen in complex
organic molecules from which it cannot easily escape, and which may, depending on the attributes of the
ecosystem in which they are growing, sequester it for long periods of time.

10 This is a desirable end over and above its eutrophication consequences. Among the various nitrates,
oxides, and other compounds containing reactive nitrogen are toxins and potent greenhouse gases.

111 could generalize to suppose that Q and R are also vectors, but there seems to be no real gain from doing
so.

12 The assumption of constant returns implies that

n(;?,.4) = tt(r/a)a.

The assumption that R is essential means

;r(o) = 0.

To a second-order approximation of 7i(R :\) around R= 0, then,

-------
n (r, a)

r(o) + x'(0)R/A + (0 )R2/A2

The first term in square brackets is zero by assumption. Setting a = n,(0) and ji = -Vi n"(0). we have
expression (2).

13 Another convenient, if less general, way in which to motivate equation (5) is to suppose that R - yR2/. I
is a constant-returns-to-scale production function in a single input polluting input R purchased at price w.
If P is the price of output, then a = P-w and p = Py.

14 It should also be noted, however, that the literature warns against generalization. The amount of
nitrogen that will be delivered to a water body depends not only on the size of the area through which it
will be filtered and retained, but also the properties of soils, the slope of the terrain, the type of vegetation
covering it, and other factors. Moreover, more nitrogen will be flushed out during storms than during more
tranquil periods, so such studies implicitly (or, occasionally, explicitly; see, e. g.,. Finally, nitrogen may
be retained to different degrees and with differing levels of certainty depending on whether it is fully
denitrified (converted back into atmospheric nitrogen, N2) or bound into complex organic molecules which
may or may not remain in the soil after the plants that produced them die.

It is also worth noting in passing that the literature generally reports nitrogen retention efficiency as a
fraction of the inflow, rather than as an absolute amount.

15 It is worth noting an interesting curiosum here. Substituting the linear deposition function
L = R-(/>().-A)

for equation (5) yields exactly the same expression for the minimum possible value of A as in (23). This is
one among many indications of the robustness of the results.

16 I hesitate to state such a conclusion without positing some final caveats and qualifications. One is that
my understanding of ecology, at least, is not such as to suggest that we can confidently suppose that
arbitrarily small ecosystems could sustainably provide arbitrarily large benefits. Put in the parlance of
production theory, there may well be nonconvexities arguing for the preservation of ecosystems of at least a
minimum scale. The other obvious caveat here is that some of the most important reasons for preserving
nature are probably the least tangible and effable. Economists considering ecosystem services might do
well to contemplate the musings of John Stuart Mill, which he may have been wise not to have attemped to
quantify:

Nor is there much satisfaction in contemplating the world with nothing left to the spontaneous
activity of nature; with every rood of land brought into cultivation, which is capable of growing
food for human beings; every flowery waste or natural pasture ploughed up, all quadrupeds or
birds which are not domesticated for man's use exterminated as his rivals for food, every
hedgerow or superfluous tree rooted out, and scarcely a place left where a wild shrub or flower
could grow without being eradicated as a weed in the name of improved agriculture. (1848).

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