Measuring the Marginal Cost of

Nonuniform Environmental Regulations

David L. Sunding

A method is presented for measuring the marginal welfare cost of environmental

regulations affecting agriculture. The method incorporates output market effects and

recognizes diversity in production conditions among crops, regions, and seasons. An

important advantage of the method is that only regional outputs and changes in

regional production costs are needed to calculate deadweight loss, thus simplifying the measurement of welfare changes. This feature of the model is significant since the

complexity and substantial data requirements of most existing impact models cause

many environmental regulations to be enacted with inadequate analysis of their economic impacts. The method also disaggregates welfare impacts by crop, place, and time, thus encouraging the implementation of nonuniform interventions that achieve a

given level of environmental quality more efficiently than uniform policies.

Key words: environmental regulations, welfare analysis, microparameter models, distributional impacts.

Regulations intended to improve environmental quality often entail changes in agricultural pro- duction processes. Policies to improve water quality, ensure worker safety, maintain soil quality, enhance wetlands, and protect endangered species frequently require adjustments in farming practices. In this paper I develop a method for calculating the marginal welfare costs of envi- ronmental regulations affecting agriculture.

To the extent that environmental regulations imply changes in farming practices, there is a natural tradeoff between environmental quality and production costs. Requiring growers to re- duce pesticide applications, for example, typi- cally reduces yields and may increase per acre production costs as growers adopt other pest control methods such as integrated pest man- agement. The result of reducing pesticide appli- cation, then, is to increase the marginal cost of production.

Agriculture differs from many other indus- tries in that farming is highly dependent on the physical and biological environment. Because

David L. Sunding is senior economist with the Council of Eco- nomic Advisers, Executive Office of the President.

This research was supported by a grant from the Office of Pesti- cide Consultation and Analysis of the California Department of Food and Agriculture. The author acknowledges helpful comments from two anonymous referees, David Zilberman, Doug Parker, Jerry Siebert, Adolfo Gallo, Steve Shaeffer, and participants in seminars at UC Riverside and UC Santa Barbara.

environmental conditions vary widely among regions, agricultural production processes also differ among regions. Factors such as soil qual- ity, drainage conditions, water availability, and pest control problems partially determine the methods and costs of production. Thus, the ef- fects of environmental regulations on agricul- ture will most likely vary among regions, and, as emphasized by Zilberman et al. and Lichtenberg, Parker, and Zilberman, environ- mental regulations frequently have significant distributional impacts.

Agriculture is also highly dependent on dy- namic conditions such as temperature, humid- ity, rainfall, and pest population growth rates. When calculating the cost of environmental regulations of agriculture, it is also important to temporally disaggregate the impact of the regu- lations as opposed to performing an annual analysis. There are several examples of time- dependent environmental regulation in agricul- ture, which are discussed below, and many more cases where varying regulations by sea- son would reduce the welfare costs of improv- ing environmental quality.

Disaggregating the marginal costs of environ- mental regulations encourages policy makers to design and implement more flexible, nonuni- form policies that tailor regulations to indi- vidual crops, regions, and seasons. This point is emphasized in the Lichtenberg, Spear, and

Amer. J. Agr. Econ. 78 (November 1996): 1098-1107 Copyright 1996 American Agricultural Economics Association

Marginal Cost of Environmental Regulations 1099

Zilberman analysis of re-entry intervals follow- ing pesticide applications that calculates first- best, region- and crop-specific regulations. The Lichtenberg, Zilberman, and Bogen study of drinking water contamination also suggests that different water quality standards should be de- veloped for urban and rural areas as a result of the significant economies of scale in urban wa- ter treatment.

A method is presented for measuring the mar- ginal costs of nonuniform environmental regu- lations that recognizes differences in produc- tion conditions among crops, regions, and sea- sons. There have been several attempts to de- velop methods for measuring marginal costs of environmental regulations affecting agriculture, most notably Lichtenberg, Parker, and Zilberman. This paper extends the existing lit- erature by explicitly considering temporal as well as spatial diversity, thus facilitating the de- sign of environmental regulations that are sea- son- and region-specific. This modification is especially important in markets for perishable commodities that have widely fluctuating prices, quantities, and market shares over time.

The formal analysis in the next section re- sults in an equation characterizing marginal welfare impacts for each crop and season com- bination as a weighted average of the changes in regional marginal production costs. This theoretical result is appealing on practical grounds because the method requires only readily obtainable information to assess the marginal costs of environmental regulations. Further, the welfare impacts can be calculated with a spreadsheet, thus making the method low-cost and accessible to noneconomist policy makers. Econometric measures of demand and supply elasticities, which are difficult to esti- mate and interpret, are only needed to partition the total welfare losses into consumer and pro- ducer surplus changes; the aggregate welfare loss does not depend on these elasticities. The welfare loss expression developed in the next section also is shown to be a close approxima- tion to true welfare loss in an important class of production models.

The practical value of the model developed in this paper depends on the ability of regulatory agencies to enforce crop, region, and time-spe- cific environmental regulations. Nonuniform regulations are feasible, as the following para- graphs demonstrate. Nationally, under the Fed- eral Insecticide, Fungicide and Rodenticide

Act, growers of a particular crop in a particular region can request a Section 18 exemption from registration requirements in case of extreme need, usually defined as large profit losses re- sulting from the absence of alternative controls. Chemical bans and the taking of arable land for critical habitat protection for endangered spe- cies are also done on a regional basis.

Physical information is being used to develop localized environmental policies affecting agri- culture. For example, the state of California is currently banning the use of pesticides likely to leach into groundwater in certain Pesticide Management Zones (PMZ). Growers operating within these areas are denied access to these chemicals through the registration process, wherein growers must file for permission to use certain agricultural chemicals at the time of purchase. The state has developed a Geographic Information System (GIS) that enables the per- mit issuer to tell whether the grower's field is within a PMZ and act accordingly. A similar pro- gram is being developed for the Corn Belt by the U.S. Environmental Protection Agency to control nutrient contamination of groundwater.

Finally, there are a small number of current environmental regulations that are seasonal. For example, some re-entry and preharvest in- tervals after pesticide applications vary by sea- son as foliar residue decay rates depend on temperature, humidity, and rainfall. Making more environmental regulations season depen- dent can have significant welfare benefits. In fact, in the empirical example of a pesticide cancellation presented below, seasonal differ- ences in the marginal welfare impacts of can- cellation within a region are as large as the variation between regions in a given season.

The formal analysis, presented in the next section, culminates in an expression for the marginal welfare costs of environmental regula- tion. The method is then used to calculate the marginal costs of banning the pesticide, mevinphos. State and federal agencies are in- vestigating whether this organophosphate in- secticide poses unreasonable risks to farm workers and consumers, particularly infants (State of California), and the state of California has recently taken steps to ban its use in the state entirely. Measures of the marginal welfare costs of banning mevinphos in California, based on information from four vegetable crops grown in various parts of the state and else- where, are presented.

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1100 November 1996

Marginal Welfare Costs of Environmental Regulation

Economic welfare is defined here as the unweighted sum of producer and consumer sur- plus; the impacts described here are gross wel- fare changes from regulation since the analysis does not quantify the benefits of regulation such as increased levels of human and environ- mental health. Denote the level of production of some crop in region i in period t by qit and the market price in period t by the inverse de- mand function p,(q,), where q, is total produc- tion of I regions at time t. The cost of produc- tion in region i in period t is denoted by the continuous and differentiable function ci,(qi,, git), where git indexes environmental regulation in region i and period t. Suppose that the pro- duction technology is characterized by

acit (qit, , it) a2Cit (qit, git ) >0; _ >0.

aqit aqit2

Thus, technology in each region exhibits con- stant or decreasing returns to size.

Consider a perfectly competitive output mar- ket. The period t profit of region i is given as

(1) it = P,qit - cit(qit, Jit).

The first-order condition for profit maximiza- tion is

- t = O Vi,t

which simply requires that price equal regional marginal cost in each time period and region. Market equilibrium is characterized by

(3) p,(qt) - pt = 0 V t

where qt is total production in period t. Totally differentiating equations (2) and (3),

and using the fact that competition implies mar- ginal cost is equal to price, we have the system

4 P dP aMCi,,(q,,, it) d) (4) -

dq, t + di i ,itqit _ 0Vit t

- dpt = 0 Vi, t

(5) P dqit - dpt = 0 Vt iel tqit

where Eit is the elasticity of supply in region i in time t, and rt, is the elasticity of demand in time t. The system of I + 1 equations can be solved to obtain marginal changes in regional produc- tion and market price, dq,, and dp,. Note that equations (4) and (5) can accommodate any type of shift in regional supply curves and that we have made no assumption about the func- tional form of regional marginal cost curves other than eliminating increasing returns to size and assuming continuity and differentiability.

Expressions for the change in producer and consumer surplus follow naturally from the cal- culated marginal changes in quantities and prices. Consumer surplus in period t is given as

a,

(6) CS, = Jq(p,)dp, Pt

where p, is a variable of integration and a, is the vertical intercept of the demand curve. The marginal change in consumer welfare is then dCS, = -qdp,.

Producer surplus in region i and period t is given as

qa7

(7) PS,, = p,q, - JMCi,(Oi,, i)di, 0

where 0, is a variable of integration. The mar- ginal change is found using Leibniz's Rule as

q' aMCi(Oit. git)

o aOit

- MCi, (i, [it)dqi,

which simplifies to

(8) dPSit = qi,dp, - aMC,, (qit, it )dqit

agit

In regions that are not directly affected by envi- ronmental regulation, this expression reduces to q,dp,. These growers should gain from the

Amer. J. Agr. Econ.

acit (qi, [tit ) (2) aqi ,

a,qit

Marginal Cost of Environmental Regulations 1101

regulation to the extent that it raises marginal costs in competing regions and increases output price as a result. Expression (8) can also be in- terpreted in terms of changes in quasi-rent: the first term is simply the change in farm revenue resulting from the regulation, while the second term is the change in production costs.

The gross marginal welfare cost of a change in environmental regulations is calculated by summing the expressions for the change in con- sumer and regional producer surplus to obtain

(9) dW, = _jI aMCit (qit, tit )dqit q (9) d = -,"-, q i,. iEl agit

The marginal change in social welfare in each time period is thus equal to a weighted average of changes in regional marginal costs of pro- duction, with weights given by preregulation output levels. Expression (9) is highly intuitive: the marginal cost of environmental regulation is equal to the increase in the value of inputs to agricultural production. This expression also shows that marginal welfare loss is separable in the change in regional marginal production costs and separable over time, a feature that greatly simplifies the computation of impacts.

Expression (9) is significant for policy analy- sis since it implies that decision makers can as- sess the total marginal welfare costs (i.e., the marginal effects on consumer and producer sur- plus) of environmental regulation with informa- tion that is simple to obtain. Lichtenberg, Parker, and Zilberman show that when marginal production costs for each region are equal to average costs, as in case of the step-function supply curve, the change in regional marginal cost at time t is equal to

( MC,it(qit, git) Ptit + (dCit/it)

ait 1- i,t

where Vrit is the percent change in regional yield, Yit is regional yield, and dCit is the change in per acre production costs, all at time t. While there may be a large number of regions and time periods considered [in fact this is pre- ferred as it increases the accuracy of equation (9), as discussed later], each individual datum in equation (10) is readily available. Prices, re- gional outputs, and yields are published by state and federal sources. Changes in per acre yield and production cost can be obtained from noneconomists via survey methods, which we discuss in more detail below. Thus, demand and

supply elasticities are not required to assess the marginal welfare impacts of environmental regulation; elasticities are needed only to de- compose aggregate deadweight loss into pro- ducer and consumer surplus components. The simplicity of the method developed here is an important practical advantage over theoretically more exact, but also more complicated, proce- dures. Currently, many environmental regula- tions affecting growers are enacted with no economic analysis of their impacts. This lack of analysis is due in part to the complexity of many existing agricultural impact models, and to the fact that the basic data used in these models, especially supply and demand elastici- ties, are difficult to obtain.

Equation (9) is a first-order approximation to the change in deadweight loss and thus is accu- rate only for small changes in marginal produc- tion costs. For large changes, it may be neces- sary to solve a system of supply and demand equations directly and compute new equilibrium prices following imposition of the environmental regulation. While more elaborate methods are re- quired to assess the impacts of quantum changes in environmental regulations, such as massive pesticide cancellations (e.g., Chambers and Lichtenberg), such regulations are the excep- tion rather than the rule. Indeed, environmental regulations affecting agriculture are increas- ingly promulgated at the state or local level.

There is an interesting connection between the impact framework in equation (9) and the "microparameter" or "putty-clay" class of pro- duction models of Hochman and Zilberman; Berck and Helfand; Paris; and Moffit, Zilberman, and Just. These authors have shown that local von Leibig production functions are consistent with Cobb-Douglas or other continu- ous aggregate production functions if there is continuous variation among individual atomis- tic production units. In the microparameter frame- work with a finite number of individual produc- tion units, each with positive measure, aggregate marginal cost is a step function, with the flat por- tion of each step given by constant marginal cost in a particular production region. Each region also faces output capacity constraints due to a limited natural resource base or the type of production technology employed. In the finite microparam- eter case, the marginal change in welfare result- ing from environmental regulation is approxi- mated by equation (9) since variation in pro- duction conditions is completely captured by inter-regional differences in marginal cost (pro- vided, of course, that the underlying yield and cost change estimates are accurately measured).

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1102 November 1996

$

p+dp p

MCI +dMC1 qI

MC1

ql

Figure 1. Welfare loss in the microparameter case

q

Figure 1 further develops the welfare loss calculations for the microparameter case. The level of each step of the base supply curve is constant marginal cost in a particular growing region, and the width of the step is given by the regional output capacity constraint. Changes in marginal cost resulting from environmental regulations alter the height of each step differ- ently depending on the nonuniformity of the regulation and regional production and environ- mental conditions; indeed, the regulation may not change marginal cost at all in some regions. The shaded area in figure 1 is the gross mar- ginal welfare loss as given by equation (9), which is the sum of the changes in regional marginal production costs. Note that this analy- sis can incorporate any type of supply shift (i.e., parallel, proportional, or more compli- cated types) as determined by the regional data.

There is some ex ante uncertainty about the yield impacts of adopting alternative produc- tion technologies. Zilberman et al. suggest that this uncertainty should be explicitly incorpo- rated into impact analyses of environmental regulations. Formally, they suggest treating the percentage yield change in a particular region and season, jit, as drawn from some density. Given this density, it is straightforward to cal- culate the mean impacts of the regulation, E(dW,), as well as the associated distribution of marginal impacts. It is convenient to describe the distribution of impacts in terms of confidence

levels, where a denotes the probability that the impacts exceed some level. Formally, define dWta as the solution to prob(dWt > dW,a) = a. In the empirical example below, dWt is calcu- lated for several different confidence levels.

There are several possible sources for the density of yield impacts of the regulation in a particular crop, region, and season. The error on statistical assessments of field trials is one possible source, but this error may not repre- sent actual farm conditions. Instead, it is prefer- able to conduct interviews with industry ex- perts, including growers, pesticide dealers, uni- versity researchers, extension agents, and chemical company representatives. The survey responses are then used to calculate the distri- bution of impacts by a Monte Carlo method. Yield change estimates for each crop, region, and season are selected randomly from the set of survey responses, and marginal welfare im- pacts are then calculated according to equation (9). This procedure is repeated many times to create a set of marginal welfare impacts. Fi- nally, the set of impact estimates is used to ob- tain dW,a for various confidence levels.

Application to Mevinphos Regulation

In this section the method developed above is applied to a specific problem: measuring the mar- ginal welfare costs of banning the mevinphos

Amer. J. Agr. Econ.

Marginal Cost of Environmental Regulations 1103

pesticide for vegetable production in Califor- nia. Mevinphos (2-carbomethyoxy-l-methylvi- nyl dimethyl phosphate) is an insecticide-acari- cide with contact and systemic activity that is most commonly used by California growers to control aphids on broccoli, cauliflower, head let- tuce, and leaf lettuce. Mevinphos is used to eradi- cate aphids just prior to harvest so that growers can meet the stringent U.S. Department of Ag- riculture quality standards.

The four crops considered here are produced in four California regions: Imperial Valley, Monterey, South Coast, and San Joaquin Valley. Output from other domestic areas, especially Arizona, Texas, and Florida, are aggregated into an "other domestic" category. Monthly crop prices and regional outputs are taken from the Federal-State Market News Service; 1990 is taken as the base year to avoid complications caused by the silverleaf whitefly infestation that began in 1991. Yields are taken from vari- ous University of California crop budgets from the counties comprising the four California pro- duction regions, and mevinphos use percent- ages for the California regions are found in the 1991 State of California Pesticide Use Report.

The basis of the marginal welfare analysis, equation (9), indicates that it is necessary to compute the effects of the cancellation on mar- ginal production costs separately for each crop, region, and season. Equation (10) relates changes in marginal cost to changes in per acre produc- tion costs and yields when growers adopt the next-highest profit alternative to mevinphos. Several alternative controls were considered: dimethoate, diazinon, thiodan, imidacloprid (available only to Imperial Valley growers un- der a Section 18 exemption), and pyrellin.

Telephone interviews were conducted with fifty-six growers, pesticide dealers and applica- tors, extension advisers, commodity group rep- resentatives, produce packers and distributors, and university researchers to assess the yield effects from switching to each of the alternative aphid controls. Interview subjects were asked to give the countywide yield change resulting from replacing mevinphos with alternative aphid controls and specifically were asked to assess actual changes rather than report the re- sults of experiments on highly managed plots. It is important to remember that the alternative chemical controls listed above have existed for many years, and survey respondents were gen- erally familiar with the actual field perfor- mance of the alternatives. These survey re-

sponses are the basis for the Monte Carlo analysis of welfare impacts described in the previous section. Changes in per acre produc- tion costs are determined by calculating per acre chemical expenditures for each of the al- ternatives (at standard application rates and market prices) and subtracting this number from the per acre cost of mevinphos applica- tion. Generally, changes in per acre cost are empirically insignificant for the set of crops considered here, since chemical cost is only a small fraction of the crop budget.

Table 1 shows the highest-profit alternatives to mevinphos for each of the crop, region, and season combinations, and also reports the asso- ciated yield and per acre cost changes. The highest-profit alternatives to mevinphos are imidacloprid (all crops in Imperial), diazinon (broccoli, cauliflower, and leaf lettuce in the re- maining regions) and dimethoate (head lettuce in regions other than Imperial). Expected yield losses obtained from the industry survey vary by season and by region; generally, expected yield losses are higher in the Monterey and South Coast areas and higher in the summer months due to weather conditions favoring aphid growth. Table 1 also gives sample stan- dard deviations for the assessed yield changes.

Table 2 presents the marginal welfare costs of banning mevinphos use in California, calcu- lated using equations (9) and (10) and the data in table 1. The expected marginal welfare costs of banning mevinphos are $53.3 million annually, as compared to total annual revenues of $924 mil- lion for these four crops. Mean monthly dead- weight losses, where the expectation is taken over the sample distribution, vary widely over the year according to market share among growing regions and yield and cost changes, thus underscoring the importance of disaggre- gating impacts over time as well as region.

The marginal welfare costs of a mevinphos ban are highest for head lettuce since this is the largest market considered and a significant share of the nation's output comes from Cali- fornia. Mean losses are largest during May- June and November-December, during which time most head lettuce is produced in California's Monterey and San Joaquin Valley regions. It is also interesting to note that mean losses are virtually zero during December-Feb- ruary, during which time nearly all output is produced in the Imperial Valley and other do- mestic regions that do not rely on mevinphos.

Since disaggregating environmental regula-

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Table 1. Changes in Yield and Per Acre Cost

Highest Profit Mean Percent Per Acre Region Alternative Change in Yielda Cost Change ($)

Broccoli and Cauliflower

Imperial Imidacloprid 0 50 (1.73)

Monterey Diazinon -10 -10 (4.08)

San Joaquin Diazinon -4 -10 (1.41)

South Coast Diazinon -8 -10 (2.89)

Head Lettuce

Imperial Imidacloprid 0 50 (0.00)

Monterey Winter Dimethoate -11 -10

(4.91) Summer Dimethoate -20 -10

(7.12) San Joaquin Dimethoate -5 -10

(5.00) South Coast

Winter Dimethoate -9 -10 (4.04)

Summer Dimethoate -12 -10 (5.13)

Leaf Lettuce

Imperial Imidacloprid 0 50 (0.00)

Monterey Winter Diazinon -17 -10

(7.53) Summer Diazinon -28 -10

(9.83) San Joaquin Diazinon -8 -10

(3.54) South Coast

Winter Diazinon -14 -10 (4.78)

Summer Diazinon -18 -10 (2.89)

a Standard deviations are in parentheses.

tions along the lines suggested in this paper has some cost implications for the administrative agency designing and enforcing the rule, it is important to assess the social welfare value of a disaggregated as opposed to a uniform regula- tion. The Lorenz Curve, which is often used to represent inequality in the distribution of in- come, is a useful way of summarizing the ben-

efit from implementing nonuniform regulations. Figure 2 is constructed by first calculating the number of pounds of mevinphos applied and the marginal welfare impact per pound applied in each crop, region, and month. Next, the per pound marginal welfare impacts are ranked in ascending order, cumulated and plotted against cumulative pounds applied.

1104 November 1996 Amer. J. Agr. Econ.

Marginal Cost of Environmental Regulations 1105

Table 2. Expected Marginal Welfare Impact of Banning Mevinphos ($ Thousands)

Month Broccoli Cauliflower Head Lettuce Leaf Lettuce Total

Jan 253 100 31 144 528 Feb 257 155 2 94 508 Mar 420 384 194 125 1,123 Apr 791 653 2,952 328 4,724 May 785 637 4,552 622 6,596 Jun 549 621 3,910 408 5,488 Jul 566 329 628 580 2,103 Aug 641 378 5,327 766 7,112 Sep 737 405 7,178 1,052 9,372 Oct 836 500 4,325 629 6,290 Nov 901 567 5,522 1,065 8,055 Dec 727 351 225 72 1,375

Total 7,463 5,080 34,846 5,885 53,274

Lorenz Curve

..0

_ '

,- '__ , _0.

~.

-- - - - 45 Degree Lie

-O..,

_ _

,-- "

'

.0

% Mevinphos Use

Figure 2. Lorenz curve for expected marginal welfare loss

The heterogeneity in the gross marginal wel- fare impacts of banning mevinphos is depicted by the size of the area below the 45? line and above the Lorenz Curve in figure 2. Of course, if all uses of the chemical generated the same level of producer and consumer surplus, then the Lorenz Curve would lie on the 45? line. The size of the area above the Lorenz Curve and be- low the 45? line shows the welfare improve- ment from using nonuniform regulations as compared to proportional use reductions that treat each crop, region, and season similarly. For example, suppose that regulators wish to reduce mevinphos use by half. Nonuniform regulations that target specific crop, region, and season combinations can reduce welfare losses by over 50% as compared to a uniform propor- tional reduction that ignores differences in mar- ginal productivity.

This type of Lorenz Curve analysis can be used to assess the benefits of many types of nonuniform environmental regulations. For ex- ample, many economists have observed that permit trading to reduce point and nonpoint source emissions can lower the welfare costs of improving air and water quality, as opposed to programs that proportionally reduce emissions. The method described here can measure the benefits of decentralized, market-based regula- tions, such as permit trading, that efficiently al- locate the burden of emissions reductions vis-a- vis proportional reduction. Other potential ap- plications of this technique include measuring the benefits of agricultural water trading and conservation reserve programs.

The Monte Carlo simulation of gross welfare impacts using the expert survey also shows the importance of explicitly accounting for yield

100

80

% Expected Deadweight

Loss

60

40

20

0 80 100

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1106 November 1996

change uncertainty when measuring marginal welfare impacts. Table 3 gives the marginal welfare impacts of canceling mevinphos at various confidence levels, represented as dif- ferent choices of a. Ex ante uncertainty about the yield impacts of switching to alter- native pest controls clearly affects the calcu- lation of marginal costs. Mean marginal wel- fare impacts of banning mevinphos in California are $53.3 million annually; due to ex ante uncer- tainty about yield changes, impacts exceed $64.8 million annually with a 25% level of con- fidence and exceed $85.9 million with a 5% level of confidence.

The magnitude of the confidence intervals on welfare impacts is significant. If producer and consumer surplus impacts are large in re- lation to total industry revenues, environ- mental regulations may result in bankruptcy and extreme consumer effects. Thus, firms and consumers may oppose environmental regulations based on worst-case impacts even if mean impacts are small in relation to the size of the industry.

Implications for Policy Design

Standard arguments in the economic theory of environmental policy suggest that regulations be set at their first- or second-best levels. In the notation of this paper, the first-best regulation satisfies max{B(git) - C(Qit)} Vi, t, where B((i,t) is the benefit from the regulation derived from higher environmental quality or public health, and C(it,) is the cost of the regulation in terms of lost producer and consumer surplus. Alternatively, the regulation may be set to min{C(Qi,)} s.t. B(iit) > , Vi, t, where P is some predetermined level of benefit. It is also possible to find efficient regulations in- corporating the uncertainty inherent in the impact analysis by using dW,, in conjunction with "safety-fixed" rules (Kataoka) for envi- ronmental quality in the manner suggested by Lichtenberg and Zilberman. The large de- gree of variation in the confidence interval estimates in table 3 implies that there is value in obtaining better scientific informa- tion about the yield impacts of environmen- tal regulations. A risk-averse regulator will change regulations significantly in response to uncertainty about marginal welfare impacts, and, thus, reducing ex ante uncertainty about yield changes will result in regulations that more accurately balance marginal costs and benefits.

Table 3. Distribution of Marginal Welfare Im- pact

Marginal Welfare Impact a ($ Thousands)

0.05 85,872 0.10 74,275 0.25 64,838 0.50 53,274 0.75 41,870 0.90 32,336 0.95 21,214

Regardless of whether environmental regula- tions affecting agriculture are set at their first- or second-best levels, it is necessary for policy makers to assess the marginal cost of the inter- vention. The method developed in this paper is a simple algorithm for performing such an analysis. Expression (9) is an improvement over previous impact assessment methods in that it gives a theoretically appealing and easily computable formula for measuring region- and time-specific welfare loss.' The method devel- oped here is valid for marginal changes in envi- ronmental regulations, including regulations promulgated at the state or local level. Global methods are needed to evaluate quantum changes in regulations.

Finally, the framework developed here can be used to integrate economic information with existing earth science data in a single regula- tory approach. Geographic Information Sys- tems are rapidly gaining acceptance among en- vironmental professionals. These data bases contain highly detailed information on spatial characteristics, such as land use patterns, and environmental conditions, such as groundwater depth and quality, soil characteristics, and mi- croclimate. These data bases may also contain dynamic information for particular locations, such as lateral groundwater flow. GIS data is increasingly used to identify environmentally sensitive areas, for example, agricultural areas where pesticides have a high probability of infil-

It is interesting to compare the regional distribution of mar- ginal costs and benefits. Since most citizens live in urban areas, the benefits from improving environmental quality will often be concentrated in these regions, particularly if environmental regula- tion results in increases in wildlife populations. The benefits from environmental regulations of agriculture can be local as well. For example, regulations to ensure farm worker safety and improve drinking water quality primarily will benefit rural residents. Pro- ducer surplus losses that are the bulk of the welfare costs of envi- ronmental regulations primarily are felt in rural areas.

Amer. J. Agr. Econ.

Marginal Cost of Environmental Regulations 1107

trating groundwater, or regions with high densi- ties of an endangered species. The model devel- oped in this paper can be used to measure the marginal costs of regulating agricultural produc- tion at a disaggregated level, and it thus can be paired with detailed GIS data to give regulators a full picture of the marginal costs and benefits of localized environmental regulation.

[Received July 1994; final revision received September 1996.]

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