Public welfare in relation to alternative pesticide policies

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<ul><li><p>JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT 2, 295-308 (1976) </p><p>Public Welfare in Relation to Alternative Pesticide Policies 1 </p><p>W. F. EDWARDS AND ~LkX l~. LANGtIAM 2 </p><p>b~&amp;tstrial Research and Extension Center and University of ,4rkansas, Little Rock, and Research Coordinator, Agricttltural Development Council, htc. </p><p>Received June 10, 1975 </p><p>This paper presents a theoretical model for examining the welfare implications of various pesticide policies and the model is empirically implemented for three such policies. For the empirical implementation, the model consists of a nonlinear objective function subject to a set of linear constraints. The objective function represents a measure of welfare con- sisting of consumers' plus producers" surplus modified for externalities that can be quantified in monetary terms. The set of constraints consists of the usual ones to insure a feasible, nonnegative solution as well as an "environmental constraint" to recognize externalities not subject to quantification in monetary terms. Policies evaluated were: Policy 1, a 50% reduction in the usage of chlorinated hydrocarbons; Policy 2, a virtual elimination in the usage of chlorinated hydrocarbons; and Policy 3, no change in present usage patterns of pesticides. Subject to qualifications explainedmore fully in the paper, Policy 1 pointed to a decline of approximately 1% in welfare while Policy 2 pointed to a decline of about 3%. </p><p>I. INTRODUCTION </p><p>This paper sets forth a methodology for evaluating the benefits and costs of a given pesticide or class of pesticides under alternative usage policies, it presents the results of a part ial implementation of the model in Dade County, F lor ida, and it describes the methodological and data gaps highlighted by this effort. 3 </p><p>Research of this sort has the potential for assisting the Environmental Protection Agency in the registration and banning of pesticides, as well as aiding other regulatory agencies in establishing policy on pesticide usage. According to the Federal Environ- mental Pesticide Control Act of 1972, 4 the Administrator of the Environmental Pro- tection Agency shall register a pesticide if he determines that "when used in accord- ance with widespread and commonly recognized practice it will not generally cause unreasonable adverse effects on the environment" (86 Stat. 981). The term "unreason- able adverse effects on the environment" means "any unreasonable risk to man or the environment, taking into account the economic, social, and environmental costs and benefits of the use of any pesticide" (86 Stat. 979). </p><p>1 Funds for this study were provided by a grant from Resources for Future, Inc. We wish to thank Professor Hugh Macaulay of Clemson University and two anonymous reviewers </p><p>for constructive comments on earlier versions of this paper. 2 On leave from the Department of Food and Resource Economics, University of Florida. 3 Some of the thoughts and suggestions made herein were stimulated by a Workshop on the Eco- </p><p>nomic and Social Aspects of Pesticides Regulation sponsored by the Criteria and Evaluation Division, Office of Pesticide Programs, U. S. Environmental Protection Agency, May 12, 13, 1975. </p><p>, Public Law 92-516, 92nd Congress, H. R. 10729, October 21, 1972. </p><p>Copyright ~ 1976 by Acadcmle Press, Inc. All rights of reproduction in any form reserved. </p><p>295 </p></li><li><p>296 EDWARDS AND LANGHAM </p><p>s </p><p>QUANTITY </p><p>FIGURE 1 </p><p>II. THE THEORETICAL MODEL </p><p>Concept of Pttblic tVelfare Used hz the Model </p><p>Though not limited to such a focus, the model presented here concerns the sub- stitution of nonpersistent for persistent pesticides. 5 It assesses the benefits and costs of two such substitution policies and it compares each of these to a third policy representing the "status quo." The concept of public welfare, which makes up the welfare function, consists of consumers' surplus plus producers' surplus modified by an estimate of externalities attributable to the pesticides. Recognizing that many (perhaps most) externalities cannot be quantified in monetary terms, we discuss a particular class of these and illustrate the inclusion of them in the model as "environ- mental constraints" on the maximization of the welfare function. </p><p>The concept of consumer/producer surplus as an approximation to public welfare has been discussed widely in the literature, and remains a concept of some contro- versy. However, it currently seems to be enjoying an increasing popularity, particularly for empirical research. G For a given product, consumer surplus is calculated as the area between the demand function and the price axis above the equilibrium price, while producer surplus is the area between the supply function and the price axis below the equilibrium price. Thus, for linear demand and supply functions, consumer/ producer surplus would be the shaded area in Fig. 1. </p><p>Diagranmtatic Profile of the Public Welfare Calculation </p><p>The objective function of the model, which we call publie welfare, can be depicted graphically as shown in Fig. 2. For a given crop, the initial position or status quo is represented by the demand function, D, and the supply function, SI, in'Fig. 2a.rFor this position a certain quantity andmix of pesticides are used'in the production of the crop and the internal costs of these pesticides are reflected in the supply function, $1. Some of these pesticides create external damages to the environment; some create </p><p>s The term "persistent" is used to describe a pesticide which tends to degrade slowly in the environ- ment and therefore may represent a hazard to the environment through its longevity. </p><p>6 For discussions of the concept, the interested reader may consult Marshall 1"14], Hicks [6-1, Hotelling [-7], Samuelson 1-16], and Bergson ['1]. </p></li><li><p>ALTERNATIVE PESTICIDE POLICIES 297 </p><p>S 2 </p><p>E 2 D </p><p>q </p><p>(a) </p><p>FIGURE 2 </p><p>P2 PI </p><p>Usage of damaging pesticides </p><p>(b) </p><p>external benefits; and some may create no externalities at ally From a policy perspec- tive, the primary interest is on the net external effects of the pesticide or class of pesticides in question. The methodology presented here applies equally well for net external benefits and the net external costs, but for simplicity of exposition we will present the methodology in terms of net external costs. Labeling those pesticides which create net external costs as "damaging pesticides," suppose a relation exists between the usage of these damaging pesticides and the level of such external damages, measured in dollar terms, as indicated in Fig. 2b. Let Pt and/71 indicate the quantity of damaging pesticides used and the resulting magnitude of external damages for the pesticide mix under supply function $1. Now imagine the introduction of a new pesticide policy which reduces the usage of the damaging pesticides but increases the marginal cost of the crop in question, thus shifting the supply function from St to S~ in Fig. 2a. At the reduced level of damaging pesticides, indicated by P~ in Fig. 2b, we have a lower level of externalities, indicated by E~. The net effect of the pesticide policy, as far as public welfare is concerned, would be the difference between the reduction in consumer/producer surplus in Fig. 2a and the reduction in external damage in Fig. 2b. From society's point of view then, the problem is one of employing that pesticide policy which maximizes the sum of these two elements of welfare (the internalities plus the externalities). </p><p>Before turning to the mathematical formulation of the model, one additional observation can be most easily made at this point. Pesticide policies can take a variety of forms. If a certain pesticide policy reduced or banned a damaging pesticide, this would be depicted as a shift along the externality function as described above. But other policies might result in a shift in the function itself. For instance, if a policy simply stated that a permit had to be obtained before purchasing the damaging pesticide, in an effort to keep the pesticide out of the hands of the completely unin- formed, then the effect on the function in Fig. 2b might be to shift the entire function to the right, thus reducing the level of externalities for all levels of usage of the damag- ing pesticide, perhaps with little or no change in Fig. 2a. For another example, several researchers have obtained results which seem to indicate that the incidence of externali- ties, at least those of an acute nature (which are usually caused by the highly toxic </p><p>7 DDT, for example, might create both external costs and external benefits--external costs via its detrimental effect on the reproduction of certain species of birds, and external benefits via its reduction in the mosquito population. </p></li><li><p>298 EDWARDS AND LANGHAM </p><p>=m mum If0 , subject to </p><p>but nonpersistent pesticides) is sensitive to the general level of public awareness. 8 A policy, therefore, to engage in a public information program also could be evaluated within the model format by visualizing the effect of the program as a shift in the externality function. As far as program costs or enforcement costs for a given policy are concerned, these could also be incorporated by shifting the function in Fig. 2b vertically by the amount of these estimated costs. In short, by using a bit of imagina- tion, one could accommodate a wide variety of pesticide policies through the formula- tion presented in Figs. 2a and 2b. </p><p>Mathematical Formulation of the Public Welfare Calculation </p><p>The model for this analysis is formally stated as follows: 9 For a set of subjectively chosen pesticide usage policies, r, r= I . . . . , s, rank the associated estimates of welfare, IV,, where: </p><p>~f~(Y,) gI(Yi)']dy,] s Ehg'(z;)-] j= l . . . . . n - - - - = 1 . . . . , m ( I ) i~l r = 1, . . . , s </p><p>s aiTyi - zi = 0, (2) j=l </p><p>Ck,(Z,) 0, (4) </p><p>where J~(yj) = demand function for the j th crop; yj = acres of the j th crop; gi'(Yi) = supply function for the j th crop under the rth policy alternative; h~'(zl) = an "externality function," a functional relationship between observed external effects expressed in dollars, and the quantity of the ith pesticide, under the rth policy alterna- tive; ~~ z~ = quantity of the ith pesticide measured in pounds of 100% active material; au" = the quantity of the ith pesticide used per acre of the j th crop under the rth policy; cki(zi) = a function describing the accumulation of the ith pesticide in the kth environmental element in response to the use of one unit of pesticide i; Ck~* = an arbitrary upper limit on the ith pesticide residue in the kth environmental e lement- -a parameter to be chosen "politically." </p><p>In this formulation, the term </p><p>Z [~(y~) - g~'(y; . /ff i l </p><p>is the sum of consumer/producer surplus across tile n crops for a given pesticide policy r, while the term </p><p>m </p><p>hir(Zi) </p><p>s This seems to be the case in Dade County, Florida, where John Davies, Department of Epi- demiology, University of Miami, has been investigating poison cases involving organic phosphates. The same general finding was made in a California study (8). </p><p>9 An abbreviated specification of the model may also be found in Langham et al. I-11]. 10 This function is of course highly aggregated in the sense that it applies to the entire geographic </p><p>region being studied, encompassing multiple crops, cultivation practices, and perhaps climatic con- ditions. Its degree of aggregation is somewhat analogous to that of the classical consumption function which encompasses multiple income levels, tastes and preferences, and geographic differences. </p></li><li><p>ALTERNATIVE PESTICIDE POLICIES 299 </p><p>represents those external damages attributable to the m damaging pesticides under policy r that can be monetarily quantified. </p><p>Constraints on the Maximization of the Public tVelfare Function </p><p>Constraints (2) and (4) are the usual ones used in mathematical programming to guarantee a feasible, nonnegative solution. Constraint (2) simply says the quantity of pesticide i under policy r called for by the solution, z;, must in fact be the amount used by the n crops in the model. Constraint (4) prohibits the model from producing negative valued solutions for y~ and z;, an outcome which might be possible from a strictly mathematical solution to the problem, but would be unrealistic from an economic point of view. Constraint (3), which we call an "environmental constraint," is the one of greatest interest. This constraint says that the residue of pesticide i in the kth environmental element shall not exceed Ck~*, a politically determined value. The constraint is extremely important from a conceptual point of view, for this is the route by which value judgments and externalities not amenable to monetary expression gain admission to the model. Ecologists are presumed to be very interested in this constraint, for they frequently argue that environmental amenities are incommensur- ables that tend to be forgotten in the materialistic world of benefit/cost analysis. Structuring the model in this way allows the analyst to introduce selected environ- mental constraints and to observe their monetary effect on the objective function. </p><p>Some studies of wildlife biology, particularly those of the Patuxent Wildlife Research Center, approach the model's concept of an environmental constraint. For example, Stickel [-17, p. 13] states, "Residues in brains of birds of several species killed under different conditions were of a similar magnitude. . . The concentration of 30 ppm of DDT plus DDD appears to be a useful approximation for the beginning of a zone of hazard." The authors are therefore saying that Ck~* should be approximately 30 ppm for brain residue of DDT/DDD in birds. </p><p>Examples for the use of the environmental constraint need not be limited to wildlife. If, for example, the analyst wishes to investigate the welfare consequences of restricting pesticide residues in ground-water tables, he could, with suitable data, formulate the appropriate environmental constraint, run the model and observe the effect on the objective function. To incorporate such a constraint, the analyst would need to estimate the relationship between usage of the pesticide and the residue build-up in the ground-water table. This relation would then constitute the function eki(ZO in the model. </p><p>The environmental constraint concept also could be activated with regard to the human health impacts of pesticides, a matter of great concern at the EPA workshop alluded to earlier. While the data requirements would be more difficult relative to the ground water constraint, the model conceptually accommodates one as well as the other. For this constraint it would probably be more meaningful to express Ck~* as the limit on human health impacts, e.g., number of carcinogenic cases attributable to the use of the damaging pesticide, rather than in terms of the residue of the damaging pesticide in the human body. The health constraint would have to be specified either by extrapolating the...</p></li></ul>

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