Download - Public welfare in relation to alternative pesticide policies

JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT 2, 295-308 (1976)

Public Welfare in Relation to Alternative Pesticide Policies 1

W. F. EDWARDS AND ~LkX l~. LANGtIAM 2

b~&tstrial Research and Extension Center and University of ,4rkansas, Little Rock, and Research Coordinator, Agricttltural Development Council, htc.

Received June 10, 1975

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%.

I. I N T R O D U C T I O N

This paper sets for th a m e t h o d o l o g y for evaluat ing the benefits and costs of a given pesticide or class of pesticides under al ternat ive usage policies, it presents the results of a par t ia l implementa t ion of the model in D a d e County , F lo r ida , and it describes the methodolog ica l and da ta gaps highlighted by this effort. 3

Research o f this sort has the potent ia l for assist ing the Env i ronmenta l Pro tec t ion Agency in the regis t ra t ion and banning o f pesticides, as well as a id ing other regu la tory agencies in establ ishing pol icy on pesticide usage. Accord ing to the Federa l Env i ronmenta l Pesticide Cont ro l Ac t o f 1972, 4 the A dmin i s t r a t o r o f the Env i ronmen ta l Pro- tect ion Agency shall register a pesticide if he determines tha t "when used in accord- ance with widespread and c o m m o n l y recognized pract ice it will no t general ly cause unreasonable adverse effects on the env i ronment" (86 Stat. 981). The term "unreasonable adverse effects on the env i ronment" means " any unreasonable r isk to man or the envi ronment , taking into account the economic , social, and envi ronmenta l costs and benefits of the use o f any pest ic ide" (86 Stat . 979).

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

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-

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.

, Public Law 92-516, 92nd Congress, H. R. 10729, October 21, 1972.

Copyright ~ 1976 by Acadcmle Press, Inc. All rights of reproduction in any form reserved.

295

296 EDWARDS AND LANGHAM

s

QUANTITY

FIGURE 1

II. THE THEORETICAL MODEL

Concept of Pttblic tVelfare Used hz the Model

Though not limited to such a focus, the model presented here concerns the substitution 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 "environmental constraints" on the maximization of the welfare function.

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 controversy. 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.

Diagranmtatic Profile of the Public Welfare Calculation

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

s The term "persistent" is used to describe a pesticide which tends to degrade slowly in the environment and therefore may represent a hazard to the environment through its longevity.

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].

ALTERNATIVE PESTICIDE POLICIES 297

S 2

E 2 D

q

(a)

FIGURE 2

P2 PI

Usage of damaging pesticides

(b)

external benefits; and some may create no externalities at ally From a policy perspec- tive, the primary interest is on the ne t 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).

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 damaging 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 externalities, at least those of an acute nature (which are usually caused by the highly toxic

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.


=m mum If0 ,

subject to

but nonpersis tent pesticides) is sensitive to the general level o f public awareness. 8 A policy, therefore, to engage in a public informat ion p r o g r a m also could be evaluated within the model fo rmat by visualizing the effect o f the p rog ram as a shift in the externali ty function. As far as p rog ram 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 amoun t of these est imated costs. In short, by using a bit o f imagina- tion, one could accommoda te a wide variety of pesticide policies through the formula- t ion presented in Figs. 2a and 2b.

Mathematical Formulation of the Public Welfare Calculation

The model for this analysis is formal ly stated as follows: 9 For a set o f subjectively chosen pesticide usage policies, r, r = I . . . . , s, r ank the associated estimates of welfare, IV,, where:

~f~(Y,) gI(Yi)']dy,] s Ehg'(z;)-] j = l . . . . . n - - - - = 1 . . . . , m ( I )

i~l r = 1 , . . . , s

s aiTyi - zi = 0, (2) j=l

Ck,(Z,) <_ C~.,*, k = 1 , . . . , p , (3)

yi, z~ > 0, (4)

where J~(yj) = demand function for the j t h crop; y j = acres of the j th crop; gi '(Yi) = supply function for the j t h c rop under the r th policy alternative; h~'(zl) = an "external i ty funct ion," a functional relationship between observed external effects expressed in dollars, and the quant i ty o f the ith pesticide, under the r th policy alternative; ~~ z~ = quanti ty of the ith pesticide measured in pounds of 100% active mater ia l ; au" = the quanti ty of the ith pesticide used per acre of the j t h c rop under the r th policy; cki(zi) = a function describing the accumulat ion of the ith pesticide in the kth envi ronmenta l element in response to the use of one unit of pesticide i; Ck~* = an arbi t rary upper limit on the ith pesticide residue in the kth environmental e l emen t - - a pa rame te r to be chosen "poli t ical ly."

In this formulat ion, the term

Z [~(y~) - g~'(y; . / f f i l

is the sum of consumer /p roduce r surplus across tile n crops for a given pesticide policy r, while the term

m

hir(Zi)

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).

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

region being studied, encompassing multiple crops, cultivation practices, and perhaps climatic conditions. 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.


represents those external damages attributable to the m damaging pesticides under policy r that can be monetarily quantified.

Constraints on the Maximization of the Public tVelfare Function

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 environmental constraints and to observe their monetary effect on the objective function.

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 m a g n i t u d e . . . 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 D D T / D D D in birds.

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.

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 results of laboratory experiments to man, or by using direct observations on the health impacts of the damaging pesticides on man. In either case, of course, the state-of-the-art is very crude. Nevertheless, as data gathering efforts improve, it will be possible to attempt to formulate such constraints. The ultimate relationship that is required in the model for an environmental constraint can be

300 EDWARDS AND LANGItAM

~g

~o

= Cki

~ Usage of damaging pesticide ~o

FIGURE 3

illustrated as in Fig. 3. Given the relationship described as ck~(zi) = Ck;, society, through its legislators or policy makers, then places a limit, C~i*, on the environmental consequence of using the damaging pesticide, and thereby limits the usage of the pesticide itself. The shadow price of the constraint then provides an estimate of the effect of the constraint on welfare, as defined in the objective function. By varying the levels of Ck~*, one cot,ld trace out a function which might be called a "marginal welfare productivity function," having an interpretation similar to tile "marginal value product function," in production economics.

It should be noted that this approach could also be used to evaluate the welfare implications of an existing residue standard, by inserting the standard as C~* in the constraint, and observing the monetary effects on the objective function. Some researchers have argt, ed that the setting of standards has tended to be myopic in that nmjor emphasis has been placed on risks, without taking sufficient account of benefits. An approach such as this would encourage a more balanced consideration of benefits as well as costs.

]II. AN EMPIRICAL IMPLEMENTATION OF TH E MODEL

The model was empirically tested in Dade County Florida. Data for the estimation of demand and supply functions were readily available but data on pesticide usage and externalities had to be gathered on site by the authors. Eight crops were covered in the analysis, which accounted for 85% of Dade County's planted acreage in 1966- 1967, the time period covered by the analysis. Further definitions and delineations for the empirical implementation were:

1. The model was oriented toward the substitution of nonpersistent pesticides (the bulk of which were organic phosphates) for the chlorinated hydrocarbons, a group of persistent pesticides which have caused considerable concern over their potential environmental hazards.

2. Policies evaluated were: a. A 50% reduction in the chlorinated hydrocarbons with a concommitant

increase in the nonpersistent pesticides in sufficient magnitude to maintain crop quality and yield per acre. II

b. A virtual elimination of the chlorinated hydrocarbons, again with an increase in the fionpersistent group to maintain crop quality and yield per acre.

c. No change in present usage patterns of pesticides.

n Historically, the Environmental Protection Agency has registered or banned individual pesticides rather than whole classes of pesticides.


3. As explained in the previous section, the model envisages a shift in the supply function of a given crop with the introduction of a new pesticide policy. The necessary shifts were deduced f rom cost o f product ion data on the crops covered in the analysis and f rom informat ion supplied by growers and scientists familiar with c rop product ion in the region. These were then applied as parallel shifts in the supply functions for the status quo. ~2 As explained previously, in addit ion to the shifts in the supply functions for the given crops, the new pesticide policy also causes either a shift a long the externality function or a shift of the entire externality function (or both) . In our case it was a shift a long the function in two s t eps - -one corresponding to a 50% reduction in the usage of chlorinated hydrocarbons and the other to an elimination of the chlorinated hydrocarbons .

T h e D e m a n d M o d e l

The model which provides the basis for estimating demand equations for the objective function was specified as follows: ~3

q(t) = T0 + r lp( t ) + z21(t) + t t ( t) (5 )

subject to

q( t ) - - q ( t - - 1) = ~[q( t ) - - q( t - - 1)], 0 < r < 2 (6)

where q(t) = the long-run equil ibrium quant i ty as of period t; p ( t ) = price of the commodi ty in period t; 1( t ) = per capita disposable income (deflated) in per iod t for the Uni ted States; q( t ) = the quant i ty demanded in per iod t; u(t) = a spherical disturbance term normal ly distributed.

The constraint (6) s imply describes the adjus tment toward the long run equil ibrium quantity. ~4

By substituting Eq. (6) into Eq. (5) one can obtain the following function, 15 which was empirically est imated: ~6

q( t ) = ~kro + (1 - - r - - 1) + r + ~7"2/(t) -{- ~ku(t). (7)

The S u p p l y M o d e l

The supply model is specified as follows:

~( t ) = Go + ~lp( t - - 1) + v(t) (8) subject to

y ( t ) - - y ( t - - I ) = ~ ( t ) -- y ( t - - 1)7, 0 < t~ < 2 (9)

where 9 ( 0 = long-run equilibrium acreage as of period t; p ( t - - 1) = price in the

lz We suggested in an unpublished memorandum to the Environmental Protection Agency that a linear programming approach might better be used to synthesize supply functions under alternative pesticide policies. These could then be inserted into the welfare model described in this paper.

x~ Since this model was used for all crops, the crop designation, j, is omitted. it If 0 < ~ < 1, q(t) approaches ~(t) asymptotically. I f6 = 1, the entire adjustment is accomplished

in one period. If 1 < ~k < 2, q(t) overadjusts, but still converges upon ~(t). Discussion of the use of lagged variables may be found in I-5, 10, 15].

15 In this equation, n(t) is only contemporaneously uncorrelated with the regressor q(t -- 1) I'9, p. 121; 13, p. 129]. The result is that the least-squares estimates are biased but have the desirable asymptotic properties of consistency and efficiency.

~e A more detailed discussion of the data base used to estimate these functions can be found in Edwards I-3].

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ALTERNATIVE PESTICIDE POLICIES 3 0 3

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previous time period; y( t ) = acres planted in period t; v(t) = a disturbance term satisfying a similar set of assumptions as those given for the demand model.

As in the demand model, the constraint described the adjustment toward the long- run equilibrium acreage. Using (9) to eliminate 9(0 in (8) yields Eq. (10), which was empirically estimated.

y( t ) = ~0 + (1 -- ~)y(t -- 1) + ~ l p ( t -- 1) + ~v(t). (10)

Results of the demand/supply analysis are presented in Tables I and II. These will not be discussed in detail since they do not represent the main focus of this paper. Suffice it to say that the signs of the regression coefficients were as predicted by theory, the R ~ values of the regression equations ranged from 0.42 to 0.96, and most of the coefficients were significant at the 0.1 level or above.

Tile Externality Ftmctions

For purposes of empirical measurement an externality was defined as any "cost" which was created by the agricultural use of pesticides but was not borne, or was only partially borne, by the producers, a7 This definition of course does not preclude the possibility of handling an external benefit as a negative cost and is not inconsistent with the definition provided by Buchanan and Stubblebine I-2-1.

The process of attempting to identify and quantify externalities attributable to the two classes of pesticides was subject to three limitations. First, there was no way to guarantee an exhaustive, yet nonduplicative enumeration of the externalities. It was felt that the more logical sources of information were utilized, but this did not mean that all externalities were uncovered nor did it give a basis for measuring the con- fidence one could place in the enumeration. The following sources were utilized:

1. Interviews with growers in the region under s tudy--for information on wildlife kills, effects on domestic animals, and incidents of health damage to farm workers.

2. Data from workman's compensation claims--for information on external health effects.

3. Data from insurance companies--for information on property damages. 4. Veterinarians--for information on external damage to domestic animals and

wildlife. 5. Biologists--for information on external damage to wildlife. 6. The Dade County Community Studies on Pesticides Program of the U. S.

Public Health Service--for information on the health effects of pesticides.

A second limitation was that by the nature of things the list of externalities was probably biased toward external costs relative to external benefits. External costs were simply easier to uncover since they generally create controversy.

The third limitation stems from the fact that all observed externalities were acute as opposed to chronic. Ecologists as a rule tend to be more concerned about the long- term, chronic effects of pesticides rather than the acute effects, but the state-of-the-art at the time of this study simply did not permit the identification and quantification of the chronic externalities. The model permits this difficulty to be partially overcome through sensitivity analysis on the externality function associated with any pesticide to get an idea of the model solution's stability across various externality functions. From the sources mentioned earlier, a point estimate of monetary externalities due

~7 The problems encountered in attempting to empirically identify the externalities in Dade County have been described elsewhere 1"12].


to the nonpersistent pesticides was synthesized, which was then paired with the estimated usage of these pesticides to obtain one point on the functional relation between these pesticides and externalities. For simplicity, a linear function was then passed through this point and the origin. The equation for the function was: ~s

pesticides

ext. = 0.034 (quantity of nonpersistent pesticides)

and the full externality function (for both classes of pesticides) was:

2

hi'(zi) = 4,(chlorinated hydrocarbons) + 0.034 (nonpersistent pesticides). i = I

As indicated above, a lack of data prohibited the empirical estimation of 4,, so a value of 0 was initially used. Sensitivity analysis was then used in an effort to partially overcome this handicap and investigate the model solutions for positive values of 4,.

Letting 4, = 0, the model results were:

Value of objective function (social

welfare) (000 $)

Policy 1 (50% reduction in chlorinated hydrocarbons) 37,500 Policy 2 (Elimination of chlorinated hydrocarbons) 36,500 Policy 3 (the status quo) 37,900 Percentage change, Policy 3 to Policy 1 -0.01 Percentage change, Policy 3 to Policy 2 -0.03

Thus, eliminating chlorinated hydrocarbons and substituting other pesticides for them in such a way as to maintain crop quality and yield per acre would result in a decline in "social welfare" as defined previously, of about 3%. Total acreage devoted to the crops covered by the analysis declined by approximately 2% with potatoes suffering the greatest decline, in the amount of five percent. .9 The usage of nonpersistent pesticides increased under Policy 3 from 134,000 to 806,000 lb, an increase of 500%. The ramifications of such a large increase in the usage of the nonpersistent but usually very toxic pesticides is a matter of great importance, but we did not attempt in this study to analyze these ramifications. The mathematical formulation of the model assumes that as the usage of the nonpersistent pesticides increases, externalities associated with their usage will increase linearly. We had no data to support or refute this assumption. Some argue that such a large increase would cause externalities to increase percentagewise by more than the increase in pesticides--due to increased health accidents, wildlife kills, etc. Others say that at least for the human health impacts, as more pesticides are used, people become educated to their proper handling and that externalities would therefore not increase as fast as pesticide usage. This question needs to be investigated further.

,8 The value, $0.034, is the slope necessary to pass the linear function through the origin and the point representing the observed externalities on the graph:

,9 Crops included in the analysis were tomatoes, potatoes, beans, corn, squash, avacados, limes, and mangos.


As in the case of the externality function, data adequate to activate the environmental constraint in the model were not empirically observable. However, some limited data, along with several assumptions, were used to demonstrate the effect of such a constraint on the model solution. The data used were:

1. Observations on the content of certain chlorinated hydrocarbons in eagle eggs in Dade County.

2. Estimates of the agricultural usage of chlorinated hydrocarbons in Dade County.

The assumptions made in order to use these data were:

1. It was assumed that the measurements included all chlorinated hydrocarbons. Actually the eggs were analyzed for only six chlorinated hydrocarbons, but the D D T group (DDT, DDD, DDE) was monitored and it was believed that this group accounted for practically all of the hydrocarbon residue.

2. It was assumed that the chlorinated hydrocarbons have an average half-life of seven years in Dade County.

3. It was assumed that farmers had been using chlorinated hydrocarbons at the 1966-1967 level of 221,000 lb since 1950.

These assumptions result in the point on Fig. 4, and for simplicity a linear function was passed through this point and the origin to represent cki(zi) in the model. This function was: ck~(zO = (5.2 • 10-6)(z0, where z~ in this case is pounds of chlorinated hydrocarbons. Next an arbitrary value of 8 ppm was chosen for Cki*, the "politically" determined value called for by the model. Thus, constraint (3) became:

(5.2)< 10-G)(lb of chlorinated hydrocarbons) < 8 ppm.

This constraint was then incorporated in the model and a new solution was generated for Policy 3 (the status quo) to demonstrate the effect on the objective function. The

�9 result was:

Environmental constraint not included Environmental constraint included

Value of objective Pounds of Pounds of function chlorinated nonpersistent (000 S) hydrocarbons pesticides 37,900 22 i,000 134,000 37, 100 147,000 l 18,000

e~

o

eg r~ o

12.09 I I I ! I

2,342,600.

ibs. of chlorinated hydrocarbons 20

FIGURE 4

20 2,342,600 lb of chlorinated hydrocarbons is the limiting value of an annual usage rate of 221,000 lb if eht half-life is 7 years.


This formulation of the model limited the usage of the persistent pesticides (chlorinated hydrocarbons) without allowing a substitution of the nonpersistent pesticides to maintain crop yield per acre. Therefore, as acreages fell, the usage of the nonpersistent pesticides also fell. 2~ Thus, this model solution might be interpreted as representing the "limiting effect" of the environmental constraint. In actuality, the final equilibrium would be somewhere between these two solutions, as farmers used more nonpersistent pesticides in response to policies designed to reduce the usage of persistent pesticides.

The "limiting cost" of the environmental constraint is thus approximately $800,000 (the difference between 537,900 and S37,100 expressed in thousands of dollars from the above table). Whether or not the cost is worth while is again a political decision, but phrasing the alternative in this way brings into clear relief the fact that if society wishes certain environmental amenities, it must be willing to pay for them. By changing C~* and rerunning the model a series of times, the researcher can trace out, via the shadow prices of C~i*, the "marginal welfare productivity" of a unit of the pesticide being constrained.

IV. M E T H O D O L O G I C A L A N D D A T A GAPS H I G H L I G H T E D BY T H E M O D E L

The attempt to implement the model described in this paper has highlighted two important areas that need further work. First, although a great deal of material has been written on the theory of externalities, most of the theoretical discussions concern externalities between two or three parties at most. The theory has limitations for the researcher who wants to empirically estimate externalities at the industry level or across a broad segment of society. Is the set of externalities that are external to the firm the same as the set that is external to the industry ? Why, or why not ? By what aggregation process can industry externalities be estimated ? When a researcher un- covers a "cost" which logic tells him may not be incorporated in the market price of the product, by what criteria does he decide whether or not it is an externality ? For example, farmers in Dade County generally carry insurance which covers pesticide accidents to their laborers. One could therefore argue that to the extent that the insurance company pays all costs of a pesticide accident, the costs have been already internalized in the insurance premium which the farmer pays. On the other hand, insurance companies advised us that they do not as a rule differentiate between a farmer who used pesticides and one who does not in setting premiums. I f this is true, one could argue the reverse, namely that there is no internal "cost" reflecting the potential health hazard, and that the costs of the pesticide accidents should be con- sidered an externality. The point is that more definitive guidelines for handling externalities in empirical research are needed if our research is to be of pragmatic value to policy makers.

2~ In response to one reviewer's question about land taken out of production as a result of some pesticide policy, we feel the need to state explicitly the rather restrictive assumptions on which the model is based: They are: (a) Agricultural inputs taken out of production can be utilized with equal productivity in activities (agricultural or nonagricultural) not included in the model. (b) Income effects of price changes have a negligible effect on the welfare function. The model also divorces itself from the question of whether or not current income distributions are optimal. (c) The model assumes a constant marginal utility of money among people affected by the policies. (d) The model is static in the sense that it ignores shifts through time in the functions that comprise the model. (e) The model assumes that demand and supply functions for a crop are independent of those in other regions, those for other crops, and those in other industries. (f) The externality functions for the classes of pesticides are assumed independent.


The second area of need is tha t deal ing with tile ob ta in ing o f parameters for the cons t ruc t ion of envi ronmenta l constraints . We need a systematic process for moni to r - ing the use of pesticides on the one hand, and the mon i to r ing of envi ronmenta l consequences on the other. When we have such a sys temat ic da ta gathering process, theories to explain the l inkages between the two bodies of da ta can be developed and tested more readily. I t may be that the magni tude o f this task is something on the order o f the magni tude of the task o f gather ing the da ta for the Na t iona l Income Accounts . However , if we are to t a k e t h e envi ronmenta l pol lu t ion p rob lem seriously, we must reconcile ourselves to the fact that expensive da ta are needed to make ra t iona l pol icy decisions for the future.

R E F E R E N C E S

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of Alternative Policies," unpublished Ph.D. thesis, University of Florida (1969). 4. Florida Department of Agriculture, in cooperation with the U. S. Department of Agriculture

and Agricultural Experiment Stations of the University of Florida, "Florida Agricultural Statistics: Vegetable Summary, 19677' Florida Crop and Livestock Reporting Service, Orlando, Fla. (1967).

5. A. S. Goldberg, "Econometric Theory," (Bradley et al., Eds.), Wiley New York (1966). 6. J. R. Hicks, The rehabilitation of consumers' surplus, in "Readings in Welfare Economics,"

eds. (Arrow and Scitovsky, Eds.), Vol. Xll, Richard D. Irwin, Inc., Homewoo.d, 111. (1969). 7. H. Hotelling, The general welfare in relation to problems of taxation and railway utility rates,

Econometrica 6 (1938). 8. R. E. tlowitt, "Pesticide Externality Policy an Optimal Control Approach," unpublished Ph.D.

thesis, University of California, Davis. 9. J. Johnston, "Econometric Methods." McGraw-Hill, New York (1963).

10. L. M. Koyck, "Distributed Lags and Investment Analysis," North-Holland Amsterdam (1954). I 1. M. R. Langham, J. C. Headley, and W. F. Edwards, Agricultural pesticides: productivity and

externalities. "Environmental Quality Analysis: Theory and Method in the Social Sciences," (Kncese and Bower, Eds.), The Johns Hopkins Press for Resources for the Future, Inc., Baltimore (1972).

12. M. R. Langham and W. F. Edwards, Externalities in pesticide use, Amer. J. Agric. Econo. 51, No. 5 (December 1969).

13. E. Malinvaud, "Statistical Methods of Econometrics TM (Silvey, Trans.), North-llolland, Amster- dam (1966).

14. A. Marshall, "Principles of Economics," Vol. 1, Ninth (Variorum) Edition with annotations by C. W. Guillebaud, Macmillan New York (1961).

15. Marc Ncrlove, "Distributed Lags and Demand Analysis for Agricultural and Other Com- modities," Agricultural tlandbook 141, U. S. Department of Agriculture (1958).

16. Paul Anthony Samuelson, "Foundations of Economic Analysis," Atheneum, New York (1965). 17. Lucille F. Stickel and William H. Stickel, Distribution of DDT residues in tissues of birds in

relation to mortality, body condition, the time, Paper presented at the Sixth Inter-American Conference on Toxicology and Occupational Medicine, Miami, Florida, August 26-29, 1968.

18. U. S. Department of Agriculture, Agricultural Statistics, 1948 through 1967, U. S. Government Printing Office, Washington, D. C.

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