Corrective taxes for pollution control

JOURNALOF ENVIRONMENTALECONOMICSAND MANAGEMENT1, 296-318 (1974)

Corrective Taxes for Pollution Control An Application of the Environmental Pricing ond Standards Systems to Agriculture 1 LAWRENCE W. ABRAMS University of Cahfornia at Santa Cruz, Santa Crttz, Californ& 95060 AND

JAMES L. BARR University of Arizona, Tucson, .4rizona 85712, an.t Wharton School of Finance and Commerce, Unirersi O' of Pennsylvania, Philadelphia, Pennsylvankt 19104

Received July 1, 1974 This paper demonstrates how a system of corrective taxes can be applied to the problem of managing surface water nitrate pollution in agricultural regions. A spatial linear programming model of the U. S. livestock-feed complex including constraint equations linking fertilizer nitrogen use by Illinois farmers to water quality in that state has been developed. The solution to this model at various desired levels of NO3-N in Illinois provides estimates of regional taxes on fertilizer nitrogen use appropriate to the "Environmental Pricing and Standards" system. In addition, other estimated changes in agricultural activity induced by this system of corrective taxes are presented. 1. I N T R O D U C T I O N The efficacy of the Pigouvian tax prescription for the resolution of externalities has long been regarded with skepticism by economists. On the theoretical level, the corrective taxes on effluents, inputs a n d / o r outputs must be "just right" to guide the e c o n o m y to a second best welfare position. Even then, the presence of externalities m a y introduce nonconvexities which prevent the attainment of a Pareto optimal allocation of resources. Speaking toward environmental externalities on the practical level, the Pigouvian prescription requires a knowledge o f the welfare losses attached to alternative pollution levels, or what can be called the (social) damage cost function. It has been argued that this cost function is either impossible to construct or so costly to estimate that the corrective tax a p p r o a c h to environmental management is rendered inoperable. Recently several authors (e.g., see Refs. E4-1 and [-117) have suggested that, if one stops short o f requiring Pareto efficient solutions, the corrective tax approach can be an effective means for managing environmental quality. The management proposal embodying this view has come to be k n o w n as the Environmental The authors gratefully acknowledge the support of the National Science Foundation, Grant Number 29926xi, and the invaluable collaboration of others on the overall project, notably Barry Commoner, John Duffy, Daniel Kohl and Georgia Shearer. In addition, the authors have been supported in part by Resources for the Future, and by the Division of Economic and Business Research, University of Arizona. 296 Copyright ~ 1974by AcademicPress. Inc. All rightsof reproductionin any form reserved.

CORRECTIVE TAXES FOR POLLUTION CONTROL

297

Pricing and Standards System (EPS). The appeal of the proposal is its capability to provide, (1) as a management system, a set of corrective taxes that will achieve a given environmental standard at minimum abatement costs, and (2) as a planning system, estimates of the (efficient) abatement costs imposed by alternative environmental standards. Realistically, the choice of the desired standard must be left to the body politic; EPS can identify the efficient set of trade-offs and the associated sets of corrective taxes needed to implement chosen control policies. This paper develops the EPS approach to the problem of managing the level of surface water nitrate pollution in agricultural regions. Specifically, by relating nitrate concentration levels to inorganic fertilizer usage, we devise a set of control programs for the nitrate problem that are sustainable by regional (corrective) taxes levied on nitrogen fertilizer. An efficient control program is presented for the State of Illinois. The EPS proposal calls for the determination of an environmental standard for a specific environmental resource(s). Enforcement of this standard would impinge on producers who contribute to the depletion of that resource. In the case of water quality, identified polluters would be confronted with additional constraints or costs. Alternatively, if a positive tax is imposed on the relevant effluent, reductions in the pollution level would be normally achieved through factor substitutions, changes in output level and mix, etc. The two problems presented by this solution proposal are: (1) the identification of the relevant effluents and the material inputs/outputs that produce them, and (2) the determination of the appropriate tax level(s) on the specific commodities. The first problem is that of determining the Environmental Linkage--the relationship between the level of production activities and the environmental quality of interest. When pollutants are emitted from measurable point sources (e.g., stack emissions, industrial dumping), it is appropriate t o tax the effluent itself, leaving the individual producers to make cost minimizing adjustments. But when the pollution sources are diffused it may be appropriate to levy taxes directly on inputs or outputs, with the adjustments now coming through the substitution effects of the price changes. In what follows we wish to emphasize the distinction between these two kinds of control problems. The administrative efficacy of the EPS approach is based on its ability to determine uniform taxes on producers in any given control region. The choice of control regions involves an important trade-off between the theoretic efficiency and the practicality of the EPS system. On the one hand, the efficiency of a uniform tax within a region requires that the "marginal physical product (in terms of the environmental quality E) of a unit of effluent be the same for all producers" [-17, p. 201~ in that region. 2 On the other hand, a proliferation of control regions so as to make producers more homogeneous within regions greatly reduces the practicality of the control system. The proper level of disaggregation in the delineation of control regions must strike a balance between these two considerations. Within a control region j the environmental linkage is deduced from the firm (i) production relations,

f,i(S,

Y, Z) = 0,

(1)

"-Sce Baumol and Oatcs [43, and Tietcnbcrg El7-1for the derivation of these efficiencyconditions. The latter author stresses the efficiencyrequirement for uniform taxes within regions. These requirements imply linkages of the form given in (2). Additionally the efficiencyof the EPS approach depends on the separability of the effects of the effluentsZ on the quality levels E, and the usual second order conditions to insure that (X*, Y*, Z*) is a minimum point.

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ABRAMS AND BARR

where X, Y, and Z are vectors of normal inputs and outputs, and of effluents respectively; along with the relationship between the aggregate flow of effluents and the environmental quality in region j, Ei: g , ( Z Z,) = Ej. iGi

(2)

Underlying (2) is the assumption that the contribution of the effluents of any producer in j to the environmental quality level Ei is additively separable. This is a necessary condition for the efficiency of a uniform tax on several producers within a control region. The determination of relation (2) can be seen to be the core of the environmental linkage problem. For the point source pollution problem, efficient taxes 3 on the effluents Z can be identified provided certain conditions on (1) and (2) are met. It has been shown that the cost minimizing production of a given level of outputs

?(=

E

Y,)

subject to (1) and (2) can be achieved via taxes on Z. The taxes are derived from the shadow prices associated with the constraints (2) limited by the chosen environmental standards Ej. It should be emphasized that the shadow prices must be evaluated at the cost minimizing solution {X*, Y*, Z*}. When pollution sources are diffused, the EPS proposal must resort to taxes on outputs or inputs. This circumstance appears to apply to agricultural pollution problems. If corrective taxes are to be applied to, say, inputs, an additional set of relations must be determined to complete the environmental linkage: Zi = Hi(X),

Viii.

(3)

In effect, then, the shadow prices on (2) can be translated to a set of taxes on X via (3) to yield an efficient EPS solution for a given environmental standard/Z' i. Independently of the authors cited above, M. Langham [-13-] has derived the conditions for efficient EPS solutions based on input taxes. 4 It is safe to say that the conditions underlying the existence of efficient EPS corrective tax solutions are stringent. At the most fundamental level one must be concerned with nonconvexities introduced by the presence of externalities [-13, 16-]. For the problem that we consider, we have not too unrealistically assumed these difficulties a w a y ) Still, the determination of relations (2) and (3) for diffused source pollution poses formidable problems for practical applications of the EPS proposal. This determination encompasses the whole design of an EPS management system: the environmental dimensions and their control regions must be chosen to insure the separability G of these technical linkages, and at the same time, the administrative practicality of these choices has to be real. 3 Efficient is used here in the sense that production costs are minimal, given/~'. In the context of a cost minimizing programming problem Min CX s.t. A X >>. Y if additional environmental constraints are imposed of the form B X ~/~', it can be shown that the shadow prices X* associated with the minimum cost solution X* are the efficient corrective taxes. That is, the tax guided solution, derived from Min C X q- X* BX, the allocation problem, s.t. A X >1 Ywill be equivalent to the original solution X*, and thus cost minimal. See Abrams 1-1]. s In effect, we assume that the level of nitrate pollution has no effect on crop production possibilities. This independence assumption is not as tenable in most point source problems such as industrial waste pollution of waterways. 6 By separability, here, we mean the homogeneity of an environmental linkage within regions and separability of individual linkages within and among control regions.

CORRECTIVE TAXES FOR POLLUTION CONTROL

299

The second problem of EPS involves the development of a procedure by which the tax rates are set initially, and adjusted to achieve a desired standard. Some proponents of EPS advocate a trial and error approach, with successive rate adjustments chosen to close the gap between the current quality level and the set standard. There are costs attached to this simplistic approach; the iterative process may be long and drawn out, but more important, such fine tuning actions may create uncertainties and a reluctance on the part of producers to adapt to their new cost structures. These considerations point up the need to apply the EPS proposal as a planning tool. If the relations (1)-(3) can be identified then it is possible to develop e x a n t e estimates of the corrective taxes needed to achieve alternative environmental qualities. Equally important, simulation modeling of the EPS approach can estimate the expected abatement costs attached to different standards, and these estimates can in turn influence the choice of the standard itself. If the costs of achieving a given standard are estimated to be prohibitive, society may wish to settle for something less. Thus EPS modeling plays an interactive role by both influencing opinion on what constitutes a desirable standard and determining the tax measures required to meet that standard. Finally it should be pointed out that, even if there is some uncertainty about the accuracy of the linkage relations (2) and (3), EPS simulations can furnish estimates of the costs attached to various tax measures. The reduction in effluents produced (Z), or specific inputs used (X) may or may not produce the predicted environmental changes; but if the modeling of producer responses to changes in their cost structure via (1) is reliable, the cost estimate of such market interventions can identify the cost trade-offs of alternative tax proposals. Our simulation results should be viewed in this light. We place more confidence in our ability to model producer responses to fertilizer taxes we do in the effect that the fertilizer reduction would have on water quality. The cost estimates of the tax induced changes are still relevant, even if the abatement effects are less certain. In Section 2 we describe the environmental program. Then, the structural model of the agricultural sector is presented, with the details of this construct relegated to an Appendix. The environmental linkage for the simulated Illinois control program is developed in Section 4, and the results of the simulations are presented in Section 5. 2. T H E E N V I R O N M E N T A L PROBLEM Our initial problem focus was on the alarmingly high concentration levels of nitratenitrogen I-NO3--N] found in many lakes and streams in the Corn Belt by the year 1970. The concentration levels of N O ~ - - N were not consistently high in this five state area, but very high readings were recorded in the predominantly agricultural regions of central lllinois, Indiana, and Iowa. In many instances, the readings exceeded the primary standard of 10 mg/liter established by the United States Public Health Service. During the previous decade, steady increases in the NO3--N concentration level in surface waters were documented by data from watershed sampling stations of the United States Geological Survey in these regions. At the same time, the use of nitrogen fertilizer increased very rapidly in these same regions, indicating that commercial fertilizer use could be a potential source of the nitrate found in surface waters. 7 Figure 1 provides an indication of the magnitude of 7A recent paper [21 documents the nitrate situation and fertilizer usage described here. The use of complementary !nputs of phosphorus and potassium increased at comparable rates during the same period.

300

ABRAMS AND BARR

o

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o a

~

o

~ ~

9) :

ee~

"_i

Itl

%

~ o

oo

Ooo i

21p

i

:;11

iiii

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."~11

E - , t i m a t e d l~,t~-~,f N AH,~i~'ali,~-',bs. N , A c r e Drait~t.d

FIG. I. Nitrate concentration vs estimated fertilizer application in various watersheds since 1948. The rate of nitrogen application was estimated for each watershed to be equal to the fraction of the watershed in corn, multiplied by the average annual rate of nitrogen application to corn for the state. Our assumptions are that all of the nitrogen used in the state of Illinois is applied to corn and that the rate of application to corn throughout the state is uniform. The nitrogen sales data for the entire state of Illinois are found in Consunlption of Commercial Fertilizers, Prhnary Plant Nutrients, USDA Statistical Bulletin no. 472. Data on the fraction of the watershed in corn is from the Illinois ,4grictdtural Statistics, Illinois Cooperative Reporting Service, Illinois Department of Agriculture. The fraction of the upstream watershed in corn was calculated from these data using the assumption that the fraction of the acreage in corn is uniform within a county. Nitrate concentration data were supplied through the courtesy of R. H. Harmeson of the Illinois State Water Survey. The annual discharge weighted mean was computed by multiplying each monthly nitrate concentration reading by the instantaneous river discharge rate (USGS) at that date, summing these and dividing by the sum of the discharge. Crop and fertilizer data were for the middle year of each three year period. Source: B. Commoner and D. Kohl, (1972), p. IV.7. these changes for the s a m p l e d Illinois watersheds. These events a n d c o n d i t i o n s p r o vided the impetus for a large interdisciplinary study, o f which this analysis was a part. s T h e possible sources o f the nitrate c o n c e n t r a t i o n include fertilizer nitrogen, soil nitrogen, a n i m a l a n d industrial wastes, nitrogen fixing legumes, and rainfall. Supp o r t i n g the positive correlation between fertilizer a p p l i c a t i o n and nitrate c o n c e n t r a t i o n were findings o f detailed isotope analyses o f g r o u n d a n d snrface water in central Illinois: it was f o u n d that in the spring of 1970 in the S a n g a m o n River watershed, 4 5 % ( d : 10%) o f the nitrate originated from i n o r g a n i c fertilizer sources ['123. Once the link between fertilizer nitrogen a p p l i c a t i o n s b y c r o p farmers a n d N O ~ - N c o n c e n t r a t i o n s in surface waters h a d been established, it r e m a i n e d to be discovered the process by which this t r a n s f o r m a t i o n occurred. It was felt t h a t there were i m p o r tant factors, not in themselves sources of nitrogen, which significantly affected the t r a n s f o r m a t i o n o f fertilizer nitrogen into N O a - N f o u n d in surface waters. These m o d i f y i n g variables included rainfall, soil type, slope o f cultivated land, a n d the extent o f field d r a i n a g e tiles. It was also felt that f a r m m a n a g e m e n t practices affected the t r a n s f o r m a t i o n . T h e relation between fertilizer nitrogen applied and resulting N O 3 - N seemed to d e p e n d on the c r o p to which the fertilizer was applied, the timing o f the a p p l i c a t i o n , the l o c a t i o n o f the land within the watershed, and the level o f a p p l i c a t i o n per acre c r o p p e d . 8 B. Commoner and D. Kohl 1-73 (Co-principal Investigators), "A Study of Certain Ecological, Public Health and Economic Consequences of the Use of Inorganic Nitrogen Fertilizer," National Science Foundation, GI 29926xl. 1971-1974. Figure 1 is only intended to be suggestive of the relationship between NO~-N and fertilizer load per acre. It is representative of more refined cross-sectional relationships found for lllinois watersheds, 1968-1971.

CORRECTIVE TAXES FOR POLLUTION CONTROL

301

Many of these complexities in this transformation process, even if they were better understood, would be unrepresentable in the regional programming model that we use to describe the agricultural sector. In view of this, the reader should maintain a degree of skepticism about the potential accuracy of our approach. Certainly, more robust specifications of the fertilizer use-nitrate transformation process can be represented in our programming format when they are available. Our present efforts at modeling this process should be regarded as exploratory. The linkage between regional nitrate-nitrogen concentration and fertilizer application rates is explained in Section 4 below. It will be seen to be rather unsophisticated in view of the many potential factors cited above. The regression estimates can be faulted for a variety of reasons, but frankly, this was the best available evidence on the linkage that we could construct. Finally, we note that the results presented here only describe the consequences that alternative fertilizer Control policies would have on agricultural producers and consumers. Consideration would have to be given at the same time to water treatment methods that might reduce the NO3-N levels in critical regions, and to alternatives that could deal directly with the possible health consequences of high nitrate concentration. Nonetheless, we feel that our findings contribute to an understanding of the costs that would be imposed by several plausible means of controlling nitrogen fertilizer usage in the Corn Belt. Our analysis is based on a structural model of the major agricultural activities in the U. S. that has the capability of evaluating control programs that concern production activities within the Corn Belt. In this paper we report on results that we have obtained for simulated environmental control programs for the State of Illinois. The primary reasons for limiting our inquiry to the state of Illinois are that: (1) the nitrate problem has been more serious there than in any other state; (2) the state's major role in feedgrain and fed-beef production; and (3) the availability of scientific evidence on the fertilizer use-nitrate linkage and watershed data on fertilizer applications and nitrate concentration levels. The last factor is most important; other Corn Belt areas could be included in the control analysis if linkagerelationships could be obtained. In this respect, the structural model has general applicability to environmental problems in agriculture, provided these linkages can be ascertained. We now describe the structural model of the agricultural sector employed in this study. 3. T H E M O D E L 9 We have sought to develop a structural model of the agricultural sector that captures regional production capabilities as well as regional demands for agricultural products. We feel that this approach is essential if we are to account for the substitution possibilities between land and fertilizer, and to examine the effects that fertilizer controls in the Corn Belt would have on that region as well as on the national market under changing demand conditions. For this construct we have drawn heavily upon the work of Earl Heady and others E6, 14, 20] at Iowa State (ISU) and of (King and Schrader ['10]) (KS). Essentially we have incorporated the model of fed-beef production of (KS) into the data base and structural models of ISU. The resulting spatial linear programming model considers 20 consuming regions, 41 producing regions, nine crop activities and eight livestock activities. Of the 41 producing regions, 23 are 9 Further description of the model is presented in the Appendix. A more extensive development of the model and its application to environmental control policy can be found in [1].

302

ABRAMS AND BARR

located in the Corn Belt? ~ For these Corn Belt regions, yield response curves were constructed for the five principal nitrogen using crops? ~ The basic data used for these constructs were the lbach and Adams estimates [-I 9-]. Piece-wise linear approximations to these yield response curves were incorporated into the linear programming model. This feature enables the model to solve for the cost-minimizing application rates of fertilizers as well as the optimal location of the production activities. At the same time, regional constraints on overall nitrogen use enable the model to solve for the optimal production patterns and fertilizer usage rates in the Corn Belt under simulated degrees of regional fertilizer rationing. Alternatively, simulated taxes levied on nitrogen fertilizer use in Corn Belt regions can direct the model to ration nitrogen fertilizer via the price system. We view the capability of this model to determine regional tax prices that yield optimal solutions that are equivalent to those obtained under direct rationing at its major strength. It enables us to consider the sensitivity of production costs and the spatial location of activities as these regional tax prices affect the optimal application rates of fertilizer and profit-ability of each crop. Farmers operating in their own (economic) self interest could achieve a desired regional usage of fertilizer nitrogen via a "correct" set of tax prices. Regional demands for fed-beef and pork are exogenous to the model. These derived demands represent the major component of the total demand for feed grains. Within the demand structure, the model captures the major substitution possibilities relevant to controlling fertilizer use. Fed-beef activities permit the ratio of roughage feeds to grain concentrates to vary according to the regional supply prices of these inputs. Additionally, the length of time on feed--a short-fed vs long-fed choice--is determined by the supply price of feeder calves vis ,t vis the roughage and concentrate prices in each region. Thus the method and location of feed lot activities will depend on regional feed grain prices, which in turn depend on fertilizer usage controls, whether they are in the form of regional tonnage allotments or tax levies. In the Corn Belt the direct substitution of fertilizer for land is governed by these controls via the choice of fertilizer application rates. Finally, regional constraints on total available cropland and pastureland present the trade-off between livestock holding capacity and crop production. 4. T H E E N V I R O N M E N T A L L I N K A G E Like other pollution problems surface water nitrate is the result of localized actions and conditions, with localized (transferable downstream) impacts. To a considerable extent this kind of problem can be solved by identifying the sources of the pollution and educating the polluters and those affected on the social costs of the polluted conditions. Altruism, social pressure, and possible legal sanctions are effective measures when the pollution sources and dangers are clearly identifiable and not greatly diffused. Unfortunately the nitrate problem cannot be characterized in this way. First, the complexity of conditions and processes that affect the movement of nitrate compounds through the soil to surface waters prevents the identification of problem polluters? -~ a0Essentially the producing regions delineated by ISU outside the Corn Belt have been aggregated up to state and two-state regions to economize on computation costs. Distortions created by this aggregation appear to be minor. n Corn, oats, barley, sorghum, and wheat. ~2Conversely, it prevents potential polluters from identifying with the problem. Conceivably, farmers in central Illinois might voluntarily reduce fertilizer use if it could be demonstrated that this is the source of the NO3-N and that it represents a real health danger. However, the free rider problem would remain and militate against such individual actions.

CORRECTIVE TAXES FOR POLLUTION CONTROL

303

Second, the consequences of high NO~-N concentrations are not well understood. Clinically detectable effects are found in newborn babies (methehomoglobinemia), but the incidence of this condition is low. The potentially more dangerous consequences may be chronic effects that result from long term exposure to high NO3-N concentrations. These circumstances surrounding the fertilizer usage-nitrate problem suggest that some form of direct intervention is needed to effect any change. A control approach with both practical and theoretical appeal involves the use of regional taxes on nitrogen fertilizer to achieve "target" usage levels. T o implement the scheme, nitrogen fertilizer usage rates must be first related to nitrate concentration levels in designated control regions. Then the regional fertilizer usage associated with target nitrate concentration levels can be incorporated into environmental constraints on regional crop production in the programming model to derive estimates of the EPS corrective taxes. Six control regions were defined, corresponding to the Illinois producing regions of the programming model. (See Fig. 1, Appendix.) Using sample data recorded by the United States Geological Survey in Illinois watersheds and county data on nitrogen sales for the years 1968-1970, we developed a multiple regression model to relate nitrate levels to fertilizer usage. ~3 The 26 watershed sample points are associated with the six control regions via dummy variable techniques. We assume that the nitrate concentrate in surface waters of the ith Illinois watershed, C;, is derived from two separable components corresponding to the contribution of soil nitrogen S;, and fertilizer nitrogen Fi: Ci = S i . F i

(1)

The contribution of soil nitrogen is assumed constant and independent of the watershed sampled: Si = a (2) There is a strong prior expectation that o~should be in the neighborhood of 2 mg/liter. This expectation is based on the fact that many of the watershed samples taken in Illinois in the late 1940's, when little fertilizer nitrogen was used, measured around 2 mg/liter? 4 It is assumed that F~ is a function of fertilizer load, defined as the ratio of total fertilizer nitrogen applied to total land area in the ith watershed, or (N~/AI). There is a strong prior expectation that d F , / d ( N , / A , ) > O, d'F~/d(N,/A,)"- > 0

(3)

This expectation is based on the work by Stanford et al., which indicates that the uptake efficiency of fertilizer nitrogen by crops ultimately declined with increasing application rates [-15, p. 8-1. This means that the amount of fertilizer nitrogen not taken up increases at an increasing rate as the level of fertilizer nitrogen applied increases. By making a "leap of faith" from Stanford's findings for a single plant to a 1~Unfortunately, fertilizer usage data is unavailable. To the extent that users buy their fertilizer locally, little bias is introduced through the use of sales data. (On the average, an Illinois producing region covers seventeen counties.) 1~Richard Parker, Data for Analysis of Application Rates of Nitrogen Fertilizer Concentrations in S t i f face Waters, and the Economic Effects Thereof, Table 1, unpublished manuscript, Center for the Biology of Natural Systems, Washington University, February, 1974.

304

ABRAMS AND BARR

whole watershed with (N~/AO as a proxy for fertilizer use, we arrive at the expectations summarized in (3). Assuming an exponential form for F~ we have, (4)

C~ = ae a'('v'l'4')

Equation (4) is a crude approximation of the relation between fertilizer nitrogen applications and resulting NO~-N concentrations in any given watershed. It assumes that the relation is independent of how the fertilizer nitrogen is applied, the crop to which the fertilizer is applied, the amount applied per acre, the timing of the application, the location of the acre within the watershed, etc. What matters is the total level of application per land area. We assume that 13i does depend on modifying factors such as the slope of the land cultivated in the watershed, the extent of drainage tiles, and soil type. These modifying factors differ among Illinois regions and to the extent that such differences are significant, the/3 for each control region should also differ. To account for these differences, dummy slope variables are used to link the location of the watersheds (i) to their control regions (j). In this way, the elasticity of the fertilizer load contribution varies across regions. The estimating equation incorporating these regional variations can be written ~5from (4) as: 8

log C, = o,, + [.3 + ~ D,](N,/A,) + u,

i E ,,,

(5)

Jt~l

where {1 D, =

iEK, otherwise,

/:watershed, K: producing region(s).

The estimated coefficients of (5) forms the basis of the Illinois environmental linkage, a set of log-linear constructs relating nitrogen usage to nitrate concentration in each control region. Letting J~i be the computed values of t3 q- D, we have, f~ffAi.N~(Xi) <_ log O~ -- a',

j = l, 6,

(6)

where Nj(Xi) is the nitrogen usage associated with crop activities Xi is j and 0j is a regional nitrate concentrate target. Notice that for a given target, the constraints (6) are linear while still capturing the nonlinear relation (3). In the presence of these constraints, the programming model solves for the optimal crop activities and nitrogen application rates. The parameters in Eq. (5) were estimated via ordinary least squares. Data consisted of pooled observations from 26 Illinois watersheds for the years 1968-1971. Because, in 1970, there was widespread Southern Corn Leaf blight in Illinois, a slope dummy for 1970 was included to test the hypothesis that the blight would affect the estimates of 13j, a component of the slope in all regions. It was expected that the coefficient associated with the 1970 slope dummy would be positive because of the lower corn uptake efficiency due to the blight. Table I presents the estimates obtained for the coefficients in Eq. (5). All of the estimated coefficients are seen to be significantly different from zero. The slope dummy for 1970, DT0, is positive, indicating that the Southern Corn Leaf blight increased the effect of a given amount of fertilizer nitrogen use on nitrates leached into surface waters. The slopes of all regional slope dummy coefficients are negative, ~sIn the cross section regression a single dummy variable was used to represent the central part of the state (Regions 22 and 23) and another for the south-southeast (Regions 24 and 25).

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TABLE I ESTIMATED COEFFICIENTS OF TIlE ENVIRONMENTAL LINKAGE'~

Coefficient

Estimate

Standard error

~j

Regression location (No.) ~

a B D, D~ D~ D~0

0.65 0.034 --0.007 --0.016 --0.040 0.006

0.15 0.004 0.003 0.005 0.009 0.003

0.034 0.027 0.018 0.00&

EC, WC (22, 23) N (21) SE, S (24, 25) SW (26)

, R 2 = 0.46; degrees of freedom = 98. b See Fig. 4, Appendix. 9 Since one cannot reject the hypothesis that Da = --0.034 we have calculated [hs as 0 rather than the more implausible value of --0.006. indicating that the modifying variables in regions outside of Region 22 and 23 are such that they tend to decrease the effect o f a given a m o u n t o f fertilizer nitrogen on nitrates leached into surface waters. T h e results give no indication of which modifying variable causes this shift. The estimated value o f a ' is consistent with our prior expectations (a = 1.92). These coefficient estimates can be used to c o m p u t e the nitrogen usage levels associated with alternative concentration targets via (6). The resultant limits on nitrogen usage for various concentrations (ppm) are presented in Table II. F o r the sake of comparison, 1959 actual usage levels are included. E m p l o y e d as upper bounds on the environmental constraints (6), these target usage levels yield the desired EPS corrective taxes as shadow prices. Simple parametric p r o g r a m m i n g techniques are used to derive the various tax prices. The tax price required to achieve a given regional target depends on the direct controls or tax prices simulated for the other regions. Put alternatively, cost minimizing cropping and fertilizer usage rates in a region depend on the supply prices of all commodities, which in turn reflect the constraints and costs prevailing in all other regions. In this way, one region can transfer environmental pressure to another region t h r o u g h the market place by restricting its output of, in this case, nitrogen using crops. Because of the regional interdependency of the effects of fertilizer control policies, tax prices designed to achieve a given set o f regional targets must be determined jointly. These prices can be determined by solving for the cost minimizing production pattern in the presence of the direct constraints (6). The shadow prices on these TABLE II ALTERNATIVE NITROGEN USAGE TARGETS, ILLINOIS PRODUCING REGIONS (1000 TONS N )

Region No.

N (21) EC (22) WC (23) SE (24) S (25) SW (26)

Estimated usage levels to achieve (ppm)

1959 Usage levels 22.3 60.4 16.3 4.6 9.7 8.2

2

5

8

8.8 7.1 2.7 2.3 6.3 .

186.4 152.7 57.8 51.1 137.0 .

286.0 227.5 85.9 76.1 204.3

.

.

10 350.0 278.4 105.2 93.1 250.0 (See Table I)

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ABRAMS AND BARR

-% PN (J) : PN~ fox (j)

PN

Targel usoge level

I

I QI (Tons)

~ ]

A

Fio. 2. Simulated regional demand for nitrogen fertilizer. constraints can be shown to equal the desired prices. Thus the duality relationship between resource availability and price in these programming models enables us to systematically investigate the interdependences of regional control policies, and the regional fertilizer prices required to support these policies. Simulated taxes on nitrogen fertilizer used in a region will have the effects of changing both crop acreages, and nitrogen application rates per acre on each crop. Since the yield response curves are concave, increases in the effective price of nitrogen will (eventually) shift production to crops using less nitrogen, and reduce the amount of nitrogen applied. A sufficiently high price would eliminate the production of crops using nitrogen altogether in the cost minimizing solutions. By varying the effective price of nitrogen on a single (or set of) region, model solutions trace out regional demand curves for nitrogen. Referring to Fig. 2, p x is the supply price of fertilizer in Region j, and/~.v(j) is the price cum tax. The quantity of nitrogen at A is that amount which is optimal when no tax is levied. Quantities at the various tax prices are the optimal usage levels for the region, given that production possibilities and costs are not altered in other producing regions. We now present the results of our simulation experiments that control regional nitrate concentration levels via (6). 5. SIMULATION RESULTS The design of the experiments was to: (1) solve the spatial production model without any constraints on nitrogen usage for 1970 demand levels, (2) then, successively constrain nitrogen usage in the six Illinois producing regions to levels that correspond to 10 ppm -- 5 ppm NO3--N at one unit intervals. In this way we are able to trace out the substitution effects, and consequent effects on prices and incomes that are associated with these intended environmental quality levels. The estimated impacts on prices, outputs and location are based on supply and demand conditions in 1970, which since have changed markedly. To achieve the estimated levels of regional environmental quality, the following taxes, derived from the shadow prices on the constraints (6), would be required. As can be seen from Table III, for the quality range (5-10 ppm) considered, the constraints (6) were only binding in three of the six regions. In the relatively unprodue~ tive southern half of the state, the nitrogen limitations never impinged on the optimal choice of activities. For the affected regions, the control program altered optimal production patterns, and in turn prompted changes in production activities outside the state. Before describing in detail the effects that the corrective tax solutions are estimated to have on cost minimizing production patterns, we present a summary of the estimated

CORRECTIVE TAXES FOR POLLUTION CONTROL

307

TABLE 11I CORRECTIVE TAXES FOR FERTILIZER NITROGEN CO,NFIROL IN ILLINOIS'j

NO~-N (mg/liter)

10 9 8 7 6 5

Location (Dollars/lb. of N) N (21)

EC (22)

WC (23)

SE, S, SW (24, 25, 26)

0.00000 0.00000 0.00000 0.00000 0.02660 0.02316

0.02055 0.02081 0.02194 0.02193 0.14483 0.15106

0.01775 0.04456 0.04602 0.04847 0.06107 0.07133

0.000(~ 0.00000 0.00000 0.00000 0.00000 0.~

See Fig. 4 for the delineation of the Illinois producing-regions. (minimum) abatement costs associated with achieving different (statewide) water qualities. It should be remembered that the abatement costs depicted in Fig. 3 are " n e t " of the tax revenues collected via the EPS procedure. Taxes are transfers and not resource costs. 16 The information contained in Fig. 3 depicts the estimated trade-offs between reduced nitrogen concentrate in Illinois surface waters and net abatement costs. If we assume that the desired level of environmental quality is that level at which the net benefits from improvement in environmental quality are maximized, Fig. 3 might be helpful in determining the target level of environmental quality. Figure 3 presents the estimated costs to society of achieving various levels of NO3-N. However, in practice such information would be extremely costly, if not impossible, to obtain, We suggest that even in the absence of any benefit function, an estimated cost function could be used to narrow the range in which the desired level of environmental quality can be expected to be found. Notice that in Fig. 3 the abatement cost function has three distinct segments. Between 10 mg/liter and the level occurring in the absence of constraints, the marginal costs of environmental improvement are relatively low. Below 7 mg/liter, the marginal costs are relatively high. A choice of environmental quality target outside the 7-10 mg/liter NO~-N range might not be warranted from these cost considerations alone. The principal response to a corrective tax on fertilizer nitrogen use in Illinois would be in the form of reduced application rates by Illinois crop farmers. Since corn production in Illinois historically has accounted for 90% of the demand for fertilizer nitrogen in the state, one would expect the corrective taxes to affect farmers producing corn the most. This response might be classified as essentially marginal. There are other responses which might be classified as essentially discrete and qualitative that farmers might make. They may switch to less fertilizer intensive crops such as soybeans, wheat, and barley. Another response might be for farmers to simply discontinue crop production altogether allowing their cropland to remain idle or to be used as pasture. In the three constrained producing-regions, fertilizer nitrogen application rates for corn production decline with higher taxes--tighter NOa-N limits--as expected. The 16Operationally, abatement costs are computed as the difference in the optimal values of the objective function of the model at the alternative constraint limitation of (6).

308

ABRAMS AND BARR TABLE IV ACREAGE CIIANGES IN ILLINOIS UNDER VARIOUS ENVIRONMENTALCONSTRAINTS

NOrN (rag/liter)

Benchmark I0 9 8 7 6 5

Millions of acres Wheat

Corn

Oats

0.0 0.0 0.23 0.39 0.57 0.78 1.02

8.32 8.32 8.08 7.92 7.75 7.54 7.30

0.0 0.0 0.0 0.0 0.0 0.0 0.0

Barley Sorghum Soybeans Hay-sil Cropland pasture 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0

6.14 6.14 6.14 6.14 6.14 6.14 6.14

1.09 1.09 1.09 1.09 1.09 0.88 0.76

5.07 5.07 5.07 5.07 5.07 5.42 5.46

rate of decline is not uniform across these regions with Regions 22 and 23 showing the steepest descent. It was expected that the taxes would stimulate substitution of small grain and soybean production for corn production. This effect was found to occur for Region 22 between the no-constraint situation and 10 mg/liter, and for Region 23 between 6 mg/liter and 5 rag/liter. An upper bound of 40% of cropland available for soybean production appeared to limit any further substitution of soybean production for corn production. If this agronomic limit was loosened, much more substitution for corn would occur in Illinois. As expected, farmers in regions outside of Illinois altered their production activities. Farmers in Region 12, East Central Indiana, and in Region 18, Central Iowa, substituted corn production for other crop activities in response to the decline in supply of corn by Illinois farmers. This change in crop mix was not accompanied by any change in application rates. Table IV summarizes the response by Illinois farmers in terms of land use. Basically, wheat and cropland pasture activities are substituted for corn and hay-silage as the environmental constraints are made more severe. One would expect that taxes on fertilizer nitrogen in Illinois would increase the supply price of corn in that state. This change also should have repercussions in terms of increases in" the supply price of corn in other regions of the country because they obtain their supplies of corn from Illinois or now obtain their supplies of corn from sources that would not otherwise be competitive with Illinois sources had no tax on fertilizer use been levied in Illinois. Table VI presents selected regional supply prices TABLE V FERTILIZER NITROGEN USE IN ILLINOIS UNDER VARIOUS ENVIRONMENTAL CONSTRAINTS

NOrN (mg/liter) 10 9 8 7 6 5

Thousands of tons State

(21)

(22)

(23)

(24)

(25)

(26)

618.4 574.6 548.3 5!9.8 471.8 397.5

234.9 234.9 234.9 234.9 221.3 186.4

278.4 246.6 227.5 206.8 181.3 152.7

105.2 93.1 85.9 78.1 68.5 57.7

0.0 0.0 0.0 0.0 0.7 0.7

0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0

CORRECTIVE TAXES FOR POLLUTION CONTROL

309

TABLE VI REGIONAL CORN PRICES UNDER ALTERNATIVE ENVIRONMENTALCONS~IRAINIS

Consuming region~ 2 5 6 10 11 12 20

Dollars/bushel

Percent (9)

10 mg/liter

5 mg/liter

1.009 1.288 1.137 0.723 1.188 1.101 1.550

1.0J,l 1.327 1.176 0.762 1.227 1.140 1.572

3 3 3 5 3 4 1

See Appendix for the delineation of consuming regions. for corn assuming two levels of NO~-N are met through the appropriate tax schemes. Taxes on fertilizer nitrogen in Illinois would cause greater increases in the supply price of those crops which use fertilizer nitrogen relatively more intensive than those crops which use fertilizer nitrogen relatively less intensively. Thus, the supply price of corn should increase more than the supply price of other small grains and wheat. This change in the relative prices of feed grains should affect livestock feeding strategies. The national demands for various grains and soybeans by livestock activities under two environmental constraints are presented in Table VII. As expected, as the target level of NO3-N is reduced from 10 rag/liter to 5 mg/iiter and taxes on fertilizer nitrogen are increased accordingly, there is a substitution by livestock producers of small grains for corn. Notice that less soybeans are fed, too. This result is due to the fact that less high protein supplement feeds such as soybeans are needed as less protein deficient feeds such as corn are fed to livestock. Only one of the possible substitutions made by livestock producers in response to the change in the relative prices of feed grains was presented in Table VII. Other responses include changes in the proportion of feed concentrates to roughage, a m o u n t of weight gain through grazing, and the location of feeding activities. Table VIII summarizes these responses made on the part of fed beef producers. Reducing the desired level of NO3-N in Illinois from 10 mg/liter to 5 mg/liter requires appropriate TABLE VII GRAIN FED TO LIVESTOCK UNDER ALTERNATIVE ENVIRONMENTAL CONSTRAINTS

Feed

Wheat Corn Oats Barley Sorghum Oilmeals~

Millions of bushels 10 mg/liter

5 mg/liter

92 3563 0 579 1117 603

260 3482 0 633 1138 589

* Soybeans and cottonseed expressed in soybean equivalents.

310

ABRAMS AND BARR. TABLE VII[ OI"ILMALBEEF FEEDINGLOCATIONSAND STRAIEGILS UNDER ALTERNATIVECONSTRAINTLEVELS"

Region

Strategy (millions of head) 6

5

4

3

Short-fed Roughage ~ Concentrates 10~

5~

l0

5

10

2

I

Long-fed Roughage ~ Concentrates 5

10

5

3.34

3.34

10

5

10

5

1

2 3 4 5 6 7

2.33 2.33 0.34 0.34

8

9 10 11 12 13 14 15 16 17 18 19 20 Total

0.34 3.81 4.00 I0.82

10.82 1.28 1.31

1.33 1.31 1.30

1.47

0.23 0.08 0.32 0.31 0.00

0.00

0.55

0.39

0.I0

5 . 1 4 5.31

15.46 15.63 4.29

4.08 0.00

0.00

" See Figure 5, Appendix for an explanation of fed beef strategies. b 10 = 10 mg/liter, NO~-N; 5 = 5 mg/liter, NO3-N. increases in the tax on fertilizer nitrogen. This increase causes all fed beef activities to leave the state, and significant reductions in the level of fed beef activities in (consuming) regions such as 14, 15, and 16 who rely on feed from the Corn Belt. This decline in supply is balanced by increases in supply of fed beef in the Great Plains regions of 12, and 13. As expected, there are shifts toward more roughage intensive feed strategies (Region 14), and shifts toward more pasture-intensive feed strategies (Region 16). One other significant substitution not shown in Table VII is the switch in the C o r n Belt from fed-beef activities to beef heard grazing. As the desired level of N O a - N is reduced from 10 mg/liter to 5 rag/liter, beef cow herds increase from 9.22 million to 9.44 million. There are no other significant changes in the location o f milk cow and beef cow activities in response to environmental controls placed on the use o f fertilizer nitrogen in Illinois. As a result of the responses summarized in Tables VII and VIII, the supply prices o f livestock products are expected to increase. Table IX presents selected price increases for milk, non-grain-fed beef and grain-fed beef as taxes are increased in order to redu=e the desired level o f N O a - N in Illinois from 10 rag/liter to 5 mg/liter. The

CORRECTIVE TAXES FOR POLLUTION CONTROL

31 l

TABLE IX 9 LIVESTOCK PRODUCT PRICE CIIANGES UNDER ALTERNATIVE ENVIRONMENTAL CONSTRAINTS

Consuming region

2 10 20

Dollars/hundredweight Milk

Grain-fed beef

Non-grain fed beef

10 mg/liter

5 rag/liter

10 mg/liter

5 mg/liter

10 mg/liter

5 rag/liter

3.23 (1)~ 3.21 (1) 3.21 (1)

3.27 3.25 3.25

37.04 (3) 35.89 (3) 38.01 (3)

38.07 36.92 39.00,

36.81 (3) 34.98 (3) 35.99 (3)

37.94 36.10 37.20

aPercent of increase. increases in the price of beef should warn the policy maker that if he desires to reduce the level of N O ~ - N in Illinois from 10 to 5 mg/liter, he better be prepared to face subsequent criticism from consumers. O n e of the most i m p o r t a n t results provided by the linear p r o g r a m m i n g model of the livestock-feed complex, which is not essential to the calculation of the a p p r o p r i a t e taxes but which might be i m p o r t a n t in deciding what level of N O 3 - N is appropriate, TABLE X REGIONAL DISTRIBUTION OF NET FARM INCOME AFTER TAXES UNDER TIlE SIMULATED EPS SYSTE,~I

Region

Millions of dollars None

10 9 8 7 6 5 rag/liter mg/liter mg/liter mg/liter rag/liter mg/liter

N (21) Net income Taxes Net income after taxes

180.1 0.0 180.i

183.6 0.0 183.6

183.6 0.0 183.6

187.3 0.0 187.3

187.3 0.0 187.3

190.0 11.8 178.2

193.3 8.6 184.7

EC (22) Net income Taxes Net income after taxes

296.6 0.0 296.4

300.4 11.4 289.0

299.9 10.3 289.6

303.1 10.0 293.1

301.9 9.1 292.8

288.1 52.5 235.6

287.1 46.1 241.0

WC (23) Net income Taxes Net income after taxes

84.6 0.0 84.6

86.1 3.7 82.4

86.4 8.3 78.1

86.0 7.9 78.1

86.0 7.6 78.4

85.6 8.4 77.2

86.9 8.2 78.7

SE (24) Net income Taxes Net income after taxes

0.0 0.0 0.0

0.0 0.0 0.0

0.0 0.0 0.0

0.0 0.0 0.0

0.0 0.0 0.0

2.8 0.0 2.8

2.8 0.0 2.8

SW (26) Net income Taxes Net income after taxes

15.2 0.0 15.2

15.4 0.0 15.4

15.4 0.0 15.4

15.6 0.0 15.6

15.6 0.0 15.6

15.6 0.0 15.6

15.9 0.0 15.9

312

ABRAMS AND BARR TABLE XI ES'FIMATED CllANGES IN FERTILIZER NI1ROGEN USE INDUCED BY STRIC-'TI~R ENVIRONMENTAL CONTROL

Producing region 9 12 13 20 30 31

Fertilizer nitrogen use (millions of pounds) I0 rag/liter

5 mg/liter

Change

17.09 920.88 82.46 172.61 95.18 93.65

3.30 990.09 107.80 147.36 102.70 95.04

- 13.79 69.21 25.34 - 25.25 7.52 1.39

is the income of Illinois farmers under various possible levels of NO3-N. The effect on income derived from crop production in Illinois due to taxes designed to reduce N O 3 - N concentrations to 5 mg/liter is shown in Table X. Net income is defined as the difference between total revenue and total variable costs excluding tax payments. Total revenue is the sum of crop output times its respective supply price. Total variable cost includes all costs of production except implicit rent on cropland used. Excluding tax payments, the table reveals that net income to farmers generally increases as corrective taxes increase (or desired level of NO3-N decreases). This result is due to the fact that reductions in output due to less fertilizer use are outweighed by increases in the prices received for crop outputs. However, after tax form incomes are estimated to decline in most instances as the target NO3-N level is decreased? 7 These estimates underscore an important aspect of the EPS management proposal: the tractability of unilateral environmental control may hinge on the distribution of tax revenues. Table X indicates that a system of lump-sum rebates could increase Illinois farm incomes, an increase made possible through higher farm prices. Finally, while results have already been presented showing the change in fertilizer nitrogen use in lllinois under various tax schemes, it is also useful to know what changes in total fertilizer nitrogen use will occur in other producing regions. This data could serve as a crude indicator of the environmental pressure directed toward other regions by the imposition of controls in Illinois. Because we did not have data to formulate environmental submodels for regions outside of Illinois, we do not know what effect the changes in fertilizer nitrogen use would have on NO3N in these regions. Table XI presents these results for six Corn Belt producing regions outside of Illinois. 6. C O N C L U S I O N The EPS approach to resource management requires a means by which environmental standards can be chosen and prices can be set to attain them. Mathematical programming models are effective vehicles for accomplishing these tasks, because the duality relationship between resource valuation and efficient resource use that under~7These results are qualitatively similar to those reported by Mayer and Hargrove 1-14"1.They considered alternative leer-acre limits on nitrogen usage, applied initially to Iowa, and then nationwide. Regionally differentiated controls on fertilizer nitrogen resulted in decreases in income for farmers in those regions subject to the relatively stricter controls. However, in the case where all regions were subject to the same level of restriction, farm income in all regions increased.

CORRECTIVE TAXES FOR POLLUTION CONTROL -- 25 20 o

I-9

9,~

~15.2

~5

! U,S. Public heallh slandord

\

.__o ~

x.~.o3.5 Ii

5

0

313

~S

I

I 6

5 Niltole

I

I

1

I1.1 ,~'-----'--;-~

7 8 9 10 ~1 12 I~ 14 concenlr~dion ( P P M )

Fz~. 3. Abatement cost estimates for Illinois water quality standards, 1970. lies the EPS proposal is at the same time central to these optimization techniques. In this study, nitrogen fertilizer use is related to nitrate concentration found in Illinois surface waters by regression analysis. These relationships constitute the Environmental Linkage in the model; they enable us to translate regional environmental (NO3-N) standards into constraints on agriculture production. The programming model embeds these environmental constraints and Illinois production alternatives into the larger national market for agriculture. Cost minimizing production patterns are determined via linear programming techniques, along with optimal nitrogen application rates on Corn Belt crops. In Illinois, nitrogen use is constrained via the environmental linkage constraints. The shadow prices on these constraints at an optimal solution can be interpreted as the corrective taxes on nitrogen fertilizer needed to effect the environmental standards implied by the constraint limits. The spatial model of agriculture is shown to produce a reasonably accurate description of actual production patterns (benchmark solution) for the year 1970. Then, by activating the environmental linkage constraints, nitrate concentration standards are imposed on Illinois producing regions. These standards are seen to impinge on production possibilities in Illinois, and to shift some nitrogen using activities elsewhere. The implication that these shifts have on land use, production, prices and income are traced out for Illinois farmers, and for the nation. The magnitude and direction of these shifts appear plausible, based on our a priori expectations. The corrective taxes needed on nitrogen to effect these changes range from one to two cents per pound to achieve the l0 ppm standard set by the United States Public Health Service up to 7-15 cents per pound to achieve a stricter standard of five ppm. The solutions indicate (Fig. 3) that the costs of achieving standards of less than seven ppm may be very expensive, in terms of increased agricultural production costs. The solutions indicate that environmental initiatives taken by a single region (Illinois) could be achieved at a modest resource cost. At the same time, the costs to Illinois farmers appear to be lower than one might reasonably expect, particularly if the tax collections are redistributed to farm interests in some way. Finally, the solutions demonstrate the extent to which a region's environmental liabilities can be transferred via the market to other regions. APPENDIX: T H E S T R U C T U R E OF T H E M O D E L is 1. Introduction In formulating a model of the agricultural sector, three considerations are crucial: (1) the recognition that the analysis is one of partial equilibrium; (2) the necessity of la A complete algebraic statement of the model and a summary of its performance can be obtained from the authors upon request.

314

ABRAMS AND BARR

competitive efficiency as the basic mechanism by which resources are allocated; and (3) an appreciation of the controls available to policy makers, and the importance of existing and potential programs in affecting the market outcome. Each of these considerations affects the choice of an appropriate model. The first consideration forces one to delimit the activities that are endogenous to the analysis. We are concerned primarily with the alternatives for producing fed beef, since these place demands on the production system for grains and roughage, and the location of feedlots. This problem focus defines the partial equilibrium setting in which to conduct the analysis. The basic substitution possibilities in the model are between feed inputs for fed beef (roughage and concentrates), and between feed inputs and feeder calves (short-fed vs long-fed beef). Other major grain and livestock activities are included to complete the supply side of the sector. The policy specific aspects of the problem can then be introduced into this framework. The effects of nitrogen fertilizer use are examined by expanding the choice of production alternatives for nitrogen using crops in regions where there exist potential nitrate pollution hazards. Additional activities are defined that permit the model to solve for the economically optimal levels of fertilizer application for each crop. At the same time, regional fertilizer constraints intended to simulate environmental standards will impinge on these choices. If sufficiently stringent, these constraints will force cutbacks on fertilizer use and/or divert crop production from the environmentally constrained regions. Moreover, the constrained solution shadow prices identify fertilizer tax prices that would achieve the desired fertilizer usage rates in lieu of the direct constraints. IL The Model

The programming model represents grain and livestock activities in the continental United States. The model is a hybrid of three linear programming models of agriculture (see Brokken ['5-], King and Sehrader [-10-], and Whittlesey [-20-}), combining in our view the best aspects of each model. The objective is to minimize the total variable costs of producing and delivering fixed quantities of final products to spatially separated markets. We consider nine crop and eight livestock activities: Crop activities 1. 2. 3. 4. 5. 6. 7. 8. 9.

Wheat Corn Oats Barley Sorghum Soybeans Cotton--lint and seed Silage--hay rotation Wild Hay

Livestock activities 1-6. Fed beef (1000 lb dressed) 7. Dairy cattle (head) 8. Beef cattle (head)

The activity levels are defined in terms of acres planted (000). There are 41 ( = n ) crop producing regions, of which 23 of these are in the Corn Belt states. These areal definitions are derived from the regional partition of Whittlesey [-20-1, which is based on the homogeneity of crop growing conditions, costs and yield potentials with a single producing region. Within the Corn Belt we have preserved his areal definitions; crop activities that require nitrogen fertilizer in these regions are further defined ac-

CORRECTIVE TAXES FOR POLLUTION CONTROL R;

315

Livestock Producing and Consuming Regions

'X L\ | i| J | 'i | | ~ X ] - ~ ' - ~ I..... -I~,L ._@_@.,-?-:r x_4

|

|

Producing Region

~

D:

~.~

Corn Belt Producing Regions

Fl~. 4. Regional definitions. cording to the amount of fertilizer used and its associated yield. Outside the Corn Belt we have used constant per acre costs and yield coefficients (that assume average fertilizer input) constructed by the Iowa State research program. Outside the Corn Belt we have aggregated producing regions so that they conform to a set of larger regions, that defines the spatial unit for which final demands are specified and for which livestock production is defined. The larger regions are collections of contiguous .crop producing regions and are dubbed consuming regions. The partition is defined so that consuming regions are collections of states. The choice of the larger partition is dictated both by demand considerations (e.g., population patterns, and the location of export--import centers) as well as the homogeneity of livestock growing conditions and costs. Figure 4 presents the partitions used in this study. Transportation costs for commodities are defined between consuming regions. It is assumed that transportation within a consuming region can be undertaken costlessly. Variable costs for the crop activities include the costs of labor, nonland capital, seed, fertilizer, and other direct expenses. Within the Corn Belt region, fertilizer using crop activities are further indexed to denote the costs and yields associated with alternative fertilizer application rates. Variable costs of livestock production are net of feed costs. They include labor, nonland capital costs, veterinary expenses, breeding expenses and other direct costs. Transportation costs of various commodities are defined in natural units, such as bushels of corn, thousand pounds of dressed beef, or hundred pounds of fluid milk.

316

ABRAMS AND BARR

Concentrates intoke per coil

2 6

3

ssed beef output per colt Rou~he~e infcke per Cc:lf

Flo. 5. Alternativefeedlotstrategies. The objective function, then, minimizes the costs of producing and delivering livestock and feedgrain products in the United States. The constraints of the model include the usual upper limits on available cropland by producing region, and the final demands for crop and livestock products by consuming regions. In addition intermediate demands for feedgrains, roughage, and feeder calves by the livestock activities are defined by a set of regional constraints which reflect feed (energy) requirements and other dietary considerations (such as corn and protein intake). Our formulation of the fed beef sector is based on the regional model of King and Schrader El0-]; it permits variations in feed composition and feeding duration, and accounts for regional cost differences net of feed and calf inputs. While our formulation ignores several important aspects of the livestock producing sector, we feel it is the best specification available, and a reasonable compromise between the intracacies of the cattle feeding described in 1-87, and the need for structural simplicity in spatial programming models. As noted above there are six fed beef activities in the model that can be construed as alternative feedlot strategies. These activities differ according to their input requirements in two ways: (1) the ratio of inputs of feed concentrates (grains) and of roughage, and (2) the duration of time the calf is kept on its feeding program. The six alternatives are depicted (for a given region) in Fig. 5. Piecewise linear combinations of these six strategies are incorporated in our model. Strategies 1, 2, and 3 use more feed and roughage than 4, 5, and 6, respectively. This reflects the fact that calves are fed for a longer period, yielding a higher weight gain per calf. Roughly speaking, feedlots located where the delivered price of calves is low vis-'t-vis grain and roughage prices would opt for the short feeding program. Finally, the model has been designed to evaluate fertilizer control policies for the Corn Belt producing region. To accommodate this end, we introduced alternative fertilizer application strategies for the principal nitrogen using crops in those regions. Crop yields at different application rates of nitrogen and its complementary nutrients were derived from the basic survey work of Ibach and Adams 1-191. Yield response curves were constructed from this data that are compatible with the average practice estimates of Whittlesey, for wheat, corn, sorghum, oats and barley, for each producing region in the Corn Belt. Referring to Fig. 6, each vertex on the piecewise linear yield curve corresponds to a feasible activity, with its associated yield and cost. This construction allows the model to solve for any convex combination of the eligible fertilizer strategies. At the same time, constraints on total fertilizer usage are introduced, with the upper limits Ni derived from the environmental linkage equations described in the accompanying paper. Practically speaking, these limits are varied parametrically, with the corresponding shadow prices on these constraints identified as the corrective taxes required to achieve

CORRECTIVE TAXES FOR POLLUTION CONTROL

Yield: Eushel$ Per Acre

/[

,

317

I

I

, I'OS t

;

Xi t rogr Pounds Per Acre

r

t I

1

2

20

60

! I 3

1 O0

11,11

FIG. 6. Cost and yield response curves.

the environmental quality levels (ppm) that relate to the N i. The environmental constraints (20) can be made less areal specific by aggregating these constraints over sets of producing regions, etc. Parametric programming techniques provide an inexpensive method of determining sets of corrective taxes that will support alternative environmental quality levels.

IlL Model Statistics and PeJfornlance The model described above consists of 435 rows and 3916 activities, including a slack activity for each row constraint. The benchmark solution, wherein no environmental constraints were imposed on Corn Belt production activities, required approximately 80 min (CPU) to reach an optimal solution using the IBM-360-65 MPS package. Additional programming time was required for the parametric analyses that (1) examined the sensitivity of solutions to parametric assumptions and (2) developed the solutions under environmental constraints. Overall, we feel that the model produced solutions that compare favorably to actual production patterns. The benchmark solution located crop and livestock activities reasonably well, with overspecialization the principal shortcoming.~ Total production of individual commodities is reasonably close to 1970 actual data, the year for which demand data was taken. The location and strategy of fed-beef activities is overspecialized but credible with actual locations constraint with regional comparative advantages. Total feed consumption in the benchmark solution contained somewhat less small grains and more sorghum. Optimal nitrogen fertilizer use in the Corn Belt, and the associated Illinois nitrate concentration levels compared reasonably well with actual 1970 data. A considerable amount of sensitivity analysis has been conducted to see how optimal solutions change when various constraints are relaxed, or in the presence of auxiliary constraints. The benchmark solution seems to us to be the best compromise between the normative and descriptive performance of the model. 19This is the expected tendency for linear models that assume homogeneous production capabilities within regions. The degree of overspecialization could be reduced by disaggregating the Corn Belt producing regions. A more complete evaluation of the model performance is presented in Abrams I-1 Chapter 8-1.

REFERENCES 1. L. A. Abrams, "Operational Use of Corrective Taxes for Pollution Control," Unpublished Ph.D. Dissertation, June, 1974. 2. J. L. Barr and L. Abrams, "Some Notes on the Use of Fertilizer and Water Quality," Paper presented at the American Agriculture Economics Association Seminar on Agricultural Productivity and Environmental Quality, Gainesville, Florida, August, 1972.

318

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