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An input-output analysis of environmental preservation
JOURNAL
OF ENVIRONMENTAL
An Input-Output
ECONOMICS
AND
Analysis IRWIN
MANAGEMENT
3,205-214 (1976)
of Environmental
Preservation’
F. LIPNOWSKI
Department of Economics, University of Manitoba, W innipeg, Manitoba, Canada Received July 21, 1975 A well-established criterion for determining the growth potential of an economy, the technology of which can be represented by a nonnegative indecomposable square matrix, is examined critically. The concept of growth upon which this criterion is established is shown to be ambiguous since the environmental repercussions of economic activity are completely ignored. Assuming that this economy possessesan antipollution technology which has hitherto been ignored, an alternative criterion to gauge growth potential in the presence of complete environmental preservation is proposed. The magnitude of the uniform rate of profit which must obtain when the economy ignores the environment if a policy of environmental preservation is to be deemed technically feasible is calculated. Finally, a number of factors which would facilitate the implementation of a policy of environmental preservation are discussed.
INTRODUCTION It is no exaggeration to assert that traditionally, the natural environment has not enjoyed pride of place in theoretical economic analysis. It held center stage in the water-diamonds paradox only long enough for economists to demonstrate that, given Nature’s abundance, Her useful bounty fails to command value in exchange. The traditional view has, by and large, regarded environmental factors as available costlessly in unlimited amounts and hence,as noneconomic goods. The extension of general equilibrium m o d e ls to the treatment of the environment as a scarceresource has been a very recent phenomenon. In a seminal paper, Ayres and Kneese [2] incorporated the fundamental law of conservation of mass (and energy) in a Wah-as-Casselgeneral equilibrium m o d e l, developing a “materials balance” approach for commodity flows within the economy. The concept of materials balance was subsequently adopted by d’Arge and Kogiku [S] in the context of a closed resource system to addressthe issue of optimal growth in a finite planning horizon. Q u ite a different approach was taken by Leontief [9] when he introduced pollution activities into the framework of an open static inputoutput m o d e l; the exogenously specified vector of final demand was enlarged to include the acceptablelevel of each pollutant generatedin the course of production and consumption. Leontief also introduced the means to achieve acceptablelevels of Gnal delivery of pollutants: n a m e ly, an antipollution technology, comprising a distinct antipollution industry for each type of pollutant generated. 1 I would like to thank Prof. E. J. Mishan, Dr. S. A. Ozga, Barbara Spencer, and two anonymous referees for their helpful comments without implicating them in the responsibility for errors or defects in the paper which remain. 205 Copyright All rights
0 1976 by Academic Press, Inc. of reproduction in any form reserved.
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Inherent in Leontiefs circular flow model of goods, pollution and antipollution is the notion that all flows are reversible. However, as has been emphasized by GeorgescuRoegen [6], with the passage of time there results inexorably the production of high entropy from low entropy, a time-irreversible process. Thus, even if one posits the presence of an antipollution technology which is capable of eliminating pollution arising in the course of production and consumption, the energy depleted in restoring the quality of the environment cannot itself be recovered. Consequently, the finite fund of energy sources must eventually disappear. Despite the Second Law of Thermodynamics, which must be regarded as an immovable datum, it is still of interest to examine the implications of a policy of complete environmental preservation within the context of a closed, static input-output model, particularly as regards the technical feasibility of such a policy. To this end, the traditional criterion for assessing an economy’s growth potential without taking any account of environmental quality is considered critically; it is argued that this well-established criterion rests upon the foundation of an ambiguous concept of growth. On the assumption that the economy does possessan antipollution technology, an alternative criterion to gauge growth potential unambiguously is proposed. Building on this new foundation, a criterion to inform the analyst of the technical feasibility of effecting a sudden transition from a situation of zero antipollution activity to one of strict environmental preservation is formulated. Various factors which would facilitate the implementation of a policy of environmental preservation are then examined. THE TRADITIONAL CRITERION FOR GAUGING GROWTH POTENTIAL Consider a closed, static Leontief economy, consisting of a labor “industry” and of m other industries. Let the technology of this economy be represented by an m + 1 by m + 1 nonnegative, indecomposable matrix, A. The initial row of A, row zero, contains elements aoi (i = 1, . . . , m), the labor input coefficients of production, while column zero consists of aio (i = 1, . . . , m), the consumption coefficients of labor; by convention, a00is defined as zero. An element in row i and columnj of A, aii (i, j = 1, . . ., m) denotes the input from industry i per unit of output in industry j. Let the dominant positive eigenvalue of A be denoted by the scalar c. Then by the PerronFrobenius theorem, there must be one and only one right-hand strictly positive eigenvector, say x, such that Ax = cx; and there must be one and only one left-hand strictly positive eigenvector, say p, such that pA = cp. The interpretation of x is as the vector of relative outputs of all industries in the economy, including labor, while that of p is as the vector of relative prices, including that of labor services. If x exceeds Ax, the latter representing a vector of relative inputs into the production processes, then c is less than 1 and may be written c = l/(1 + g), where g is positive and is interpreted as the maximum balanced rate of growth which the economy can attain. Since the same dominant eigenvalue obtains for the left-hand eigenvector, if p exceeds pA, the latter denoting a vector of the relative costs of production at the unit level in each industry, then c may be written as l/(1 + r), where I is the uniform rate of profit which obtains in all industries, and we may conclude that g = r, a duality first noted explicitly by von Neumann [ 131. The traditional criterion for judging the possibility of balanced growth in the economy emerges directly from these properties of the technology matrix A: if c < 1, it is claimed that the economy is capable of positive balanced growth at the rate g, with all industries realizing (in equilibrium) a positive uniform rate of profit, r; from the condition c = 1, it is inferred that the
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207
economy is just capable of reproducing itself on a constant scale, the case of “simple reproduction;” and c > 1 is taken to indicate that the economy faces imminent balanced contraction at the absolute rate of g/period [4, 81. The traditional formulation of the criterion for discerning the growth potential of an economy would be unexceptionable were it not for its complete omission of the environmental repercussions arising from economic activity. Once it is allowed that pollution is generated in the course of production, the balanced expansion in the output of the m + 1 industries, accompanied by a balanced increase in the quantity of pollutants discharged into the environment, would characterize a situation which could hardly be described, unambiguously, as one of growth. What underlies this assertion is a conception of unambiguous growth which entails an increase in the provision of at least one commodity or service and a decrease in none, where the class of economic services includes those rendered by the environment. It m ight be noted in passing that even if environmental degradation were inconsequential, some ambiguity remains in the notion of balanced growth along a von Neumann ray, since the increased “output” of the labor industry m ight entail a decreasein the availability of the “commodity” leisure. Although there are a number of more or less satisfactory ways to deal with this particular source of ambiguity in the concept of growth,2 this possible difficulty will be ignored. If our concept of unambiguous growth is accepted, it would follow that the only circumstance in which the criterion to gauge the growth potential of an economy could be the traditional one which examines the dominant eigenvalue of A, would be one in which the quantity of pollution generated could be neutralized completely by Nature, thereby permitting environmental quality to remain intact. This condition would be fulfilled only if the scale at which the economy operated did not exceed some critical level beyond which Nature could no longer assimilate pollutants harmlessly. However, since x depicts output proportions so that Ax = cx holds for any scalar multiple of x, it seems ill-advised to adopt a criterion to assessgrowth potential which has validity only for a lim ited range in the scale of operation of the economy. The objections raised against the traditional criterion can be met by formulating an alternative criterion on the basis of an enlarged technology matrix A*, which is constructed in the next section. ENVIRONMENTAL PRESERVATlON AND THE POTENTIAL FOR BALANCED GROWTH The construction of matrix A* from A requires that n - m additional rows and columns be added to A, given that there are II - m types of pollution generation arising 2 If the size of the workforce does not expand, the only way in which the economy’s advance along the von Neumann ray would not be impeded would be if productivity happened to increase at the appropriate rate. To assume, for example, that aio are consumption coefficients expressed in terms of labor efficiency units and that as the wage basket grows at the rate g, there would occur HarrodNeutral technical progress also at the rate g, would be so arbitrary an assumption as to render the model worthless. The usual interpretation of the von Neumann model involves the implicit assumption that there is a pool of potential workers outside the economy whose services can be drawn upon as required. Robinson gives the following interpretation [15]: As the flow of output of wage goods increases, employment of labor grows (either the population is growing at just the right rate or there is an indefinite reserve of potential labor, living on nuts in the jungles, ready to take employment when the standard real wage is offered). Although the total input of labor would be rising, at least the leisure available to the existing workforce would not have to decline as the economy advances along the von Neumann ray. Whether this can justifiably be characterized as unambiguous growth is a moot point.
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from production and consumption, with one antipollution industry for each type of pollutant. Each additional row and column consists of n + 1 elements and the (n + l)order square matrix A* is assumed to be nonnegative and indecomposable. Subscript 0 represents the labor sector; i, j = 1, . . . , m represent “useful” industries; and g,k=m+l, . . . . n represent types of pollutant generated or eliminated. The following notation, in addition to that introduced previously in connection with A, is adopted : aoo = input of labor service per unit elimination of pollutant g; agO= pollutant g generated by the consumption of the basket of wage goods paid for one unit of labor service; ai, = input of commodity i per unit of elimination of pollutant g; arri = pollutant g generated per unit of output of commodity i; and u!,~ = pollutant g generated per unit elimination of pollutant k. The enlarged closed economy-environment technology matrix A* would appear as follows: a00
a01
i al0
a11
.
. aom
~O,?n,l
. .
a0,
.
ah
&,m,l
..
%L
amm
am,m+l
..
amn
.
am+b
Ga+1,?n+1
. .
urn+]
anm
an,m+l
..
Qnn
Applying the Perron-Frobenius theorem to A*, the dominant eigenvalue c* can be associated with the strictly positive right-hand eigenvector X and with the strictly positive left-hand eigenvector P, so that the following two systems of equations emerge: A*X=
c*X, . . . .
(1)
PA* = c*P, . . . .
(2)
The interpretation of these equations is straightforward. The first m + 1 equations in (1) differ from the right-hand eigenequation associated with A only inasmuch as A*X includes as an additional component the intermediate product destined for the antipollution sectors. The last n - m equations in (1) indicate, on the left-hand side of the equations, the quantities of each type of pollutant generated by the act of consumption in the labor sector, by the production of the m “useful” goods at their respective levels of operation, and by the operation of the antipollution sectors themselves at their respective levels. Similarly, the price equations differ from those associated with A as a result of including in the price of the first m + 1 goods and services (including labor service) a cost component corresponding to the cost of restoring the environmental damage arising from the supply of one unit of the respective good or service. The tixity of the wage basket of consumption in the closed Leontief model permits the pollution coefficient us0 (g = m + 1, . . ., n) to be associated with payment for one unit of labor services; thus, wages will be sufficient, assuming c* < 1, to afford workers their customary wage basket as well as to cover the cost of offsetting the environmental
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PRESERVATION
209
damage arising from the consumption of this basket of goods.3 The final it - m equations in (2) indicate that the antipollution services are assigned prices which not only cover their direct inputs of labor and products from the m “useful” sectors, but also internalize the cost of offsetting the damage to the environment which results from the provision of one unit of antipollution service. The obvious question to pose with respect to Eqs. (1) and (2) is, What is their significance? If c* < 1, this would immediately inform the analyst that the economy is capable, simultaneously, of maintaining the quality of the environment and growing at the balanced rate of (1 - c*)/c*. Thus we are provided directly with a criterion for ascertaining unambiguous growth potential. Moreover, from c* = 1, one may infer that the economy could just reproduce itself on a constant scale while preserving the environment; while c* > 1 implies that the economy lacks this capability. In assessingthe broader significance of these equations, it is essential to bear in m ind that the technology matrix A* merely sets lim its within which the actual behavior of the economy is a matter of discretion. In examining actual behavior, economic institutions certainly cannot be neglected. Thus, c* < 1 merely indicates the possibility of a positive rate of balanced growth and of a positive uniform rate of profit; the technology alone cannot guarantee that these possibilities will be realized. Further institutional and behavioral assumptions are needed before it can be claimed that these possibilities would occur. A uniform rate of profit could arise in long-run equilibrium under competitive capitalism or as a consequence of the deliberate policy of socialist planners; either institutional setting would require the P price structure. However, neither institutional context could achieve maximal balanced growth without adopting a “Golden Rule” of accumulation whereby the entire social surplus would be reinvested period after period. Such dedicated accumulation could be carried out by “disembodied capitalist spirits” [l l] whose consumption is, naturally, zero; or by a Central Planning Bureau, bent on attaining maximal growth and which also consumes nothing. Unless the economy’s stock of pollutants has reached critical levels such that an ecological disaster would result from an increment in this stock, there is nothing compelling about P for any value of c*. Society m ight conceivably attach no value to environmental preservation, opting instead for the maximal balanced expansion in its m “useful” industries at the rate (1 - c)/c. In this case, the price vector for the first m + 1 industries would be p while a zero price would obtain for each of the n - m antipollution serviceswhich could be provided but which would all remain inoperative. There is, moreover, no compelling reason to assume that, in general, the social surplus must be divided among industries in proportion to the value of their capital which is tied up for one production period, as is assumed implicitly in (2). An alternative principle which could govern the distribution of social surplus through the price mechanism would involve raising the subsistence wage rate by such a uniform percentage-calculated by dividing the physical surplus of each of the “useful” commodities by the supply of man-hours and adding the resultant quantities of each commodity to the hourly wage basket-as absorbs the entire social surplus. The price ratios would then be equal “to the (new) embodied labour ratios” [12, p. xxxvi]. It is, perhaps, also worthwhile noting that even if P is the actual price vector in the economy for the case of c* < 1, there would be no reason to suppose that production would be undertaken in the proportions indicated by X. In other words, the equaliza8 The derivation of the au0 coefficients appears in a forthcoming paper by the author.
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F. LIPNOWSKI
tion of the rate of profit in all sectors, including the antipollution industries, does not imply that the economy is situated on the von Neumann ray. Indeed, an economy which is off the von Neumann ray might experience considerable difficulty in moving onto it. The improbability of P or of X actually occurring does not, however, vitiate their significance as norms against which the actual price and output proportions can be measured. P represents a price structure wherein the marginal social cost of production of each commodity and service is equated to its price. Thus, the divergence between the actual price of a commodity and the corresponding component in P-assuming one primary input,4 say labor, and setting the price of one man-hour equal to 1 for both the actual price vector and for P-indicates the extent to which the actual price of that commodity fails to internalize its externality. Likewise, a knowledge of X could be of particular value to planners contemplating the pursuit of a policy of environmental preservation. For example, if c* = 1, then only production in the relative proportions of X would permit the economy to maintain fully the quality of the environment while achieving simple reproduction in the first m + 1 industries. For c* < 1, X indicates what the output proportions must be if a policy of environmental preservation is to be pursued together with one of maximal balanced growth. A question which might be of interest to planners but which is not answered directly by Eqs. (1) or (2) is the following: Assuming that the economy with technology matrix A is equalizing profit rates in its m + 1 operative sectors, with no antipollution activity being undertaken; assuming further that the dominant eigenvalue of A is c = l/(1 + r) where r > 0; and assuming that antipollution industries for each of the n - m types of pollutants being generated, although not in operation, have a known technology, what is the minimum rate of profit which would render a policy of environmental preservation feasible ? In this context, we mean by “feasible” that the economy could preserve the environment fully while at least reproducing itself on a constant scale in its first m + 1 sectors. In other words, what is sought is a critical minimum rate of profit, say r. such that c = l/(1 + r,) would imply that c* = 1. THE
CRITICAL
RATE
OF PROFIT
To set the analysis in a more definite context, imagine that an economy amends its Constitution at some point in time t, enshrining the following inviolable provision: that the quality of the environment be preserved at the level which obtains at time t; and that any and all polluting agents be assessed a tax per unit of production or consumption equal to the cost to be incurred by the antipollution industries in offsetting the damage inflicted upon the environment by the respective pollution-generating activity. It is assumed that the administrative and enforcement costs of this provision are zero. It is obvious that the proposed Constitutional amendment could be implemented only if the economy were realizing a sufficient surplus prior to t. The pre-t social surplus would have to be greater than or equal to the resource cost of complete 4 The genus of “closed” linear models embracessuch diverse speciesas the von Neumann growth model and the static Leontief model. The former treats labor as a produced commodity and has, in consequence,earned the description of being a model of a slave economy. While one could view labor in the closed Leontief model in this manner, one need not do so. By defining U~O (i = 1, . . . , m) as a “vector of final demand coefficients” [14] labor can be regarded as a primary input; such an interpretation would not alter the structure of the closed static Leontief model. See also [17, p. lo].
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environmental preservation for the amendment to be deemed feasible. The comparison of these two magnitudes is in terms of the pre-t price structure, since the value of the pre-t social surplus, namely px - PAX, which is the same as rpAx, involves the simultaneous solution of r and p; hence, the uniform rate of profit, r, could not be associated with a different price structure for technology matrix A. To calculate the resource cost of preserving the environment in terms of p, the enlarged technology matrix A* is partitioned into four submatrices, consisting of the m + 1 by m + 1 matrix A, the rectangular submatrix comprising the first m + 1 rows of the final n - m columns, A12,the rectangular submatrix comprising the first m + 1 columns of the final n - m rows, AZ1, and the square submatrix consisting of the elements in the final n - m rows and columns is denoted AZ,. Thus, A* appears as follows :
An. A*=[A Azi1 A22
To translate the prices of the antipollution services into real costs in terms of p, let pk = (pm+l, . . . , pn). Since pk must be the social cost of antipollution services at the unit level, the following equations are formed. p” = PA,Z i- pk& = (p-4&1
- AdL.
The expression (pA12) represents an II - m dimension row vector of coefficients which indicate the direct real cost, measured in terms of labor and the m “useful” products at p prices, of operating each of the antipollution industries at the unit level. The square matrix [I - Az2]-’ is of dimension y1- m; its element in row g and column k indicates the quantity of pollutant g which is generated directly and indirectly by the operation of antipollution industry k at the unit level. Hence, the inner product of (PA,,) and the kth column of [I - Az2]-’ represents the total, i.e., direct plus indirect, cost of one unit of antipollution service k, which is to say, pk. Let xk be an n - m dimension column vector of antipollution activity levels which would be required to preserve the environment of the pre-t economy operating at x, and let
x*=[IXk’ X
an II + 1 dimension column vector. Then [AzlA2.Jx*, an n - m dimension column vector, shows the quantity of each type of pollutant generated directly by the operation of the economy at the x* level. Therefore, the social cost of eliminating this vector of pollutants, expressedin terms of the first m + 1 industries at the p prices, would be Thus, the feasibility of implementing the proposed (pA12)CI Am]-‘[A2~42lx*. Constitutional amendment would require that rpAx 2 (pA12)[I - Azz]-1[AzlAzz]x*.5 This provides an expression for the critical m inimum rate of profit, rc, in terms of the pre-t prices: rc = f(pA12)[I - A22]-1[A21A22]x*]/pAx. It will be recalled that if the pre-t rate of profit, realized uniformly in all sectors, is rO,then the enlarged technology 6 The implicit pair of products of initial prices, when the MRT
assumption in our analysis is that the marginal rate of transformation between any is constant. A problem in calculating the real cost of a proposed program, in terms when the program is of sufficient magnitude to alter those prices, is confronted only between any pair of products is not linear in the relevant range.
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matrix A* would have a dominant eigenvalue c* = 1; planners would thus be informed of the feasibility of the policy of environmental preservation from a knowledge of the value of re. However, it is obvious that the information needed to calculate Y?is not less than that needed to calculate c*. FLEXIBILITY IN THE ECONOMY AND THE CRITICAL RATE OF PROFIT It must be emphasized that the critical minimum rate of profit prior to time t which would permit the complete internalization of externalities while allowing simple reproduction to occur would be as high as Y, only in the limiting case of fixed production and consumption coefficients and in the absence of technological progress. The relaxation of these rigid conditions would entail that a lower social surplus would have to be forthcoming from the A economy in order to implement the Constitutional amendment. The nonsubstitution theorem of Samuelson [ 161 and Georgescu-Roegen[7] proved that the choice of an input combination to minimize the cost of production within each industry remains unaltered by a change in the scale of production in any industry or in the composition of final demand, assuming that constant returns to scale obtain. However, a change in the relative price structure, such as would accompany an internalization of externalities, would be likely to induce (assuming substitution possibilities in production) a switch to lower pollution-generating processes.The incentive for such switches is implicit in the realignment of relative prices, since the Constitutional amendment would impose the highest indirect tax per unit of output on the commodity processed by a technique which necessitatesthe most costly environmental restoration. Further, if the possibility of substitution in consumption is admitted, the imposition of a consumption tax which internalizes the resultant damage to the environment would induce utility-maximizing households to shift their pattern of consumption away from commodities which generate relatively high pollution in the act of their consumption. Such factors as the packaging and the extent to which the material of which the product is made is biodegradable, would figure more prominently in the calculus of the prospective consumer. Since technological progress could take various forms, each of which would reduce the resource cost of implementing the proposed Constitutional amendment, the following taxonomy classifies several guises under which advances in the state of the arts might conceivably occur: Al, A2. Bl. B2.
lowering lowering lowering lowering
the the the the
uLj coefficients for some i and j; czigcoefficients for some i and g; a,i coefficients for some g and i; aok coefficients for some g and k.
To interpret reductions in each category of coefficients as unambiguous manifestations of technological progress, it must be assumed that offsetting increases in the coefficients of the same category do not occur. Cases Al and A2 reflect a conventional form of technological progress; in each case, it becomes possible, comparing best-practice techniques, to produce one unit of output (or of antipollution service) at a lower real cost, with gains accruing to society from the direct and indirect effects.
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213
Technological improvements of the Bl and B2 variety would reduce the generation of pollution and are thus “preventive” in nature. The actual magnitude of the decrease in pollution-generation would arise from the ensuing direct and indirect effects of Bl and B2. Deliberate changes in the nature of the commodities produced could reduce the environmentally damaging characteristics of the product, yet leave the desirable attributes intact or perhaps even improved. For example, if the consumer’s utility from some commodity is unaffected by its packaging, the a,,, term m ight be lowered significantly by altering the packaging with no concomitant loss in welfare from consumption. Similarly, improvements in the technology of consumption (a la Lancaster) m ight arise from greater flexibility in combining desirable attributes while excluding hitherto jointly-supplied characteristics to which the consumer is indifferent. An example m ight be increased specialization in newspapers, with the classified advertisements and the news being divided into separate entities. As Bonus [3, p. 2601 has noted, the consumer’s waste decision is implicit in his consumption decision if a commodity’s final price includes the entire social cost. In models featuring demand equations, the optimal consumption bundle of consumers would be sensitive, in general, to the level of an indirect tax component added onto the basic prices of commodities to cover the cost of restoring the environment from the damage caused by the act of consumption of the respective commodities. It is therefore clear that flexibility in production or consumption, with substitution occurring in response to a realignment in the relative price structure, as well as various forms of technological progress (occurring, say, at time t) would lower the critical rate of profit needed to implement the proposed Constitutional amendment. Thus, the calculation of re yielded an upper bound for the size of the social surplus which must obtain in the economy prior to time t. This calculated value of rC is binding only in the absence of cost-reducing technical substitutions in production, technological improvements, or adjustments in the pattern of final consumption in the direction of commodities which result in less pollution generation. CONCLUSION A well-established criterion for gauging the growth potential of an economy, the technology of which can be represented by a nonnegative indecomposable square matrix, was reexamined critically. The concept of growth upon which this traditional criterion is based was shown to be ambiguous inasmuch as the environmental repercussions are left out of the account. On the assumption that such an economy possessesan antipollution technology which may be included in an enlarged technology-environment matrix (which is also nonnegative and indecomposable), a criterion to gauge growth potential in the presenceof complete environmental preservation was proposed. Then the magnitude of the uniform rate of profit which would have to obtain in such an economy when it disregards the environment in order for a policy of environmental preservation to be technically feasible was calculated. Finally, a number of factors which would facilitate the implementation of a policy of environmental preservation were considered. REFERENCES 1. K. J. Arrow and D. A. Starrett, Cost- and demand-theoretical approaches to the theory of price determination, in “Carl Menger and the Austrian School of Economics” (J. R. Hicks and W. Weber, Eds.), Oxford Univ. Press, London/New York (1973).
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2. R. U. Ayres and A. V. Kneese, Production, consumption and externalities, Amer. Ecorr. Rev. 59, 282-297 (1969). 3. H. Bonus, On the consumer’s waste decision, Z. ges. ?&&SW. 128, 257-268 (1972). 4. A. Brady, “Proportions, Prices and Planning, A Mathematical Restatement of the Labor Theory of Value,” North-Holland, Budapest (1970). 5. R. C. d’Arge and K. C. Kogiku, Economic growth and the environment, Rev. Econ. Stud. 40, 61-77 (1973). 6. N. Georgescu-Roegen, “The Entropy Law and the Economic Process,” Harvard Univ. Press, Cambridge, Mass. (1971). 7. N. Georgescu-Roegen, Some properties of a generalized Leontief model, in “Activity Analysis of Production and Allocation” (T. C. Koopmans, Ed.), Wiley, New York (1951). 8. L. Johansen, The rate of growth in dynamic input-output models. Some observations along lines suggested by 0. Lange and A. Br6dy, Memorandum from Institute of Economics, University of Oslo (1972). 9. W. W. Leontief, Environmental repercussions and the economic structure: an input&output approach, Rev. Econ. Stat. 52,262-271, (1970). 10. W. W. Leontief, National income, economic structure, and environmental externalities, in “The Measurement of Economic and Social Performance” (M. Moss, Ed.), Columbia Univ. Press, New York (1973). 11. G. Mathur, “Planning for Steady Growth,” Oxford Univ. Press, London/New York (1965). 12. R. L. Meek, “Studies in the Labour Theory of Value,” 2nd Ed., Lawrence and Wishart Ltd., London (1973). 13. J. von Neumann, A model of general economic equilibrium, Rev. Ecou. Stud. 13, l-9 (1945-46). 14. L. L. Pasinetti, “Growth and Income Distribution, Essays in Economic Theory,” Cambridge Univ. Press, London/New York (1974). 15. J. Robinson, “Economic Heresies, Some Old-Fashioned Questions in Economic Theory,” Basic Books, New York (1973). 16. P. A. Sam,ielson, Abstract of a theorem concerning substitutability in open Leontief models, in “Activity Analysis of Production and Allocation” (T. C. Koopmans, Ed.), Wiley, New York (1951). 17. P. Sraffa, “The Production of Commodities by Means of Commodities, Prelude to a Critique of Economic Theory,” Cambridge Univ. Press, London/New York (1960). 18. R. Stone, The evaluation of pollution: balancing gains and losses, Mirwva 10, 412-425, (1972).
OF ENVIRONMENTAL
An Input-Output
ECONOMICS
AND
Analysis IRWIN
MANAGEMENT
3,205-214 (1976)
of Environmental
Preservation’
F. LIPNOWSKI
Department of Economics, University of Manitoba, W innipeg, Manitoba, Canada Received July 21, 1975 A well-established criterion for determining the growth potential of an economy, the technology of which can be represented by a nonnegative indecomposable square matrix, is examined critically. The concept of growth upon which this criterion is established is shown to be ambiguous since the environmental repercussions of economic activity are completely ignored. Assuming that this economy possessesan antipollution technology which has hitherto been ignored, an alternative criterion to gauge growth potential in the presence of complete environmental preservation is proposed. The magnitude of the uniform rate of profit which must obtain when the economy ignores the environment if a policy of environmental preservation is to be deemed technically feasible is calculated. Finally, a number of factors which would facilitate the implementation of a policy of environmental preservation are discussed.
INTRODUCTION It is no exaggeration to assert that traditionally, the natural environment has not enjoyed pride of place in theoretical economic analysis. It held center stage in the water-diamonds paradox only long enough for economists to demonstrate that, given Nature’s abundance, Her useful bounty fails to command value in exchange. The traditional view has, by and large, regarded environmental factors as available costlessly in unlimited amounts and hence,as noneconomic goods. The extension of general equilibrium m o d e ls to the treatment of the environment as a scarceresource has been a very recent phenomenon. In a seminal paper, Ayres and Kneese [2] incorporated the fundamental law of conservation of mass (and energy) in a Wah-as-Casselgeneral equilibrium m o d e l, developing a “materials balance” approach for commodity flows within the economy. The concept of materials balance was subsequently adopted by d’Arge and Kogiku [S] in the context of a closed resource system to addressthe issue of optimal growth in a finite planning horizon. Q u ite a different approach was taken by Leontief [9] when he introduced pollution activities into the framework of an open static inputoutput m o d e l; the exogenously specified vector of final demand was enlarged to include the acceptablelevel of each pollutant generatedin the course of production and consumption. Leontief also introduced the means to achieve acceptablelevels of Gnal delivery of pollutants: n a m e ly, an antipollution technology, comprising a distinct antipollution industry for each type of pollutant generated. 1 I would like to thank Prof. E. J. Mishan, Dr. S. A. Ozga, Barbara Spencer, and two anonymous referees for their helpful comments without implicating them in the responsibility for errors or defects in the paper which remain. 205 Copyright All rights
0 1976 by Academic Press, Inc. of reproduction in any form reserved.
206
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Inherent in Leontiefs circular flow model of goods, pollution and antipollution is the notion that all flows are reversible. However, as has been emphasized by GeorgescuRoegen [6], with the passage of time there results inexorably the production of high entropy from low entropy, a time-irreversible process. Thus, even if one posits the presence of an antipollution technology which is capable of eliminating pollution arising in the course of production and consumption, the energy depleted in restoring the quality of the environment cannot itself be recovered. Consequently, the finite fund of energy sources must eventually disappear. Despite the Second Law of Thermodynamics, which must be regarded as an immovable datum, it is still of interest to examine the implications of a policy of complete environmental preservation within the context of a closed, static input-output model, particularly as regards the technical feasibility of such a policy. To this end, the traditional criterion for assessing an economy’s growth potential without taking any account of environmental quality is considered critically; it is argued that this well-established criterion rests upon the foundation of an ambiguous concept of growth. On the assumption that the economy does possessan antipollution technology, an alternative criterion to gauge growth potential unambiguously is proposed. Building on this new foundation, a criterion to inform the analyst of the technical feasibility of effecting a sudden transition from a situation of zero antipollution activity to one of strict environmental preservation is formulated. Various factors which would facilitate the implementation of a policy of environmental preservation are then examined. THE TRADITIONAL CRITERION FOR GAUGING GROWTH POTENTIAL Consider a closed, static Leontief economy, consisting of a labor “industry” and of m other industries. Let the technology of this economy be represented by an m + 1 by m + 1 nonnegative, indecomposable matrix, A. The initial row of A, row zero, contains elements aoi (i = 1, . . . , m), the labor input coefficients of production, while column zero consists of aio (i = 1, . . . , m), the consumption coefficients of labor; by convention, a00is defined as zero. An element in row i and columnj of A, aii (i, j = 1, . . ., m) denotes the input from industry i per unit of output in industry j. Let the dominant positive eigenvalue of A be denoted by the scalar c. Then by the PerronFrobenius theorem, there must be one and only one right-hand strictly positive eigenvector, say x, such that Ax = cx; and there must be one and only one left-hand strictly positive eigenvector, say p, such that pA = cp. The interpretation of x is as the vector of relative outputs of all industries in the economy, including labor, while that of p is as the vector of relative prices, including that of labor services. If x exceeds Ax, the latter representing a vector of relative inputs into the production processes, then c is less than 1 and may be written c = l/(1 + g), where g is positive and is interpreted as the maximum balanced rate of growth which the economy can attain. Since the same dominant eigenvalue obtains for the left-hand eigenvector, if p exceeds pA, the latter denoting a vector of the relative costs of production at the unit level in each industry, then c may be written as l/(1 + r), where I is the uniform rate of profit which obtains in all industries, and we may conclude that g = r, a duality first noted explicitly by von Neumann [ 131. The traditional criterion for judging the possibility of balanced growth in the economy emerges directly from these properties of the technology matrix A: if c < 1, it is claimed that the economy is capable of positive balanced growth at the rate g, with all industries realizing (in equilibrium) a positive uniform rate of profit, r; from the condition c = 1, it is inferred that the
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economy is just capable of reproducing itself on a constant scale, the case of “simple reproduction;” and c > 1 is taken to indicate that the economy faces imminent balanced contraction at the absolute rate of g/period [4, 81. The traditional formulation of the criterion for discerning the growth potential of an economy would be unexceptionable were it not for its complete omission of the environmental repercussions arising from economic activity. Once it is allowed that pollution is generated in the course of production, the balanced expansion in the output of the m + 1 industries, accompanied by a balanced increase in the quantity of pollutants discharged into the environment, would characterize a situation which could hardly be described, unambiguously, as one of growth. What underlies this assertion is a conception of unambiguous growth which entails an increase in the provision of at least one commodity or service and a decrease in none, where the class of economic services includes those rendered by the environment. It m ight be noted in passing that even if environmental degradation were inconsequential, some ambiguity remains in the notion of balanced growth along a von Neumann ray, since the increased “output” of the labor industry m ight entail a decreasein the availability of the “commodity” leisure. Although there are a number of more or less satisfactory ways to deal with this particular source of ambiguity in the concept of growth,2 this possible difficulty will be ignored. If our concept of unambiguous growth is accepted, it would follow that the only circumstance in which the criterion to gauge the growth potential of an economy could be the traditional one which examines the dominant eigenvalue of A, would be one in which the quantity of pollution generated could be neutralized completely by Nature, thereby permitting environmental quality to remain intact. This condition would be fulfilled only if the scale at which the economy operated did not exceed some critical level beyond which Nature could no longer assimilate pollutants harmlessly. However, since x depicts output proportions so that Ax = cx holds for any scalar multiple of x, it seems ill-advised to adopt a criterion to assessgrowth potential which has validity only for a lim ited range in the scale of operation of the economy. The objections raised against the traditional criterion can be met by formulating an alternative criterion on the basis of an enlarged technology matrix A*, which is constructed in the next section. ENVIRONMENTAL PRESERVATlON AND THE POTENTIAL FOR BALANCED GROWTH The construction of matrix A* from A requires that n - m additional rows and columns be added to A, given that there are II - m types of pollution generation arising 2 If the size of the workforce does not expand, the only way in which the economy’s advance along the von Neumann ray would not be impeded would be if productivity happened to increase at the appropriate rate. To assume, for example, that aio are consumption coefficients expressed in terms of labor efficiency units and that as the wage basket grows at the rate g, there would occur HarrodNeutral technical progress also at the rate g, would be so arbitrary an assumption as to render the model worthless. The usual interpretation of the von Neumann model involves the implicit assumption that there is a pool of potential workers outside the economy whose services can be drawn upon as required. Robinson gives the following interpretation [15]: As the flow of output of wage goods increases, employment of labor grows (either the population is growing at just the right rate or there is an indefinite reserve of potential labor, living on nuts in the jungles, ready to take employment when the standard real wage is offered). Although the total input of labor would be rising, at least the leisure available to the existing workforce would not have to decline as the economy advances along the von Neumann ray. Whether this can justifiably be characterized as unambiguous growth is a moot point.
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from production and consumption, with one antipollution industry for each type of pollutant. Each additional row and column consists of n + 1 elements and the (n + l)order square matrix A* is assumed to be nonnegative and indecomposable. Subscript 0 represents the labor sector; i, j = 1, . . . , m represent “useful” industries; and g,k=m+l, . . . . n represent types of pollutant generated or eliminated. The following notation, in addition to that introduced previously in connection with A, is adopted : aoo = input of labor service per unit elimination of pollutant g; agO= pollutant g generated by the consumption of the basket of wage goods paid for one unit of labor service; ai, = input of commodity i per unit of elimination of pollutant g; arri = pollutant g generated per unit of output of commodity i; and u!,~ = pollutant g generated per unit elimination of pollutant k. The enlarged closed economy-environment technology matrix A* would appear as follows: a00
a01
i al0
a11
.
. aom
~O,?n,l
. .
a0,
.
ah
&,m,l
..
%L
amm
am,m+l
..
amn
.
am+b
Ga+1,?n+1
. .
urn+]
anm
an,m+l
..
Qnn
Applying the Perron-Frobenius theorem to A*, the dominant eigenvalue c* can be associated with the strictly positive right-hand eigenvector X and with the strictly positive left-hand eigenvector P, so that the following two systems of equations emerge: A*X=
c*X, . . . .
(1)
PA* = c*P, . . . .
(2)
The interpretation of these equations is straightforward. The first m + 1 equations in (1) differ from the right-hand eigenequation associated with A only inasmuch as A*X includes as an additional component the intermediate product destined for the antipollution sectors. The last n - m equations in (1) indicate, on the left-hand side of the equations, the quantities of each type of pollutant generated by the act of consumption in the labor sector, by the production of the m “useful” goods at their respective levels of operation, and by the operation of the antipollution sectors themselves at their respective levels. Similarly, the price equations differ from those associated with A as a result of including in the price of the first m + 1 goods and services (including labor service) a cost component corresponding to the cost of restoring the environmental damage arising from the supply of one unit of the respective good or service. The tixity of the wage basket of consumption in the closed Leontief model permits the pollution coefficient us0 (g = m + 1, . . ., n) to be associated with payment for one unit of labor services; thus, wages will be sufficient, assuming c* < 1, to afford workers their customary wage basket as well as to cover the cost of offsetting the environmental
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damage arising from the consumption of this basket of goods.3 The final it - m equations in (2) indicate that the antipollution services are assigned prices which not only cover their direct inputs of labor and products from the m “useful” sectors, but also internalize the cost of offsetting the damage to the environment which results from the provision of one unit of antipollution service. The obvious question to pose with respect to Eqs. (1) and (2) is, What is their significance? If c* < 1, this would immediately inform the analyst that the economy is capable, simultaneously, of maintaining the quality of the environment and growing at the balanced rate of (1 - c*)/c*. Thus we are provided directly with a criterion for ascertaining unambiguous growth potential. Moreover, from c* = 1, one may infer that the economy could just reproduce itself on a constant scale while preserving the environment; while c* > 1 implies that the economy lacks this capability. In assessingthe broader significance of these equations, it is essential to bear in m ind that the technology matrix A* merely sets lim its within which the actual behavior of the economy is a matter of discretion. In examining actual behavior, economic institutions certainly cannot be neglected. Thus, c* < 1 merely indicates the possibility of a positive rate of balanced growth and of a positive uniform rate of profit; the technology alone cannot guarantee that these possibilities will be realized. Further institutional and behavioral assumptions are needed before it can be claimed that these possibilities would occur. A uniform rate of profit could arise in long-run equilibrium under competitive capitalism or as a consequence of the deliberate policy of socialist planners; either institutional setting would require the P price structure. However, neither institutional context could achieve maximal balanced growth without adopting a “Golden Rule” of accumulation whereby the entire social surplus would be reinvested period after period. Such dedicated accumulation could be carried out by “disembodied capitalist spirits” [l l] whose consumption is, naturally, zero; or by a Central Planning Bureau, bent on attaining maximal growth and which also consumes nothing. Unless the economy’s stock of pollutants has reached critical levels such that an ecological disaster would result from an increment in this stock, there is nothing compelling about P for any value of c*. Society m ight conceivably attach no value to environmental preservation, opting instead for the maximal balanced expansion in its m “useful” industries at the rate (1 - c)/c. In this case, the price vector for the first m + 1 industries would be p while a zero price would obtain for each of the n - m antipollution serviceswhich could be provided but which would all remain inoperative. There is, moreover, no compelling reason to assume that, in general, the social surplus must be divided among industries in proportion to the value of their capital which is tied up for one production period, as is assumed implicitly in (2). An alternative principle which could govern the distribution of social surplus through the price mechanism would involve raising the subsistence wage rate by such a uniform percentage-calculated by dividing the physical surplus of each of the “useful” commodities by the supply of man-hours and adding the resultant quantities of each commodity to the hourly wage basket-as absorbs the entire social surplus. The price ratios would then be equal “to the (new) embodied labour ratios” [12, p. xxxvi]. It is, perhaps, also worthwhile noting that even if P is the actual price vector in the economy for the case of c* < 1, there would be no reason to suppose that production would be undertaken in the proportions indicated by X. In other words, the equaliza8 The derivation of the au0 coefficients appears in a forthcoming paper by the author.
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tion of the rate of profit in all sectors, including the antipollution industries, does not imply that the economy is situated on the von Neumann ray. Indeed, an economy which is off the von Neumann ray might experience considerable difficulty in moving onto it. The improbability of P or of X actually occurring does not, however, vitiate their significance as norms against which the actual price and output proportions can be measured. P represents a price structure wherein the marginal social cost of production of each commodity and service is equated to its price. Thus, the divergence between the actual price of a commodity and the corresponding component in P-assuming one primary input,4 say labor, and setting the price of one man-hour equal to 1 for both the actual price vector and for P-indicates the extent to which the actual price of that commodity fails to internalize its externality. Likewise, a knowledge of X could be of particular value to planners contemplating the pursuit of a policy of environmental preservation. For example, if c* = 1, then only production in the relative proportions of X would permit the economy to maintain fully the quality of the environment while achieving simple reproduction in the first m + 1 industries. For c* < 1, X indicates what the output proportions must be if a policy of environmental preservation is to be pursued together with one of maximal balanced growth. A question which might be of interest to planners but which is not answered directly by Eqs. (1) or (2) is the following: Assuming that the economy with technology matrix A is equalizing profit rates in its m + 1 operative sectors, with no antipollution activity being undertaken; assuming further that the dominant eigenvalue of A is c = l/(1 + r) where r > 0; and assuming that antipollution industries for each of the n - m types of pollutants being generated, although not in operation, have a known technology, what is the minimum rate of profit which would render a policy of environmental preservation feasible ? In this context, we mean by “feasible” that the economy could preserve the environment fully while at least reproducing itself on a constant scale in its first m + 1 sectors. In other words, what is sought is a critical minimum rate of profit, say r. such that c = l/(1 + r,) would imply that c* = 1. THE
CRITICAL
RATE
OF PROFIT
To set the analysis in a more definite context, imagine that an economy amends its Constitution at some point in time t, enshrining the following inviolable provision: that the quality of the environment be preserved at the level which obtains at time t; and that any and all polluting agents be assessed a tax per unit of production or consumption equal to the cost to be incurred by the antipollution industries in offsetting the damage inflicted upon the environment by the respective pollution-generating activity. It is assumed that the administrative and enforcement costs of this provision are zero. It is obvious that the proposed Constitutional amendment could be implemented only if the economy were realizing a sufficient surplus prior to t. The pre-t social surplus would have to be greater than or equal to the resource cost of complete 4 The genus of “closed” linear models embracessuch diverse speciesas the von Neumann growth model and the static Leontief model. The former treats labor as a produced commodity and has, in consequence,earned the description of being a model of a slave economy. While one could view labor in the closed Leontief model in this manner, one need not do so. By defining U~O (i = 1, . . . , m) as a “vector of final demand coefficients” [14] labor can be regarded as a primary input; such an interpretation would not alter the structure of the closed static Leontief model. See also [17, p. lo].
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environmental preservation for the amendment to be deemed feasible. The comparison of these two magnitudes is in terms of the pre-t price structure, since the value of the pre-t social surplus, namely px - PAX, which is the same as rpAx, involves the simultaneous solution of r and p; hence, the uniform rate of profit, r, could not be associated with a different price structure for technology matrix A. To calculate the resource cost of preserving the environment in terms of p, the enlarged technology matrix A* is partitioned into four submatrices, consisting of the m + 1 by m + 1 matrix A, the rectangular submatrix comprising the first m + 1 rows of the final n - m columns, A12,the rectangular submatrix comprising the first m + 1 columns of the final n - m rows, AZ1, and the square submatrix consisting of the elements in the final n - m rows and columns is denoted AZ,. Thus, A* appears as follows :
An. A*=[A Azi1 A22
To translate the prices of the antipollution services into real costs in terms of p, let pk = (pm+l, . . . , pn). Since pk must be the social cost of antipollution services at the unit level, the following equations are formed. p” = PA,Z i- pk& = (p-4&1
- AdL.
The expression (pA12) represents an II - m dimension row vector of coefficients which indicate the direct real cost, measured in terms of labor and the m “useful” products at p prices, of operating each of the antipollution industries at the unit level. The square matrix [I - Az2]-’ is of dimension y1- m; its element in row g and column k indicates the quantity of pollutant g which is generated directly and indirectly by the operation of antipollution industry k at the unit level. Hence, the inner product of (PA,,) and the kth column of [I - Az2]-’ represents the total, i.e., direct plus indirect, cost of one unit of antipollution service k, which is to say, pk. Let xk be an n - m dimension column vector of antipollution activity levels which would be required to preserve the environment of the pre-t economy operating at x, and let
x*=[IXk’ X
an II + 1 dimension column vector. Then [AzlA2.Jx*, an n - m dimension column vector, shows the quantity of each type of pollutant generated directly by the operation of the economy at the x* level. Therefore, the social cost of eliminating this vector of pollutants, expressedin terms of the first m + 1 industries at the p prices, would be Thus, the feasibility of implementing the proposed (pA12)CI Am]-‘[A2~42lx*. Constitutional amendment would require that rpAx 2 (pA12)[I - Azz]-1[AzlAzz]x*.5 This provides an expression for the critical m inimum rate of profit, rc, in terms of the pre-t prices: rc = f(pA12)[I - A22]-1[A21A22]x*]/pAx. It will be recalled that if the pre-t rate of profit, realized uniformly in all sectors, is rO,then the enlarged technology 6 The implicit pair of products of initial prices, when the MRT
assumption in our analysis is that the marginal rate of transformation between any is constant. A problem in calculating the real cost of a proposed program, in terms when the program is of sufficient magnitude to alter those prices, is confronted only between any pair of products is not linear in the relevant range.
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matrix A* would have a dominant eigenvalue c* = 1; planners would thus be informed of the feasibility of the policy of environmental preservation from a knowledge of the value of re. However, it is obvious that the information needed to calculate Y?is not less than that needed to calculate c*. FLEXIBILITY IN THE ECONOMY AND THE CRITICAL RATE OF PROFIT It must be emphasized that the critical minimum rate of profit prior to time t which would permit the complete internalization of externalities while allowing simple reproduction to occur would be as high as Y, only in the limiting case of fixed production and consumption coefficients and in the absence of technological progress. The relaxation of these rigid conditions would entail that a lower social surplus would have to be forthcoming from the A economy in order to implement the Constitutional amendment. The nonsubstitution theorem of Samuelson [ 161 and Georgescu-Roegen[7] proved that the choice of an input combination to minimize the cost of production within each industry remains unaltered by a change in the scale of production in any industry or in the composition of final demand, assuming that constant returns to scale obtain. However, a change in the relative price structure, such as would accompany an internalization of externalities, would be likely to induce (assuming substitution possibilities in production) a switch to lower pollution-generating processes.The incentive for such switches is implicit in the realignment of relative prices, since the Constitutional amendment would impose the highest indirect tax per unit of output on the commodity processed by a technique which necessitatesthe most costly environmental restoration. Further, if the possibility of substitution in consumption is admitted, the imposition of a consumption tax which internalizes the resultant damage to the environment would induce utility-maximizing households to shift their pattern of consumption away from commodities which generate relatively high pollution in the act of their consumption. Such factors as the packaging and the extent to which the material of which the product is made is biodegradable, would figure more prominently in the calculus of the prospective consumer. Since technological progress could take various forms, each of which would reduce the resource cost of implementing the proposed Constitutional amendment, the following taxonomy classifies several guises under which advances in the state of the arts might conceivably occur: Al, A2. Bl. B2.
lowering lowering lowering lowering
the the the the
uLj coefficients for some i and j; czigcoefficients for some i and g; a,i coefficients for some g and i; aok coefficients for some g and k.
To interpret reductions in each category of coefficients as unambiguous manifestations of technological progress, it must be assumed that offsetting increases in the coefficients of the same category do not occur. Cases Al and A2 reflect a conventional form of technological progress; in each case, it becomes possible, comparing best-practice techniques, to produce one unit of output (or of antipollution service) at a lower real cost, with gains accruing to society from the direct and indirect effects.
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AND
ENVIRONMENTAL
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Technological improvements of the Bl and B2 variety would reduce the generation of pollution and are thus “preventive” in nature. The actual magnitude of the decrease in pollution-generation would arise from the ensuing direct and indirect effects of Bl and B2. Deliberate changes in the nature of the commodities produced could reduce the environmentally damaging characteristics of the product, yet leave the desirable attributes intact or perhaps even improved. For example, if the consumer’s utility from some commodity is unaffected by its packaging, the a,,, term m ight be lowered significantly by altering the packaging with no concomitant loss in welfare from consumption. Similarly, improvements in the technology of consumption (a la Lancaster) m ight arise from greater flexibility in combining desirable attributes while excluding hitherto jointly-supplied characteristics to which the consumer is indifferent. An example m ight be increased specialization in newspapers, with the classified advertisements and the news being divided into separate entities. As Bonus [3, p. 2601 has noted, the consumer’s waste decision is implicit in his consumption decision if a commodity’s final price includes the entire social cost. In models featuring demand equations, the optimal consumption bundle of consumers would be sensitive, in general, to the level of an indirect tax component added onto the basic prices of commodities to cover the cost of restoring the environment from the damage caused by the act of consumption of the respective commodities. It is therefore clear that flexibility in production or consumption, with substitution occurring in response to a realignment in the relative price structure, as well as various forms of technological progress (occurring, say, at time t) would lower the critical rate of profit needed to implement the proposed Constitutional amendment. Thus, the calculation of re yielded an upper bound for the size of the social surplus which must obtain in the economy prior to time t. This calculated value of rC is binding only in the absence of cost-reducing technical substitutions in production, technological improvements, or adjustments in the pattern of final consumption in the direction of commodities which result in less pollution generation. CONCLUSION A well-established criterion for gauging the growth potential of an economy, the technology of which can be represented by a nonnegative indecomposable square matrix, was reexamined critically. The concept of growth upon which this traditional criterion is based was shown to be ambiguous inasmuch as the environmental repercussions are left out of the account. On the assumption that such an economy possessesan antipollution technology which may be included in an enlarged technology-environment matrix (which is also nonnegative and indecomposable), a criterion to gauge growth potential in the presenceof complete environmental preservation was proposed. Then the magnitude of the uniform rate of profit which would have to obtain in such an economy when it disregards the environment in order for a policy of environmental preservation to be technically feasible was calculated. Finally, a number of factors which would facilitate the implementation of a policy of environmental preservation were considered. REFERENCES 1. K. J. Arrow and D. A. Starrett, Cost- and demand-theoretical approaches to the theory of price determination, in “Carl Menger and the Austrian School of Economics” (J. R. Hicks and W. Weber, Eds.), Oxford Univ. Press, London/New York (1973).
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2. R. U. Ayres and A. V. Kneese, Production, consumption and externalities, Amer. Ecorr. Rev. 59, 282-297 (1969). 3. H. Bonus, On the consumer’s waste decision, Z. ges. ?&&SW. 128, 257-268 (1972). 4. A. Brady, “Proportions, Prices and Planning, A Mathematical Restatement of the Labor Theory of Value,” North-Holland, Budapest (1970). 5. R. C. d’Arge and K. C. Kogiku, Economic growth and the environment, Rev. Econ. Stud. 40, 61-77 (1973). 6. N. Georgescu-Roegen, “The Entropy Law and the Economic Process,” Harvard Univ. Press, Cambridge, Mass. (1971). 7. N. Georgescu-Roegen, Some properties of a generalized Leontief model, in “Activity Analysis of Production and Allocation” (T. C. Koopmans, Ed.), Wiley, New York (1951). 8. L. Johansen, The rate of growth in dynamic input-output models. Some observations along lines suggested by 0. Lange and A. Br6dy, Memorandum from Institute of Economics, University of Oslo (1972). 9. W. W. Leontief, Environmental repercussions and the economic structure: an input&output approach, Rev. Econ. Stat. 52,262-271, (1970). 10. W. W. Leontief, National income, economic structure, and environmental externalities, in “The Measurement of Economic and Social Performance” (M. Moss, Ed.), Columbia Univ. Press, New York (1973). 11. G. Mathur, “Planning for Steady Growth,” Oxford Univ. Press, London/New York (1965). 12. R. L. Meek, “Studies in the Labour Theory of Value,” 2nd Ed., Lawrence and Wishart Ltd., London (1973). 13. J. von Neumann, A model of general economic equilibrium, Rev. Ecou. Stud. 13, l-9 (1945-46). 14. L. L. Pasinetti, “Growth and Income Distribution, Essays in Economic Theory,” Cambridge Univ. Press, London/New York (1974). 15. J. Robinson, “Economic Heresies, Some Old-Fashioned Questions in Economic Theory,” Basic Books, New York (1973). 16. P. A. Sam,ielson, Abstract of a theorem concerning substitutability in open Leontief models, in “Activity Analysis of Production and Allocation” (T. C. Koopmans, Ed.), Wiley, New York (1951). 17. P. Sraffa, “The Production of Commodities by Means of Commodities, Prelude to a Critique of Economic Theory,” Cambridge Univ. Press, London/New York (1960). 18. R. Stone, The evaluation of pollution: balancing gains and losses, Mirwva 10, 412-425, (1972).