young (1991) - is the entropy law relevant to the economics of natural resource scarcity

JOURNAL OF ENVIRONMENTAL ECONOMICS AND MANAGEMENT 21, 169-179 (1991)

Is the Entropy Law Relevant to the Economics of Natural Resource Scarcity?

JEFFREY T. YOUNG

Department of Economics, St. Lawrence University, Canton, New York 13617

Received January 2, 1991; revised February 15, 1991

Nicholas Georgescu-Roegen and Herman Daly have argued that the entropy law imposes an absolute resource scarcity which cannot be overcome with technological change, exploration, or substitution. On the contrary this paper argues that their critique is fundamental ly f lawed. The pessimistic scenario requires a concept of materials entropy which is highly problematic. Materials entropy cannot be def ined independent ly of technology and it is impossible to aggregate over different types of materials to meaningful ly talk about available versus unavai lable matter in the aggregate. Failing a concept of materials entropy the critique fails since the earth is not c losed with respect to energy. Q lvvl Academic press, WC.

Despite the protests of a few heterodox economists, conventional economic analysis of environmental and natural resource issues has largely ignored the entropy law while incorporating the laws of conservation of matter and energy into standard sorts of neoclassical mode ls of production and economic growth. Burness et al. reflect a common attitude when they state that

it seems fair to say that the interface between economic and thermodynamic laws for resources policy, in the sense of something not already reflected in market solutions, is not at all clear. [5, p. 21

In a way this attitude of resource economists to thermodynamic laws is paradoxi- cal. Not only is there a strong resemblance between entropy and classical diminishing returns but also there exists a strong affinity between entropy and the concept of scarcity. These similarities notwithstanding, I shall argue in this paper that the ma instream economists are right. The entropy law does not add anything which is not already considered in economic mode ls of long-run economic growth in relation to the availability of environmental resources.

The crux of the argument revolves around the treatment of material resources. This is because the entropy law as a physical principle applies only in a closed system and then only to energy. However, since the earth is an open system with respect to energy any inevitable entropic decay or dissipation in the earth which sets a long-run physical lim it on economic activity must occur for matter, not for energy. Proponents of the entropy law as a physical constraint on economic growth must show that it applies to matter as well as to energy. Georgescu-Roegen, the leading such proponent, is well aware of this [8]. Since the law is about energy it can be extended to matter only by analogy. The law, therefore, loses its law-like character. Production and consumption are not required to obey this revised law.

Professors Charles W. Howe and Kenneth E. Boulding both read and commented on an earlier draft of the paper. I acknowledge their help and encouragement . Naturally the views expressed in the paper as well as remaining errors are solely my responsibility.

169 00950696/91 $3.00

Copyright 8 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.

170 JEFFREY T. YOUNG

Indeed, as I argue, they do not obey this law, or more specifically, there is no way to know if they obey the law.

The entropy law is also being recommended to us as the basis of a new energy and/or entropy theory of value [S, 51. From this perspective the argument is made that energy efficiency rather than traditional sorts of economic efficiency should guide technology selection and resource allocation decisions. This is an interesting and important issue which ultimately deals with the efficacy of a one-factor value theory and with the philosophical issue of the nature of the concept of value used in economic analysis. It is, however, beyond the scope of this paper. Here I am concerned only with the claim that entropy imposes a long-run, absolute scarcity which technological change, resource substitution, and exploration cannot reverse. I am particularly concerned to stress the extent to which such a claim requires a concept of materials entropy and the validity of such a concept.

The paper is divided into two parts. In the first part I survey some of the relevant literature which deals with the relationship between economics and certain physical principles, namely the laws of conservation of matter and energy and the entropy law. In the second part I construct a simple model of an economy which explicitly obeys all of these laws. In so doing 1 try to construct a strong case in favor of the relevance of the entropy law. However, in considering the role of technological change and the nature of material resources I conclude that the law cannot be extended to cover material resources, even by analogy, and, thus, the case for entropy fails. To show this I construct a simple counterexample in which entropy (assuming it can be defined) decreases in a closed system. I then argue that the distinction made in physics between available and unavailable energy (necessary to the entropy law) becomes highly problematic when applied to matter and that this is the underlying reason why the counterexample is important.

PART I

In a path breaking article Ayres and Kneese introduced the law of conservation of matter into the realm of neoclassical economic discourse [2]. This yielded the important insight that technological external diseconomies are not freakish anomalies in the process of production and consumption but an inherent and normal part of them [p. 2871. In addition, one can use the Ayres/Kneese materials balance to clarify that consumption does not destroy matter, and that, therefore, exhaustion must be an economic as opposed to a physical phenomenon [12, pp. 24-251. If the importance of the conservation principles for economic analysis, especially in natural resource and environmental economics, has been established, the same cannot be said of the entropy law which stands alongside the conservation laws as the second law of thermodynamics. This is indeed a curious phenomenon. If matter and energy are neither created in production nor destroyed in consumption it is logical to conclude that they are dissipated, a point which immediately suggests that the entropy law is intimately connected with the depletion of natural resources and the buildup of pollutants in the environment.

The energy and environmental crises of the 1970s touched off an explosion of interest in the economics of resource exhaustion, resource scarcity, the sustainability of growth, and increasing scarcity of natural resources. Among leading economists contributing to this vast literature only a few have made the entropy

ENTROPY AND ECONOMICS 171

law an important element in their analysis. Georgescu-Roegen is, of course, the leading advocate of the view that the economic process is inherently entropic and that the entropy law is the taproot of economic scarcity with low entropy being a necessary, but not a sufficient, condition, for the existence of economic value [8, pp. 1041-10421. Daly has taken up the same theme in his various works on the steady-state economy arguing that nature really dues impose an inescapable general scarcity (added emphasis) and it is a serious delusion to believe otherwise [6, p. 691. In Dalys hands the entropy law is not just a deeper explanation of the economists concept of relative scarcity. Rather it is the basis of an absolute scarcity which will always increase regardless of the pace or direction of technological change. This in turn leads to the steady-state economy as a necessary policy conclusion in order to m inimize this inexorable trend. Although not sympathetic to Dalys belief in the efficacy of the steady-state economy, Georgescu-Roegen has been very critical of economic growth 193.

If the entropy law is the basis of scarcity and also of an absolute scarcity, then certainly economists should take notice. Surprisingly, such has not been the case. Recent texts in Natural Resources and Environmental Economics either make no mention of the law or pass over it lightly, although the materials balance is usually presented [IO-12, 16, 7, 191. The only exception I am aware of is Pearce and Turner, who consider the entropy law to be a constraint which is not reflected in market prices and must be taken into account by adding a sustainability criterion to the normal models of the maximization of the present value of net benefits [13, p. 241.

Outside of the textbooks the neoclassical models of growth and resource exhaustion have also been silent on the role of entropy in economic processes. There are only a few exceptions. Ayres, for one, has attempted to come to grips with the relationship between the laws of thermodynamics and of economics. In his 1978 book, Resources, Environment and Economics, he observes:

It is interesting to note that the classical economic theory of exhaustible resources as developed by Hotelling, Herfendahl, and others, does predict the exploitation of the highest quality (i.e., lowest cost) reserves first, but has not so far, allowed for the positive feedback between decreasing quality (negentropy) of the remaining resources and the rate of extinc- tion. Nor have the increasing environmental costs of this entropic buildup been incorporated in models of optimal extraction. [1, pp. 46-471.

In subsequent work Ayres and M iller found that for a production function that is consistent with conservation of matter/energy, and subject to the assumptions that both capital and consumption goods embody energy (the ultimate resource), the optimal path leads to a stationary state with finite capital and finite technical knowledge, resulting in maximum technical efficiency less than unity. [3, p. 3701

This presents a stark contrast to typical neoclassical formulations wherein a constant per capita output with an exhaustible natural resource is possible

if any of the following three conditions are satisfied: (a) the elasticity of substitution between natural resources and capital is greater than unity, (b) the elasticity of substitution is unity (Cobb-Douglas) and the share of capital is greater than that of resources, or (c) there is resource augmenting technical change.. the simple fact that resources are finite and are necessary for production, does not imply that the resource-using economy must eventually stagnate and decline. 114, p. 7011; see also [17, 181.

It is relatively easy to show this latter conclusion is erroneous. Although neoclassical formulations of the type Y = AKaLpRY (where (Y + /3 + y = 1 is a typical


assumption) show that R (the flow of natural resources> must be greater than zero for production to take place, they exhibit asymptotic properties which violate the law of conservation of matter. It clearly will not be possible to reduce R to an infinitesimally small value simply by allowing K to increase rapidly enough, regardless of the value of the elasticity of substitution between capital and resources. A capital stock must have more than a vanishingly small flow of material resources in order to produce material output for an expanding (or even stationary) population. And, as Ayres and Miller assume, energy is necessary to produce capital. Seen in this light the Georgescu-Roegen/Daly/Ayres thermodynamic critique appears to have something to offer. However, these results are based on the conservation laws, not entropy. It would be an easy matter to constrain the value of R in the production function such that R 2 R,, where R, is strictly greater than zero. This would certainly not produce any earth-shattering revolution in economic theory, although it may constrain our optimism with regard to the sustainability of economic growth. More importantly, it in no way clarifies the role of entropy in the economics of long-run resource scarcity.

While the erudite mathematical literature has largely ignored both physical laws there is some evidence that economists have come to think of the entropy law as a glorified law of diminishing returns. Boulding has treated it as a phenomenon reminiscent of classical diminishing returns, and I have argued elsewhere that there are important similarities between the two concepts [4, 201. This similarity may account for the cool reception Georgescu-Roegens ideas have received in the profession. Since the Ricardian model of growth leading to the stationary state predates the first appearance of the entropy law by about 50 years economists may implicitly feel a sense of pride in having modeled entropic processes prior to their discovery in physics, and would thus be reluctant to rename an old, familiar concept. More importantly economics would not need the entropy law if it were classical diminishing returns in fancier clothing. However, as I will argue more fully below, they are not the same in all respects. Ricardo is not an important precursor of Boltzmann. Ricardian diminishing returns presupposes a certain order of use of natural resources from a known stock while the entropy law does not require the same kind of ordering assumption, but more on this below.

PART II

It will be useful to place before ourselves a simple model of the economic process which attempts to incorporate the conservation laws and the entropy law [21]. Picture an economy which utilizes two generalized but nonhomogeneous natural resources, matter and energy, in its production processes along with capital and labor. We will assume that the conservation laws and entropy laws impose the following constraints upon the system:

(1) all production requires matter and energy, including the production of labor and capital;

(2) all materials and energy must be accounted for both before and after production has taken place;

(3) matter and energy are constant stocks equal to the total amount of each in the earths crust. At a point in time these stocks are partly in situ and partly dissipated from previous extraction and partly embodied in durable goods (material


stocks only). The entropy law requires the orderliness of these stocks to decrease over time, provided the system is closed.

For the sake of simplicity, I am assuming that the generalized energy resource is embodied in a stock of fossil fuels rather than available as a free flow of solar energy. This amounts to the assumption that our economy is an isolated system in the physical sense that no matter or energy flows between the system and the rest of the universe.

Although neoclassical theory usually treats capital as a produced input, this is not normally the case with labor. However, if our aim is to construct a model of a system which obeys the physical laws of time and matter we must insist on the classical methodology of treating labor as a produced input. Although this may strike the modern economist as archaic or even inhuman since it ignores the preference structure of the supplier of labor, it is undeniably true that in a physical sense human work and know-how cannot be provided to the production process without consuming matter and energy. Thus, we must assume that we have a general equilibrium system of a Physiocratic type which focuses on reproduction in which, therefore, output is also simultaneously input.

In neoclassical terms we might depict four production functions in which input consists of capital (K), labor CL), refined energy (E), and refined matter (M) with each function of the following general form:

Y=f(K,L,E,M,t). (1)

Neoclassical models insert time to capture the process of technological change over time and its effect on the production process. Our task here is to examine in more detail the effect of the passage of time on this system under the assumption that it is in a self-replacing state; i.e., all business and household capital is maintained at a constant level.

The conservation laws and entropy law allow us to formalize this. Let

M,(t) = net addition of material to stocks of durable goods at time t. MS(t) = flow of extracted raw material from matter in situ. ES(t) = flow of extracted energy from energy in situ. S,(t) = stock of material resources. S,(t) = stock of energy resources. D,(t) = matter discharged at time t in the form of pollution which is diffuse

and not recyclable. D,(t) = energy discharged in the form of heat and not recyclable. G(t) = matter discharged in the form of solid waste which is recyclable. AS,(t) = stock of available material resources at time t. AS,(t) = stock of available energy resources at time t. QM = quality index of th e entire stock of material resources. QE = quality index of the entire stock of energy resources. AQM = quality index of available matter. AQE = quality index of available energy.

Since matter and energy can be neither created nor destroyed we have

S.&t) = S,(O) - lMS(t) dt + /dl&( t) dt + iMS(t) dt + kG(t) dt, (2)


which is the materials balance. Verbally it says that all matter extracted from the ground since the initial time period (t = 0) must have been discharged back into the environment or else embodied in other stocks of currently used durable goods such as machines, tables, and automobiles. A similar relation holds for energy,

S,(t) = S,( 0) - /kS( t) dt + jf&( t) dt, (3) 0 0

which implies

S,(t) = SE(O) since j-kS( t) dt = jb,( t) dt. 0 0

It will be helpful to consider another stock, namely, the stock of material resources in situ plus the stock of recyclable matter as the available stock of material resources or negentropy [l, p. 45ff.l. This was defined above as AS,(t). Thus

AS,(t) = S,( 0) - ~ifS( t) dt + lrG( t) dt. 0

(5)

For energy we have

AS,(t) = S,( 0) - j-ES( t) dt. 0

Verbally (5) and (6) state that currently available matter and energy exist in situ as the stock remaining after cumulative extraction is subtracted from the initial stocks in situ. In the case of matter recyclable materials are also considered to be available.

The identities between the original and current stocks of matter and energy reflect the conservation laws, while the distinction between the total stock, reflect- ing the earths entire crust, and the available stocks implies the existence of entropic dissipation as the stocks are used over time. This, of course, assumes that we know what it means for a resource to be available and that the entire crust is indeed available. For the time being I will simply make these assumptions, since to do otherwise would put the cart before the horse, as will become apparent.

Entropic dissipation can be explicitly introduced. Since Q,,,(t) and D,(t) are both greater than zero, the entropy of the original stocks will increase. We could think of this phenomenon of dissipation as altering the quality rankings of the various sources of the resources such that a unit of material or energy in situ would have a higher quality ranking than the same material widely dispersed in the environment. Thus, the process of production, even in a self-replacing state, causes each unit of matter and energy used to become of lower quality. To formalize this a bit, we have

QM = g,(Ms, t), (7) QE = g,(Es, t), (8)


n n

I

M M MM MM MM MM I

M M M M

M M M M M M M M M M

M M M M

FIGURE

where the entropy law asserts that

aQM -


discharged resources, entropy clearly increases regardless of the order in which resources are extracted provided in situ sources are always more orderly, or concentrated, than discharged resources.

It should be clear that as these various indices change over time they will exert important impacts on the various production processes in our hypothetical economy. Replacing the time variable with these indices yields the following general form of the production functions,

Y = f( K, L, M, E, Q, AQ) 7

where Q and AQ are the quality indices for matter and energy. The effect of the AQ indices is straightforward. Lower quality resources in situ draw off progres- sively more labor and capital to mine and process, thus causing diminishing returns in the aggregate. Thus,

ay - > 0. aAQ

The Q indices affect production independently of the AQ indices because of the negative impact of harmful discharges of spent matter and energy on the production process. It seems to me that the effect is qualitatively the same even if there are strict pollution controls. The materials balance tells us that pollution controls do not cause pollution to physically disappear. There will still be discharges although perhaps not as harmful. However, capital and labor will be diverted from the production of other goods and services, producing a diminishing returns situation similar to the case above. Thus

ay - > 0. aQ

It is reasonable to assume that resources will be used from best to worst within the confines of existing knowledge. Moreover, the entropy law asserts that the Q index will always be falling. This is the absolute general scarcity which I believe Daly and Georgescu-Roegen are talking about, and the fact that aY/aQ > 0 indicates the negative impact on growth which falling Q, i.e., increasing entropy, will eventually cause. This I believe is a model faithful to their conception of the economic process, one which clearly indicates a role for the entropy law in economic analysis. If this were the end of the matter the case would be firmly established.

However, as anyone familiar with classical dynamics knows, technological change represents a counterforce to diminishing returns. Significantly, Boulding counter- poses processes which create potential [41. He finds the theory of autopoiesis relevant as an explanation of how order can be spontaneously created in stochastic systems. The application of this idea to economics opens an

intriguing and as yet very little explored field of inquiry. The dynamics of Adam Smiths invisible hand is remarkably like an example of autopoiesis, for it is a process by which order is built out of independent decisions of varying probability. [4, p. 1871

Can technological change be viewed as a spontaneous order creating process; i.e., is knowledge, which is not conserved when it is used (communicated), fundamen-


A bbb

a ab a a a

aa a

bb bb aa

b aa b bb

FIGURE 3

tally antientropic? A straightforward, resource augmenting technological change which increases the output per unit of matter and/or energy input would only change the rates of change of the two quality indexes, causing dissipation to proceed at a slower pace. However, this is not the only type of technological change possible. The most important changes have created resources out of noneconomic material.

This type of case presents a very interesting problem, since it raises a question which I have purposely pushed aside. I have implicitly assumed that we know what negentropy, or low entropy matter and energy, is; but do we? Is it not in fact an anthropomorphic concept intimately associated with what is useful and, therefore, defined by current technology? In reality we do not have a single material and/or energy resource. We have numerous m inerals, fossil fuels, etc. To illustrate the problem, suppose that there are two chemical elements found in ore deposits in situ which represent our material resource. Suppose further that they are desig- nated a and b in Fig. 3 and that initially only a is considered a resource; i.e., there is no known use for b. Figure 3A shows a and b in situ, while Fig. 3B shows that no discharge or dissipation has occurred.

As a is depleted we get the situation of Fig. 4. As long as b is not a resource it is clear that AQ,,,, and QM are behaving as they did before. However, suppose that a technological change occurs which makes b a resource. Is the situation depicted by Fig. 3 or Fig. 4 more orderly, given that b is not useful in Fig 3 but is useful in Fig. 4? Alternatively, suppose that a technology for collecting dissipated a and recycling it becomes available. Which figure now represents the most orderly situation?

bbb bbb a a ab ab

a a a a a a a

a a bb bb bb bb

b b a b b bb bb a a

FIGURE 4 FIGURE 4


In these counterexamples it is very possible for entropy, or our intuitive notion of entropy as disorderliness or unavailability, to be decreasing even though the system is closed. It is, however, open with respect to knowledge which has exogeneously increased.

Energy resources can be reduced to common physical measures of available energy which is then measured independently of the existence of a technology to convert the energy into useful work. This is not the case with matter. Is b available matter when there are no known uses for it? If so, then how can we know that dissipated a is unavailable? The absence of a technology for using dissipated a would not mean it is unavailable matter. The point is that available matter is dependent on the existence of appropriate technologies. It is not a purely physical concept. In the absence of a measure of the entropy of the matter in a closed system there is no way of defining the materials entropy of the system or, assuming such a definition, knowing whether it is spontaneously increasing or decreasing over time.

There is also a classic aggregation problem in applying entropy to matter which does not exist for energy. Without some neutral aggregation principle it is impossible to tell whether a resource system is becoming more or less orderly if there is more than one type of material resource. When one kind of matter is being dissipated in the process of collecting and recycling another, making it more available, is entropy for the system as a whole increasing or decreasing? It is impossible to say.

Attempts to apply entropy to matter go beyond the physical principle of entropy measured in terms of unavailable energy in a closed system and it becomes difficult if not impossible to quantify the concept even in principle. In the absence of such quantification it is difficult to know whether entropy imposes an inescapable, absolute scarcity on the human race or not. Indeed it is impossible even to define the concept.

CONCLUSION

The way the entropy law is being recommended to us borders very closely on the kind of scientism which Hayek and Popper have warned us against. Principles of physical science are being used in ways quite alien to the domain in which they are believed to be valid. In this case entropy is being applied to both energy and matter. What is even worse, in the hands of some popularizers the entropy law becomes a law of universal decay in society, institutions, and the economy [15]. Even in the sophisticated hands of Georgescu-Roegen and Daly a concept of order is invoked to talk about the entropic dissipation of matter in a situation where it can only be quantified if we are talking about a single material resource and a single unchanging technology.

This would not be a difficult problem if the disorder occurs outside the system. Increasing order in a subsystem of a larger open system is perfectly consistent with entropy. Negentropy can be imported as the earth imports energy from the sun. However, the model of entropic decay is not relevant for modeling open systems.

I am led to the conclusion that either the entropic analogy is not relevant for material resources or the system boundaries must be drawn in very peculiar ways. In either case the entropy law is not particularly relevant to the economics of


long-run resource scarcity. If it is confined to energy resources only, as it should be, the relevant system is not closed, although the continual flow of solar energy, being beyond human control, may impose a long-run, ultimate constraint on energy use. This however, is so far into the future that it is hardly relevant to current resource allocation issues. Attempts to extend it to matter fail because of the problems associated with defining available matter in a technically progressive world with numerous kinds of material resources. Provided that the materials/energy balance is satisfied, consideration of the entropy law, though different from classical diminishing returns, adds nothing to traditional models based on the tension between depletion- and pollution-induced scarcity and certain scarcity m itigating factors.

REFERENCES

1. R. Ayres, Resources, Environment, and Economics; Applications of the Materials/Energy Bal- ance Principle, Wiley, New York (19781.

2. R. Ayres and A. Kneese, Production, consumption, and externalities, Amer. Econom. Rev. 59, 282-297 (1969).

3. R. Ayres and S. Miller, The role of technological change, J. Enuiron. Econom. Management 7, 353-371 (1980).

4. K. Boulding, Equilibrium, entropy, development, and auotpoiesis: Towards a disequilibrium economics, Eastern Econom. J. VI, 179-187 (19801.

5. S. Burness, R. Cummings, G. Morris, and I. Paik, Thermodynamic and economic concepts as related to resource-use policies, Land Econom. 56, l-9 (1980).

6. H. Daly, Entropy, growth, and the political economy of scarcity, in Scarcity and Growth Reconsidered (V. K. Smith, Ed.), Johns Hopkins Univ. Press, Baltimore (19791.

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young (1991) - is the entropy law relevant to the economics of natural resource scarcity

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