Shmuel Amir.pdf

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ECOLOGICALECONOMICS

ELSEVIER Ecological Economics 10 (1994) 125-147

The role of thermodynamics in the studyof economic and ecological systems

Shmuel AmirQual it y of the Enrir onment Di cision, Resources for t he Future, 1616 P Street, N . W.. Washington, D C 20036, USA

The Departm ent of Appl i ed P hysics and M athemati cs. Soreq N uclear R esearch Center. YaL,ne. 70600, I srael

(Accepted 23 May 1993)

Abstract

Economic theory has always maintained that economic value is generated solely within the economy where it isfully distributed among the factors of production before being consumed. According to this theory, the economy isan isolated system that does not need flows to pass across its boundaries in support of its steady state (generalequilibrium). From a thermodynamic point of view this idea is unacceptable. According to thermodynamic theory,any open system, which allows flows of matter and energy to cross its boundaries, is capable of maintaining itself insteady state only because it transports &ue from its environment to restore the value that has been consumedwithin the system and dissipated. Drawing on the analogy with thermodynamics. this paper replaces the traditionalsystemic analog of the economy, which is the closed circular flow process, with the steady flow process. Accordingto this analog, any efficient economy is an open system both physically and economically requiring a flow ofeconomic value to maintain its steady state. In other words, an economically isolated system has to be inefficient andis bound to misallocate and overuse environmental resources. Whether the economy behaves as an economicallyisolated (inefficient) or open (efficient) system is an empirical question. However, if real economies are economicallyopen and efficient, and environmental resources are abused due to the economys unrestrained material growth,parts of traditional economic theory, especially those related to benefit evaluation, will have to be modified. Policyrecommendations will be affected in any case because internalization. the panacea of resource misallocations. cannotbe more than a temporary solution. Instead of opening the economy, internalization encloses the harmed resourceand saves it by abusing excessively other environmental resources.

Key words: Efficiency; Environmental externality; Resource allocation; Thermodynamics

1 Introduction

The interfaceeconomic theory

between thermodynamics andhas developed in two widely

different directions. The first direction is analyti-cal, and it has been little explored (Davis, 1942;Samuelson, 1983). It consists of an attempt toexpose the similarity of the theories and to delin-eate the formal relations, in Samuelsons words,that exist between them. Although Samuelsons

Correspondence to Israel. study succeeds in identifying analytical overlaps

0921-8009/94/$07.00 0 1994 Elsevier Science B.V. All rights reservedSSDI 092 1-8009(93)E0063-M


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126 S. Ami r/E cological Economics 10 1994) 125-142

between thermodynamic formalism and neoclassi- rgescu-Roegen, 1979). Thus, the question ofcal economics, it has not generated enthusiasm, whether or not it is necessary to include explicitlydebate, or an agenda of yet-to-be-solved prob- the laws of thermodynamics in economic theorylems. Lismans investigations of this interface led in general, and in the theory of natural resource

him to doubt whether the theory of analogies use in particular, has not been yet resolved.will still produce important or practical results Moreover, an even more fundamental question,(Lisman, 19491, a view that is held by many i.e., whether or not economic theory disregardseconomists and physicists alike (Faber and the laws of thermodynamics, has not been dealtProops, 198.5). with satisfactorily in the literature either.

This view, however, is no more substantiatedthan the view outlined by the second direction inwhich the interface between thermodynamics andeconomic theory has developed. Basically thisdirection consists of an informal claim that eco-nomic theory neglects absolute scarcity as dic-tated by the laws of thermodynamics (Underwoodand King, 1989), and disregards the laws of ther-modynamics altogether (see e.g., Soddy, 1912,1933, 1934; Boulding, 1966; Georgescu-Roegen,1971; Odum, 1971; Daly, 1973). Moreover, it con-sists of the less committing assertion that eco-nomic theory has lost its physical and biophysicalfoundations (Ayres and Nair, 1984; Faber, 1985;Daly, 1987; Faber et al., 1987).

To put matters in proper perspective, it mustbe said that nobody claims that economic orecological systems operate in violation of thermo-

dynamic laws. Rather, the claim is that economicand policy theorists are precluded from suggest-ing appropriate measures to curb the excessiveuse of natural resources because in their theoriesthey ignore constraints imposed on these systemsby these laws. This claim, which asserts that theexplicit inclusion of thermodynamic laws in eco-nomic theory could have generated more efficienteconomic instruments, has not been left unchal-lenged; however, both advocates and critics havenot presented their positions formally, makingthem hard to judge (see e.g., Solow, 1972; Nord-haus and Tobin, 1973; Simon. 1980, 1981). EvenGeorgescu-Roegen, who is critical of the mecha-nistic view of traditional economic theory, statesclearly that one cannot rectify the resulting prob-lems merely by imposing the laws of thermody-namics on the theory. Moreover, he rejects theidea that economic value is related by a definitelaw to common thermodynamic functions (Geo-

To discuss the latter question properly re-quires one to establish a formal analogy betweenthe basic terms of the two theories (Amir, 1987).Since each theory is considered sound by its ownpractitioners, the analogy must be developedwhile the terms of each theory are left intact. Asa starting point, this requires one to recognize thefollowing observations. First, although economictheory only is explicit in assuming agents to be-have rationally (i.e., to optimize), optimizationand thermodynamics are not alien to each other.A well-known approach to thermodynamics de-veloped by Hatsopouios and Keenan (1965) as-sumes that systems undergo changes as long as a(constrained) state function does not reach a sta-ble position. A stable position is a time-independ-ent state that solely determines the value of thesaid function, and this value can always be inter-

preted as a minimal or maximal value of theconstrained function. Thus, although thermody-namics is at most implicit with respect to its useof optimization, economics and thermodynamicsare methodologically analogous. Second, pricesand quantities of commodities in economic sys-tems are the analogs of the intensive and exten-sive variables, respectively, of a thermodynamicsystem. However, to the best of our knowledge,no study of this analogy - including the mostrecent ones (Bryant, 1982; Ayres and Nair, 1984;Proops, 1985; Amir, 1987) - has yet been able toelucidate fully the analogy between an economyand a reactive laboratory beaker. The missinglink for establishing this analogy may plausibly bethat human welfare, and hence the welfare func-tion of the economy, is a nonconserved function(Amir, 1992a). In contrast to traditional economicthinking, human welfare changes when an iso-lated system, consisting of the economy and its


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S. Amir / Ecological Economics 10 1994) 125-142 117

surroundings, undergoes any economic process,including a steady flow process.

This idea is not only plausible, it is also ex-tremely fruitful. Whereas the welfare derived

from an economy in steady state is constant,irrespective of the nature of the welfare function,only a nonconserved welfare function is able todirectly measure the real value of the environ-mental resources that are lost or damaged inmaintaining the economy in its state. For a con-served function, whose global level is also con-stant, this value, by definition, is equal to zero. Itis unfortunate, therefore, that theory alone can-not determine whether the welfare function of aneconomy is conserved or nonconserved. Thisquestion is empirical. The answer to it has to befound in the observed variables of the economy.Fortunately, the theory predicts that the statevariables, the prices, the stocks, and the flows ofthe conserved and nonconserved systems will dif-fer markedly, and provides the equations neededto study these differences. Moreover, the theorydemonstrates that the welfare function of anyefficient system cannot be conservative and that ifthe decentralized free market economy operatesaccording to the rules prescribed by traditionaleconomic theory, it is necessarily conservative

and inefficient. This demonstration immediately

A state-dependent function is said to be conserved if itassumes a constant value when an isolated system, i.e.. onethat does not have any interac tion with its surroundings. isundergoing a process in which its state changes. A system isnonkonsetved if its approach to an equilibrium state or to a

steady state, as the case may be, is guided by a nonkon-served function. Observe that this definition is equivalent tothe more common one that states that a system property is aconserved quantity if it is derived by summation from the

same property of any number of separate systems, whenever

the latter are merged and isolated. Consider systems of reac-tive chemicals that are merged into a system and isolated.Before a chemical process starts, any extensive property of themerged system, conserved or nonconserved, is derived bysummation from the respective properties of the originalsystems. However, when the process ends, the value reachedwill stay unchanged only if the property is conserved. Otherconcepts and terms borrowed from thermodynamics are ex-

plained in any textbook on thermodynamics or in my earlier

studies Arnir, 1987, 1991). Readers in need are stronglyencouraged to acquaint themselves with one of these sources.

implies that the free market misallocates environ-mental resources by producing inappropriate eco-nomic signals. These signals cause the L&e ofthe resources lost in maintaining the state of the

economy to be higher than is necessary. Contraryto common knowledge, even from a theoreticalpoint of view alone, Pigouvian taxes and otherinternalizing measures cannot rectify this misallo-cation without abusing other resources. It is asymptom of the efficient states of the economythat the real value of the inflows is higher thanthe real value of the outflows, so that the realtransactions carried out across the boundariesbetween the economy and its environment arenot balanced. Pigouvian taxes that are set propor-tional to real values cannot be effective unlesscomplemented by mechanisms that will keepmonetary transactions unbalanced as well.

Furthermore, in view of the structural andfunctional analogy between economic and ecolog-ical systems (Arnir, 1987), optimization and theensuing valuation multipliers (biotic potentials)will become cornerstones of efficient resourceallocation in ecological systems as well. Exceptfor rare occasions (see e.g., Fretwell and Lucas,1969), the concept of the biotic potential as aforce that guides the spatial and temporal distri-

bution of biomasses is alien to ecological theoryand has never been integrated into communityand ecosystem models. In addition to providingecological systems with their intensive variables(biotic potentials), our analysis gives rise to sev-eral summary measures that characterize the stateand functioning of economic and ecological sys-tems. Since theory alone cannot specify the exactform of the welfare function, and no law, thermo-dynamic or otherwise, dictates a specific objec-tive function of a system, these measures alsoshould be derived from an empirically testedfunction. Most measures are linear expressions,formed by summing up products of either thestocks or the flows of the system concerned withtheir respective valuation multipliers. This makesthem look like conventional measures of thefunctioning of economic systems. There is, how-ever, one distinction. Conventional measures,both in economics and in ecology, are derivedfrom an accounting system that is forced to obey


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128 S. Amir/ Ecological Economics 10 1994) 125-142

a law of value conservation, and they manifest theprinciple of a balanced budget. If the summarymeasures of a nonconserved system are con-structed to be proportional to the real values, the

resulting expressions, whether they are monetizedor not, must satisfy the condition that transac-tions remain unbalanced in steady state.

To derive the results described above, thispaper pursues the following objectives: (a) topresent an analogy between economic and ther-modynamic theories; (b) to examine this analogyand establish its validity for economic and ecolog-ical analysis; and Cc) to study its implications forthe analysis of the optimal use of environmentalresources.

This paper is multidisciplinary and touches onthree different scientific fields: economics, ecol-ogy, and thermodynamics. To help readers, itavoids rigorous mathematical presentations andfocuses on the main issues. It is not intended tobe analytical, but to discuss the issues compre-hensively without presenting formal mathematicalproofs.

In the first of the following sections, a formalmodel of an economic (ecological) system is pre-sented. The next section analyzes the steady statebehavior of this system and explicates the differ-

ences in the analysis between the present and thetraditional economic theories. In the last section,the implications of this analysis for the study ofthe efficient use of natural resources is discussed.

2. The model

In this section we present a model of an opensystem. The model represents any economic orecological system starting from the individualagent (organism1 and ending with the globaleconomy (ecosystem). In order to render theanalysis more accessible, the assumption is madethat the system may be represented by a general-ized-production-, linear-activity-type model (vanNeumann, 1945; Koopmans, 1951; Malinvaud,1953; Gale, 19601. This assumption does not re-strict the generality of the model and the derivedconclusions.

Let there be in the system and its surroundings

SurroundingsOpen Boundar

/,,,,,,,,,,,,, ,,,,,,,,,,,I , , l, ,

K:CX

4 4Yi>0 , BX - AX : Yi m. A commodityis a chemical compound or any mixture of suchcompounds. An activity is a linear way of trans-forming commodities into other commodities; itmay be considered to be an unscaled chemicalreaction. Whatever the system is doing must be

done by employing activities (Lancaster, 1966;Amir, 19791, so that the term activity applies tothe exchange as well as to the production andconsumption of commodities (and services). Asubsystem may be any part of the original system:individuals, firms, industries, economic sectors,national economies, populations, guilds, commu-nities, and general ecological assemblages. Thedefinition of the subsystems may change accord-ing to our study goals. However, all systems andsubsystems are thermodynamically open, and theyexchange matter and energy with their surround-ings at the same time that they operate activities.To simplify notation, we may henceforth disre-gard the subdivision of a system into its compo-nent subsystems. Alternatively, we may assumethat each subsystem has only one activity.

Let Xi be the level of the jth activity, b, bethe amount of commodity i produced by the jthactivity (per unit of time and activity), and aij bethe amount of commodity i consumed by the jth


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activity (per unit of time and activity). Denote byY (YE Em) the flow of commodities associatedwith the system (Fig. 1). If Y. > 0, the ith com-modity flows out of the system. If Y < 0, the ith

commodity flows into the system. Let d K (d K EE) denote the change of the stocks of the sys-tem during the production period. dKi is positivefor an increase in the ith stock and is negative fora decrease. Thus, K , denotes the stock of the ithcommodity held within the boundaries of thesystem.

Viewing activities as chemical reactions, inwhich products (outputs) are formed from reac-tants (inputs), we associate the inputs to thereaction with the stocks K, and the inflows -Y-during the period of reaction dt. Hence,

AXdt< -Y- dt+K,. (I)

Similarly, we associate the outputs with the finalstocks K, + , and the outflows Yc. Hence,

BXdt>Y+ dt+K,+,,,, (2)

where A and B - the input and output matrices,respectively - are m x .I matrices and X E E/,.

Recalling the definition of dK and dividingthe equation by dt, we derive a fundamentalexpression for the operation of the system.

BX-AXa dK/dt +Y,where Y = Y+ + Y-.

(3)

An activity cannot be operated in a vacuum.Stocks of commodities are needed as well asflows. Let cij be the amount of commodity ineeded per unit of process j. We write:

CX


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130 S. Amir / Ecological Economics 10 1994) X25-142

merely an accounting medium, it cannot flowacross the system boundaries.

Assuming W is linear homogeneous in K, wecan write W = c~(t)p(X t)K where it is assumed

that the derivative of W with respect to Kj isap, E E. The net gain in welfare (profits or sav-ings), 7r, may be written as follows:

x( K, t) = dW/dr = 6W/6t + n(d,dr)( xp;K,).

6)

where SW/St = pK and & = da/dt. Eq. 6 be-comes:

+ C pi + C 6p,/6Ki)K, ii,I 1 I )

6)

where 6, = 6p,/6t is the partial derivative of p,with respect to t and K, = dK,/dt.

3. Steady state analysis

This section is divided into two parts. In thefirst part, the optimality criterion of the presentmodel is presented, interpreted and analyzed. Inthe second part, the process of discounting isintroduced and its role in regulating the activitiesof the system is delineated.

3.1. The optimafity criterionIn steady state the vectors dt )p( K, t) and Y,

of intensive variables and flows. respectively, aretime independeat, and the stocks K stay un-changed, i.e., K = 0. Every commodity must belocated somewhere, either in the system or in itssurroundings. If it is placed only in the system, itis part of the stock vector K. Hence, in steadystate it must be completely recycled. If it is placedonly in the surroundings, it enters into the systemor leaves it as a flow, which is included in theflow vector Y. Hence, in steady state it will flow

at a constant rate in one of two directions, intothe system or out of it. If stocks of a givencommodity are available both in the system andin its surroundings, in steady state there is no

change in the stock within the system, but possi-ble losses or gains may be balanced by flows thatcross the boundaries rather than by the stockbeing fully recycled.

Consider an unconstrained change of W(K t>.Welfare will be time independent, assuming anypath is possible, if the net gain r is maximized,and the maximum of r, i.e., r* equals 0. Sinced = 0 in steady state, r is given by Eq. 6 asfollows:

rr(K, t) =6W/St+ ;;K;

=(Y{(cS/(Y)~K+J?K}. (6)

A change in welfare can be brought about intwo ways. First, it can be brought about by earn-ing income I, i.e., an increase in welfare mea-sured by the accounting value of the outputs andincluding the revalue of the stocks and the valueof the outflows. Second, it may be brought aboutby incurring costs E, i.e., a decrease in welfaregiven by the accounting value of the inputs. Thus,we define:

dW=rrdt=Idt-Edt

=(r(pBX dt -p/IX dt). (7)

The maximization of WCK, t) can be brokeninto two independent problems: a linear pro-duction problem and a nonlinear consumptionproblem. The production problem is that ofmaximizing the value of the net product. Dueto Eqs. 3 and 7, this product is given as follows:

p,BXdt -p,mdt =~,+dtK,,dr -P,K, +P,Y dt,

8)

where pr and prtdl are the price vectors of thecurrent and the next period, respectively. Assum-ing plcdr =p, + dp, =p + dp, Eq. 8 may be writ-ten as follows:

pBX-pAX=;K+p@+Y). (8)

Observe that the right-hand side of Eq. 8 is


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131 S. Amir / Ecological Economi cs JO 1994) 125-142

on the circulation of this accounting medium.According to Eq. 12, the physical stocks withinthe system remain steady. The only sources of apossible change are the flows Y. These flows

cannot be avoided in steady state because even inthermodynamically closed systems the flows oflight and heat continue. These two flowshave no matching stock equations because lightis derived from an external source, and heatflows into an external heat bath. When the con-straints of the optimization problem are satisfiedwith equalities, light is completely used by thesystem and any heat generated leaves the sys-tem. However, the heat generated is not neces-sarily equal to the light used. Light andheat differ, and cannot be forced to be equal.Thus, the answer must be formulated in the fol-lowing way. If value is real, by definition, itcannot be accumulated in or depleted from asystem in steady state (Keenan, 1941; Denbigh,1951; van Wylen, 19.59). Hence, in a closed systemthe value associated with the incoming lightmust be equal to the value associated with theoutgoing heat. The extension of this answer toany open system in steady state will simply re-quire that the following equation is satisfied:

qY=O,(14)

where the qjs are the values per unit of theflows of the Ys. This equation asserts that valueis conserved, and it may be called the law ofvalue conservation.

If, as suggested above, u* Y equals zero, thenU* Y = qY, and the accounting medium is subjectto a global conservation law. This is shown asfollows: The amount of accounting medium in thesurroundings does not change because u * Y = 0.Since the basic solution is efficient, all the 5,shave the same sign (Dorfman et al., 1958), i.e.,they must be equal to zero. Therefore, the p,sand the amount of accounting medium within thesystem do not change either, i.e., the accountingmedium is globally conserved.

There are two problems with this solution.First, Eq. 14 is not part of the optimization prob-lem in the first place because we have taken intoaccount all observed flows and stocks, and wehave not been able to observe any (real) flow of

value independent of light, heat, and mat-ter. Second, there is no law whatsoever, physicalor otherwise, forcing u*Y to take certain valuesin the steady state. If u * Y f 0, not all the 5s can

be zero. Actually, since the basic solution is effi-cient, they all will have the same sign, eitherpositive or negative.

As a result of the optimization problem andthe fact that d = 0, W(K, t 1 is constant in steadystate. Hence, if W(K, t) is not a conserved func-tion, u *Y differs from zero, and global changesin welfare, given by u*Y, must be attributed tochanges that have occurred in the surroundings.This implies that the fact that W( K, t) is constantin steady state has nothing to do with whether ornot it is a conserved function and U* Y = 0.Therefore, it is important to note the followingpoints. First, steady states satisfying the condi-tions u* Y # 0 and fi # 0 cannot be excluded.Second, the function U* Y measures the net real(w el fare) L-due of the resources that are takenfrom the environment or disposed into it in sup-port of the steady state, i.e., u*Y is a measure ofthe environmental cost of maintaining the econ-omy in steady state. Third, if W(K, I) is a con-served function, u*Y is equal to zero, and noenvironmental cost is involved with maintaining

the economy in steady state.As a consequence of the preceding discussion,

W(K, t) will be a conserved function and will becalled an internal energy-like function if 5 = 0,i.e., U* Y = 0 in steady state. If welfare is con-served, we face a particular case of the first lawof thermodynamics. This law says that, with re-spect to energy-like functions, any change withinthe system (whether or not the system is in steadystate) is matched by an opposite change in thesurroundings (cf. Eq. 12 after a zero is substitutedfor 8). However, Wt K, t) does not have to be aconserved function. If it is not, fi f 0. In this case,W(K, t) is called a free energy-like function (i.e.,in steady state u * Y G 0 whenever p > 0, and u * Y2 ;O whenever p < 0) or an entropy-like function(i.e., in steady state u * Y G 0 whenever p < 0, andu * Y 2 ;O whenever p > 0). Note the essential roleof the qualifier like, which has been added tosignify that W(K, t) does nor have to be a ther-modynamic function.


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S. Ami r/ Ecological Economics I O 1994) 125-142 133

If u * Y # 0 we face the second case:

value = free energy

= abstract (accounting) money. (13)

Since the accounting medium is a ghost, noth-ing real is changed in the system, which is claimedto be in steady state. However, we still have toreconcile two facts, i.e., that 6 may differ fromzero whereas p is a constant. The solution isfound in the process of discounting.

3.2. The discounting process and efficiencyThe present model departs from the main body

of economic theory in not assuming that INK, t)is a conserved quantity, This departure allows 3

to differ from zero, and the last assumption keepsEq. 12 from becoming trivial. Hence, Eq. 12 canbe used as a single constraint, summarizing theproductive side of the model, in the maximiza-tion of W(KJ t). The other part of the problem,the consumption problem, can now be writtenas follows:

The first-order necessary conditions for a max-imum are:

mF{W(K, f): fiKO,and m= -u*Y>O.

6W (K, t)/6Kj- -~8~~0, i= l,..., m, ( 16)

where u > 0, the Lagrange multiplier, is equal to6W(K, t)/6m.

Solving these equations for the K,s and C, andcomparing the result with the definition of thep,s and with the value equation, the solutioncan be closed, provided the following equationsare satisfied:

O


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134 S. Am ir /Ecological Economics 10 (1994) 125-142

that fi = 0 in steady state and W(K t) is a con-served function. 7

By assuming that fi = 0 in steady state, eco-nomic theory has ignored the possibility that 5 # 0

and that W(K t) is a nonconserved function. Italso has discounted the possibility that the follow-ing assumption, which now we are ready to make,is always true, and can become a law of theeconomic process. For any change of state of theeconomy (ecosystem) and any nonconserved wel-fare function W( K, t 1, the weak inequality f iK > 0is always satisfied. Moreover, an equality sign ispossible only if the process that leads to thechange of state is reversible, i.e., is completedwithout leaving any change in the surroundings. s

In the present context of a steady flow process,this assumption means that while the value of theoutputs is already embodied in the value of theinputs for a maximizing function, the value of theinflows is higher than the value of the outflowsfor any real process. In the more general case ofa growing open system, this assumption impliesthat the real value of the resources withdrawnfrom the environment is always higher than thereal value of the stocks incorporated in the sys-tem during the same period. Equipped with thisplausible assumption. we turn to the last stage of

our analysis.One question still remains: What is the physi-

Other substantial parts of economic theory also maintain

that economic welfare is a conserved quantity. No basis or

justification for this assumption i\ ever provided. In general

equilibrium theory, the assumptton IS made that all inputs to

the production process are variables. i.e.. the stock vector K

for the productive sector is equal to zero. Since the economy

must contain some stocks to operate. as is evidenced by the

initial holdings of the consumers. but the budget constraint

does not include a term for fiK. the assumptton is. again. thatc = 0, implyi ng welfare to be a conserved function. The cl aim

that value is a conserved function is explicitly made only in

one place Dorfman et al.. 1958, p. 322). where, surprisingly,

the value of the economy has become a constant irrespective

of its state. which mi ght be growing. declining. or remaining

steady. Very recently, this claim has been repeated with

regard to the same van Neumann economic growth model

Samuelson, 1990), which essentially describes an isolated

economy in no need of any surroundings for its growth and

survival.

cal meaning of the discounting process. Thisquestion has been pondered by Amir (1983).Consider the economy or the ecosystem as eithera cyclic engine or a steady flow process. In steady

state any sequence of chemical reactions can beviewed in either way (Denbigh, 1951). The econ-omy produces outputs from inputs and returns tothe input stage after the outputs are consumed.During this cycle the economy is absorbing mate-rial resources and light from its surroundings.The material resources become different materialresources, and the light is emitted as heat. Effi-ciency is a measure of the initial value that hasbeen transformed successfully into the finalvalue along the cycle. It is defined as E =-uy+/uy- = (fiK + uu-)/uY-= 1 +BK/uY_.

The efficiency of the system increases with thelength of the cycle. The exact dependency is notof any importance, but its extent is limited be-cause j? 2 0. Thus, r( K, m, t) = p, /8, < m and E< 1 for any real economic process. To increaseefficiency, f iK must be decreased without a con-comitant decrease of uY-. Since a decrease in Kwill affect SK and uY- similarly, the effectiveroute is to decrease i; by slowing down the pro-

Although several equations have to be slightly modified if

the assumption of footnote 5 holds. this law and other basic

concepts presented in the paper remain valid. To see this

point, note that Eq. 8 would have to be rewritten as

a,p,BX df -rr,p,AXdr

,a r+JlPl+dr K r+*r -Y,P,K, +a,p,Ydf

or

apBX - apAX - apY > 6pK + a;K + npd.

making the expression c p + ab)K + apti + Y )- crp(B -A)X the objective function of Eq. 9. Eqs. 12 and 12 become(Gp+a;)K* +apt?* = up(B-A)X-u*Y and ap(B-A)X * = u * Y respectively. However, the original equations

remain valid because once Eq. 16 is reached. i; has to bedefined as p(A - E)C-. Hence, apt - B)X =abK andregarding ;K > 0 to be an expression of the law of theeconomic process is equivalent to claiming that p(A - B)X >0 serv es this purpose. Given the last equality, the definitionsof conserved and nonconserved functions, the discussion on

the efficiency of the economic process, and other conclusions

are left intact, although the integrand in Eq. 18, which now

should be read e -@p(K rH(B - A)X - Yldr, and Eqs. 20and 21, which now include dB - A)X(Sp/GK) as an addi-tional term, have to be inconsequentially changed.


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S. Ar k/Ecol ogical Economics 10 1994) 125-142 135

o j ; turnovertlme

Fig. 2. The optimal period of production of an open system in

steady state.

cess. This is achieved by increasing the complex-ity and roundaboutness of the process and bywidening its capital base (Fig. 2). At any givenmoment, however, the extent of roundaboutnessis constrained by the rate of time preference.Since it is assumed that the present is preferredover the future, the rate of time preference j? ispositive. According to Eqs. 17 or 21, the cycle

length (turnover time or period of production) isconstrained at the optimum point because7(Ic m, f) must equal l/p for maximum effi-ciency to be achieved. At the point of maximumefficiency, - f i K is minimized, 14Y is maximized,and -J?K * = u* Y. Higher efficiencies are ob-tainable only if the rate of time preference issomehow decreased. This will allow slower pro-cesses - which are more complex, roundabout,and capital intensive - to take place.

It is important to understand two points. First.the moment we realize that W(K, t) may be anonconserved function, we must also see that theway the sum - f iK + u* Y is divided between its

) Based on this fact, some may argue for a biological or

perhaps a thermodynamical basis for time preference, but this

is not what has been meant by claiming that economic theory

ignores the laws of thermodynamics.

terms -5K and u*Y is path dependent whereasthat sum is always equal to zero in steady state.Given the stocks of the economy. the economicprocess can be carried out in various ways, most

of which are inefficient. The efficient way equatesthe rate of time preference p to p(K m, t).p(K m, t)= 1/7(K, m, t), and dK, m, t ) is thevariable that guides the response to the physicalenvironment. 7( K, m, t) is determined independ-entZy of j3. It is the average time it takes for a unitof Y- to circulate in the system until it shows upas a unit of Y+ - that is, the period of productionof the economy operating as an irreversible steadyflow process. Second, the economy is not merelya reactive beaker through which a steady flowprocess is forced, and W(K, t) is not a simplethermodynamic function. Hence, the optimumreached is of a social (ecological), rather than of aphysical, importance, and Prigogines assertion(1961) that thermodynamic entropy productionis minimized in steady state is unlikely to beapplicable in the present context. However, withrespect to the welfare function that guides theeconomy in question, it can be said that, at theoptimum, the loss of welfare is minimized, pro-vided welfare is a nonconserved function.

We now turn to an examination of the neces-

sary role played by the last condition which as-sumes welfare to be a nonconserved function.Assume for a moment that W(K, t) is a con-served function. This assumption implies that 6= 0 and u*Y = 0. The only way to satisfy Eq. 17with p > 0 is to let p(K, m, t> approach zero anddK, m, t ) approach infinity. Assuming the pre-sent is preferred over the future, /3 > 0, and Eq.21 is satisfied by equating p to (~/u,MK *Y/~?K,for every i. This means that U* Y is not a maxi-mum, l/p does not satisfy Eq. 17, and the result-ing state is not efficient. Moreover, as the follow-ing argument shows, this state is also intertempo-rally inefficient.

The only way to satisfy both Eq. 17 and Eq. 21when W CK, t) is a conserved function is to dis-miss time preference and to equate p with zero.If W(K, t) is conservative, holding a positive rateof time preference is myopic. This rate can beforsaken with no welfare loss. No sacrifice isincurred by anybody if p is reduced to zero and


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136 S. Amir / Ecological Economics 10 1994) 125-142

the economic process is slowed down. As thisprocess continues, u * Y is maintained at its zerolevel, and K and W(K t ) can be increased at nosocial cost until B = B( K, m, t ) = 0 and T( K, m, t >

approaches infinity. When the final state isreached, the transformation of Y- to Y+ isaccomplished by passing from one activity to an-other along a definite sequence in a mannersimilar to that suggested for a sequence of heatengines by Ondrechen et al. (1981). Since eachactivity takes an infinite amount of time to becompleted, the resulting process is reversible anddoes not affect the systems surroundings. No lossof welfare is incurred, since no free energy-likeentity is consumed and no entropy-like entity isgenerated and dissipated. When the cycle iscompleted, not only the internal energy-like en-tity, but any value function is globally conserved.Given this situation, U* Y = 0 and 6u*Y/6Kj = 0irrespective of the welfare function. In the my-opic case, which is identified with the reversibleand unrealistic case. conservative and nonconser-vative criteria coincide and the resulting unitvalues are proportional.

Real processes are finite. and the activities inthe said sequence must be completed in a finitetime. Moreover, in the belief that real sacrifices

are involved, i.e., that II* Y is not constant andthat it may have to change as the process contin-ues, people will stick to their temporal prefer-ences which are represented by B > 0. In thiscase, true welfare is a nonconserved function.However, due to Eq. 21. d,/p, = PC , m, t) = p,and the turnover time T( K, m. t ). which is de-rived from Eq. 17. equals l/B. To satisfy Eq. 21with i;, = 0. the average period of production inthe case in which the welfare function is con-served is defined as 1 B. Since (l/u* )6u*Y/6K, = 0 in one case and (l/u,*)Su* Y/SK, = /? > 0 in the other case, the twosteady states. the one guided by the noncon-served function and the one guided by theconserved function, differ but share the sameperiod of production. Hence, in the initial state,the value u * Y as derived from the nonconservedfunction is not maximized, - f iK * is not mini-mized, and a process can be found that allows theproduction period to remain unaltered while the

flows decrease and the stocks increase. Thismeans that the initial steady state is again in-tertemporally inefficient. Assuming that theeconomy behaves efficiently, it cannot be guided

by a conserved function.This statement does not mean that, in steady

state, mass, energy or monetary budgets are notsatisfied. These budgets are automatically satis-fied when the steady state is reached becausethey are based on the idea that the entire valueof the outputs is always incorporated into thevalue of the inputs. These budgets cannot guidethe system because they satisfy the condition UY+bK = 0 identically when J? = 0, whereas theguiding function and the unit values this func-tion gives rise to satisfy the condition UY + {K = 0only at the optimum. Take mass for example.Commodities are composed of other commodi-ties, and their composition is assumed to be fixedboth in terms of the more elementary commodi-ties and ultimately in terms of the basic chemicalelements. Hence, if 9; denotes the mass of theith commodity, it is fully determined by the com-position of ith and the mass of its components.Since chemical elements are neither destroyednor formed in chemical reactions, it must be truethat q(Y+dt + K +,,,I = TBXdt = qAXdt = q(K,

- Y-dt). Hence, q( Y + K ) = 0. In steady stateR = 0 and qY = 0. The same argument applieswhen qi measures the energy or the fixed mon-etary value of one unit of the ith commodity.Therefore, the equation qY = 0 is satisfied insteady state, irrespective of the value of u * Y. Asa constraint it is more than superfluous if, inaddition, u * and q are required to be propor-tional. This requirement leads to a system thatmay behave efficiently to act inefficiently.

Similarly, forcing the economy to behave con-servatively by requiring that real (welfare) valuesand exchange prices be proportional, is bound tocreate inefficiencies and resource misallocations.The behavior of the decentralized free marketeconomy, if in fact it follows traditional economictheory, provides an example of this case. Con-sider this economy when equilibrium is reached.Economic goods are positively priced and arecirculated within the economy between the pro-duction and consumption sectors, whereas flows


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S. Amir / Ecological Economics IO 1994) 125-142 137

that either originate or end up in the systemsurroundings are priced at zero. Denoting theprice vector of the decentralized economy by pand the respective flow vector by Y , the result is

pY = 0 (y = 0 if p; > 0, and p; = 0 if yi # 0).Traditional theory assumes that real (welfare)values and exchange prices are proportional sothat p = u = 4~. Hence, pY= uY= 0, and thefunction W(K, t) that corresponds to the processof the decentralized market economy is con-served. Since conserved systems cannot be effi-cient, either the decentralized market economybehaves as prescribed by the theory and is ineffi-cient, or it is efficient but does not follow thetheory. If empirically the economy is found to beefficient, those aspects of the traditional theorythat are based on the proportionality require-ment, including most aspects of benefit evalua-tion, will have to be abandoned or at least modi-fied.

rium analysis will show the resulting valuationmultipliers to be the steady state (equilibriumin economic terminology) prices of a multi-com-ponent system. This approach is particularly sig-

nificant for studying aggregates of partially inde-pendent open systems, e.g., natural ecosystems,for which the existence of exchange prices oreven of thermodynamic-like potentials in steadystate is not self-evident (Amir, 1979, 1987).

4. Discussion

The observation that general equilibrium anal-ysis is useful for the study of natural ecosystems isimportant on three counts. First, in this way asingle accounting framework for the various com-ponents of any open system can be established.Components are integrated through the use of acommon set of valuation multipliers (the US andLS). Although not directly observed, these multi-pliers are computable as functions of observedstocks and flows. In this way, the accountingframework generates several computable ecoindi-caters that define states of efficient resource allo-cations, and provides policy and economic ana-lysts with the means to estimate the value of thenatural capital (Amir, 1989).

This exposition presents the main features of Second, it provides a basis for the existenceopen systems and analyzes their (moving) steady and determination of a steady state based on thestate behavior. The analysis applies to any open principle of system autonomy, which states that

system, ecological or economic, because these no subsystem can be completely controlled bysystems are analogous structurally and function- other subsystems and that any steady state, ifally and behave similarly (Amir, 1979, 1987). In reached at all, must be maintained in a decentral-addition, similar behavioral principles are pre- ized way. In this context, it is important to notedicted for these systems based on the consistent the possible consequences of the alternative,parts of two independent theories: neoclassical fully controlled, approach. To understand whyeconomics and thermodynamics. The analysis these consequences arise, it is sufficient to recallshows the valuation multipliers (efficiency prices, that the immediate surroundings, i.e., the envi-biotic potentials) to be the intensive variables of ronment as discussed in economics, are only parteconomic and ecological systems. They are the of the overall surroundings of the economy. Ifthermodynamic-like potenrials of the system, these overall surroundings are divided into oneand like thermodynamic potentials in physical part. called the inner surroundings, that com-systems, they are not immutable constants of pletely envelopes the economy within environ-nature. These potentials are present-value prices mental open bounds, and a separate part, calledthat are system and state dependent and that are the outer surroundings, that does not interactdetermined as-if an optimally devised plan has with the economy at all, then the flows of thebeen executed by the system. Although the analy- inner surroundings are divided into two compo-sis is based on the maximization of a single wel- nents. The first component, denoted by Y,,, de-fare function, its extension to many independent scribes flows that cross the boundaries of thesubsystems, as was shown by Arrow and Debreu economy. The second component, denoted by(1954), is immediate. In this case, general equilib- Y,,, describes flows that do not cross the bound-


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138 S. Atnir/ Ecological Economics 10 19941 125-142

aries of the economy. In steady state, the condi-tion UY G 0 must be satisfied by each system withrespect to its boundaries since both the economyand the inner surroundings are open systems.Hence, the lower the value of uYce is at theboundaries with the economy, the lower the valueof uYes is at the other boundaries of the innersurroundings (uY of the inner environment isequal to uYe, - uY~~). By definition, these bound-aries do not have any interface with the economyand are left uncontrolled. Since the dynamicversion of the fundamental equation of the opti-mization problem (Eq. 12) must be satisfied byany open system that undergoes a moving steadystate process, if not enough external stocks areavailable near these boundaries of the inner sur-

roundings to make uYes sufficiently negative, thesaid requirement cannot be met and the outersurroundings start to disintegrate as indicated bythe increasing globalization of todays environ-mental problems.

Third, since the system is less constrained whendisequilibrated, its convergence to steady statealso has to be achieved in a decentralized way.Although the mass of a certain mineral or metalmay be held fixed at severe regulatory costs, thealternative of maintaining mass balance over the

entire economy is not practical. Neither this al-ternative nor any other global principle, such asthat of energy conservation, can provide recourseagainst the possible breakdown of the system dueto efforts forcing it toward the steady state. Openmacroscopic systems are not subject to anyconstraint other than the resource constraintsgiven by Eqs. 3 and 4. If these systems areguided by nonconserved functions and are inprinciple efficient, they do not have to obey thelaws of conservation by keeping their mass orenergy content constant while approaching a

steady state. In fact. they are precluded fromreaching efficient states if required to obey theseadditional constraints.

Claims have been made that economic theorydisregards the energy and other thermodynamicconstraints that are placed on real systems. Theseclaims are unsubstantiated. UY does not have tobe a thermodynamic function. Even if it were, itis not an independent constraint. No independent

constraints exist, other than those specified byEqs. 3 and 4. Other constraints are derived con-straints. They do not have any significance with-out the production side of the system, whichtransforms the resources into a single accountingmedium.

Like any thermodynamic value function, if se-lected to guide an efficient system. WK, f 1must be finite irrespective of the combined size ofthe system and its surroundings. Implicit in theassumption of traditional economic theory thatno economic value flows across the boundariesof a steady state economy is another assumptionthat the surroundings are capable of providinginfinite welfare. Hence, a claim may be made infavor of the idea that economic theory ignores

absolute scarcity (Underwood and King, 1989).However, W(K, t> is not a real entity and, cer-tainly, it is not an independent resource. Thus,economic theory does not ignore either relativeor absolute scarcity as much as it is blind to thefact that human welfare is not likely to be aconserved function. Ignoring this possibility, neo-classical economics explains the behavior of con-served systems only, which are either economi-cally isolated and inefficient or reversible andunreal. Thermodynamics is a wider theory of

value than neoclassical economics. It explains thebehavior of any efficient system, conserved ornonconserved. If, from a methodological point ofview, the analogy with thermodynamics is essen-tial to the study of economic behavior, i.e., ifhuman welfare is a nonconserved function, it isimpossible to sustain welfare without incurringsome environmental costs (Amir, 1992b). There isno free lunch not only within the economy, as isrecognized by traditional theory, but globally aswell. In this sense only, economic theory hasignored absolute scarcity.

The fact that the laws of thermodynamics donot require economic systems to be in steadystate, let alone any particular steady state, doesnot mean that the analogy between thermody-namics and economic theory is fruitless or with-out implications for economic policy. To examinethis point we have to note differences, as well assimilarities, between the theories. The theories ofthermodynamics and neoclassical economics dif-


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S. Amir / Ecological Economics 10 1994) 125 -142 130

fer in one important respect. In thermodynamicsthe boundaries of the studied system are prede-fined. In economics the boundaries are delin-eated once the system reaches a state of eco-

nomic equilibrium. This fact bears both favor-able and unfavorable implications.

On the positive side, it must be admitted thateconomic theory is richer than thermodynamicsin providing functional rules for the distributionof matter among component subsystems. On thenegative side, a decentralized, free market econ-omy necessarily isolates itself, i.e., it behaves con-servatively if it follows traditional economic the-ory. This theory assumes that anything of eco-nomic value is incorporated info the system, sothat whatever is left in the surroundings does nothave any economic value. Our analysis shows thatrequiring real (welfare) values and exchangeprices to be proportional and insisting that trans-actions be balanced imply that welfare must be aconserved function. Although the economy inter-acts with its surroundings, and the flows thatcross its boundaries are essential for its survival,they are considered economically valueless. Thisis the essence of all environmental externalitiesand the crux of a common difficulty that has ledsome economists to believe, without ground. that

the economy is self-sustained and others to be-lieve. equally without ground, that the economyhas lost its (biojphysical foundations. We nowturn to address the policy implications of thiscommon difficulty.

Several facts are clear. First, a state of eco-nomic equilibrium is a steady state. It is main-tained by flows that might be thought of as eco-nomically irrelevant but that, nevertheless. areabsolutely indispensable for the survival of thesystem as an active entity enabled to maintainwell-defined boundaries around its stocks. Sec-ond, modern environmental problems, such as airand water pollution, deforestation, and ozonedepletion, have become part of our daily experi-ence. Their causes are easily pinpointed to belocated in our economic activities. Although theproblems mentioned are accompanied by eco-nomic growth and development, to the extentthat social welfare is decreased or at least is notmaximized in their presence, resources are misal-

located. Third, whether the free market is inher-ently inefficient and operates as suggested bytraditional economic theory or is efficient butdynamic, its capital structure is not compatible

with the external resources available. Hence. nei-ther the lowest rate of welfare loss nor the lowestrate of time preference has been achieved.

The realization that resource misallocationsare widespread and that they do not result fromthe existence of thermodynamic constraints yetunrecognized by economic theory leaves twoquestions. First, are conventional economic solu-tions, known to rectify resource misallocations ingeneral, sufficient to mitigate and redress envi-ronmental externalities? Second, does thermody-namics offer alternative solutions to those alreadyknown to economists for identifying unknown al-location problems or for dictating certain pricesrather than others?

The first question arises because environmen-tal economics has not yet departed from thetraditional view of welfare economics, which con-siders the environment as another sector withinthe economy. Due to this view, environmentalproblems are regarded as another case of thedivergence of private and social costs, a problemthat could be evaluated according to traditional

procedures and that should be redressed by inter-nalization. However, partial internalization is nota solution, and complete internalization, whichcalls for an up front subsidization of the environ-ment, is no more than wishful thinking. Partialinternalization is not a solution because it savesharmed resources by abusing other environmcn-tal resources. Following traditional theory, once aresource is internalized by being positively val-ued, it is eliminated from the Y vector because itstarts to circulate within the economy. the bound-aries of which have been extended to encompassthe resource. Therefore LI* Y,, is still required toequal to zero, and the welfare function remainsconserved. This means that the economy is ineffi-cient and overuses other external resources.Hence, even if traditional economic theory werevalid, and if welfare were a conserved function,resource misallocations would have to be recti-fied by slowing down the economic process, i.e.,by reducing the rate of time preference and


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140 S. Am ir / Ecological Economrcs IO 1994) 125-142

lengthening the period of production, rather thanby internalization. lo

The only way to avoid these problems is torecognize that the economy is an open system

from the perspective of economics as well as fromthe perspective of thermodynamics. Thus, anyscientific discipline that will attempt to addressthese issues of internal and external resourcecompatibility will have to accept that part of theenvironment that will always remain within thesurroundings as a legitimate part of its agenda.This requires us to find a way to internalize thesurroundings into the theory without, at the sametime, internalizing it into the economic system.The study of the economy as an economicallyopen, nonconserved system is a niche that hasbeen left vacant and is available for occupation.For this to happen, the successful discipline willhave to depart from traditional economic andecological analysis. One such departure is pro-vided by the nonconserved welfare function thatshould be defined on any open system. This func-tion is unique in its ability to measure the real(w elf are) w fue of the environmental resourceslost in support of the state of the system while thefunction itself is defined solely on the systemsinternal resources.

Having said this. we recognize the immenserole traditional theory has allotted to the Pigou-vian system of taxes and subsidies in addressingexternality problems. In a utopian world, whereinformation is perfect and consumption and pro-duction could be halted until markets clear,Pigouvian taxes and subsidies might have beenthe signals required to achieve efficiency, i.e., tominimize the loss of social welfare. Our world,however. is real, and the appropriate signals,reflecting true social costs, cannot be derived byanything but experience. Experience is built on

Partial internalization is a strategy widely used throughoutthe biological world for coping with resource constraints. In

this case. it is highly li kely that resources are overused tem-

porarily by natural populations that behave dynamically while

approaching an efficient steady state. When this steady stateis no longer a desirable goal. as is true for humans, the entire

process loses its rationale. For an extensive discussion of this

case, see Amir 1992b).

trial and error, and it affects the state of theworld and changes the appropriate signals. Theproblem of the dependency of the appropriatesignal on the state of the system prevails when-

ever social and private costs diverge.In the present instance, a more serious prob-

lem crops up. Even if the appropriate signalscould be produced by a system of Pigouvian prices,or by Lindahls system of prices, the resultingcondition u*Y,, < 0 cannot be maintained in afree market economy. Satisfying this condition bymaking transactions on behalf of the environmentis necessary for achieving economic efficiencywhenever W(K tl is nonconserved. However, thiscondition only makes explicit the real subsidiza-tion of the economy u*YCzl, whichnever could be reflected by the flows of thecompetitive system that satisfy the conditionpY,_ = 0. To affect the appropriate change inflows, the flows have to be taxed. This will in-crease the value of the inflows and decrease thevalue of the outflows. If taxes are required to beproportional to real values, budgets cannot bebalanced, and if budgets are required to be bal-anced, the resulting taxes can bear no generalrelation to the real values. For each casespecifically, the appropriate taxes have to be de-

termined by modeling the interactions betweenthe economy and its environment.

Our last conclusion is in reference to possibleapplications of the present study in the context ofthe general equilibrium approach. The possibilityof deriving valuation multipliers for any opensystem is important not only for deriving nonan-thropocentric ecoindicators and summary mea-sures of the health of ecosystems. It also allowsthe derivation of an integrated set of intensivevariables for a system composed of economic and

Assuming the real values are specified in terms of a mone-tary uni t of account, the condition - m = u* Y,, < 0 means

that the unit of account has to leak out of the system as

long as the U*S and the ps, the real values and the taxes, areproportional. Thus, if M monetary units are distributed ini-

tially among economic agents, I/+)m = PM > 0 will be the

rate at which they are taken out of circulation. If budgets are

required to be balanced. no leakage is possible, and the

proportionality rule cannot hold.


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ecological agents. In this way, a single accountingframework is founded, and this framework couldbe used to determine the value to man of particu-lar natural resources and environmental wealth in

general. Furthermore, the possibility of comput-ing the state variables of the composed system isinvaluable for the study and prediction of futureecological impacts of alternative economic poli-cies. One, however, has to bear in mind that theobserved states, and hence the simulated ones,are possibly guided by a nonconserved functionthat requires transactions across the bound-aries to remain unbalanced.

cknowledgement

I would like to thank Paul Samuelson, JulianSimon, Matthias Ruth, Jean Koch, RobertHerendeen, Allen Kneese, David Simpson, Ray-mond Kopp, Martin David, Jeffrey Hyman, MarioGiampietro, Robert Costanza, the editor of thisjournal, and several anonymous referees for theirvaluable comments on earlier versions of thispaper. 1 have especially benefitted from fruitfuldiscussions with Bruce Hannon during years ofour collaboration, and from the editorial assis-

tance of Melissa Edeburn. Although I am grate-ful to them all, the views expressed here and,certainly, any remaining errors or misconceptionsare my sole responsibility.

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