Is Neoclassical Microeconomics Formally Valid? an Approach Based on an Analogy with Equilibrium Thermodynamics

Home , Irreversible process

Ecological Economics 58 (2006) 160–169 www.elsevier.com/locate/ecolecon ANALYSIS Is neoclassical microeconomics formally valid? An approach based on an analogy with equilibrium thermodynamics

Taˆnia Sousa *, Tiago Domingos

Environment and Energy Section, DEM, Instituto Superior Te´cnico, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal Received 13 July 2005; accepted 16 July 2005 Available online 12 September 2005

Abstract

The relation between Thermodynamics and Economics is a paramount issue in Ecological Economics. Two different levels can be distinguished when discussing it: formal and substantive. At the formal level, a mathematical framework is used to describe both thermodynamic and economic systems. At the substantive level, thermodynamic laws are applied to economic processes. In Ecological Economics, there is a widespread claim that neoclassical economics has the same mathematical formulation as classical mechanics and is therefore fundamentally flawed because: 1) utility does not obey a conservation law as energy does; 2) an equilibrium theory cannot be used to study irreversible processes. Here, we show that neoclassical economics is based on a wrong formulation of classical mechanics, being in fact formally analogous to equilibrium thermodynamics. The similarity between both formalisms, namely that they are both cases of constrained optimisation, is easily perceived when thermodynamics is looked upon using the Tisza–Callen axiomatisation. In this paper, we take the formal analogy between equilibrium thermodynamics and economic systems far enough to answer the formal criticisms, proving that the formalism of neoclassical economics has irreversibility embedded in it. However, the formal similarity between equilibrium thermodynamics and neoclassical microeconomics does not mean that economic models are in accordance with mass, energy and entropy balance equations. In fact, neoclassical theory suffers from flaws in the substantive integration with thermodynamic laws as has already been fully demonstrated by valuable work done by ecological economists in this field. D 2005 Elsevier B.V. All rights reserved.

Keywords: Thermodynamics; Entropy; Neoclassical economics; Analogy and irreversibility

1. Introduction

The relation between Thermodynamics and Eco- * Corresponding author. Tel.: +351 218419290; fax: +351 nomics is a paramount issue in Ecological Economics. 218417365. Two different levels can be distinguished when dis- E-mail address: [email protected] (T. Sousa). cussing it: formal and substantive.

At the formal level, a mathematical framework is law as energy does; an equilibrium theory cannot be used to describe both thermodynamic and economic used to study irreversible processes. systems. This allows for insights that were gained in Here, we argue that neoclassical economics is not one field of knowledge to be transposed to another. formally identical to classical mechanics and that the However, this has to be done with great care identifying correct identification of the formalism that underlies the whether the conditions that have to be met in the construction of neoclassical economics is vital in the original field are also met in the field where the analogy evaluation of its internal coherence. We show that eco- is taken. nomics is formally identical to thermodynamics because At the substantive level, thermodynamic laws are they are both problems of static constrained optimisa- applied to economic processes. The integration between tion. The similarity between both formalisms has already economics and thermodynamics at the substantive level been explored in the literature since the 40T (Davis, is of crucial importance because economic processes 1941; Lisman, 1949; Samuelson, 1960a,b) and more obey thermodynamic laws and therefore a sound eco- recently (Saslow, 1999; Berry et al., 2000; Candeal et nomic theory must be coherent with thermodynamics. al., 2001a,b; Tsirlin and AmelTkin, 2001; Tsirlin et al., This integration highlights the dependence between the 2001; Amel’kin et al., 2002; Smith and Foley, 2004). economic system and the biophysical framework con- The formal analogies of Saslow (1999), Berry et al. tributing to the analysis of the sustainability of economic (2000) and Amel’kin et al. (2002) are driven from systems. superficial similarities between the entities of economy This distinction between formal analogy and sub- and thermodynamics instead of being derived from stantive integration is not a new issue, e.g., Martinez- fundamental principles. Therefore, these analogies are Alier (1997) says that dthe mathematical description of not helpful in answering the criticisms raised by eco- economic phenomena in the language of physics is logical economists concerning the formal coherence of different from applying the concepts of physicsT. economic theory. Also, Baumga¨rtner (2004b) discussing the different Candeal et al. (2001a,b) prove that the mathematical ways in which thermodynamics can be incorporated representations of entropy and utility are analogous. in economic analysis, considers the isomorphism of Candeal et al. (2001a) and Cooper (1967) investigate formal structure and the thermodynamic constraints the mathematical foundations of the entropy represen- on economic action among others, which are respec- tation where the entropy is built as an order preserving tively, the formal analogy and the substantive integra- function that satisfies a continuity property. Candeal et tion discussed in this paper. al. (2001b) establish a formal relation between the en- The belief that neoclassical economics is based tropy function and the utility function for the axioms that on a formal analogy to classical mechanics is establish the existence of both ordering functions. Al- common among ecological economists. For exam- though, these authors do not develop their analysis any ple, Amir (1995) argues that dmost physical analo- further, the formal analogy obtained at the function level gies in economic theory are borrowed from is important and it lies behind the optimisation analogy mechanicsT, Martinez-Alier (1997) argues that pursued here. deconomic science has used the mathematics of me- The claim that neoclassical economics is formally chanics since the first neoclassical economistsT and identical to classical mechanics has also led many Eco- Costanza et al. (1997) say that dthe market model has logical Economists to the substantive assertion that neo- been formalized using the same mathematics as used by classical economics is fundamentally flawed because it Newton for mechanical systemsT. Outside ecological ignores thermodynamics. This argument lacks coher- economics, this thesis has been most extensively ar- ence because the existence of a formal analogy does gued by Mirowski (1999), who considers that neoclas- not imply the existence of a substantive integration and sical economics is an attempt to emulate classical vice-versa. This statement about the non-equivalence mechanics. between the formal analogy and the substantive integra- Based on this supposed analogy to classical me- tion is easily argued, in this case, because the formal chanics, the main formal criticisms of neoclassical analogy uses the entities that are part of economic theory, economics are: utility does not obey a conservation i.e., utility, while the substantive integration uses the 162 T. Sousa, T. Domingos / Ecological Economics 58 (2006) 160–169 mass, energy and entropy flows in economic systems. ogies from classical mechanics. Mirowski (1999) Another argument that should help clarifying this issue gives some examples of the use of mechanical con- is that different physical phenomena are described with cepts and metaphors: (1) the lever rule by Nicolas different mathematical formalisms although they all Canard, (2) gravitation theory by Stanley Jevons, (3) have to obey thermodynamic laws. Whether neoclassi- force by Herman Go¨ssen, (4) power by Frederick cal economics is formally identical to classical mechan- Soddy and (5) the Energy Minimum Principle by ics is not straightforwardly related to its substantive Francis Edgeworth. relation with thermodynamic laws. This approach of establishing analogies between For the same reason, although here we show that mechanics and economics was taken to its extreme by neoclassical economics is formally identical to thermo- Irving Fisher who in 1892 established the most exten- dynamics, this does not imply that it is substantively sive relation between mechanics and economics compatible with thermodynamic laws. Whether neoclas- (Table 1). According to Fisher (1991), while econom- sical economics is in agreement with thermodynamic ic equilibrium corresponds to maximum profit, me- laws should be evaluated by looking at the dentropic chanical equilibrium corresponds to minimum energy. flow of energy and materials that runs through the Given the history of economic analogies to mechan- economyT (Martinez-Alier, 1997) instead of being ics, there is a widespread claim that neoclassical eco- based on the use of formal arguments. We would like nomics is fundamentally flawed because the assumptions to emphasize that ecological economics has already on which classical mechanics is based do not apply to given many important contributions to this substantive consumer theory. The most important aspects usually integration between thermodynamics and economics referred in the literature are: 1) utility does not obey a with, among many others, the works of Georgescu- conservation law as energy does; 2) an equilibrium Roegen (1971), Daly (1991), Biancardi et al. (1993), theory cannot be used to study irreversible processes. Ruth (1993, 1995), Stern (1997), Ayres (1998, 1999, Some of the examples of this are described below. 2001), Baumga¨rtner et al. (2001), Ayres et al. (2003), Mirowski (1999) considers that dforgetting the con- Tiezzi (2002) and Frondel and Schmidt (2004). servation of energy while simultaneously appealing to The roadmap of this paper is as follows. In Section 2, the metaphor of energy ... is the Achilles heel of all we motivate the reader for our formal analogy: (1) by neoclassical economicsT because, according to Mir- explaining why there is the widespread idea that owski, although utility cannot be a conserved entity, neoclassical economics is formally analogous to clas- the results obtained in consumer theory assume that it is. sical mechanics and (2) by reviewing some of the Amir (1995, 1998) claims that the utility function incorrect formal criticisms of neoclassical economics. is unlikely to be a conserved quantity, but that eco- In Section 3, we present a unified formalism for nomic theory assumes that it is, which is supposedly thermodynamic and economic systems, based on the formalism of constrained optimisation. In Section 4, some of the formalismTs characteristics, namely its Table 1 limits and scope and other related issues, are clarified. The analogy between mechanics and economics proposed by Fisher Section 5 concludes and argues that although there is (1991, p. 85) a formal analogy between thermodynamics and neo- Mechanics Economics classical economics, these two fields are not substan- Particle Individual tively compatible. Space (vector) Commodity (vector) Force (vector) Marginal utility (vector) Work=force space Disutility=marginal utility commodity 2. Is the formalism of neoclassical economics (scalar) (scalar) Energy=force space Utility=marginal utility commodity wrong? (scalar) (scalar) Equilibrium: impelling Equilibrium: marginal utility and It is generally claimed that neoclassical economics and resisting forces marginal disutility along each is based on classical mechanics because throughout along each axis are axis are equal the history of economics many economists used anal- equal T. Sousa, T. Domingos / Ecological Economics 58 (2006) 160–169 163 patent in the use of the proportionality between mar- developed in the general case and then applied to ther- ginal utilities and market prices in equilibrium. modynamic and to economic systems. Georgescu-Roegen (1971) argues that Jevons and Walras, whose aim was to create an economic science 3.1. General formalism similar to mechanics, built an economic theory that only describes reversible and qualityless motion. Geor- The constrained optimisation problem describes gescu-Roegen also argues that deconomics...is mech- the behaviour of the system that evolves in order to anistic in the same strong sense...[that] classical maximize some function y subject to a set of con- mechanics...because neither induces any qualitative straints1. In equilibrium the values acquired by the change nor is affected by the qualitative change of the variables, xi, i =1,...,n, maximize the potential y, environmentT. given the constraints. Lozada (1995) states that the entropy law is not This maximization is constrained because the vari- reducible to mechanics by saying that dthe inconsisten- ables in equilibrium have to obey a set of constraints, cy between the logical structure of the entropy law and gz =0, z =1,...,m. These constraints are a function of 0 the logical structure of neoclassical economic analysis the initial values of the variables, xi , and of some is that the former is evolutionary and the other is parameters kj, j =1,...,l: arithmomorphic and hence non-evolutionaryT. However it is important to emphasize that some max yxðÞ1; ...; xn s:t: x1;...;xn authors do disagree with the supposed analogy between 0 0 gz x1; ...; xn; x ; ...; x ; k1; ...; k1 ¼ 0: ð1Þ classical mechanics and neoclassical economics, e.g., 1 n T Varian (1991), in a review of Mirowski s book, argues This problem is solved with the Method of Lagran- that if the energy conservation principle implies that gean Multipliers.2 The Lagrangean function, L,is utility is not a coherent concept then this implies that defined as: utility is not energyT, Marchionatti and Gambino (1997) say that da critique, such as that of Mirowski, of the LxðÞ1; ...; xn; k1; ...; k1; k1; ...; km mechanical analogy in neoclassical economics, seems ¼ yxðÞ; ...; x largely unhelpful and based on a misunderstandingT 1 n and Hands (1993) argues that the standard Slutsky Xm 0 0 conditions, that are sufficient for the integrability of þ kzgz x1; ...; xn; x1; ...; xn; k1; ...; k1 : demand, do not seem to be sufficient to guarantee, as z¼1 Mirowski argues, that prices form a conservative vector The values of the variables that maximize the field. objective function subject to the constraints are We agree that if neoclassical economics were indeed obtained solving the system of m +n equations: formally identical to classical mechanics it would be internally incoherent. However, we argue that neoclas- BL ¼ 0; i ¼ 1; ...; n; sical economics is based on a wrong formulation of Bxi classical mechanics, being in fact formally identical to BL ¼ 0; z ¼ 1; ...; m: thermodynamics. Both neoclassical economics and Bkz thermodynamics are equilibrium theories and can be developed as formalisms of constrained optimisation as which is equivalent to: Xn shown in the next section. By Bgz B ¼ kz ; i ¼ 1; ...; n xi Bx z¼1 i g 0; z 1; ...; m 3. A unified formalism for neoclassical economics z ¼ ¼ ð2Þ and equilibrium thermodynamics 1 Minimization is an equivalent problem. In this section, a mathematical unified formalism 2 For a more detailed description of this method see, e.g., Jehle based on the axiomatization of Tisza-Callen is first (1991). 164 T. Sousa, T. Domingos / Ecological Economics 58 (2006) 160–169

If the function y and the constraints gz are real The variables are S, the entropy, U, the internal valued and differentiable, if the number of constraints, energy, V, the volume, and N the number of moles. m, is less than the number of variables, n, and if the The problem of the maximization of entropy for a gradient vectors of the constraint equations are line- composite system4 comprising two simple systems (1 arly independent, the maximum exists. In this case, and 2) is formalized as:5 LagrangeTs Method gives the first order equilibrium conditions (Jehle, 1991), Eq. (2), which define the max S ¼ S1ðÞþU1; V1; N1 S2ðÞU2; V2; N2 ; state of the system. These equilibrium conditions U1;U2;V1;V2;N1;N2 give the optimal values of each x , x *, as a function i i s. t. of the parameters kj and of the initial conditions:

0 0 0 0 U1 þ U2 ¼ U1 þ U2 ; xi ¼ fk1; ...; k1; x1; ...; xn : ð3Þ 0 0 V1 þ V2 ¼ V1 þ V2 ; With the set of Eq. (3) the optimal value of y, y*, 0 0 N1 þ N2 ¼ N1 þ N2 ð6Þ can also be written as: where the constraints are that, over the two systems, ; ; ; 0; ; 0 : y ¼ fk1 ... k1 x1 ... xn ð4Þ the sums of the internal energies, the mole numbers and the volumes are kept constant. The initial condi- In the initial state, the system is characterized by 0 0 0 tions are the internal energy Uj , the mole numbers Nj the values xi ; which are called initial conditions. In and the volume V0 for j =1,2. the final state, the system is characterized by the j Defining temperature, Tj, pressure, Pj, and chemi- optimal values assumed by the variables, xi*. The cal potential, lj, for j =1, 2, as: evolution of the system from the initial to the final state is called a process. In a reversible process, the BSj 1 initial and final states have the same y*. In an u ; BU T irreversible process, the final state has a higher j j B value of y* than the initial state. The amount of Sj u Pj B ; irreversibility (always positive) produced in an irre- Vj Tj versible process can be measured by the increase in BS l j u j : ð7Þ y. An impossible process is a process that will BNj Tj never occur because if it did the final state would have a lower value of y*. with Sj=Sj(Uj, Vj, Nj), j= 1, 2, the equilibrium conditions, see Eq. (2), for the thermodynamic system 3.2. Thermodynamic systems subject to the previous constraints are:

The constrained optimisation problem in thermody- 1 1 P P l l namics is the maximization of the entropy of a com- ¼ 1 ¼ 2 : 1 ¼ 2 posite system with constant total internal energy, T1 T2 T1 T2 T1 T2 constant total volume and constant total mole numbers. The entropy of a homogeneous thermodynamic That is, equilibrium is established when both sys- system can be obtained from the fundamental equa- tems have the same temperature, the same chemical tion (Tisza, 1966; Callen, 1985):3 potentials and the same pressure. Thus, an isolated

S ¼ SUðÞ; V ; N : ð5Þ 4 Caratheo´dory introduced the concept of composite systems because the entropy is axiomatically only defined for equilibrium 3 Where, for simplicity, we consider a system with a single systems. chemical component. 5 For simplicity, we consider only two subsystems. T. Sousa, T. Domingos / Ecological Economics 58 (2006) 160–169 165 composite system whose constraints are defined 3.3. Consumer system above increases its entropy towards the maximum value by turning into a system with a homogeneous The extremum principle, in consumer theory, is the temperature, homogeneous pressure and homoge- maximization of utility of a consumer at constant mar- neous chemical potential. ket prices and constant endowment. When allowed to These equilibrium conditions are also explainable by trade with the market, the consumer maximizes his reductio ad absurdum. Suppose that, in the equilibrium utility, U. state, the temperatures of the two systems were not equal, The consumerTs utility maximization problem is e.g., T1 NT2. If energy would flow (in the form of heat) from system 1 to system 2, system 2 would increase its maxU ¼ UxðÞ1; ...; xn x1;...;xn entropy and system 1 would decrease its entropy because the derivative of the entropy in relation with s.t. energy, Eq. (7), is always positive given that the 0 0 absolute temperature is always positive. The increase p1x1 þ ... þ pnxn ¼ p1x1 þ ... þ pnxn: ð10Þ in entropy of system 2 would be higher than the decrease in entropy of the other system because its where the constraint is that the total cost of goods that temperature is lower, again by Eq. (7). Therefore, the will be bought (left hand side term of the constraint) is global change in entropy would be positive and con- equal to his initial endowment p x0+. . .+p x 0. The sequently the initial equilibrium state did not have the 1 1 n n variables are the different amounts of goods, x , the highest entropy possible, which means it was not an i parameters are the market price p of good i, i= equilibrium state. i 1,. . .,n. The initial conditions are the amounts of Each optimal variable, see Eq. (3), can be written each good i in the initial state, x 0. as: i Defining marginal utilities as: 0 0 0 0 0 0 BU Uj ¼ fV1 ; V2 ; U1 ; U2 ; N1 ; N2 ; j ¼ 1; 2; uMU i; i ¼ 1; ...; n; ð11Þ Bxi N ¼ fV0; V 0; U 0; U 0; N 0; N 0 ; j ¼ 1; 2; j 1 2 1 2 1 2 0 0 0 0 0 0 Vj ¼ fV1 ; V2 ; U1 ; U2 ; N1 ; N2 ; j ¼ 1; 2: ð8Þ with U =U(x1,. . .,xn), the equilibrium conditions, see Eq. (2), for the consumer are: These equations give the optimal value of the MU 1 MU n variables of each system as a function of the initial ¼ ... ¼ : P P conditions. The maximum entropy, see Eq. (4), as a 1 n function of the same arguments is: A consumer system whose constraints are that the endowment and the prices remain constant increases his utility towards the maximum value by exchanging S ¼ fV0; V 0; U 0; U 0; N 0; N 0 : ð9Þ 1 2 1 2 1 2 with the market until the ratio between marginal utility and price is the same for all products. Reversible processes in a thermodynamic system Varian (1996) proves this optimum condition by are processes that occur in an isolated system at reductio ad absurdum using the following argument. constant maximal entropy. Impossible processes are Suppose that the consumerTs utility is maximum but processes that do not occur because the isolated sys- that the ratio between marginal utilities of product i tem would decrease its maximum entropy. Irreversible and product j is two and the ratio of prices is one. processes in a thermodynamic system are processes Then, the consumer will exchange one unit of product that occur in an isolated system at increasing maximal j for one unit of product i obeying the endowment entropy. The amount of irreversibility produced is constraint (they are worth the same) and increase his equal to the variation in entropy between the initial utility. This means that the initial state was not at the state and the equilibrium state. maximum utility. 166 T. Sousa, T. Domingos / Ecological Economics 58 (2006) 160–169

Each optimal value, see Eq. (3), can be written as: dynamic analysis of economic systems should be based on the thermodynamics of non-equilibrium open systems (Kondepudi and Prigogine, 1998; Pri- x ¼ fp; p ; ...; p ; x0; ...; x0 ; j ¼ 1; ...; n: j 1 2 n 1 n gogine, 1961; Onsager, 1931a,b; de Groot and Mazur, ð12Þ 1962).

4.2. On the concept of equilibrium These equations give the optimal amount of product j as a function of the prices and initial amounts of In the formalism of constrained optimization, equi- each product. The maximum utility as a function of librium is the extremum point subject to the constraints the same arguments is the equilibrium condition anal- considered. It is equilibrium because the system will ogous to Eq. (4), not move from that point unless the constraints are changed. For example, for a certain amount of total 0 0 internal energy, total volume and total number of U ¼ fp1; ...; pn; x1; ...; xn : ð13Þ moles, a thermodynamic system is in equilibrium if its entropy is at the maximum level (S*). This entropy Reversible processes for the same consumer are equilibrium value (S*) can only be changed if the processes in which he trades with the market but constraints are changed, e.g., the system receives a does not increase his maximum utility. Impossible heat flow from the exterior hence increasing its total processes are trades that do not occur because the energy. The same is applicable to the consumer: for a consumer would decrease his maximum utility. Ir- certain total cost of goods, a consumer system is in reversible processes for the consumer are processes equilibrium if its utility is at the maximum level (U*). characterized by an increase in utility: if a consumer This utility level (U*) can only be changed if the engages in a trade that increases his utility, he will constraints are changed, e.g., the consumer receives not reverse the trade. The amount of irreversibility an additional endowment. produced is equal to the amount of utility increase The formal equilibrium considered for the consum- between the initial state and the equilibrium state.6 er problem is not the thermodynamic equilibrium of the consumer. The thermodynamic equilibrium of the consumer would be a dead consumer. 4. Discussing the formalism 4.3. On the ordinal concept of utility In this section we clarify some of the points of the formalism presented. Utility is usually considered in an ordinal framework, i.e, utility functions order the consumption 4.1. On the correct thermodynamic framework for bundles according to the preferences of the consumer substantive integration but the absolute values of utility have no meaning. This means that if utility function U(x1,..., xn), repre- We would like to emphasize that the substantive sents the preferences of the consumer, then so does any other utility function obtained through a positive integration between thermodynamics and economic u systems should not be based on the thermodynamic monotonic transformation U =f(U(x1,...,xn)), (Jehle, theory of isolated systems that we present in this 1991), i.e., paper. Economic systems are open thermodynamic systems far from equilibrium and therefore a thermo- BU h BfUðÞ ¼ N0: ð14Þ BU BU

6 This statement does not mean that we are considering that utility Our proposed formalism does not entail a cardinal is a cardinal concept. This is further discussed in Section 4.3. concept of utility and is fully compatible with the T. Sousa, T. Domingos / Ecological Economics 58 (2006) 160–169 167 ordinal framework because (1) the equilibrium condi- We concluded that formal criticisms are wrong be- tions obtained and (2) the ranking of the amount of cause they are either based on mixing up the substan- irreversibilities produced are both independent of the tive and formal levels (Daly, 1995; Sollner, 1997)or specific utility function chosen within the family of they are based on the wrong assumption that the monotonic transformations. (1) is proved by Samuel- microeconomic formalism is analogous to the classi- son (1983) and (2) is obtained below. cal mechanics formalism (Mirowski, 1999; Lozada, The amount of irreversibility produced between an 1995; Georgescu-Roegen, 1971; Amir, 1995, 1998). initial state characterized by x1,..., xn and a final We have shown that the argument that the neoclas- equilibrium state x1*,..., xn* can be measured using sical formalism is wrong because it was built from the utility function U or any other positive monotonic mechanics, is not valid; in fact, the neoclassical for- transformation Uu=f(U): malism is identical to the Tisza–Callen axiomatization of thermodynamics. For both thermodynamic and economic systems, we have identified the constrained r ¼ U ðÞx1 ; ...; xn UxðÞ1; ...; xn optimisation problems along with the equilibrium con- h h h r ¼ U ðÞx1 ; ...; xn U ðÞx1; ...; xn : ð15Þ ditions. We have proved that the formalism of neoclassical economics does not consider utility to be a conserved entity because it predicts the existence of We prove that ru is a positive monotonic transform irreversible processes characterized by increasing util- of r, using Eq. (14), ity at constant market prices. Smith and Foley (2004) also present a formal analogy between neoclassical economics and thermo- h h h Br B U ðÞx1 ; ...; xn U ðÞx1; ...; xn dynamics based on constrained optimisation. These ¼ authors consider that the main difference between the Br BðÞU ðÞx1 ; ...; xn UxðÞ1; ...; xn two fields is that dthere is no counterpart in physics for h h BU ðÞx1 ; ...; xn BU ðÞx1; ...; xn the way neoclassical economists attach importance to N0: ¼ þ BU ðÞx1 ; ...; xn BUxðÞ1; ...; xn transformations respecting initial endowments ...and there seems to be no counterpart in economics to the importance thermodynamics attaches to reversible Summarizing, the amount of irreversibilities pro- transformations.T The first remark is not correct be- duced between any initial state and the equilibrium cause initial endowments in consumer theory (initial state has an ordinal meaning, i.e., if the amount of amounts of goods) are similar to the initial extensive irreversibilities produced going from state A to equi- parameters characterizing an isolated composite sys- librium is higher than the amount of irreversibilities tem (volume, internal energy and number of moles). produced going from state B to equilibrium, then the The second remark is not correct because in consumer consumer will behave such as to move from state A to theory many results are also obtained for reversible state B but not the reverse. transformations, e.g., the compensating and the equivalent variations. In both fields, reversible transformations are just limiting cases of actual transformations 5. Conclusions but their study is important because they set limits on real transformations. In the ecological economics literature, the validity Finally, it is of fundamental importance that the of neoclassical economics has been widely discussed. fact that neoclassical economics is formally identical This discussion has not been as fruitful as expected to thermodynamics does not mean that it is compat- because the distinction between formal and substan- ible with thermodynamic laws. Examples of flaws in tive criticisms is blurred in many of the arguments the integration between economic theory and ther- presented. modynamic laws already identified are: economic In this paper, we present and explore the validity of theory considers a circular flow between households the formal criticisms of neoclassical economic theory. and firms without considering the one-way flow that 168 T. Sousa, T. Domingos / Ecological Economics 58 (2006) 160–169 begins with resources and ends with waste (Geor- Acknowledgments gescu-Roegen, 1971); energy and capital are generally not substitutes, as assumed by production functions, This paper was written with financial support from but complements (Ruth, 1993; Daly, 1997; Stern, 1997); PRODEP III (Taˆnia Sousa) and from FCT through grant the Inada conditions are inconsistent with mass conser- POCI/AMB/55701/2004 (Taˆnia Sousa and Tiago Dom- vation (Baumga¨rtner, 2004a); and production theory ingos). The authors thank Stephan Baumga¨rtner, Joa˜o does not fully possess thermodynamic irreversibility Rodrigues, Ralph Winkler and two anonymous re- (Baumga¨rtner, 2005). viewers for helpful comments and suggestions on this However these flaws do not result from the similar- paper. ities between the formal structure of economics and mechanics. 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