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

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Is Neoclassical Microeconomics Formally Valid? an Approach Based on an Analogy with Equilibrium Thermodynamics 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 thermody- namics 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. 0921-8009/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolecon.2005.07.004 T. Sousa, T. Domingos / Ecological Economics 58 (2006) 160–169 161 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
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