آیا اقتصاد خرد نئوکلاسیک به طور رسمی معتبر است ؟ رویکرد مبتنی بر قیاس با ترمودینامیک تعادل

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.

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. This allows for insights that were gained in one field of knowledge to be transposed to another. However, this has to be done with great care identifying whether the conditions that have to be met in the original field are also met in the field where the analogy is taken. At the substantive level, thermodynamic laws are applied to economic processes. The integration between economics and thermodynamics at the substantive level is of crucial importance because economic processes obey thermodynamic laws and therefore a sound economic theory must be coherent with thermodynamics. This integration highlights the dependence between the economic system and the biophysical framework contributing to the analysis of the sustainability of economic systems. This distinction between formal analogy and substantive integration is not a new issue, e.g., Martinez-Alier (1997) says that ‘the mathematical description of economic phenomena in the language of physics is different from applying the concepts of physics’. Also, Baumgärtner (2004b) discussing the different ways in which thermodynamics can be incorporated in economic analysis, considers the isomorphism of formal structure and the thermodynamic constraints on economic action among others, which are respectively, the formal analogy and the substantive integration discussed in this paper. The belief that neoclassical economics is based on a formal analogy to classical mechanics is common among ecological economists. For example, Amir (1995) argues that ‘most physical analogies in economic theory are borrowed from mechanics’, Martinez-Alier (1997) argues that ‘economic science has used the mathematics of mechanics since the first neoclassical economists’ and Costanza et al. (1997) say that ‘the market model has been formalized using the same mathematics as used by Newton for mechanical systems’. Outside ecological economics, this thesis has been most extensively argued by Mirowski (1999), who considers that neoclassical economics is an attempt to emulate classical mechanics. Based on this supposed analogy to classical mechanics, the main formal criticisms of neoclassical economics are: utility does not obey a conservation law as energy does; an equilibrium theory cannot be used to study irreversible processes. Here, we argue that neoclassical economics is not formally identical to classical mechanics and that the correct identification of the formalism that underlies the construction of neoclassical economics is vital in the evaluation of its internal coherence. We show that economics is formally identical to thermodynamics because they are both problems of static constrained optimisation. The similarity between both formalisms has already been explored in the literature since the 40’ (Davis, 1941, Lisman, 1949, Samuelson, 1960a and Samuelson, 1960b) and more recently (Saslow, 1999, Berry et al., 2000, Candeal et al., 2001a, Candeal et al., 2001b, Tsirlin and Amel’kin, 2001, Tsirlin et al., 2001, Amel'kin et al., 2002 and Smith and Foley, 2004). The formal analogies of Saslow (1999), Berry et al. (2000) and Amel'kin et al. (2002) are driven from superficial similarities between the entities of economy and thermodynamics instead of being derived from fundamental principles. Therefore, these analogies are not helpful in answering the criticisms raised by ecological economists concerning the formal coherence of economic theory. Candeal et al., 2001a and Candeal et al., 2001b prove that the mathematical representations of entropy and utility are analogous. Candeal et al. (2001a) and Cooper (1967) investigate the mathematical foundations of the entropy representation where the entropy is built as an order preserving function that satisfies a continuity property. Candeal et al. (2001b) establish a formal relation between the entropy function and the utility function for the axioms that establish the existence of both ordering functions. Although, these authors do not develop their analysis any further, the formal analogy obtained at the function level is important and it lies behind the optimisation analogy pursued here. The claim that neoclassical economics is formally identical to classical mechanics has also led many Ecological Economists to the substantive assertion that neoclassical economics is fundamentally flawed because it ignores thermodynamics. This argument lacks coherence because the existence of a formal analogy does not imply the existence of a substantive integration and vice-versa. This statement about the non-equivalence between the formal analogy and the substantive integration is easily argued, in this case, because the formal analogy uses the entities that are part of economic theory, i.e., utility, while the substantive integration uses the mass, energy and entropy flows in economic systems. Another argument that should help clarifying this issue is that different physical phenomena are described with different mathematical formalisms although they all have to obey thermodynamic laws. Whether neoclassical economics is formally identical to classical mechanics is not straightforwardly related to its substantive relation with thermodynamic laws. For the same reason, although here we show that neoclassical economics is formally identical to thermodynamics, this does not imply that it is substantively compatible with thermodynamic laws. Whether neoclassical economics is in agreement with thermodynamic laws should be evaluated by looking at the ‘entropic flow of energy and materials that runs through the economy’ (Martinez-Alier, 1997) instead of being based on the use of formal arguments. We would like to emphasize that ecological economics has already given many important contributions to this substantive integration between thermodynamics and economics with, among many others, the works of Georgescu-Roegen (1971), Daly (1991), Biancardi et al. (1993), Ruth, 1993 and Ruth, 1995, Stern (1997), Ayres, 1998, Ayres, 1999 and Ayres, 2001, Baumgärtner et al. (2001), Ayres et al. (2003), Tiezzi (2002) and Frondel and Schmidt (2004). The roadmap of this paper is as follows. In Section 2, we motivate the reader for our formal analogy: (1) by explaining why there is the widespread idea that neoclassical economics is formally analogous to classical mechanics and (2) by reviewing some of the incorrect formal criticisms of neoclassical economics. In Section 3, we present a unified formalism for thermodynamic and economic systems, based on the formalism of constrained optimisation. In Section 4, some of the formalism’s characteristics, namely its limits and scope and other related issues, are clarified. Section 5 concludes and argues that although there is a formal analogy between thermodynamics and neoclassical economics, these two fields are not substantively compatible.

In the ecological economics literature, the validity of neoclassical economics has been widely discussed. This discussion has not been as fruitful as expected because the distinction between formal and substantive criticisms is blurred in many of the arguments presented. In this paper, we present and explore the validity of the formal criticisms of neoclassical economic theory. We concluded that formal criticisms are wrong because they are either based on mixing up the substantive and formal levels (Daly, 1995 and Sollner, 1997) or they are based on the wrong assumption that the microeconomic formalism is analogous to the classical mechanics formalism (Mirowski, 1999, Lozada, 1995, Georgescu-Roegen, 1971, Amir, 1995 and Amir, 1998). We have shown that the argument that the neoclassical formalism is wrong because it was built from mechanics, is not valid; in fact, the neoclassical formalism is identical to the Tisza–Callen axiomatization of thermodynamics. For both thermodynamic and economic systems, we have identified the constrained optimisation problems along with the equilibrium conditions. We have proved that the formalism of neoclassical economics does not consider utility to be a conserved entity because it predicts the existence of irreversible processes characterized by increasing utility at constant market prices. Smith and Foley (2004) also present a formal analogy between neoclassical economics and thermodynamics based on constrained optimisation. These authors consider that the main difference between the two fields is that ‘there is no counterpart in physics for the way neoclassical economists attach importance to transformations respecting initial endowments … and there seems to be no counterpart in economics to the importance thermodynamics attaches to reversible transformations.’ The first remark is not correct because initial endowments in consumer theory (initial amounts of goods) are similar to the initial extensive parameters characterizing an isolated composite system (volume, internal energy and number of moles). The second remark is not correct because in consumer theory many results are also obtained for reversible transformations, e.g., the compensating and the equivalent variations. In both fields, reversible transformations are just limiting cases of actual transformations but their study is important because they set limits on real transformations. Finally, it is of fundamental importance that the fact that neoclassical economics is formally identical to thermodynamics does not mean that it is compatible with thermodynamic laws. Examples of flaws in the integration between economic theory and thermodynamic laws already identified are: economic theory considers a circular flow between households and firms without considering the one-way flow that begins with resources and ends with waste (Georgescu-Roegen, 1971); energy and capital are generally not substitutes, as assumed by production functions, but complements (Ruth, 1993, Daly, 1997 and Stern, 1997); the Inada conditions are inconsistent with mass conservation (Baumgärtner, 2004a); and production theory does not fully possess thermodynamic irreversibility (Baumgärtner, 2005). However these flaws do not result from the similarities between the formal structure of economics and mechanics. This misconception, which results from the use of the formal to argue the substantive, is present in many works like Daly (1995), Sollner (1997) and Georgescu-Roegen (1971). Daly (1995) argues that standard economics explains circular flows because they are mechanistic in nature (reversible and qualityless) and that it does not explain the one-way flow of resources into waste because it is irreversible and mechanistic models cannot deal with irreversibility. We have proved that formally standard economics has irreversibility embedded in it; therefore, the fact that standard economics does not explain the physical directionality of economic flows cannot be accounted for by its formal structure. Sollner (1997) considers that the definition of value in economic theory is incompatible with the entropy law because it was taken from neoclassical mechanics. However, to exemplify this formal flaw, Sollner uses substantive arguments analogous to the ones provided by Georgescu-Roegen. We argue that the flaws in the economic theory, referred by Sollner (1997), Daly (1995) and Georgescu-Roegen (1971) do exist, but the causality relation used to explain these flaws is not correct. These flaws are due to a lack of substantive integration between thermodynamics and economics instead of being rooted in the supposed ‘mechanistic’ nature of neoclassical economics. Concluding, we proved that the analogies to classical mechanics used by economists to build up neoclassical economic theory were wrongly formulated and that instead, neoclassical economic theory was built formally analogous to thermodynamics. Additionally, by clarifying the distinction between formal analogy and substantive integration we made clear that although neoclassical economics and thermodynamics are both formalisms of constrained optimisation they are not substantively compatible.