ترمودینامیک کلاسیک و نظریه اقتصادی تعادل عمومی

A long history of analogy making between neoclassical economics and physical thermodynamics has unfortunately served to obscure two important relations between the two fields: their definitions of equilibria stem from essentially the same three axioms for the mathematical representations of systems, while the classes of transformation each has chosen to emphasize, and their responses to the problem of path dependence, have led them to very different interpretations of duality in those representations. Despite these conventional differences, we show that economies in which all agents have preferences quasi-linear in some good have a trading-constraint structure isomorphic to the structure of physical systems with classical thermodynamic equations of state. Exact equivalents of thermodynamic potentials, including entropy, can be constructed, and function as the economic counterparts to free energies. Quasi-linear economies are the most general in which the Walrasian idea of price formation as an analog of force balance can be realized. More general economic models raise the same methodological problems as more complex physical models that exhibit path-dependence. We show how the degree of aggregatability of an economic model corresponds to which properties of equilibria retain path-independence, and to the extent to which a social-welfare function exists. A new contour money-metric utility defines the maximal generalization of social-welfare functions in arbitrary economies, but depends on the endowments and composition of the economy in non-quasi-linear cases, and is limited to one-dimensional contours of equilibria in non-aggregatable cases. The differences between economic and thermodynamic methodology lies in the economic focus on the irreversible movement from initial disequilibrium endowments to equilibrium through voluntary trade, in contrast to the thermodynamic recognition that only reversible transformations lead to measurement of system structure. The consequences of respecting reversibility for economic method are sketched, and alternative interpretations of the Walrasian notion of wealth preservation are presented.

The relation between economic and physical (particularly thermodynamic) concepts of equilibrium has been a topic of recurrent interest throughout the development of neoclassical economic theory. As systems for defining equilibria, proving their existence, and computing their properties, neoclassical economics (Mas-Collel et al., 1995 and Varian, 1992) and classical thermodynamics (Fermi, 1956) undeniably have numerous formal and methodological similarities. Both fields seek to describe system phenomena in terms of solutions to constrained optimization problems. Both rely on dual representations of interacting subsystems: the state of each subsystem is represented by pairs of variables, one variable from each pair characterizing the subsystem's content, and the other characterizing the way it interacts with other subsystems. In physics the content variables are quantities like a subsystem's total energy or the volume in space it occupies; in economics they are amounts of various commodities held by agents. In physics the interaction variables are quantities like temperature and pressure that can be measured on the system boundaries; in economics they are prices that can be measured by an agent's willingness to trade one commodity for another. The significance attached to these similarities has changed considerably, however, in the time from the first mathematical formulation of utility (Walras, 1909) to the full axiomatization of general equilibrium theory (Debreu, 1987). Léon Walras appears (Mirowski, 1989) to have conceptualized economic equilibrium as a balance of the gradients of utilities, more for the sake of similarity to the concept of force balance in mechanics, than to account for any observations about the outcomes of trade. Fisher (1892) (a student of J. Willard Gibbs) attempted to update Walrasian metaphors from mechanics to thermodynamics, but retained Walras's program of seeking an explicit parallelism between physics and economics. As mathematical economics has become more sophisticated (Debreu, 1987) the naı¨ve parallelism of Walras and Fisher has progressively been abandoned, and with it the sense that it matters whether neoclassical economics resembles any branch of physics. The cardinalization of utility that Walras thought of as a counterpart to energy has been discarded, apparently removing the possibility of comparing utility with any empirically measurable quantity. A long history of logically inconsistent (or simply unproductive) analogy making (see Section 7.2) has further caused the topic of parallels to fall out of favor. Samuelson (1960) summarizes well the current view among many economists, at the end of a one of the few methodologically sound analyses of the parallel roles of dual representation in economics and physics: The formal mathematical analogy between classical thermodynamics and mathematic economic systems has now been explored. This does not warrant the commonly met attempt to find more exact analogies of physical magnitudes – such as entropy or energy – in the economic realm. Why should there be laws like the first or second laws of thermodynamics holding in the economic realm? Why should ‘utility’ be literally identified with entropy, energy, or anything else? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematical isomorphism that does exist between minimum systems that arise in different disciplines? The view that neoclassical economics is now mathematically mature, and that it is mere coincidence and no longer relevant whether it overlaps with any body of physical theory, is reflected in the complete omission of the topic of parallels from contemporary graduate texts (Mas-Collel et al., 1995). We argue here that, despite its long history of discussion, there are important insights still to be gleaned from considering the relation of neoclassical economics to classical thermodynamics. The new results concerning this relation we present here have significant implications, both for the interpretation of economic theory and for econometrics. The most important point of this paper (more important than the establishment of formal parallels between thermodynamics and utility economics) is that economics, because it does not recognize an equation of state or define prices intrinsically in terms of equilibrium, lacks the close relation between measurement and theory physical thermodynamics enjoys.

In representing the behavior of individuals (or households) as the maximization of well-behaved utility functions (which represent transitive, convex preference orderings) under constraints, marginalist and neoclassical economics effectively regards individuals as equilibrated thermodynamic systems in which a well-defined equation of state links extensive variables (commodity bundles) to intensive variables (marginal rates of substitution). This point of view has become very widely propagated through its adoption as the foundation of the economics curriculum and as the starting point for an enormous theoretical – empirical literature on economic problems. This conception of the individual leads to an analysis of real economic phenomena as the interaction of the individual agents (analogous to equilibrated subsystems in thermodynamics) and hence as a version of thermodynamic equilibrium. History seems to show that no economist has had a clear understanding of the full methodological implications of this thermodynamic perspective for economics as an explanatory science. The stumbling blocks appear to have been that in thermodynamics there is no natural role for accumulated heat flow as a state variable, and thus no reason to expand the equation of state into a quasi-linear function akin to a utility. Conversely, economists have appropriately regarded quasi-linear economies as too constrained to represent the full range of economic phenomena. As a result economics has developed a general theory (Walrasian general equilibrium theory), but on methodologically flawed foundations which foreclose the tight and scientifically fertile connection between theory and measurement enjoyed by thermodynamics. Economics unwittingly found itself coping with the complex phenomenon of path-dependency in its attempt to theorize general economic interactions not constrained to the quasi-linear case. The device of the Walrasian auctioneer is an unsuccessful attempt to finesse the issues raised by path-dependency without coming to grips with them (through positing a determinate transactions path for irreversible transformations from disequilibrium endowments to the Pareto set). In the process both economics and physics lost sight of the common ground that underlies their approach to complex systems. We hope that a better understanding of the fact that physics and economics face the same problems in applying thermodynamic reasoning to path-dependent systems can foster a more fertile interchange of ideas. This paper takes no stand on how appropriate the abstract thermodynamic point of view is to understanding real economic phenomena. It is possible to argue that the formal equivalence of utility-based economics and thermodynamics reveals the inadequacy of this approach to deal with human social phenomena. It is also possible to argue that a correct application of the methodology implied by the thermodynamic approach can greatly strengthen the empirical explanatory power of economic theory. However, one argues, though, those economists who commit themselves to utility theory as a basic framework of analysis will posses a clearer conceptual system when the theory of preferences and duality is disentangled from the problems associated with disequilibrium, dynamics, and inevitably institutions.