Thermodynamics formulation of economics

Abstract

We consider a group of information-symmetric consumers with one type of commodity in an efficient market. The commodity is fixed asset and is non-disposable. We are interested in seeing if there is some connection of thermodynamics formulation to microeconomics. We follow Carathéodory approach which requires empirical existence of equation of state (EoS) and coordinates before performing maximization of variables. In investigating EoS of various system for constructing the economics EoS, unexpectedly new insights of thermodynamics are discovered. With definition of truly endogenous function, criteria rules and diagrams are proposed in identifying the status of EoS for an empirical equation. The rules and diagrams are named effect structure rules and the effect structure diagrams. With the rules, EoS are classified into two classes. Applying the conventional thermodynamics and the new rules, we can identify demand-side economics EoS. The price takes a role of intensive variable, demand quantity as extensive variable and average personal wealth possessed by consumers as temperature. The economics EoS is of the new class, the Class III. We proposed exact form of the economics EoS for econometrics analysis. At last we propose the way to perform Monte-Carlo simulation for the EoS. Having explicitly known EoS of the economy and its coordinates lays reasonable assumptions of Hamiltonian and partition function which are central aspects in application of statistical mechanics to economics and finance.