Use of Euler’s theorem in the elucidation of economic concepts in goods exchange

A system of economic agents that simulate the exchange of goods is studied following a methodology equivalent to that used in the mechanical-statistical determination of the distribution of energies in physical systems. It is shown that the price of the exchanged goods emerges naturally, as well as the well-known “Law of Demand”, provided that the Lagrange multiplier [Formula: see text] is identified as the unit price. It is shown that using Euler’s Theorem for homogeneous functions the unit price is an intensive property, and it is evident that “wholesale” prices are always lower than “retail” prices. It is found that Total Revenue is the product of two factors: configurational entropy and another of the “free energy” type. The case where agents exchange money is studied numerically, where there is a “roof” to the amount of money that they can possess, making the existence of negative prices possible. It is shown that the increase in the amount of money in the hands of the agents leads to its depreciation, and only the expansion of the economy minimizes this loss of purchasing power. The concept of indexation is discussed as a way of maintaining the purchasing power of money.