Equilibrium in an exchange economy with multiple indivisible commodities and money

Abstract

We introduce an economy in which agents exchange their indivisible commodities and money. There are finitely many agents and finitely many different types of indivisible commodities. Commodities of the same type are subject to quality differentiation but have the same function for the agents. Each agent is initially endowed with several units of each type of indivisible commodities and a positive amount of money. Money is treated as a perfectly divisible commodity. We demonstrate that there exists at least one competitive equilibrium in this economy under some conditions on the utility functions of the agents. The results obtained in this paper generalize those of Quinzii [Quinzii, M., 1984. Core and competitive equilibria with indivisibilities. Int. J. Game Theory 13, 41–60] and Yamamoto [Yamamoto, Y., 1987. Competitive equilibria in the market with indivisibility. In: Talman, A.J.J., van der Laan, G. (Eds.), The Computation and Modelling of Economic Equilibria. North-Holland, Amsterdam, pp. 193–204] by whom economic models with one type of indivisible commodity are considered.