Competitive equilibria in economies with multiple indivisible and multiple divisible commodities

Abstract

In this paper we consider a general equilibrium model with a finite number of divisible and a finite number of indivisible commodities. In models with indivisibilities it is typically assumed that there is only one divisible good, which serves as money. The presence of money in the model is used to transfer the value of certain amounts of indivisible goods. For such economies with only one divisible commodity Danilov et al. showed the existence of a general equilibrium if the individual demands and supplies belong to a same class of discrete convexity. For economies with multiple divisible goods and money van der Laan et al. proved existence of a general equilibrium if the divisible goods are produced out of money using a linear production technology and no other producers are present in the model. In the model to be presented in this paper we consider an economy without production and with multiple divisible and multiple indivisible commodities. Convexity is replaced by pseudoconvexity, while the indivisible parts of individual demands should belong to some class of discrete convexity. One of the divisible commodities serves as money. Money is strictly desired by all consumers and there should be enough money present in the economy. To guarantee existence of a general equilibrium individual demands should be products of divisible and indivisible parts. In case there is no money, at least one linear production technology besides possibly other producers should be present in order to produce divisible goods.