Existence of an equilibrium in a competitive economy with indivisibilities and money

In this paper we introduce a model of an exchange economy with indivisible goods and money, There are finitely many agents each of whom owns one unit of finitely many different types of indivisible goods and a certain amount of money. Each type of indivisible goods is subject to quality differentiation. We demonstrate that under fairly mild conditions on demand the economy has a price equilibrium. The proof is based on a generalization of the well-known lemma of Knaster, Kuratowski and Mazurkiewicz (KKM) in combinatorial topology, The results in the paper generalize those of Gale in the case of just one type of indivisible good present in the economy.