Buying several indivisible goods

Abstract

This paper studies economies where agents exchange indivisible goods and money. Agents have potencial use for all indivisible goods and the indivisible goods are differentiated. We assume that agents have quasilinear utilities in money, have sufficiently money endowments to afford any group of objects priced below their reservation values, have reservation values which are submodular and satisfy the Cardinality Condition. This Cardinality Condition requires that for each agent the marginal utility of an object only depends on the number of objects to which it is added, not an their characteristics. Under these assumptions, we show that the set of competitive equilibrium prices is a non empty lattice and that, in any equilibrium, the price of an object is between the social value of the object and its second best use.