Existence of a competitive equilibrium when all goods are indivisible

Abstract

We study a production economy where all consumption goods are indivisible at the individual level but perfectly divisible at the overall economy level. In order to facilitate the exchange in this setting, we introduce a perfectly divisible parameter that does not enter into consumer preferences (fiat money). When consumption goods are indivisible, a Walras equilibrium does not necessarily exist. We introduce a rationing equilibrium concept and proof its existence. Unlike the standard Arrow-Debreu model, fiat money can always have a strictly positive price at the rationing equilibrium. In our set up a rationing equilibrium is a Walras equilibrium, provided that the initially endowed of fiat money is dispersed