A Model of Commodity Differentiation with Indivisibilities and Production

This paper presents an existence theorem in a general equilibrium model of a production economy with commodity differentiation and indivisibilities. The model is motivated by the existence of markets with indivisible commodities, such as the markets for automobiles and computers. As is standard in the literature, the space of commodity characteristics is described by a compact metric space and a commodity vector is described by an integer-valued Borel measure on the space of commodity characteristics. An atomless measure space of producers and consumers is assumed to overcome the problem of non-convexity of the production and consumption sets induced by indivisibilities. This paper is based on a chapter from James Marton’s dissertation. We would like to thank Marcus Berliant, Wilhelm Neuefeind, and an anonymous referee for their valuable comments and suggestions.