Equilibrium of an Economy with Infinitely Many Indivisible Commodities and Consumers

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This paper examines an economy that is a special case of what Ostroy (1984) has termed “large-square” economies. The economy can also be thought of as the “large- square” version of a “small-square” economy with indivisible goods presented by Shapley and Scarf (1974). In their economy, each consumer is endowed with a single indivisible good, which they call a house, and has preferences over houses such that they want exactly one house. Shapley and Scarf show that an equilibrium exists for this economy. The “large-square” version of this that is examined below has a continuum of indivisible goods and a continuum of agents each being endowed with exactly one indivisible good. Each agent has a utility function defined over these indivisible goods and wants to consume exactly one such good. It will be assumed that there are finitely many such utility functions. A quasi-equilibrium is shown to exist for this special kind of “large-square” economy.