Price Taking Equilibrium in Club Economies with Multiple Memberships and Unbounded Club Sizes

Economics

Further details

(with Myrna Wooders)

This paper develops a model of an economy with clubs where individuals may belong to multiple clubs and where there may be ever increasing returns to club size. The main condition required is that sufficient wealth can compensate for memberships in larger and larger clubs. Notions of price-taking equilibrium and the core, both with communication costs, are introduced. These notions require that there is a small cost, called a communication cost, of deviating from a given outcome. With the additional standard sorts of assumptions on preferences, we demonstrate that, for given communication costs, the core is not empty for sufficiently large economies and contains states of the economy that are in the core of the replicated economy for all replications (Edgeworth states of the economy). Moreover, for any given economy, every state in the economy that is in the core for all replications of that economy can be supported as a price-taking equilibrium with communication costs. Together these two results imply that, given the communication costs, for all sufficintly large economies there exists Edgeworth states of the economy and every Edgeworth state can be supported as a price-taking equilibrium.