Nizar Allouch

Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes

We model an economy with clubs (or jurisdictions) where individuals may belong to multiple clubs and where clubs sizes are arbitrary--clubs may be restricted to consist of only one or two persons, or as large as the entire economy, or anything in-between. Notions of price-taking equilibrium and the core, both with communication costs, are introduced. These notions take into account that there is a small communication cost of deviating from a given outcome. We demonstrate that, given communication costs, for all sufficiently large economies the core is nonempty and the set of price-taking equilibrium outcomes is equivalent to the core.

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

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. Clubs may be large, as large as the total agent set. 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 some additional standard sorts of assumptions on preferences, we demonstrate that, given communication costs parameterized by e > 0, for all sufficiently large economies, the core is non-empty 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 of 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 sufficiently large economies there exists Edgeworth states of the economy and every Edgeworth state can be supported as a price-taking equilibrium.

The cost of segregation in (social) networks

This paper investigates the private provision of public goods in segregated societies. While most research agrees that segregation undermines public provision, the findings are mixed for private provision: social interactions, being strong within groups and limited across groups, may either increase or impede voluntary contributions. Moreover, although efficiency concerns generally provide a rationale for government intervention, surprisingly, little light is shed in the literature on the potential effectiveness of such intervention in a segregated society. This paper first develops an index based on social interactions, which, roughly speaking, measures the welfare impact of income redistribution in an arbitrary society. It then shows that the proposed index vanishes when applied to large segregated societies, which suggests an “asymptotic neutrality” of redistributive policies.