On Heterogeneity in a Fundamental Model of Money

In this preliminary version we consider different types of ex-ante heterogeneity (production cost, preferences, market access, etc.) in a Lagos-Wright (2003) framework. Such heterogeneity generates equilibrium inequality in nominal wealth, or money holdings. We have two basic objectives. First, we want to understand under what types of heterogeneity a simple monetary policy a' la Friedman is capable to generate optimal trades, and under what types it does not. Second if the Friedman rule cannot achieve efficiency, we ask if some redistributive monetary policy can achieve efficiency. Finally, we briefly examine the relationship between inflation and consumption inequality in the economy