Inflation and unemployment in general equilibrium

When labor is indivisible, there exist efficient outcomes with some agents randomly unemployed, as in Rogerson (1988). We integrate this idea into the modern theory of monetary exchange, where some trade occurs in centralized markets and some in decentralized markets, as in Lagos and Wright (2005). This delivers a general equilibrium model of unemployment and money, with explicit microeconomic foundations. We show that the implied relation between inflation and unemployment can be positive or negative, depending on simple preference conditions. Our Phillips curve provides a long-run, exploitable, trade-off for monetary policy; it turns out, however, that the optimal policy is the Friedman rule.