Inflation and Welfare in a Competitive Search Equilibrium with Asymmetric Information

We study an economy characterized by competitive search and asymmetric information. Money is essential. Buyers decide their cash holdings after observing the contracts posted by firms and experience match-specific preference shocks which remain unknown to sellers. Firms are allowed to post general contracts. In the baseline model with indivisible goods, we show that, when the number of potential buyers is fixed, inflation decreases markups. This, in turn, increases aggregate output and ex ante welfare. When goods are divisible the negative effect of inflation on markups holds for unconstrained agents but is ambiguous for constrained agents. Still, optimal monetary policy implies a positive nominal rate. When there is buyers' free entry, asymmetric information causes a congestion effect that can be corrected by monetary policy.