Banking, Liquidity and Inflation∗

This paper develops a search-theoretic model to study the interaction between bank-ing and monetary policy and how this interaction affects the allocation and welfare. In decentralized monetary economies, uncertainty regarding opportunities to trade typ-ically implies an inefficiency in allocation due to liquidity constraints. This paper studies how banking arises endogenously in a monetary economy to improve the al-location by reallocating liquidities across agents. We show that banking can always improve allocation in the decentralized market, but the existence and welfare impli-cation of banking depend on the monetary policy. For low inflation rates, banking does not exist. For high inflation rates, banking exists and is welfare-improving. For moderate inflation rates, banking exists and is welfare-reducing. Owing to general equilibrium feedback, banking can be supported in equilibrium even though welfare is higher without banking. One implication is that, due to the non-linear effect of infla-tion on the welfare, measuring the welfare cost of inflation by extrapolating historical data may underestimate the actual cost