Inflation, prices, and information in competitive search

Inflation, as a tax on money, induces buyers to reduce their money balances. Sellers are aware of this, so to attract costumers, they post price offers that reduce the need for buyers to carry precautionary money balances. We study this effect of inflation in a competitive search environment where buyers experience preference shocks after they are matched with a seller. With full information, equilibrium price offers consist of a flat fee which is independent of the quantities purchased. With private information of buyers' preferences, equilibrium price offers are restricted by incentive compatibility constraints. As a result, the price schedule that maps quantities purchased onto payments must be increasing. As inflation rises, these price schedules become relatively flat, so the marginal cost of purchasing goods is low. Consequently, buyers that are not liquidity constrained (with a low desire to consume) purchase inefficiently large quantities. Meanwhile, buyers with a high desire to consume typically purchase inefficiently low quantities because, as their money balances fall, they become liquidity constrained. This is in contrast with the full information benchmark where inflation reduces the quantities purchased by all buyers.