Precautionary balances and the velocity of circulation of money

Inflation, as a tax on money, gives buyers an incentive to reduce their money balances. Sellers are aware of this incentive and try to attract buyers by announcing price offers that induce buyers to spend a larger fraction of their money. We examine the effect of inflation on equilibrium price offers and associated trades 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 applied equally to all buyers independently of the quantities they purchase. If buyers'preferences are private information, sellers must charge more to buyers who purchase larger quantities due to incentive compatibility restrictions. In this case, equilibrium price offers consist of a non-linear price schedule. However, as inflation rises, price schedules become relatively flat. This implies that buyers with a low desire to consume purchase higher quantities and spend their cash more rapidly. Buyers with a high desire to consume purchase lower 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. The equilibrium is efficient at the Friedman rule and inflation reduces welfare both with full and private information