Money and price posting under private information

We study price posting with undirected search in a search-theoretic monetary model with divisible money and divisible goods. Ex ante homogeneous buyers experience match specific preference shocks in bilateral trades. The shocks follow a continuous distribution and the realization of the shocks is private information. We show that generically there exists a unique price posting monetary equilibrium. In equilibrium, each seller posts a continuous pricing schedule that exhibits quantity discounts. Buyers spend only when they have high enough preferences. As their preferences are higher, they spend more till they become cash constrained. Since inflation reduces the future purchasing power of money and the value of retaining money, buyers tend to spend their money faster in response to higher inflation. In particular, more buyers choose to spend money and buyers spend on average a higher fraction of their money. The model naturally captures the hot potato effect of inflation along both the intensive margin and the extensive margin.