We compare three market structures for monetary economies: bargaining (search equilibrium); price taking (competitive equilibrium); and price posting (competitive search equilibrium). We also extend work on the microfoundations of money by allowing a general matching technology and entry. We study how equilibrium and the effects of policy depend on market structure. Under bargaining, trade and entry are both inefficient, and inflation implies first-order welfare losses. Under price taking, the Friedman rule solves the first inefficiency but not the second, and inflation may actually improve welfare. Under posting, the Friedman rule yields the first best, and inflation implies second-order welfare losses.

We survey the literature on search-theoretic models of the labor market. We show how this approach addresses many issues, including the following: Why do workers sometimes choose to remain unemployed? What determines the lengths of employment and unemployment spells? How can there simultaneously exist unemployed workers and unfilled vacancies? What determines aggregate unemployment and vacancies? How can homogeneous workers earn different wages? What are the tradeoffs firms face from different wages? How do wages and turnover interact? What determines efficient turnover? We discuss various modeling choices concerning wage determination and the meeting process, including recent models of directed search.

Search‐theoretic models of monetary exchange are based on explicit descriptions of the frictions that make money essential. However, tractable versions of these models typically make strong assumptions that render them ill suited for monetary policy analysis. We propose a new framework, based on explicit micro foundations, within which macro policy can be studied. The framework is analytically tractable and easily quantifiable. We calibrate the model to standard observations and use it to measure the cost of inflation. We find that going from 10 percent to 0 percent inflation is worth between 3 and 5 percent of consumption—much higher than previous estimates.