This paper extends recent findings in the search-theoretic literature on monetary exchange regarding the welfare costs of inflation. We present first estimates of the welfare cost of inflation using the "welfare triangle" methodology of Bailey (1958) and Lucas (2000). We then derive a money demand function from the search-theoretic model of Lagos and Wright (2005) and we estimate it from U.S. data over the period 1900-2000. We show that the welfare cost of inflation predicted by the model accords with the welfare-triangle measure when pricing mechanisms are such that buyers appropriate the social marginal benefit of their real balances. For other mechanisms, welfare triangles underestimate the true welfare cost of inflation because of a rent-sharing externality. We also point out other inefficiencies associated with noncompetitive pricing, which matter for estimating the cost of inflation. We then illustrate how endogenous participation decisions can mitigate or exacerbate the cost of inflation, and we provide calibrated examples in which a deviation from the Friedman rule is optimal. Finally, we discuss distributional effects of inflation.