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We analyze the welfare cost of inflation in a model with a cash‐in‐advance constraint and an endogenous distribution of establishments' productivities. Inflation distorts aggregate productivity through firm entry dynamics. The model is calibrated to the U.S. economy and the long‐run equilibrium properties are compared at low and high inflation. When the period over which the cash‐in‐advance constraint is binding is one quarter, an annual inflation rate of 10% leads to a decrease in average productivity of roughly 0.5% compared to the optimum. This decrease is not innocuous: it leads to a doubling of the welfare cost of inflation.