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This paper studies the welfare costs and the redistributive effects of inflation in the presence of idiosyncratic liquidity risk, in a microfounded search‐theoretical monetary model. We calibrate the model to match the empirical aggregate money demand and the distribution of money holdings across households and study the effects of inflation under the implied degree of market incompleteness. We show that in the presence of imperfect insurance the estimated long‐run welfare costs of inflation are on average 40% to 55% smaller compared to a complete markets, representative agent economy, and that inflation induces important redistributive effects across households.