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We investigate the welfare effects of inflation in economies with search frictions and menu costs. We first analyze an economy where there is no transaction demand for money balances: Money is a mere unit of account. We determine a condition under which strictly positive inflation is desirable. We relate this condition to a standard efficiency condition for search economies. Second, we consider a related economy in which there is a transaction role for money. In the absence of menu costs, the Friedman rule is optimal. In the presence of menu costs, the optimal inflation rate is negative for our numerical examples provided menu costs are small. A deviation from the Friedman rule can be optimal depending on the extent of the search externalities.