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We examine the responses of prices and inflation to monetary shocks in an inventory-theoretic model of money demand. We show that the price level responds sluggishly to an exogenous increase in the money stock because the dynamics of households' money inventories leads to a partially offsetting endogenous reduction in velocity. We also show that inflation responds sluggishly to an exogenous increase in the nominal interest rate because changes in monetary policy affect the real interest rate. In a quantitative example, we show that this nominal sluggishness is substantial and persistent if inventories in the model are calibrated to match U.S. households' holdings of M2.