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We show that deviations from long-run stability of product prices are optimal in the presence of endogenous producer entry and product variety in a sticky-price model with monopolistic competition in which price stability would be optimal in the absence of entry. Specifically, a long-run positive (negative) rate of inflation is optimal when the benefit of variety to consumers falls short of (exceeds) the market incentives for creating that variety under flexible prices, governed by the desired markup. Plausible preference specifications and parameter values justify a long-run inflation rate of two percent or higher. Price indexation implies even larger deviations from long-run price stability. However, price stability (around this non-zero trend) is close to optimal in the short run, even in the presence of time-varying flexible-price markups that distort the allocation of resources across time and states. The central bank uses its leverage over real activity in the long run, but not in the short run. Our results point to the need for continued empirical research on the determinants of markups and investigation of the benefit of product variety to consumers.