Deviations from long-run price stability are optimal in the presence of endogenous entry and product variety in a sticky-price model in which price stability would be optimal otherwise Long-run inflation (deflation) is optimal when the benefit of variety to consumers falls short of (exceeds) the market incentive for creating that variety—the desired markup; Price indexation exacerbates this mechanism. Plausible preference specifications and parameter values justify positive long-run inflation rates. However, short-run price stability (around this non-zero trend) is close to optimal, even in the presence of endogenously time-varying desired markups that distort the intertemporal allocation of resources. •Long-run inflation is optimal when variety benefit to consumer is lower than markup.•Plausible preferences imply optimal long-run inflation of at least 1 percent yearly.•Short-run price stability is nearly optimal even for large dynamic entry distortion.•Welfare loss from fully stabilizing prices can be large.•Policymaker has an extra incentive to renege on (timeless-)optimal policy.