In this study, we analyze the relationship between inflation and economic growth. To this end, we construct a model of endogenous growth with creative destruction, incorporating sticky prices due to menu costs. Inflation and deflation reduce the reward for innovation via menu cost payments and, thus, lower the frequency of creative destruction. Central banks can maximize the rate of economic growth by setting their target inflation rate at the negative of a fundamental growth rate that would be realized without price stickiness. The optimal inflation rate, however, may differ from the growth-maximizing inflation rate because of overinvestment in R&D and indeterminacy. Both mechanisms indicate a higher optimal inflation rate than the negative of a fundamental growth rate. Our calibrated model shows that the optimal inflation rate is close to the growth-maximizing inflation rate and that a deviation from the optimal level has sizable impacts on economic growth.