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We study the joint implications of heterogeneity of total factor productivity and strategic price interactions between firms on the dynamics of inflation and the design of optimal monetary policy. In this setting, more productive firms respond less to shocks affecting their marginal costs than less productive firms. As a consequence, economies with a larger proportion of highly productive firms face a flatter Phillips curve. Moreover, when these two features concur, the Ramsey problem gives rise to an optimal non-zero long run inflation that amplifies the differences in relative prices between more efficient and less efficient firms, thus increasing the market share of the former. Nevertheless, in the presence of transitory technology shocks, optimal short term deviations from this positive long run inflation are negligible.