Optimal Inflation, Average Markups and Asymmetric Sticky Prices

In state-of-the-art New Keynesian model firms are monopolistically competitive and prices are sticky. However, the average markup resulting from the monopolistic competition is usually assumed away either by production subsidy or by the zero-inflation steady state. Also, in models of an open economy the same level of price stickiness is assumed for both countries. In this paper I study the optimal rate of inflation in a two country model keeping the average markup and allowing price stickiness to differ between countries. There are two channels that govern the optimal rate of inflation. First, with local currencies an inflation tax is partly imposed on the foreign country, so it is optimal to inflate. Second, the average markup constitutes a cost of holding money so it is optimal to deflate, to compensate this cost. The paper has four novel findings: 1) in the local currencies regime the first motive dominates and the optimal inflation is positive. 2) In a monetary union the first motive is absent and the optimal inflation is negative and below the Friedman rule. 3) A monetary union improves global welfare even when stickiness is different in two countries. However, when this difference is large, only one country (the one with higher stickiness) benefits from the integration. 4) A monetary union can be welfare improving for each of both countries, if a transfer is introduced from the more sticky to the more flexible country of (depending on the parameters up to) 2% of its GDP.