In this paper we integrate the recent development in monetary theory with international finance, in order to examine the coordination between two currency areas in setting long-run inflation. The model determines the value of each currency and the size of each currency area without requiring buyers to use a particular currency to buy a country's goods. We show that the two countries inflate above the Friedman rule in a non-cooperative game. Coordination between the two areas reduces inflation to the Friedman rule, increases consumption, and improves welfare of both countries. This gain from coordination increases as the two areas become more integrated in trade. These results arise from the new features of the model, such as the deviations from the law of one price and the extensive margin of trade. To illustrate these new features, we show that introducing a direct tax on foreign holdings of a currency does not eliminate a country's incentive to inflate, while it does in traditional models.
