Currency areas and monetary coordination

We integrate a monetary search model into open-economy macro to analyze the gains from coordinating on inflation. Search frictions and local congestion lead to a determinate exchange rate between two currencies. Relative prices deviate from the law of one price. Because the deviations depend on the cross-country differential in money growth, each country is tempted to inflate to exploit the deviations. Policy coordination reduces inflation and improves welfare for all countries. In contrast to traditional models, the gains from coordination continue to exist even after each country optimally sets a direct tax on the foreign use of the country's currency.