What are the welfare gains from being in a currency union? I explore this question in the context of a dynamic stochastic general equilibrium model with monetary barriers to trade, local currency pricing and incomplete markets. The model generates a tradeoff between monetary independence and monetary union. On one hand, distinct national monetary authorities with separate currencies can address business cycles in a countryspecific way, which is not possible for a single central bank. On the other hand, short-run violations of the law of one price and long-run losses of international trade occur if different currencies are adopted, due to the inertia of prices in local currencies and to the presence of trade frictions. I quantify the welfare gap between these two international monetary arrangements in consumption equivalents over the lifetime of households, and decompose it into the contributions of different frictions. I show that the welfare ordering of alternative currency systems depends crucially on the international correlation of macroeconomic shocks and on the strength of the monetary barriers affecting trade with separate currencies. I estimate the model on data from Italy, France, Germany and Spain using standard Bayesian tools, and I find that the tradeoff is resolved in favour of a currency union among these countries.