We develop a simple general equilibrium framework to study the effect of the exchange rate system on trade and welfare. An important feature of the model is deviations from purchasing power parity, caused by rigid price setting in buyers' currency. We find the following. First, exchange rate stability is not necessarily associated with more trade.In a simple benchmark model with separable preferences and only monetary shocks, trade is unaffected by the exchange rate system, consistent with most evidence. Second, both trade and welfare can be higher under either exchange rate system, depending on preferences and on the monetary policy rules followed under each system. Finally, in general there is no one-to-one relationship between the levels of trade and welfare across exchange rate systems.