This paper compares the monetary policy problem in open economies with that in closed economies. It is found that the monetary policy problems in open and closed economies are isomorphic even in the presence of distortions in a steady state and hence the optimal monetary policies have similar properties. On the other hand, the monetary policy maker in open economies has a distorted incentive to manipulate the terms-of-trade. Because of the additional distortion in open economies, there exist gains from international monetary policy cooperation even in the case of a unit intertemporal elasticity of substitution, in contrast to the literature that abstracts from distortions in a steady state. Also, it is found that in the presence of distortions inflation bias is decreasing in openness, which is line with empirical evidence. In addition, this paper presents a simple transformation so that methods in closedeconomy models are easily applicable to open-economy models.