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A two-country general equilibrium model with large wage setters and conservative monetary authorities is employed to investigate the welfare implications of three international monetary regimes: i) non-cooperative, ii) cooperative, and iii) monetary union. The analysis shows that the unions’ wage claims depend on three strategic effects which are substantially different between the international policy arrangements. In contrast with recent studies, a switch from non-cooperation to monetary union is welfare improving with a sufficiently conservative central bank because unions perceive wage hikes as delivering lower terms-of-trade gains; while a switch from non-cooperation to cooperation is always beneficial because wage hikes do not yield any terms-of-trade gain. Finally, the paper qualifies Lippi’s (2003) findings