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On the international scene, away from national legal rules, the use of different currencies is largely due to the operation of the "Invisible Hand" The paper develops a three-country model of the world economy. This links real trade patterns with currency exchange structures in a general equilibrium framework which includes transaction costs on foreign exchange markets. In the presence of strategic complementarities, there are multiple equilibrium structures of currency exchange for a given underlying real trade pattern. The existence conditions of these different equilibria are characterized, using the trade links between countries as the key parameters. Finally, repercussions on world output of the choice of a currency exchange structure are analysed.