How to share money creation among the members of the European Monetary Union? To address this issue, we construct a two-country New Open-economy Macroeconomics model of an asymmetric monetary union with an incomplete financial market and home bias in consumption. We consider two sharing rules consistent with the current regulations of the European System of Central Banks. First, each participating National Central Bank supplies half of the European Central Bank determined money creation in the monetary union. Secondly, each National Central Bank adapts the national increase in money demand, under the constraint that the total money creation in the union does not exceed the level determined by the ECB for the whole union. We show that the current sharing rule, which ignores countries’ heterogeneity, is superior in terms of welfare. The key role of the current account is emphasized. It proves an efficient decentralized mechanism for allocation of money.