We analyze the economic consequences of forming a monetary union among countries with varying degrees of financial distortions, which interact with the firms' pricing decisions because of customer-market considerations. In response to a financial shock, firms in financially weak countries (the periphery) maintain cashflows by raising markups--in both domestic and export markets--while firms in financially strong countries (the core) reduce markups, undercutting their financially constrained competitors to gain market share. When the two regions are experiencing different shocks, common monetary policy results in a substantially higher macroeconomic volatility in the periphery, compared with a flexible exchange rate regime; this translates into a welfare loss for the union as a whole, with the loss borne entirely by the periphery. By helping firms from the core internalize the pecuniary externality engendered by the interaction of financial frictions and customer markets, a unilateral fiscal devaluation by the periphery can improve the union's overall welfare.