This paper presents a model designed to study the dynamic response of the economy under a fixed peg to the dollar to an international (and exogenous) real appreciation of the dollar, when there is wage and price stickiness, perfect capital mobility subject to sudden stops, and predominantly dollar denominated foreign debts with predominantly non-dollar trade. Assuming perfect foresight, we take the simple case in which the world is composed of the U.S.A., Europe, and Argentina and while all foreign debts are dollar denominated, all foreign trade is done with Europe. Hence, an important parameter in the model is the exogenous euro/dollar real exchange rate. PPP prevails in the export sector and there is monopolistically competitive price setting in the domestic sector and monopolistically competitive wage setting by households. Both are subject to adjustment cost functions that generate stickiness and domestic price and wage gaps, which result in "Phillips curve" equations for domestic prices and wages, respectively. Money demand is generated by a transactions technology. The first order conditions for firms and households under symmetric monopolistic competition equilibriums and the budget constraints result in a four dimensional dynamical system in the multilateral real exchange rate (MRER), the real wage, the rate of domestic price inflation and the rate of wage inflation. This system has a saddle-path stable equilibrium which is dependent on the marginal utility of wealth. Under the assumption that the economy is what is called a Domestically Biased Economy in Production relative to Consumption (DBE), it is seen that strong dollar shocks, which require an inter-temporally smoothened fall in consumption (and hence an increase in the marginal utility of wealth), have perverse impact effects. The peso appreciates in real terms and the real wage increases. These effects generate foreign indebtedness and increased vulnerability to (exogenous and unexpected) sudden stops. The DBE assumption essentially entails that real depreciations require reductions in the real wage to preserve (long run) labor market equilibrium. A story is developed to explain the main features of the functioning and ultimate collapse of Convertibility in Argentina, by assuming a strong dollar shock which is believed to be temporary and has the effect of generating unemployment, recession and debt accumulation. But before the new steady state is reached it is revealed that the shock is permanent, which triggers a sudden stop, a default, a devaluation, a debt restructuring, fiscal reform, and the return to capital market access. A more flexible exchange regime could avoid the debt accumulation that triggers the sudden stop, as well as the long period of unemployment, recession, and deflation.