The relation between current accounts and budgetary deficit in open economies has been a central subject of macroeconomics for a long  time. The traditional approach of fundamental macroeconomic identity,
used for the determination of the current account, has been subject to criticism because of absence of intertemporal considerations that are central when determining the trade balance and the current account. The recognition of these dynamic aspects has lead to an ample supply of literature on the intertemporal approach to the current account. Through such a model relating the current account to governmental budgetary deficit, which is determined by the solution of consumption and taxes smoothing problems, we try to show a mathematical development that leads us to the equation that represents the model and that relates current  accounts to public deficit.