A Technical Remark on the Problem of the Optimum income taxation

This paper presents a method for treating problems of the Pontriyagin type, when we allow them to contain constraints restricting some functions to be of bounded variation. Among the list of economic models including this kind of constraints, Mirrlees´ formulation of the optimum income tax problem has been analyzed under the proposed procedure. The necessary conditions found hardly differ from those in the literature, excepting intervals where the monotonous z(n) happens to be, simultaneously, singular and strictly increasing.