This paper presents a method of solving a practical optimization problem which arose in the context of private households' reactions to income tax levied from couples. Since the problem of constrained maximization of the household's life-time utility function in n prospective periods is complicated and sizeable, a two-stage dynamic programming approach is proposed. Splitting the problem into two-sub problems: finding the optimum policy and approximation in the policy space, is based on the dynamic nature of problems of this type, which can be seen as a multi-period decision process. Some provisional results obtained by experimental application appear to be sufficiently promising to justify elaboration.