This paper studies a life-cycle model in which the consumption good is assumed to be indivisible. This assumption requires the number of units of the good purchased in each period to be an integer. It is shown that, if the discount factor is sufficiently small, the policy function takes the form...

This note provides a simple proof of the necessity of the transversality condition for the differentiable reduced-form model. The proof uses only an elementary perturbation argument without relying on dynamic programming. The proof makes it clear that, contrary to common belief, the necessity of...

This note provides a simple proof of the necessity of the transversality condition for the differentiable reduced-form model. The proof uses only an elementary perturbation argument without relying on dynamic programming. The proof makes it clear that, contrary to common belief, the necessity of...