Optimal Savings with Finite Planning Horizon

Abstract

OPTIMAL SAVINGS programs for a nation have been discussed in the economic literature with an infinite time horizon in view. We may mention in particular the pioneering work of Ramsey on this question2. This approach is logical beeause without explicitly introducing uncertainty it is not possible, on the national plane, to choose a particular cut-off point and at the same time avoid being arbitrary. For individuals, there is only a span of life, but a nation's life may reasonably be assumed to extend indefinitely in time. The problem is that unless we introduce some crucial boundedness assumption (explicitly or implicitly) at some stage of the argument, infinite programs give rise to conceptual difficulties which may be briefly described as paradoxes of infinity.3 Examples of such boundedness assumptions are Ramsey's use of the concept of a finite bliss, defined as a maximum conceivable state of satisfaction attained for a level of consumption, or the common practice of using a pure rate of time preference in discounting future satisfaction. Neither of these assumptions is entirely unobjectionable.