Management of a Capital Stock by Strotz's Naive Planner

Abstract

A generalized version of the capital management problem posed in a classic paper by R. H. Strotz is analyzed for the case of the "naive" planner who fails to anticipate any impending change in his own preferences. By imposing progressively stronger restrictions on the primitives of the problem --- namely, the planner's discounting function, his utility index function, and the investment technology --- the path of the capital stock is characterized first implicitly as the solution to a differential equation and then explicitly via formulae that may or may not be expressible in closed form. Inasmuch as this procedure turns out to leave the discounting function essentially unrestricted, the theory can accommodate, in particular, decision makers who discount time according to the type of hyperbolic curve said to be suggested by psychological studies. Strategies for numerical computation of capital paths are discussed and are demonstrated in sample planning problems.consumption, computation, hyperbolic discounting, time preference.