Management of a Capital Stock by Strotz's Naive Planner

Christopher J. Tyson

Nuffield College, Oxford


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.

JEL classification codes: C60, D91, E21.

Keywords: consumption, computation, hyperbolic discounting, time
preference.