Terminal-Year Investment In Finite-Horizon Planninq Models (Notes & Comments)

Abstract

A common problem of finite-horizon planning models is that there is no logical determinant of investment in the final year (s). Where post-horizon production is not valued by a model, later-year investment, whose sole function is creation of capacity for post-horizon output, looks as incongruous as last rites for an atheist. A number of artificial devices have been developed to handle this difficulty1, but one predominates: to assume that terminal-year investment is a function of terminal-year output. The purpose of this note is to show: 1) how varied and arbitrary are the assumed functions (Section I); 2) that the terminal-year variables and the apparent feasibility of the resulting Plan are highly sensitive to the choice of function (Section II); and 3) that the arbitrariness of functional form is inevitable in the sense that generally acceptable criteria do not much restrict the choice (Section III). Throughout this note, we shall neglect four complexities that are not essential to the problem at hand. One, the marginal capital-output ratio (<r) is assumed fixed and known. Two, the most simple gestation-lag structure of investment is assumed, namely, that investment during period t permits an in¬crease in the output of period (t+1) over the output of t. Three, net investment is considered and depreciation complexities are assumed away. And four, we neglect all intersectoral and foreign-trade complications. The addition of complexity on any of the above counts obscures, but does not alter, the basic problem of the choice of a terminal-year investment determinant.