Why the Rich Get Richer and the Poor Get Poorer

Abstract

The usual procedure in the field of optimal growth consists in maximizing a (discounted or not) sum of instantaneous utilities, called welfare. Such an optimality criterion implies that preferences are independent over time. Following in the tradition of Irwing Fisher, Koopmans presented an alternative for the case of discrete time periods; he used an assumption of limited non-complementarity over time, and showed that there exist welfare functions for which the rate of time preference is variable. Later he and others showed that the implications are that even in the simplest situations described by the neoclassical growth model initial conditions affect the long run optimal path. Equivalent results for the case of continuous time have been reached by the present author. A similar approach by Uzawa reaches different results due to his particular assumptions; his optimal paths are, in the long run, independent of initial wealth. Blanchard and Fischer have critizised Uzawa’s increasing rate of time prKeywords: Rich, Poor.