Time preference and dynamic stability in an N-country world economy

We examine stability of competitive equilibrium in an N-country world economy with capital accumulation, where each country can have either increasing marginal impatience (IMI) or decreasing marginal impatience (DMI). The necessary and sufficient condition for stability is shown as positive definiteness of a simple matrix. The condition requires that any positive perturbation in one country's wealth, adjusted for international spill-over effects on other country's savings, reduces the country's wealth accumulation. In the presence of a DMI country, the number of countries should be sufficiently small for stability. Particularly, the existence of two or more than two DMI countries implies instablility.