Maximin Paths of Heterogeneous Capital Accumulation and the Instability of Paradoxical Steady States

Abstract

If there exist heterogeneous capital goods, a steady state may be in the sense that increasing the rate of interest above the Golden Rule level may lead to an increase in consumption or utility, rather than to the decrease which always occurs in one-sector models. It is shown that, in many cases, a path of capital accumulation which maximizes the minimum consumption or utility level is unlikely to converge to a paradoxical steady state of this kind. IN A ONE-SECTOR SOLOW-SWAN MODEL with homogeneous capital, a fall in the steady state interest rate always is associated with a rise in the steady state value of per capita utility, provided we are considering interest rates above the Golden Rule value. One aspect of the Cambridge controversy in capital theory concerns the fact that such steady state behavior does not always prevail in models with heterogeneous capital: lower interest rates can be associated with steady state equilibria having lower per capita utility. Might such steady states be unstable in some sense so that they would almost never be observed in an economy following some dynamic maximizing rules? Solow conjectured such a relationship, but until recently the question has been ignored.2 Burmeister and Long [5] have studied this question when the dynamic maximization rule is