Endogenous Growth in Multisector Ramsey Models

Abstract

In this paper, I give sufficient conditions for the existence of endogenously growing optimal paths in a general multisector Ramsey model of optimal capital accumulation. The key assumption involves the existence of a positive vector of capital stocks which admits strictly positive consumption and expansibility in inverse proportion to the utility discount factor. If the technology set contains the ray through such a point, in addition to standard convexity and interiority assumptions, then optimal paths grow without bound from any strictly positive initial stocks. The result unifies a number of existing models in the growth theory literature. Within both capital theory and macroeconomics there has been a resurgence of interest in models of capital accumulation which display endogenous growth-models without time-dependent technologies which nonetheless have the property that the optimal or equilibrium paths of capital and consumption which they generate grow without bound. It is thus surprising that little work has been done in establishing conditions which guarantee this property. A recent exception is Jones and Manuelli (1990), working in a variant of the standard one-sector Ramsey model of optimal growth. Earlier, Gale and Sutherland (1968) also proved a growth result for an undiscounted one-sector Ramsey model. By and large, though, this research program has been carried out in a series of particular examples with little suggestion of a general framework for achieving endogenous growth. This essay attempts to fill that gap, at least for models which may be cast in the convex Ramsey optimal growth framework.2 The results below provide sufficient conditions for the existence of endogenously growing optimal paths in a convex multisector Ramsey model of optimal capital accumulation, thus unifying a number of particular examples in the growth literature, as well as providing simple conditions for guaranteeing growth in more complex models. By way of motivation, consider the simplest of all endogenous growth models, the one-sector linear model, or A-k model, used by Rebelo (1991). There is a single, all-purpose consumption-investment good. An infinitely-lived representative con