Sustained endogenous growth with decreasing returns and heterogeneous capital

Abstract

Abstract The possibility of sustained long-run growth is typically associated with the presence of some endogenous `engine of growth'. It may allow the economy to grow without bound despite the use of some non-reproducible resources. Such situations can lead to dynamic models combining the features of sustainable growth and decreasing returns. One-sector models of this kind have recently attracted much attention in macroeconomics applications. Their approximate linearity for the purposes of long-run analysis has been noted. This paper is aimed at establishing the general fact: dynamic models (one- or multi-sector) which are characterized by sustained endogenous growth with non-increasing returns display the patterns of optimal growth asymptotically equivalent to those generated by models with linear technology. I consider a neoclassical growth model with heterogeneous capital, develop its linear counterpart, and prove their asymptotic equivalence in terms of long-run optimal growth rates and cross-sectoral profiles of consumption, real interest rates and relative prices. This result also implies the `non-substitution' theorem for the neoclassical dynamic model of sustained growth: optimal input profiles, relative prices, and interest rates are asymptotically independent of intertemporal preferences.