A Note on Modelling Endogenous Growth

Abstract

The Note explores the conditions for the existence of a steady state in an neo-classical model with factor-augmenting technical progress. Under the assumption that saving is automatically invested, I.e., investment is a linear function of output, the Harrod neutral type of technical progress is the only case consistent with the steady state equilibrium. But for the case of nonlinear investment function which allows for the diminishing returns, the ecomomy with a general factor augmenting technical progress may be consistent wih the steady state equilibirum. The necessary condition for this is that the consumption function be homogenous of degree two, or the investment function of degree zero. This paper presents several sufficient conditions consistent with the solutions of the optimal control, when the central planner determines the optimal level of factor-augmenting technical progress.