On Equilibrium Dynamics under Externalities in a Model of Economic Development

This paper studies a discrete-time version of a model of economic development proposed by Lucas, in which the average stock of human capital produces a positive externality in the production of the physical capital good. It establishes the existence of equilibrium programmes from arbitrary initial conditions, and of an equilibrium steady-state programme. The principal results are concerned with the global dynamic behaviour of equilibrium programmes off the steady state. They show that the asymptotic growth rates of consumption, physical and human capital on any equilibrium programme will equal the growth rates of the respective variables along the equilibrium steady state.