Optimal Growth with Resource Exhaustibility and Pollution Externality

Abstract

This paper investigates a problem of optimal growth with resource exhaustibility and pollution externality, based on a unified framework that explicitly considers augmentable man-made capital, exhaustible resource reserves, and accumulative environmental pollutants as three stock variables for optimal control analysis. Characterizations of the social optimum show that for any given man-made capital and resource reserves, resource extraction flows generated in optimal growth with both resource exhaustibility and pollution externality are smaller than those with only resource exhaustibility, and taking account of pollution externality resulting from resource extraction reduces the growth rate of consumption if man-made capital and natural resources are complements in final goods production. Existence, uniqueness and comparative statics of the steady state are analyzed. Conditions for transitional dynamics stability of optimal growth with resource exhaustibility and pollution externality are established. Expositions are made on whether allocations in a market equilibrium are consistent with the social optimum outcomes.

Keywords: Sustainability; Economic Growth; Exhaustible Resources; Pollution Externality; Environmental Damage; Optimal Control Problems

JEL Classification: Q54; H23; Q43; Q32; O13; O44; C61