Constant Savings Rates and Quasi-Arithmetic Population Growth Under Exhaustible Resource Constraints
31 Pages Posted: 11 Nov 2005
Date Written: October 2005
In the Dasgupta-Heal-Solow-Stiglitz model of capital accumulation and resource depletion we show the following equivalence: If an efficient path has constant (gross and net of population growth) savings rates, then population growth must be quasi-arithmetic and the path is a maximin or a classical utilitarian optimum. Conversely, if a path is optimal according to maximin or classical utilitarianism (with constant elasticity of marginal utility) under quasiarithmetic population growth, then the (gross and net of population growth) savings rates converge asymptotically to constants.
Keywords: constant savings rate, quasi-arithmetic population growth
JEL Classification: Q10, Q32
Suggested Citation: Suggested Citation