In the Dasgupta-Heal-Solow-Stiglitz (DHSS) 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 quasi-arithmetic population growth, then the (gross and net of population growth) savings rates converge asymptotically to constants. © 2006 Elsevier Inc. All rights reserved.
Asheim, G., Buchholz, W., Hartwick, J., Mitra, T., & Withagen, C. A. A. M. (2007). Constant Savings Rates and Quasi-arithmetic Population Growth under Exhaustible Resource Constraints. Journal of Environmental Economics and Management, 53(2), 213-229. https://doi.org/10.1016/j.jeem.2006.09.001