Resource depletion under uncertainty: implications for mine depreciation, Hartwick’s Rule and national accounting

Lozada’s equation [Resource and Energy Economics 17 (1995) 137] for the change in value of a non-autonomous dynamic program is generalized to stochastic control and applied to the depreciation of a competitive mine facing price, reserve and discount rate uncertainty. Mine depreciation includes the costs of these risks, as well as an adjustment to the ‘net price’ used to value depletion and revisions. The change in value equation also provides the basis for a stochastic version of Hartwick’s Rule [American Economic Review 67 (1977) 972] for sustainable consumption, that the risk adjusted value of net investment equal zero. The analysis has implications for the Weitzman [Quarterly Journal of Economics 90 (1976) 156] welfare measure and the stochasic Hamiltonian.