Intergenerational natural-capital equality in an overlapping-generations model with logistic regeneration

Following Mourmouras [Scandinavian Journal of Economics 93 (1991): 585–591], in a Diamond [American Economic Review 55 (1965): 1126–1150] type overlapping-generations model with renewable natural resources a competitive path of manmade capital accumulation exists which meets the sustainability criterion of intergenerational natural-capital equ(al)ity (= sustainable growth). The alleged compatibility of decentralized optimization with natural-capital sustainability is appealing, but the rel-evance of this compatibility result is questionable: the growth factor of the renewable natural resource is assumed to be independent of the resource stock. Employing instead a nonlinear (logistic) regeneration function, this paper reconsiders Mourmouras' compatibility statement in another natural environment. It is shown that only under a certain complex relationship between the parameters of the utility, production, and natural-growth function does a nontrivial stationary state exist which is saddle-point stable. It exhibits by definition intergenerational natural-capital equality, but the non-linear setting precludes in general, natural-capital equality across generations on the growth path towards the stationary state.