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 overlap ping-generations model with renewable natural resources a competitive path of manmade capital accumulation exists which meets the sustainability crite rion of intergenerational natural-capital equ(al)ity (= sustainable growth) . The alleged compatibility of decentralized optimization with natural-capi tal sustainability is appealing, but the relevance of this compatibility re sult is questionable: the growth factor of the renewable natural resource i s assumed to be independent of the resource stock. Employing instead a nonl inear (logistic) regeneration function. this paper reconsiders Mourmouras' compatibility statement in another natural environment. It is shown that on ly under a certain complex relationship between the parameters of the utili ty, production, and natural-growth function does a nontrivial stationary st ate exist which is saddle-point stable, it exhibits by definition intergene rational natural-capital equality, but the nonlinear setting precludes in g eneral, natural-capital equality across generations on the growth path towa rds the stationary state.