Genuine Savings and Sustainability with Resource Diffusion

We consider a spatial extension of genuine savings and wealth as a capital-based indicator of sustainability. In both inefficient and efficient economies, where well-being is locally or globally maximized, respectively, the well-known Hotelling rule and Hartwick (Dixit–Hammond–Hoel) investment rules and results are extended, depending on the extent of the spatial diffusion of natural capital. It is shown that the net present value of any future change in neighboring resource stocks affects the current change in intergenerational well-being. Numerical examples show the relevance of such parameters as the diffusion rate, discount rate, and marginal utility of consumption. Moreover, they suggest the exact adjustments to be made in aggregating or disaggregating the sustainability of different spatial units, which is not addressed in the current practice of green or wealth accounting.