The just rate of depletion of a natural resource

The optimal pricing and use of a natural resource is reconsidered with respect to intergenerational equity considerations. It is assumed that in a just economy, each generation chooses the plan that maximizes its own utility, subject to the constraint that the plan should not be exploitative in the sense that each generation does not take advantage of its earlier point in time with respect to future generations. It is shown that if the cost of production of an alternative energy source (e.g., solar) is sufficiently high relative to the stock of naturally stored energy, the constraints of justice result in a lower rate of energy use initially, but a higher rate later.