Economically exhaustible resources in an oligopoly-fringe model with renewables

We consider a game between oligopolistic and fringe suppliers of fossil fuel from an exhaustible resource, and producers of a renewable perfect substitute. Extraction costs are stock-dependent and strictly convex in the rate of extraction. We characterize the open-loop Nash equilibrium analytically and perform numerical simulations with calibrated parameter values. The effects of our cost assumptions are (i) to have asymptotic economical instead of physical exhaustion of the non-renewable resource and (ii) the existence of a limit-pricing phase in which both fossil and renewables suppliers are active. We decompose the welfare loss of imperfect competition in a conservation and a sequence effect, and show that both can be substantial: 3.8 and 4.2 trillion US$ in the calibrated model, respectively. We also examine Green Paradox effects and find that initial carbon emissions depend non-monotonically on the renewables subsidy rate.