Inspired by empirical evidence from the oil market, we build a model of an oligopoly facing a fringe as well as competition from renewable resources. We explore different subclasses of HARA utility functions (Cobb-Douglas, power and quadratic utility) to check the robustness of results found in...

We consider a game between oligopolistic and fringe suppliers of fossil fuel from an exhaustible resource, and of producers of a renewable perfect substitute. Extraction costs are stock-dependent and strictly convex in the rate of extraction. We characterize the open-loop equilibrium...

In the dominant firm model, we show that an increase of the fringe's reserves of a nonrenewable resource may lead to a decrease in aggregate discounted social welfare. This happens when the difference between the fringe's extraction cost and the dominant firm's is positive and large enough. We...

We give a full characterization of the open-loop Nash equilibrium of a nonrenewable resource game between two types of firms differing in extraction costs. We show that (i) there almost always exists a phase where both types of firms supply simultaneously, (ii) when the high cost mines are...

We give a full characterization of the open-loop Nash equilibrium of a non-renewable resource asymmetric game. We show that (i) there almost always exists a phase where both supply simultaneously positive quantities, (ii) when the high cost mine is exploited by a number of firms that goes to...

We revisit the seminal growth model with exhaustible resources, the so called Dasgupta-Heal-Stiglitz-Solow model (DHSS). For this optimal control problem with two state variables, we explicitly characterize the dynamics of all the variables in the model and from all possible initial values of...

We specify and solve a closed-loop dominant firm nonrenewable resource game, with a price-taking fringe. We show that (i) the outcomes of the closed-loop and the open-loop dominant firm nonrenewable resource game (à la Salant 1976) coincide and (ii) when the number of fringe firms becomes...

We provide the closed form solution to the Dasgupta-Heal-Solow-Stiglitz (DHSS) model. The DHSS model is based on the seminal articles Dasgupta and Heal (Rev. Econ. Stud.,1974), Solow (Rev. Econ. Stud.,1974) and Stiglitz (Rev. Econ. Stud.,1974) and describes an economy with two assets, man-made...