Pollution-adjusted optimal leasing value of oil and gas reserves

This paper investigates the optimal extraction strategy, the royalty of an equilibrium leasing contract, and the behavior of equilibrium oil or gas spot prices while considering two different market structures: pure monopoly and pure competition. The idea of sustainable development, or more specifically, the harmony between economy, ecology, and society, is the foundation for the modeling of the oil or gas lease. The stochastic optimal control approach is used through the derivation of a Hamilton-Jacobi Bellman (HJB) equation to specify an explicit solution to the optimal profit problem for investors with the power utility function under a monopolistic market structure and a competitive market structure without discoveries. Based on an isoelastic demand function, this paper creates net price models that consider changes in reserve levels, the policy for extraction rates, the pollution level, and the risk of oil and gas reserves being developed and produced. The equilibrium rental is established by balancing the time value of the rental with the expected present value of profits. The model is considered an American option when examining the ideal period for oil and gas exploration. The findings indicate that the extraction level is an increasing function of stock, depending on whether a monopolistic or competitive system is in place. The profit-tax cost function linked to environmental emissions is determined by modeling the physical quantity of pollution generated by the lessee during extraction, in line with the "polluter pays" principle. Price increases proportionally to the physical amount of pollution, but only to a limited extent; after that, price increases become less significant. When negotiating the contract, the government charges the lessee a higher rental cost proportional to the pollution level.