Resource Extraction with a Carbon Tax and Regime Switching Prices

Abstract

This paper develops a model of a profit maximizing firm with the option to exploit a non-renewable resource, choosing the timing and pace of development. The resource price is modelled as a regime switching process, which is calibrated to oil futures prices. A Hamilton-Jacobi-Bellman equation is specified that describes the profit maximization decision of the firm. The model is applied to a problem of optimal investment in a typical oils sands in situ operation, and solved for critical levels of oil prices that would motivate a firm to make the large scale investment needed for oil sands extraction, as well to operate, mothball or abandon the facility. Regime shifts can have an important effect on the optimal timing of investment and extraction. The paper examines the effect of several carbon tax schemes on optimal timing of construction, production and abandonment. A form of Green Paradox is identified.

Keywords: non-renewable natural resources, oil sands, optimal control, HJB equation, carbon tax, regime switching

JEL Classification: Q30, Q40, C61, C63