Optimal extraction and taxation of strategic natural resources: a differential game approach

Moustapha Pemy

Abstract

This paper studies the optimal extraction and taxation of nonrenewable natural resources. It is well known that the market values of our main strategic resources – eg, oil, natural gas, uranium and copper – fluctuate randomly following global and seasonal macroeconomic parameters; these values are modeled using Markov switching Levy processes. We formulate this problem as a differential game. The two players in this differential game are a mining company, whose aim is to maximize the revenues generated by its extracting activities, and a government agency, who is in charge of regulating and taxing natural resources.We prove the existence of a Nash equilibrium. The corresponding Hamilton–Jacobi–Isaacs equations are completely solved, and the value functions as well as the optimal extraction and taxation rates are derived in closed form. Numerical examples are presented to illustrate our findings.