Optimal Pricing, Use and Exploration of Uncertain Natural Resource Stocks.

摘要

Units of natural resources, to be called 'mines', are assumed distributed over the unexplored territory according to a Poisson process in space. At any moment, total reserves, R, and unexplored land, X, are given. Society can determine the rate of consumption, c, and the rate of exploration (space per unit time), x. Reserves, R, are drawn down by consumption and increased by discoveries made during exploration; X is decreased by exploration. At any moment, the payoff to society is a concave function of c less a linear function of x. Payoffs in the future are discounted back to the present at a constant rate.