Fair Allocation of an Exhaustible Resource

There is little agreement on the social objective that should guide the intergenerational allocation of an exhaustible resource. Thus, remaining agnostic about a broad class of possible societal goals, we propose assessing feasible consumption paths by a fairness index that measures the worst relative performance across generations. Each generation's performance ratio compares its attained welfare with the maximum welfare achievable for that generation in isolation. The resulting fairness criterion is robust with respect to a broad canonical class of social objectives (symmetric, increasing, and concave). The fair consumption path, which maximizes the fairness index subject to basic economic consistency, is characterized by three primitive requirements: implementability (a nonincreasing path), exhaustiveness (full use of the resource), and balancedness (equalized ratios across cohorts). Together, these conditions yield a unique allocation that is Pareto-efficient, Lorenz-undominated, and guarantees strictly positive consumption for all future generations. In the benchmark case of constant absolute risk aversion (CARA), the model admits a semi-closed-form solution, including an explicit value function and a unique fairness level. The proposed criterion provides a transparent standard, without the need for society to endorse any particular social welfare function, while guaranteeing evenhanded treatment to all cohorts.