Fair Resource Sharing Across Generations

Using a nonrenewable resource today reduces what remains for tomorrow. Even when societies agree that future generations deserve consideration, different views of social welfare can justify very different consumption plans. Maximizing total discounted welfare can favor early use, while placing greater emphasis on the least advantaged can support more restraint. This disagreement makes it difficult to select a common rule for sharing an exhaustible stock.

The paper [1] starts by calculating a benchmark for each generation. This is the greatest lifetime benefit achievable if the consumption plan is designed specifically in that generation's interest, subject to the same resource and economic constraints. Each generation's actual welfare is then expressed as a percentage of its benchmark. The lowest percentage across all generations defines the fairness index, and the fair allocation makes this minimum guarantee as large as possible.

Three requirements determine the resulting consumption plan. Consumption never increases over time, reflecting the opportunity cost of postponing resource use. The resource is fully used in the long run. Finally, every generation receives the same fraction of its own benchmark welfare. Together, these conditions yield a unique allocation that is also efficient, meaning that improving one generation's welfare requires reducing another's. Fairness rests on equal relative achievement, with each benchmark accounting for the opportunities available to that generation.

The paper's leading application for agents with constant absolute risk aversion shows how the rule changes resource use. A conventional plan optimized for the initial generation exhausts the stock after a finite time. Under the fair plan, consumption gradually approaches zero while remaining positive for every future generation, and the stock is exhausted only in the infinite-time limit. In the given numerical example, every generation receives approximately 84% of its own best attainable lifetime benefit. This percentage also has a broader interpretation. The same relative guarantee applies across a class of social objectives that value higher welfare, treat generations symmetrically, and do not reward inequality. The class includes both utilitarian and egalitarian criteria. Under each criterion, the fair allocation is compared with the best outcome that criterion could achieve. The approach therefore accommodates disagreement about social priorities while retaining a common standard for evaluating performance.

The analysis provides a theoretical benchmark for intergenerational resource stewardship. It considers a known resource stock, no replenishment or technological change, and a given social discount rate. These assumptions isolate the tradeoff between present use and future access, providing a starting point for studying richer settings with production, innovation, or uncertainty.

This research extends the fairness framework developed by Goel, Meyerson, and Weber [2] to resource allocation over time. It contributes to the research program on relative robustness at EPFL's Chair of Operations, Economics and Strategy (OES) [3-10], including recent work on the timing of medical tests under ambiguous prevalence dynamics [5].

Abstract: 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 even-handed treatment to all cohorts.