Decision-making processes increasingly rely on the use of algorithms. Yet, algorithms' predictive ability frequently exhibits systematic variation across subgroups of the population. While both fairness and accuracy are desirable properties of an algorithm, they often come at the cost of one another. What should a fairness-minded policymaker do then, when confronted with finite data? In this paper, we provide a consistent estimator for a theoretical fairness-accuracy (FA) frontier put forward by Liang, Lu, Mu, and Okumura [2024, https://arxiv.org/abs/2112.09975]. To do so, we recognize that the FA-frontier is a part of the boundary of a convex set---the feasible set of group-specific expected losses associated with all possible algorithms---that can be fully represented by its support function. We provide an estimator of this support function and show that it converges to a tight Gaussian process as the sample size increases.