This chapter analyzes beta fairness, which maximizes the average utility of the fraction \(\beta \) of the population having the smallest utilities. It represents an attempt to compromise between a purely utilitarian and a purely maximin objective. The chapter presents a linear programming model of beta fairness from the literature and describes, in closed form, the optimal solution that results when beta fairness is achieved subject to a budget constraint. It observes that the solution is very often the same as a maximin solution except when \(\beta \) is close to 1, which suggests that beta fairness is more useful for avoiding overprivileged stakeholders at the top of the distribution than underprivileged stakeholders at the bottom. The chapter also presents a marginal analysis of incentives for efficiency improvements.