This is the last of three chapters that analyze threshold-based fairness criteria, which are designed to combine a purely utilitarian metric with a maximin or leximax fairness criterion. The chapter focuses on a utility threshold criterion that applies a leximax criterion until the utility cost crosses a threshold, at which point it begins to apply a utilitarian criterion. The threshold is user-specified by a parameter \(\Delta \) , where larger values of \(\Delta \) correspond to greater fairness. The socially optimal solution is found by solving a sequence of optimization models. The chapter presents mixed integer/linear programming formulations of these models, whose validity is proved in the literature. It describes the optimal solution subject to a budget constraint in closed form and establishes its correctness with a lengthy argument that relies on a series of lemmas. In particular, it shows that the stakeholder utility allotments in the solution are step functions of \(\Delta \) . The chapter concludes with a marginal analysis of stakeholder incentives to improve efficiency.