This is the second 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 an equity threshold criterion that applies a utilitarian criterion until the degree of inequality crosses a threshold, at which point it begins to apply a maximin criterion. The threshold is user-specified by a parameter \(\Delta \) , where smaller values of \(\Delta \) correspond to greater fairness. The chapter presents a linear programming model of the resulting optimization problem and proves its validity. It describes the optimal solution subject to a budget constraint on closed form. It also shows that when the feasible set is closed under domination, there is an optimal solution that lies in the utilitarian portion of the feasible set, while this is not true in general. It shows by counterexample that the problem is not regionally decomposable. Finally, it offers an extensive marginal analysis that describes in detail the incentives stakeholders have to improve efficiency.