In this study, we develop a simple, two-person economy model based on the capability approach. We show that the two distribution rules of goods equalizing capabilities (i.e., the least disparity of capabilities and the largest value of an intersection of capabilities) satisfy the weak equity axiom (Sen, 1973) defined over our framework. The results suggest that equality of capabilities can deal appropriately with hard case issues (i.e., issues related to the treatment of the disabled). Finally, we present two examples that illustrate an optimal solution for each rule.