The Optimal Distribution of Income

Abstract

What is the optimal distribution of income? As any constrained optimisation problem, this depends on the form of the objective function and that of the constraint. Since we are interested in optimality from the social point of view, the relevant objective function is the SWF. The relevant constraint can be expressed as a utility possibility frontier if we agree that social welfare is a function of individual utilities. (Or individual welfares. Abstracting away the differences between preference and welfare, the two are equivalent; see Section 1.3.) Factors other than individual utilities are either regarded as not relevant to social welfare or are being held constant. In Section 2.2.1 we derived a utility possibility frontier by taking the outer envelope of the numerous utility possibility curves each corresponding to a specific collection of goods. This may be regarded as rather restrictive or purely economic, since, by varying only the collection of goods, other (social, etc.) factors must be held constant. By changing these other factors, a different utility possibility frontier may emerge. Conceptually, this generalisation can easily be taken into account by taking the outer envelope of the various utility possibility frontier, calling it the grand utility possibility frontier. Second, we may also take account of the possible costs of and constraints on redistribution which reduces the grand utility possibility frontier into the grand utility feasibility frontier (GUFF).