Efficient Social Welfare Function and Optimal Income Distribution

By showing that increases in the sum of aggregate income and aggregate Marshallian consumer surplus represent potential Pareto improvement, this paper builds a theoretical ground for using aggregate Marshallian consumer surplus as a social welfare indicator. The optimal income distribution that potentially Pareto dominates any other income distribution is studied. It is shown that the income distribution is optimal if and only if the marginal aggregate Marshallian consumer surplus of income is equalized across all consumers. An index that measures income distribution non-optimality rather than inequality is then developed. It is found that the social cost of income distribution non-optimality in a perfect competitive market could be surprisingly high. Finally, a new approach of social welfare function is developed and it is shown that a social welfare function can be expressed by the sum of aggregate income and aggregate Marshallian consumer surplus if and only if the marginal social welfare of a good is equal to its market price