Competitive Market Efficiency and Income Distribution Non-Optimality : A Theorem on Income Redistribution

Government redistribution is increasingly important in today's world. The effect of income distribution on industrialization and growth, and the causes of income redistribution have been studied in the contemporary literature. The normative significance of income redistribution, however, which is the focus of this paper, has been rarely studied. In this paper we analyze how income redistribution makes a potential Pareto improvement. For a given amount of total income, redistributing more income to consumers who spend relatively more on more elastically supplied goods increases the aggregate expenditure on more elastically supplied goods, while reducing the aggregate expenditure on less elastically supplied goods at the same amount. This paper shows that such reallocation of expenditures results in an increase in the equilibrium output of more elastically supplied goods, more than compensating for the decrease in equilibrium output of less elastically supplied goods. The aggregate Marshallian consumer surplus is raised and the potential Pareto improvement is then achieved. A perfectly competitive market is Pareto optimal for any income distribution at the individual level: all consumers maximize utilities for given income distribution and firms maximize profits. However, the Pareto optimal at the individual level does not ensure that the potential Pareto optimal at aggregate level is realized due to income distribution non-optimality. It is usually believed that income redistribution is aimed to improve social justice. We show in this paper that income redistribution can significantly improve efficiency at aggregate level. Using an example, we show that redistribution can improve social welfare more than 25%. If rich people spend relatively more on inelastically supplied goods than poor people do, the improvements of social justice and aggregate efficiency could move in the same direction. We give a testable condition for efficiency improving redistribution in the general case: if the consumer's sum of expenditure shares, weighted by inverse of 1 plus elasticities of supplies is less than the others' sum, redistributing more income to the consumer will make the potential Pareto improvement