Optimal Income Redistribution When Individual Welfare Depends Upon Relative Income

The purpose of the present note is to explore the structure of optimal income taxation/redistribution in an economy where the welfare of individuals depends in part on relative after-tax consumption, i.e., we specify individual welfare as a function of absolute and relative after-tax consumption, with diminishing marginal utility to each. With such a specification, of course, an additional incentive for income redistribution from wealthy to poor citizens is created and the logical impossibility of increasing tax rates to the point where disincentive effects actually reduce tax revenues is potentially removed. The analysis highlights the importance of the marginal valuation placed on upward social mobility in various ranges of the income distribution and its interaction with the elasticity of the marginal utility of consumption; of course, "labor supply" elasticities, the form of the social welfare function, and the skill distribution continue to play an important role.