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A transfer from a richer individual to a poorer one seems to be the most intuitive and straightforward way of reducing income inequality in a society. However, can such a transfer reduce the welfare of the society? We show that a rich-to-poor transfer can induce a response in the individuals’ behaviors which actually exacerbates, rather than reduces, income inequality as measured by the Gini index. We use this result as an input in assessing the social welfare consequence of the transfer. Measuring social welfare by Sen’s social welfare function, we show that the transfer reduces social welfare. These two results are possible even for individuals whose utility functions are relatively simple (namely, at most quadratic in all terms) and incorporate a distaste for low relative income. We first present the two results for a population of two individuals. We subsequently provide several generalizations. We show that our argument holds for a population of any size, and that the choice of utility functions which trigger this response is not singular – the results obtain for an open set of the space of admissible utility functions. In addition, we show that a rich-to-poor transfer can exacerbate inequality when we employ Lorenz-domination, and that it can decrease social welfare when we draw on any increasing, Schur-concave welfare function.

Let there be two individuals: “rich,” and “poor.” Due to inefficiency of the income redistribution policy, if a social planner were to tax the rich in order to transfer to the poor, only a fraction of the taxed income would be given to the poor. Under such inefficiency and a standard utility specification, a Rawlsian social planner who seeks to maximize the utility of the worst-off individual will select a different allocation of incomes than a utilitarian social planner who seeks to maximize the sum of the individuals’ utilities. However, when individuals prefer not only to have more income but also not to have low status conceptualized as low relative income, and when this distaste is incorporated in the individuals’ utility functions with a weight that is greater than a specified critical level, then a utilitarian social planner will select the very same income distribution as a Rawlsian social planner.