Can a concern for status reconcile diverse social welfare programs?

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