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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.

We study the assimilation behavior of a group of migrants who live in a city populated by native inhabitants. We conceptualize the group as a community, and the city as a social space. Assimilation increases the productivity of migrants and, consequently, their earnings. However, assimilation also brings the migrants closer in social space to the richer native inhabitants. This proximity subjects the migrants to relative deprivation. We consider a community of migrants whose members are at an equilibrium level of assimilation that was chosen as a result of the maximization of a utility function that has as its arguments income, the cost of assimilation effort, and a measure of relative deprivation. We ask how vulnerable this assimilation equilibrium is to the appearance of a "mutant" - a member of the community who is exogenously endowed with a superior capacity to assimilate. If the mutant were to act on his enhanced ability, his earnings would be higher than those of his fellow migrants, which will expose them to greater relative deprivation. We find that the stability of the pre-mutation assimilation equilibrium depends on the cohesion of the migrants' community, expressed as an ability to effectively sanction and discourage the mutant from deviating. The equilibrium level of assimilation of a tightly knit community is stable in the sense of not being vulnerable to the appearance of a member becoming better able to assimilate. However, if the community is loose-knit, the appearance of a mutant will destabilize the pre-mutation assimilation equilibrium, and will result in a higher equilibrium level of assimilation.

In determining the optimal redistribution of a given population's income, we ask which factor is more important: the social planner's aversion to inequality, embedded in an isoelastic social welfare function indexed by a parameter alpha, or the individuals' concern at having a low relative income, indexed by a parameter beta in a utility function that is a convex combination of (absolute) income and low relative income. Assuming that the redistribution comes at a cost (because only a fraction of a taxed income can be transferred), we find that there exists a critical level of beta below which different isoelastic social planners choose different optimal allocations of incomes. However, if beta is above that critical level, all isoelastic social planners choose the same allocation of incomes because they then find that an equal distribution of incomes maximizes social welfare regardless of the magnitude of alpha.

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.