Essays on sorting and inequality

Abstract

This thesis consists of three papers that examine sorting and inequality. In the first paper I present a model in which people sort into groups according to income and as a result become about the shape of the income distribution. Their beliefs in turn a§ect who they choose to interact with, and hence there is a two-way interaction between segregation and misperceptions about society. I show one possible application of this novel framework to the question of income inequality and the demand for redistribution. I demonstrate that under segregation an increase in income inequality can lead to a decline in perceived inequality and therefore to a fall in people's support for redistribution. I motivate my main assumptions with empirical evidence from a small survey that I conducted via Amazon Mechanical Turk. In the second paper I develop a general model of how social segregation and beliefs interact. Sorting decisions will be affected by beliefs about society, but these beliefs about society are in turn influenced by social interactions. In my model, people sort into social groups according to income, but become about the income distribution once they interact only with their own social circle. I define biased sorting equilibria, which are stable partitions in which people want to stay in their chosen group, despite their acquired misperceptions about the other groups. I introduce a refinement criterion - the consistency requirement - and find necessary and sufficient conditions for existence and uniqueness of sorting equilibria. In the third paper I present a model in which a monopolist offers citizens the opportunity to segregate into groups according to income. I focus initially on the case of two groups and show that a monopolist with fixed costs of offering the sorting technology will see profits increase as income inequality increases. I then analyze how the monopolist's optimal group partition varies with inequality and show that for a broad field of income distributions, monopolist profits increase with inequality, while at the same time total welfare of sorting given the monopolist's optimal schedule decreases. In the last section I examine how these findings generalize if the monopolist doesn't face costs of offering the sorting technology and can therefore offer as many groups as she wants.