Essays in Applied Microeconomic Theory

Abstract

This dissertation consists of three essays in microeconomic theory: two focusing on insurance theory and one on matching theory. The first chapter is concerned with catastrophe insurance. Motivated by the aftermath of hurricane Katrina, it studies a strategic model of catastrophe insurance in which consumers know that they may not get reimbursed if too many other people file claims at the same time. The model predicts that the demand for catastrophe insurance can ``bend backwards'' to zero, resulting in multiple equilibria and especially in market failure, which is always an equilibrium. This shows that a catastrophe market can fail entirely due to demand-driven reasons, a result new to the literature. The model suggests that pricing is key for the credibility of catastrophe insurers: instead of increasing demand, price cuts may backfire and instead cause a ``race to the bottom.'' However, small amounts of extra liquidity can restore the system to stable equilibrium, highlighting the importance of a functioning reinsurance market for large risks. These results remain robust both for expected utility consumer preferences and for expected utility's most popular alternative, rank-dependent expected utility. The second chapter develops a model of quality differentiation in insurance markets, focusing on two of their specific features: the fact that costs are uncertain, and the fact that firms are averse to risk. Cornerstone models of price competition predict that firms specialize in products of different quality (differentiate their products) as a way of softening price competition. However, real-world insurance markets feature very little differentiation. This chapter offers an explanation to this phenomenon by showing that cost uncertainty fundamentally alters the nature of price competition among risk-averse firms by creating a drive against differentiation. This force becomes particularly pronounced when consumers are picky about quality, and is capable of reversing standard results, leading to minimum differentiation instead. The chapter concludes with a study of how the costs of quality affect differentiation by considering two benchmark cases: when quality is costless and when quality costs are convex (quadratic). The third chapter focuses on the theory of two-sided matching. Its main topic are inefficiencies that arise when agent preferences permit indifferences. It is well-known that two-sided matching under weak preferences can result in matchings that are stable, but not Pareto efficient, which creates bad incentives for inefficiently matched agents to stay together. In this chapter I show that in one-to-one matching with weak preferences, the fraction of inefficiently matched agents decreases with market size if agents are sufficiently diverse; in particular, the proportion of agents who can Pareto improve in a randomly chosen stable matching approaches zero when the number of agents goes to infinity. This result shows that the relative degree of the inefficiency vanishes in sufficiently large markets, but this does not provide a "cure-all'' solution in absolute terms, because inefficient individuals remain even when their fraction is vanishing. Agent diversity is represented by the diversity of each person's preferences, which are assumed randomly drawn, i.i.d. from the set of all possible weak preferences. To demonstrate its main result, the chapter relies on the combinatorial properties of random weak preferences.