Essays in search theory

This thesis contains three essays. The first essay, “Matching with Multiple Applications: A Correction,” is a directed search model analyzing the implications of multiple applications by job seekers on the matching function. This paper shows why the matching function provided by Albrecht et al. (2003) is not correct when the numbers of firms and workers agents are finite, and shows how to derive the correct matching function. The second essay, “Search, Heterogeneity, and Segmentation” is joint work with Nicolas Jacquet, the first of a two-part project where we look at segmentation of markets when agents are heterogeneous, and deals with the special case when agents are of two types: either they are desirable (high-type) or not (low-type); the companion paper analyzes an economy where agents\u27 heterogeneity is on a continuum. We first characterize all steady state equilibria, and show that the segmented equilibrium can be an equilibrium. Welfare analysis is next carried out and it is shown that the economy with segmentation leads to at least as high an aggregate welfare as the economy when everyone is mixing in one meeting place. Out-of-steady-state dynamics is then analyzed. The third essay, “Directed Search and Firm Size,” shows how the size-wage differential, where larger firms paying their workers higher wages, can be obtained in a directed search setting. Directed search models generally predict that large firms, by promising the worker a higher probability of getting hired, pay lower wages. What I do here is to assume that there is an “optimal” size associated with a firm: if a firm hires less workers than capacity, it cannot be run properly and hence produces less. To avoid this potential loss in production, large firms have an incentive to post higher wages in order to get the right queue length. I show that if the penalty from not operating at the optimal capacity is large, there always exist parameter where the size-wage differential hold. I also endogenize the fractions of large and small firms in the economy