Essays in directed search with private information

This dissertation consists of two chapters, each of which is based on a theoretical research paper. The two chapters are related in that in both chapters I study models of directed (competitive) search with private information. However, some details of the environments and the questions addressed in each chapter are different. In Chapter 1, I mainly address a normative question about the (in)efficiency of equilibrium, while the main question in Chapter 2 is how to characterize the equilibrium and what properties the equilibrium has.;In Chapter 1, I characterize the constrained efficient or planner's allocation in a directed search model with private information. In this economy, buyers post contracts and sellers with private information observe all postings and direct their search toward their preferred contract. Then buyers and sellers match bilaterally and trade. I define a planner whose objective is to maximize social welfare subject to the information and matching frictions of the environment. I show in my main result that if the market economy fails to achieve the first best, then the planner, using a direct mechanism, achieves strictly higher welfare than the market economy. I also derive conditions under which the planner achieves the first best. I show that the planner can implement the direct mechanism by imposing submarket-specific taxes and subsidies on buyers conditional on trade (sales tax).;In an asset market application, I show that in general the efficient sales tax schedule is non-monotone in the price of assets. This non-monotonicity makes the implementation of the direct mechanism difficult in practice. I show that if in addition to sales tax the planner can use entry tax, submarket-specific taxes and subsidies imposed on buyers conditional on entry to each submarket whether they find a match or not, then the planner can implement the direct mechanism by using monotone tax schedules, increasing sales tax and decreasing entry tax.;In Chapter 2, I study a model in which firms invest in capital and post wages, and heterogeneous workers, who have private information about their skills, choose where to apply. Workers and firms match bilaterally. Each matched agent gets an exogenous payoff from the match before wages are paid. Each of these payoffs displays complementarity in capital and skill. I derive conditions under which the market exhibits PAM, positive assortative matching. Under these conditions, the firms over-invest in capital compared to the first best, because capital is used as a screening device.;I show that the fact that firms need to screen workers in the presence of private information changes the predictions of the model compared to that in the presence of complete information. In particular, I show that the complete information allocation exhibiting PAM is not necessary nor sufficient for the market allocation to exhibit PAM.