This dissertation consists of two chapters, both of there describing economic environments that are characterized by frictions. Chapter 1 (joint with Philipp Kircher) develops an equilibrium directed search model of the labor market where workers can simultaneously apply for multiple jobs. Wage dispersion arises despite the fact that workers and firms are homogeneous and it is driven by the simultaneity of application choice. Risk-neutral workers apply for both 'safe' and 'risky' jobs. The former yield a high probability of a job offer, but for low pay, and act as a fallback option; the latter provide higher potential payoff, but are harder to get. Consistent with stylized facts, the density of wages is decreasing and higher wage firms receive more applications per vacancy. These predictions are not typically found in random search models and they are driven by the fact that firms compete for labor in a more immediate way due to the directed nature of the search process. Unlike most models of directed search, the equilibria are not constrained efficient. Chapter 2 (joint with Philipp Kircher) considers a monetary economy with multilateral meetings between buyers and sellers. Every seller has a single indivisible good and all buyers have the same valuation for the good, though they may hold different amounts of money. The number of buyers that visit a particular seller is random due to lack of coordination. The good is allocated using a second price auction. We show that in equilibrium ex ante identical buyers choose different money holdings: carrying more money is costly but it increases the probability of winning the auction. The unique equilibrium distribution of money holdings is explicitly characterized and it is shown to be non-degenerate and continuous. When the inflation rate is above the Friedman rule, the entry of sellers is suboptimal. At the Friedman rule efficiency obtains and the distribution of money collapses to a mass point at the real valuation for the good.
