This dissertation studies opportunity and equity in college admissions, as well as how higher education affects labor market outcomes. The first two chapters explore how state policies affect enrollment at public institutions of higher education. The third chapter characterizes outcomes in a labor market in which agents with different skill levels (levels of education) choose roles and match with each other. In each chapter, I build a theoretical two-sided matching framework to explore how limited opportunities are allocated, and motivate theoretical predictions with empirical evidence. Chapter 1: Performance Funding and Equity of Access to Public Universities While state appropriations to public universities have historically been determined by student headcount (enrollment funding), an alternative is to fund based on completion metrics such as number of degrees conferred (performance funding). Advocates argue that performance funding incentivizes universities to decrease inefficient over-enrollment, while critics argue that performance funding incentivizes universities to admit fewer under-represented minority applicants, as they are less likely to graduate. I develop a framework in which a social planner and universities systematically differ in their expected returns to enrolling students and show that there exist many enrollment and performance funding rules that realign the university's enrollment problem with the social planner's problem. Ultimately, level of funding affects enrollment, not structure of the funding rule. I also identify conditions such that funding changes disproportionately affect under-represented minority enrollment. To assess theoretical predictions, I estimate changes in selectivity and demographic composition of incoming first-time, full-time cohorts at public four-year universities in Ohio and Tennessee, states that switched to performance funding in 2009 and 2010 respectively. Ohio decreased funding in the long-run, while Tennessee did not; as predicted, I find evidence of increased long-run selectivity in Ohio but not in Tennessee. I also find the proportion of Black enrollment in Ohio decreased by 1.13 percentage points in the long-run, while it increased by 2.93 percentage points in Tennessee. Chapter 2: The Enrollment Effects of Regional Campuses The Ohio public university system has several institutions, including its flagship Ohio State University (OSU), that are split between "main" and "regional" campuses. While OSU's regional campuses are independently accredited institutions, they also have a strong transfer function: if a regional campus student has a minimum 2.0 GPA and 30 credit hours, they are guaranteed the option to transfer into the main campus. I build a general theoretical framework of first-time and transfer admissions with multiple institutions; the theory predicts that opening a regional campus causes community colleges to enroll a less academically prepared first-time student body, and may cause community college students to be crowded out by less prepared regional campus students in transfer admissions. As such, there are always both students who are strictly better and worse off after a regional campus opens, and opening a regional campus is not always welfare increasing. I show that a social planner prefers to modestly expand enrollment at a main campus over opening a larger regional campus if the regional campus is insufficiently differentiated from a community college. Chapter 3: Choosing Sides in a Two-Sided Matching Market I model a competitive labor market in which agents of different skill levels (e.g., college educated or not) decide whether to enter the market as a manager or as a worker. After roles are chosen, a two-sided matching market is realized and a cooperative assignment game occurs. There exists a unique rational expectations equilibrium that induces a stable many-to-one matching and wage structure. Positive assortative matching occurs if and only if the production function exhibits a condition that I call "role supermodularity", which is stronger than the strict supermodularity condition commonly used in the matching literature because a high skilled agent with a role choice is only willing to enter the market as a worker if she expects that it is more profitable to cluster with only other high skilled agents than to exclusively manage. The wage structure in equilibrium is consistent with empirical evidence that the wage gap is driven both by increased within-firm positive sorting as well as between-firm segregation. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]