There is much to discuss, and debate, about the sources and effects of inequality on economic growth and social mobility, and the relationship between education and economic growth. However, an undergraduate degree from a highly selective and elite college gives students a strong advantage in gaining employment in jobs that promise greater lifetime earnings. The widely held assumption is that the prestige of the college is a useful proxy for the quality of the graduates of that institution. Irrespective of the relationship between education and economic growth, post-secondary education is imperative to the enhancement of human capital and a rich source of talent for employers. If there are significant bottlenecks, or structural impediments, that block equal opportunity for students of high ability that do not go to elite colleges, we should identify the problem and attempt to reduce or eliminate it. In the United States, achieving equal opportunity in post-secondary education is typically described in terms of enrolling more underrepresented groups in selective colleges. The belief is that if this step is accomplished, it will have a fundamental impact on the problem of inequality at the national level. However, what if there are not enough places for students in selective colleges to accomplish this goal? What if selective colleges do not have enough capacity to make a significant impact on the problem of serving students from underrepresented groups with demonstrated high abilities? These questions are addressed in this report.