A Supply and Demand Model of the College Admissions Problem

We consider a decentralized college admissions problem with uncertainty. We assume that a continuum of heterogeneous students apply to two colleges. College application choices are nontrivial because they are costly and their evaluations are noisy. Colleges set admissions standards for signals of student caliber. We develop the supply and demand framework where admissions standards act like prices that allocate scarce slots to students. We explore comparative statics in the game between colleges, and find that the better college is affected by the lesser college’s admissions standard in this decentralized world. Our analysis is complicated by the students’ application portfolio shifts. Noisy applications not only distorts outcomes, but even strategies: We find that the best students apply to the best college, and the best college sets higher standards only when the colleges differ sufficiently in quality, and the lesser school is not too small. Applying the model, we find that racial affirmative action at the better college is optimally met by a discriminatory admissions policy at the weaker school; and that binding early admissions programs are more effective than non-binding programs when a college competes with a rival that does not use early admissions. An earlier version was called “The College Admissions Problem with Uncertainty.” Lones is grateful for the financial support of the National Science Foundation. We have benefited from seminars at BU, UCLA, Georgetown, HBS, the 2006 Two-Sided Matching Conference (Bonn), 2006 SED (Vancouver), 2006 Latin American Econometric Society Meetings (Mexico City), and 2007 American Econometric Society Meetings (New Orleans). Arizona State University, Department of Economics, Tempe, AZ 85287-3806. Harvard University, Department of Economics, Cambridge, MA 02138. University of Michigan, Economics Department, Ann Arbor, MI 48109-1220.