A Supply and Demand Model of the College Admissions Problem∗

We develop a positive theory of decentralized college admissions problems with uncertainty, in which a continuum of heterogeneous students apply to two colleges. Student college application choices are nontrivial since they are costly and they are noisily evaluated. Colleges set admissions standards for signals of student caliber. With a heterogeneous student population, we first characterize how the student acceptance chances at the colleges co-move in caliber. We then deduce how college application portfolios vary across students. In the spirit of supply and demand, admissions standards act like prices that allocate scarce slots to students. Noisy and costly applications prevent student-college sorting: Unless the colleges differ sufficiently in quality and the lesser one is not too small, better students need not apply most aggressively, nor need the better college set higher standards. We explore comparative statics, showing that shifts in capacity or application costs at one school affect both the standards and student body compositions at both. We extend the model, to find that affirmative action at the better college may be met by a discriminatory admissions policy at the weaker school, and that the lesser college may poach students from its rival using 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), Iowa State, Harvard/MIT, the 2009 Atlanta NBER Conference, and Concordia. Parag Pathak and Philipp Kircher provided useful discussions of our paper. 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.