Seminar by Rajiv Sethi (Barnard College, Columbia University)

We examine the problem faced by an educational authority tasked with setting a passing standard for a cohort of students with varying levels of prior preparation. Learning requires costly effort. If the standard is too demanding, many will fail, and those who anticipate failing will put in low levels of effort. If the standard is too lenient, many will pass effortlessly, and learning will again be limited. We characterize the equilibrium standard and the resulting distribution of effort and learning, and examine the manner in which mean achieved learning varies with the degree of heterogeneity in student preparation. We also consider the effects of tracking, which allows for different standards to be applied to different subgroups of the student population. Finally, we allow for parental investments to increase preparedness, and heterogeneity across parents in levels of wealth. We show that poor parents will sometimes prefer a higher standard than rich parents, and that the standard chosen by the authority may vary non-monotonically in the fraction of poor parents in the population.