There is a growing interest in the use of income-share agreements to finance higher education. This paper aims to offer the first game-theoretic model of how such ISAs could affect the incentives of students to acquire human capital, and the incentives of universities to supply education. I find that ISAs highlight a tension between different policy goals: relative to tuition pricing, ISAs increase the availability of education, but reduce student productivity. In a duopoly environment, where both universities can choose a pricing model, the dominant strategy equilibrium is for both universities to choose tuition pricing. Furthermore, this equilibrium is efficient: tuition pricing maximizes both the availability of education and the productivity of education, so it is socially superior to ISA pricing.
I study a two-period labor market model to examine how inaccurate beliefs can be identified in a dynamic labor market, and how they might lead to inaccurate statistical discrimination. I show that partial unravelling, in which some workers of a group identity contract early while others do not, is impossible when firms have accurate beliefs about different groups: the presence of partial unravelling in a labor market implies that some firms have inaccurate beliefs. Furthermore, timing is an essential part of inaccurate statistical discrimination in this market: firms are inaccurately discriminatory when hiring early. In contrast, a policy that banned early contracting eliminates inaccurate statistical discrimination through providing more accurate information to firms. These results demonstrate a practical way to infer the beliefs from firms in real labor markets, and they highlight the importance of considering the beliefs of firms in labor markets when analyzing equilibria.