Education, distributive justice, and adverse selection

We consider a model of education planning in an economy in which agents differ in their costs of acquiring education. The agents' cost parameter, called 'talent', is not observed. The principal is endowed with a fixed sum of money, with which two types of transfer can be made: in cash and in kind. The principal can finance transfers in kind, called 'help', by means of schooling expenditures, which reduce the agent's education cost. The principal seeks to maximize a social welfare function which is a CES index of utility levels. We study the optimal allocation of individual education effort, schooling expenditures (help), and cash, under self-selection and budget constraints. Assuming first that the set of types is finite, and that help and effort are sufficiently substitutable, we find that individual education investment levels are an increasing function, and help is a decreasing function of talent. Utility levels cannot be equalized because of self-selection constraints. More aversion for inequality unequivocally leads to more inequality of educational achievements, and to more assistance through redistribution. This remains true in the limit, under strictly egalitarian preferences of the principal. The same qualitative properties hold in the general case of a continuum of types. Bunching at the lower end of the talent scale is a feature of the solution for sufficiently high degrees of inequality aversion.