On the Optimal Allocation of Resources in the Production of Human Capital

The problem considered here is the allocation of limited school resources over the school-life of students so as to maximize their human capital stock at the end of the schooling period. The constraints faced by school authorities in maximizing the terminal human capital stock include the production technology, a limited budget per pupil, and the constraint that the level of knowledge exceed some minimum level before the pupil can pass to the succeeding grade. The problem is solved using optimal control theory. Both the results obtained generally and those derived for specific examples indicate the optimal allocation is one where the level of expenditure per pupil increases with the grade level of the pupil.