Educational production and optimal class size

Lazear (2001) (Quarterly Journal of Economics, v. 116, p. 777-803) provided a model of a private school with a particular profit function. Using an alternative, related profit function I show that an optimal solution has nearly equal class sizes. I also offer a conjecture about the roots of a certain family of polynomials, which if true, allows one to conclude that if students become less disruptive or teacher cost increases, then the optimal solution for a profit maximizing school is generally, but not always, to use fewer classes. I also show that if the school has s>1 types of students, then the optimal solution will have at most s-1 mixed classes and its bipartite graph is a forest.