Suppose that a worker's cost of going to school is c(x,) , where x is the amount of school and is the worker's ability / productivity.

a) suppose that c is differentiable and x2c(x,)0 . Interpret this condition in words in the context of the model.

b) Now suppose that firms can observe education but not ability, and thus offer wages w(x) which depend only on education. The workers utility is given by w(x)c(x,). Is there any wage function which will induce higher ability workers to choose lower levels of education?