Use the following FOC for schooling: f'(s) = r(f(s) + c(s)), in which s is total time in school (e.g., years of school attained), f(s) is the adult wage while working, and c(s) is the direct cost of school (tuition, transport, uniforms, etc.). For this problem, let f(s) = as + b and c(s) = c, in which a, b, and c are positive constants.

The government subsidizes the cost of schooling by an amount d. What is the net gain (or loss) to society, in terms of a, b, c, and d? Treat the government's issuance of the subsidy as a cost and the student's receipt as a benefit. Suppose that the tax is levied on someone besides the student and that other prices that the student faces do not change. Your answers should be in terms of a, b, c, and d.