Use the following FOC for schooling in the simplified model: 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, transportation, uniforms, etc.). For this problem, let f(s) = as+b and c(s) = c, in which a, b, and c are positive constants.
Suppose r(b+c) < a. Show that this implies f'(s) > rc(s). Explain why s* is nevertheless infinite. Additionally, solve for s* and interpret the dependence of s* on r, a, b, and c.