Suppose Mandy's earnings are given by w(S, A) = (SA+1)^(1/2) , where S denotes years of schooling and A denotes ability. Assume that Mandy lives forever, discounts future income at a rate of r, earns nothing while in school, and supplies labor inelastically thereafter. Assume that A is exogenous and time is continuous, Mandy's objective is to choose S to maximize the present value of lifetime earnings.

(a) Calculate Mandy's present value of lifetime earnings.

(b) Find Mandy's optimal choice of years of schooling S* .

(c) Find the partial derivatives of S* with respect to A. Is the relationship between S* and A intuitively reasonable? Explain