3. Suppose that an individual's utility function for consumption, C, and leisure, L, is given by U(C, L) = C 0.5L 0.5 This person is constrained by two equations: (1) an income constraint that shows how consumption can be financed, C = wH + V, where H is hours of work and V is nonlabor income; and (2) a total time constraint (T = 1) L + H = 1 Assume V = 0, then the expenditure-minimization problem is minimize C w(1 L) s.t. U(C, L) = C 0.5L 0.5 = U 3 (a) Use this approach to derive the expenditure function for this problem. 2 (b) Use the envelope theorem to derive the compensated demand functions for consumption and leisure. 2 (c) Derive the compensated labor supply function. Show that Hc/w > 0. In working following parts it is important not to impose the V = 0 condition until after taking all derivatives. 4 (d) Assume V 6= 0, determine uncompensated supply function for labor and compare with the compensated labor supply function from part (c). 2 (e) Determine maximum utility, U, using the expenditure function derived in part (a), assume V = E, 2 (f) Use the Slutsky equation to show that income and substitution effects of a change in the real wage cancel out.