need help on economics question

4. Suppose that an individual's utility function for consumption, C, and leisure, L, is given by U(C, L) : 00-51505 This person is constrained by two equations: (1) an income constraint that shows how con- sumption can be nanced, C=wH+V, -h 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 expenditureminimization problem is minimize C w(l L) at. U(C,L) = CO'5L0'5 = U (a) Use this approach to derive the expenditure function for this problem. (b) Use the envelope theorem to derive the compensated demand functions for consumption and leisure. (c) Derive the compensated labor supply function. Show that (NP/610 > 0. In working following parts it is important not to impose the V = 0 condition until after taking all derivatives. ((1) Assume V 75 0, determine uncompensated supply function for labor and compare with the compensated labor supply function from part (c). (e) Determine maximum utility, U , using the expenditure function derived in part (a), assume V=E, (f) Use the Slutsky equation to show that income and substitution effects of a change in the real wage cancel out