4. Suppose that an individual's utility function for consumption, C, and leisure, L, is given by ow, L) = (SD-5L\" This person is constrained by two equations: (1} an income constraint. that shows how con sumption can be nanced, C = tUH + V? Page 2 of 3 Name: ECON 2030 A where H is hours of work and V is nonlabor income; and (2) a total time constraint {T = 1) L + H = 1 Assume V = I], then the expenditureminimization problem is minimize C w(1 L) at. mfg! L) = 00.51505 2 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 suppl},r function. Show that BHCfaw 2 0. In working following parts it is important not to impose the V = 0 condition until after taking all derivatives. E {d} Assume V 7E I], determine uncompensated supply function for labor and compare with the compensated labor supply hinction from part {c} {e} Determine maximum utility, F, using the expenditure function derived in part. [a], assume V = E, {f} Use the Slutsk},r equation to show that income and substitution effects of a change in the real wage cancel out