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Suppose that an individual's utility function for consumption, C, and leisure, L, is given by U(C, L) = C 0

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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 5

(a) Use this approach to derive the expenditure function for this problem. 5

(b) Use the envelope theorem to derive the compensated demand functions for consumption and leisure. 5

(c) Derive the compensated labor supply function. Show that ∂Hc/∂w > 0.