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3. Suppose that an individual’s utility function for consumption, C, and leisure, L, is given by...

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 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

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