Suppose that an individual's utility function for consumption, C, and leisure, L, is given by UC L (C, L) = 0505 This person is constrained by two equations: (1) an income constraint that shows how con sumption can be fifinanced, 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 C w(1 1 L) s

Suppose that an individual's utility function for consumption, C, and leisure, L, is given by UC L (C, L) = 0505

This person is constrained by two equations: (1) an income constraint that shows how con

sumption can be fifinanced,

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 C w(1 1 L) s.t.

U(C, L) = C0.5L0.5 = U

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

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(b) Use the envelope theorem to derive the compensated demand functions for consumption

and leisure.

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