question archive Suppose that an individual's utility function for consumption, C, and leisure, L, is given by U(C, L) = C0
Suppose that an individual's utility function for consumption, C, and leisure, L, is given by U(C, L) = C0
Subject:EconomicsPrice: Bought3
Suppose that an individual's utility function for consumption, C, and leisure, L, is given by
U(C, L) = C0.5L0.5
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
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.
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(c) Derive the compensated labor supply function. Show that ∂Hc/∂w > 0.
