3.

Suppose that an individual's utility function for consumption, C, and leisure, L, is given byU(C,L) =C0.5L0.5

This person is constrained by two equations: (1) an income constraint that shows how con- sumption can be financed,

C=wH+V,

whereHis hours of work andVis nonlabor income; and (2) a total time constraint (T= 1)

L+H=1

AssumeV= 0, then the expenditure-minimization problem is

minimizeCw(1L) s.t.U(C,L)=C0.5L0.5=U

1. (a)Use this approach to derive the expenditure function for this problem.
2. (b)Use the envelope theorem to derive the compensated demand functions for consumption and leisure.
3. (c)Derive thecompensatedlabor supply function. Show thatHc/w >0.
4. In working following parts it is important not to impose theV= 0condition until after
5. taking all derivatives.
6. (d)AssumeV= 0, determineuncompensatedsupply function for labor and compare with the compensated labor supply function from part (c).
7. (e)Determine maximum utility,U, using the expenditure function derived in part (a), assumeV=E,
8. (f)Use the Slutsky equation to show that income and substitution effects of a change in the real wage cancel out.