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. AssumeV= 0, determineuncompensatedsupply function for labor and compare with the compensated labor supply function from part (c).
2. Determine maximum utility,U, using the expenditure function derived in part (a), assumeV=E,
3. Use the Slutsky equation to show that income and substitution effects of a change in the real wage cancel out.