Consider the model of labor supply. Specifically an individual who seeks to maximize U(C) +V(leisure) subject to the budget constraint: PC=W L where P is the price of consumption, W is the nominal wage rate, and L is time devoted to work.

(a) Argue that if W and P both increase proportionately the optimal choice of how much to work does not change.

(b) Analyze what happens to labor supply if P increases. Specifically, does our theory predict what will happen? Explain your answer. If income and substitution effects are roughly offsetting onaverage, what would you predict would happen to average desired labor supply in the eventof an increase in P?

(c) Assume that U(C) =log(C) and V(leisure) =log(leisure). Normalize P=1, and let W=20. Assume the total available time H for an individual is 3600 hours a year (about 10 hours a day). Therefore, leisure=HL=3600L. Solve for the optimal labor supply L and consumption C. (Hint: U(C) =1/C and V(leisure) =1/leisure = 1/(3600L)).

(d) Continue from part (c). Now assume W=10, so the wage rate is cut in half, whereas other parameters remain the same. Solve for the optimal labor supply L and consumption C. Will this individual work more or fewer hours compared to part (c)? What can you say about the income and substitution effects caused by the wage increase?