help with question 3

3. [25 points total] Jim lives for two periods. In period 1, he has no income. So he bor- rows in at the interest rate r > 0 and consumes c1 in period 1. [31 = b In period 2, Jim works for L hours at the wage rate 11;. With the labor income wL, he consumes :22 and repays the debt and interest (1 + r} b. In addition, he should pay income tax r x (mL rb) , with a constant tax rate r E [0,1] . The income tax function indicates that the interest payment H3 is deducted from taxable income. Jim's budget constraint for period 2 is therefore written as .22 =w(l T)L [l+r(l T)]b. Subject to the two budget constraints, Jim maximizes the utility 1 Incl +f3 [Inez 5L2], where {3 E (0, 1) is the utility discount factor. (a) [10 points] Find (:21, .22, Lb) that solves Jim's problem. (b) [7 points] Explain the substitution effect and income effect of an increase in 1- on (:1. Which effect dominates? (c) [8 points] What is the tax rate 1"\" that maximizes tax revenue 1- (wL Tb)