Problem 2: Nash Wage Bargaining and Labor Income Taxes (20 points). The labor income tax rate in period : is 7 . Suppose that the real wage in period t w, arises through Nash bargaining between the potential new employee and the potential new employer. Define the potential new employee's "effective" Nash bargaining power as 17 7+ (1-n) . 1 - in which ne [0, 1]. The potential new employee and potential new employer determine the bargained wage by jointly maximizing the Nash maximand Nash maximand = max (W(w.) - U)" J(w, )'-5 . in which the value expressions are W(w)= w,, U(w,) =b", and J(w.) = A, -w . (Note: there is no typo in the value expression W(w,).) For the sake of simplicity, there are no "long-lasting jobs" throughout this question - i.e., the job turnover parameter is fixed at p =1. a. (8 points) Based on the Nash maximand stated above, construct the surplus-sharing condition. (Hint: This requires computing the first-order condition with respect to the real wage w, ) The final solution should be expressed in the form W( W. ) - U= ... in which the term in ellipsis ("...") on the right-hand side is left to you to determine.b. (12 points) Based on the surplus-sharing condition obtained in part a, re-write it using the value expressions stated above to obtain the real wage equation. The real wage equation should be expressed in the form W NASH in which the term in ellipsis ("...") on the right-hand side is left to you to determine. In the final solution, the effective bargaining power & should NOT appear on the right-hand side