Macro PS9 Solutions.pdf - Department of Applied Economics...

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PS 9 Solutions | © Sanjay K. Chugh 1 Department of Applied Economics Johns Hopkins University Economics 602 Macroeconomic Theory and Policy Practice Problem Set 9 Suggested Solutions Professor Sanjay Chugh
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PS 9 Solutions | © Sanjay K. Chugh 2 a.The main goal of this part of the question is to compute the first-order condition of the Nash maximand with respect to the real wage tw, and display your final solution in TWO different ways:1.One that contains ONLYthe terms η, tW, and tJ. 2.One that contains a real wage equation of the form ...twin which the right-hand side contains NEITHERtWNORtJ. (You must determine the term in ellipsis (“…”) on the right-hand side.) Display each version of the final solution clearly by drawing a box around it, and clearly and carefully provide the algebraic steps/logic that lead to the two versions of the final solution. Solution: To conserve somewhat on notation, let )'(DtttmpnA fnstand for the marginal product of labor. The first-order condition of the Nash maximand wt-b()hmpnt-wt()1-hwith respect to the real wage twis (be careful to use the Chain Rule of Calculus and the rules of exponents) hwt-b()hmpnt-wt()1-hwt-b()-1+(-1)×(1-h)wt-b()hmpnt-wt()1-hmpnt-wt()-1=0The term wt-b()h(which is simplytW) cancels out, as does the term 1ttmpnw(which is simply tJ). Rewriting the resulting expression, we have , which allows us to display the final solution in the two different versions requested. First, re-express the previous expression as h×Jt=1-h()×Wt, (1)
PS 9 Solutions | © Sanjay K. Chugh 3 which contains only η, tW, and tJ. Since you are given the definitions of tWand tJ, we can equivalently state this as h×(mpnt-wt)=1-h()×wt-b().After a few steps of algebra to isolate tw, we have wt=h×mpnt+(1-h)×b, (2) which contains neither tWnor tJ. b.Many economists share the view that workers’ “bargaining power”ηhas declined in

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