Question 2: Efficiency Wage Model Consider the following extension to the Efficiency-Wage Model (by Shapiro and Stiglitz, 1984, AER) that we covered in class in which the wage rate is W, cost of working is E, probability of job separation of any worker is p and the extra probability of job termination due to shirking is q. In addicion to what we covered in class, workers have a third option, semi- shirking, the cost of which to the employee is aE and which raises the probability of job separation by r (from p). (The economic contribution of workers to the firm by semi-shirking is less than no-shirking but more than shirking). a. Write the value of working, value of shirking, and value of semi-shirking. Also, write the no-shirking and no-semi-shirking conditions b. Suppose that the firm wants its workers to work properly, i.e., it does not want its workers either to shirk or semi-shirk. Then, what condition ensures that workers do work indeed, and what is the wage the firm optimally chooses to offer for this goal? How does this wage depend on a and r? c. Suppose that the cost of working is actually a function of the wage rate, i.e., E(W)= VW = w05, In addition, suppose you are provided with the following parameter values: p=0.10 r=0.10, q=0.40 and a=0.5. In order to make sure that its workers do work properly (and not shirk or semi-shirk), what wage would the firm offer?