2. Monitoring technology with false positives. Consider the labor market model of Shapiro and Stiglitz (1984). Suppose that the firm's monitoring technology returns both false negatives and false positives. Specifically, the monitoring technology correctly identifies a shirking worker with probability q and mistakes him for a diligent worker with probability 1 9,9 (0,1). Moreover, the monitoring technology correctly identifies a diligent worker with probability 1-m, and mistakes him for a shirking worker with probability m,m (0,9). The firm fires all workers identified (correctly or not) as shirkers. a. Write down an expression for the lifetime utility of a worker employed at the wage w. Explain the meaning of each term in the expression. b. Derive a condition under which the worker chooses to exert effort. c. Given the monitoring technology described above, the equilibrium employment N* and the equilibrium wage w* satisfy the following labor supply and the no-shirking conditions F'(N*) = w*, (LD) e --] . (1-(1-8)N* w* = (e +b) + B(1-5) (NS) Blq-m) 1- N* Draw the locus of (w*, N*) that satisfies the labor supply and no-shirking conditions and identify the equilibrium of the economy. d. What happens to equilibrium wages and employment if the probability m of firing a diligent worker increases? e. What happens to equilibrium wages and employment if the probability m of firing a diligent worker approaches q? 2. Monitoring technology with false positives. Consider the labor market model of Shapiro and Stiglitz (1984). Suppose that the firm's monitoring technology returns both false negatives and false positives. Specifically, the monitoring technology correctly identifies a shirking worker with probability q and mistakes him for a diligent worker with probability 1 9,9 (0,1). Moreover, the monitoring technology correctly identifies a diligent worker with probability 1-m, and mistakes him for a shirking worker with probability m,m (0,9). The firm fires all workers identified (correctly or not) as shirkers. a. Write down an expression for the lifetime utility of a worker employed at the wage w. Explain the meaning of each term in the expression. b. Derive a condition under which the worker chooses to exert effort. c. Given the monitoring technology described above, the equilibrium employment N* and the equilibrium wage w* satisfy the following labor supply and the no-shirking conditions F'(N*) = w*, (LD) e --] . (1-(1-8)N* w* = (e +b) + B(1-5) (NS) Blq-m) 1- N* Draw the locus of (w*, N*) that satisfies the labor supply and no-shirking conditions and identify the equilibrium of the economy. d. What happens to equilibrium wages and employment if the probability m of firing a diligent worker increases? e. What happens to equilibrium wages and employment if the probability m of firing a diligent worker approaches