The Labor Discipline Model The Economy Chapter 6

The Labor Discipline Model The Economy, Chapter 6 Prof. David Clingingsmith Case Western Reserve University

Employment Rent, Work Effort, Wages • An employer cannot directly measure the worker’s effort. They get only indirect/incomplete information about it. • The higher the employment rent, the more workers value staying in their job because the losses from losing it are greater. • If employers are more likely to fire workers who put in low effort, workers will put in more effort when their employment rent is higher. • One way to increase the cost of job loss and thus get the worker to exert effort is for the firm to have higher wages.

Labor Discipline Game I • Model of where firms chose wages and whether to fire a worker and workers choose effort given the wage. • A repeated, sequential game with many periods (Chapter 4).

Labor Discipline Game II • Players: Employer and Employee • Strategies: Employer decides what wage to w offer. Employee chooses how much effort e to exert given the offered wage w. Employer then decides to keep or fire. • Information and sequence: 1. 2. 3. The employer moves first. The employer knows the best response effort level e=E(w) by the employee for each wage. The employers offers the wage w* The employee knows the wage offer w* of the employer and choses the best response level of effort e*=E(w*). The employer fires the worker if the expected level of effort is not provided. • Payoffs: Employer: worker’s output minus cost of employing worker. Employee: employment rent.

Employee’s Best Response Function e=E(w) 1. 0 Effort percentage of max) 0. 9 Slope = MRT 0. 8 0. 7 0. 6 0. 5 0. 4 0. 3 0. 2 0. 1 0. 0 0 Reservation wage 5 10 15 Wage ($/hour) 20 25 30

Labor Discipline Game III Sequence of play 1. Employer chooses the wage level w* knowing the employee’s best response curve E(w) but not their actual choice e. 2. Employee selects the best response level of effort e knowing w*. 3. Employer fires employee if best response level of effort e is not given. Important: Since the employee knows they will be fired if they don’t exert e*=E(w*), they always exert e*.

Employer’s Best Response to E(w)

Isocost Lines for Effort 2. 5 1. 0 5 7. 5 10 12. 5 15 17. 5 20 22. 5 25 Effort e percentage of max) 0. 9 27. 5 30 35 0. 8 40 0. 7 45 0. 6 50 0. 5 55 60 0. 4 0. 3 0. 2 0. 1 0. 0 0 5 10 15 20 Wage w ($/hour) 25 30

Employer’s BR to Employee’s BR Function The employer wants to maximize profit by purchasing effort as cheaply as possible. Here that is $20/unit of effort. The wage will be $9. 50/hr and the employee will put in an effort level of 0. 466. 5 7. 5 10 12. 5 15 17. 5 20 22. 5 25 0. 9 Effort e percentage of max) They select the cheapest isocost line that is on the employee’s BR function, which is where MRS=MRT. 2. 5 1. 0 27. 5 30 35 0. 8 40 0. 7 45 0. 6 50 0. 5 55 60 0. 4 0. 3 0. 2 0. 1 0. 0 0 5 10 15 20 Wage w ($/hour) 25 30

Determining Wages 2. 5 1. 0 5 7. 5 10 12. 5 15 17. 5 20 22. 5 25 Effort e percentage of max) 0. 9 27. 5 30 35 0. 8 40 0. 7 45 0. 6 50 0. 5 55 60 0. 4 0. 3 0. 2 0. 1 0. 0 0 Reservation wage 5 10 15 20 Wage w ($/hour) 25 30

Involuntary Unemployment Involuntary unemployment = being out of work, but preferring to have a job at the wages and working conditions that otherwise identical employed workers have. There must always be involuntary unemployment in the labor discipline model. Why? In equilibrium, both wages and involuntary unemployment have to be high enough to ensure employment rent is high enough for workers to put in effort.

Factors Shifting the Equilibrium The employee’s best response function will shift in reaction to changes in: • the utility of the things that the wage can buy • the disutility of effort • the reservation wage, which depends on duration of unemployment and availability of unemployment benefits. • the probability of getting fired at each effort level

Changes in the Reservation Wage 2. 5 1. 0 5 7. 5 10 12. 5 15 17. 5 20 22. 5 25 Effort e percentage of max) 0. 9 27. 5 30 35 0. 8 40 0. 7 45 0. 6 50 0. 5 55 60 0. 4 0. 3 0. 2 0. 1 0. 0 0 2 Low w. R 5 7 Med. High w. R 10 15 20 Wage w ($/hour) 25 30