Question

A monopsonist faces a labor supply curve given by L s = −400 + 0.01w , where w is the annual salary.

(a) What is the lowest salary the firm can pay yet still induce one worker to want to work for the firm? What is lowest salary the firm must pay to induce two workers to work for the firm?

(b) What is the marginal cost to the firm of adding a second worker given that it must pay all employees the same salary? Is this greater than, less than, or equal to the salary paid to each of the two workers?

(c) In general, the marginal cost of hiring additional labor for this firm is given by MEL = 40, 000 + 200L. If the firm’s marginal revenue product of labor (MRPL) curve is given by L = 160− w 300 , what is the profit-maximizing number of workers the monopsonist should hire? What is the salary the workers will be paid? (Hint: Optimal labor (L ∗ ) can be found where MRPL and MEL intersect.)

(d) Suppose now the workers employed (and potentially employed) by the monopsonist become unionized and successfully get the monopsonist to agree to a fixed salary of $42,500 per worker. How does the firm’s profit-maximizing wage and employment level change under the new union agreement? Calculate the new values and graph the aggregate labor supply and demand curves, as well as the original and new Marginal Expense of Labor (MEL) lines under the union agreement.

Answer 1

1. The minimum salary is 40,100. For two, the minimum salary will instead be 40,200.
2. Per the answer above, the total compensation paid when the firm hires one worker is 40,100, when the firm hires two it is 80,400, and the marginal cost of hiring the second worker is therefore 40,300, greater than the salary paid to the two workers.
3. The profit-maximizing number of workers is found at the intersection of the ME and L curves, so that L = 16. The wage paid, however will be found on the labor supply curve, below ME: 41,600.

a. The lowest salary the firm can pay yet still induce one worker to want to work for the firm will be one where LS= 1.

So, 1 = -400 + 0.01W

W = 401*100 = 40100

For 2 workers, LS=2

2 =-400 + 0.01W

W = 402/100 = 40200

b. Marginal cost of addition of second worker = Total cost of 2 workers - Total cost of 1 worker

= 2*40200 - 40100

= 40300

It is higher then the wage as 40300 >40200

d. As seen in the graph below, the union’s monopoly power partly counterbalances the monopsony power of management. The new agreement raises wage and employment, which the monopsony power had pushed below their competitive levels.