A monopsonist faces a labor supply curve given by LS = 300 + 0.01w , where w is

Question

A monopsonist faces a labor supply curve given by LS = 300 + 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 wage? Is this greater than, less than, or equal to the wage paid to each of the two workers?

c. In general, the marginal cost of hiring additional labor for this firm is given by MW C = 29, 900 + 200L. If the firm’s labor demand curve is given by LD = 398 0.01w, what is the profit-maximizing number of workers the monopsonist should hire? What is the salary the workers will be paid?

Explanation / Answer

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 = 300 + 0.01W

W = 301*100 = 30100

For 2 worlers, LS=2

2 =300 + 0.01W

W = 302/100 = 30200

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

= 2*30200 - 30100

= 30300

It is higher then the wage as 30300 >30200

c. The profit will maximzing at the point where MC = MD

MC = 29, 900 + 200L

LD = 398 0.01W or W = 39800 - 100L

So, Profit = 29, 900 + 200L -  (398 - 100L).L

dProfit/dL = 200 - 3.98 +200L

Putting  dProfit/dL = 200 - 3.98 + 200L = 0

L = 196.02/.0/200 = 0.9801

and W =

Putting L =9801 in labour suppply

0.9801 =  300 + 0.01w

W = 30098.01

If you didn't understand , you can comment , I'ill be happy to explain in detail.

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