My textbook had the following question: A certain area has 7500 workers who are
ID: 1249843 • Letter: M
Question
My textbook had the following question:A certain area has 7500 workers who are willing to work at any salary. The area has two places of employment, A and B.
At A, the value of the marginal production of the workers is
w = 1800-0.1L
At B, it is
w = 1800-0.2L
where L is the number of workers and w is their salary per day.
Which company earns more money?
The answer given in the book is that B earns twice as much as A. They explain as follows:
At equilibrium, A employs a third of the workforce and B employs 2 thirds of the workforce. The salary the 2 companies pay their workers is identical. Therefore, B earns twice as much as A.
Please explain this. Thank you.
Explanation / Answer
There are 7500 workers who are willing to work at any salary, so all workers WILL be employed. They will work at the firm that gives them the highest wage (even though they will work at any salary). They want the highest wage possible. So the wage at each firm will have to be the same, because if one has a higher wage, then all workers will work for one firm and the other will have no workers. Since w is the same for both, you can equate the two equations and solve for La and Lb. We find that La=2Lb. This means that firm B hires twice as many workers as firm A. Since there are 7500 total workers, firm A hires 5000 and firm B hires 2500. Because firm B hires half as many workers for the same wage and same marginal production of labor (MPL), they earn twice as much money as firm A. That is to say that firm B employs half as many workers as A to do the same amount of work.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.