My textbook said that the average profit earned by a particular company is $1,00

Question

My textbook said that the average profit earned by a particular company is $1,000. It said it arrived at this figure because of the following data:

During the first 6 months of the year, the company’s demand for workers is expressed in the formula:

w = 180 – 2L

where w = wages and L = the numbr of workers it hires

During this period, they hire 40 workers.

During the other half of the year, its demand for workers is expressed as

w = 140 – 2L

During this period, they hire 20 workers

In both periods, the workers are paid a salary of $100 per day.

Please explain how this data shows that the company earns an average of $1,000

(Note that a few weeks ago I asked another question at Cramster similar to the question I am asking now, and no one was able to answer it, although some people tried.

Here is the link to that question:

http://www.cramster.com/answers-jun-11/economics/determining-profit-based-textbook-questiona-area-75_1369063.aspx?rec=0

Since both questions are taken from the same book of governmental exams, they use the same assumptions and logic.)


Thank you

Explanation / Answer

A company hires up to the point where the marginal revenue product (the additional revenue generated by a hire) equals the wage rate. Therefore the total revenue generated by all the hires can be interpreted as the area under the demand curve for labor. If we look at the area under the demand curve for labor in the first six months of the year we have 180-2l. Therefore if they hire 40 workers, the area will be a triangle with base of 40 and a height of (180-100)=80. Since area is 1/2 bh we have a total of 80*40/2 or 1600. Similarly in the second half of the year we have a demand curve of 140-2l. So at 100 the base is 20 and the height is (140-100)=40. So total revenue is 1/2* 40*20=400. So in the two periods the average revenue is 1600+400/2= 1,000.

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