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profit maximization

Hi,

Having difficulites solving the following problems, can someone give me some clues?
Thanks.

Number Of
Workers Output
0 0
1 50
2 110
3 300
4 450
5 590
6 665
7 700
8 725
9 710
10 705

1) The table above shows the weekly relationship between output and number of workers for a factory with a fixed size of plant.
a. Calculate the marginal product of labor.
b. At what point does diminishing returns set in?
c. Calculate the average product of labor.
d. Find the three stages of production.

2) Based on the table above, if the wage rate is $500 and the price of output is $5, how many workers should the firm hire?

3) A firm has two plants, one in the United States and one in Mexico, and it cannot change the size of the plants or the amount of capital equipment. The wage in Mexico is $5. The wage in the U.S. is $20. Given current employment, the marginal product of the last worker in Mexico is 100, and the marginal product of the last worker in the U.S. is 500.
a. Is the firm maximizing output relative to its labour cost? Show how you know.
b. If it is not, what should the firm do?

4) A firm is making a long-run planning decision. It wants to decide on the optimal size of plant and labor force. It is considering building a medium-sized plant and hiring 100 workers. Engineering estimates suggest that at those levels, the marginal product of capital will be 100 and the marginal product of labor will be 75. If the wage rate is $5 and the rental rate on capital is $10, is the firm making the right decision? Support your answer.

Solution Preview

See the attached file. Hope this will help. Thanks

No. of Workers Output Marginal Product of labor Average Product
0 0
1 50 50 50.00
2 110 60 55.00
3 300 190 100.00
4 450 150 112.50
5 590 140 118.00
6 665 75 110.83
7 700 35 100.00
8 725 25 90.63
9 710 -15 78.89
10 705 -5 70.50

1) The table above shows the weekly relationship between output and number of workers for a factory with a fixed size of plant.
a. Calculate the marginal product of labor.
See the above table

b. At what point does diminishing returns set in?
The diminishing return start when marginal product of labor starts decreasing. The marginal product of labor increases as we increase the number of workers from 0 to 3, attains its maximum at 3 (190) and when we add the fourth worker it starts decreasing. Thus, diminishing return starts from 4th worker.

c. Calculate the average product of labor.
See the above table.

d. Find the three stages of production.
Stage I: From ...

Solution Summary

This job examines profit maximization.

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