New Question Consider Exercise 3 again. Suppose the owner of the trawler can sell all the fish caught for $75 per 100 pounds and can hire as many crew members as desired by paying them $150 per week. Assuming that the owner of the trawler is interested in maximizing profits, determine the optimal crew size.
The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed:
| CREW SIZE (NUMBER OF WORKERS) |
AMOUNT OF FISH CAUGHT PER WEEK (HUNDREDS OF LBS) |
|
2 3 4 5 6 7 8 9 10 11 12 |
3 6 11 19 24 28 31 33 34 34 33 |
a. Over what ranges of workers are there (i) increasing, (ii) constant, (iii) decreasing, and (iv) negative returns?
b. How large a crew should be used if the trawler owner is interested in maximizing the total amount of fish caught?
c. How large a crew should be used if the trawler owner is interested in maximizing the average amount of fish caught per worker?
The marginal and average product of the worker or labor is useful in calculating the amount of fish that the workers can catch as well as in the real industries also. If the company calculates the average and marginal products, the company can decide on how to increase or decrease the amounts of labor.
|
Crew Size |
Amount of fish caught |
MPL |
APL |
|
2 |
3 |
- |
1.5 |
|
3 |
6 |
3 |
2 |
|
4 |
11 |
5 |
2.75 |
|
5 |
19 |
8 |
3.8 |
|
6 |
24 |
5 |
4 |
|
7 |
28 |
4 |
4 |
|
8 |
31 |
3 |
3.87 |
|
9 |
33 |
2 |
3.67 |
|
10 |
34 |
1 |
3.4 |
|
11 |
34 |
0 |
3.09 |
|
12 |
33 |
-1 |
2.75 |
a. The returns can be seen through the marginal product of labor as:-
- Increasing returns- The returns move from worker 3 to worker 5.
- Constant returns- There are no constant returns.
- Decreasing returns- The returns move from worker 5 to worker 11.
- Negative returns- The returns move from worker 11 to worker 12.
b. If the trawler owner is interested in maximizing the fishes, the maximum fishes lies at 34 where the marginal product is 1 while 34 where the marginal product is 0. So, the crew size would be 10.
c. The highest average amount of fish will be at the highest average product of the labor which will be 4 at worker 6 and worker 7. So, the crew sixe would be 6&7 workers.
Hence, the marginal and the average products of labor are solely responsible for knowing the highest and the lowest amounts in the range and help in generating the ideal positions for the company or an individual.
New Question
Consider Exercise 3 again. Suppose the owner of the trawler can sell all the fish caught for $75 per 100 pounds and can hire as many crew members as desired by paying them $150 per week. Assuming that the owner of the trawler is interested in maximizing profits, determine the optimal crew size.
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