Question
In: Economics
Suppose college graduates earn $20 an hour and high school graduates earn $10 an hour. Suppose...
Suppose college graduates earn $20 an hour and high school
graduates earn $10 an hour. Suppose too that the marginal product
of college graduates at Johnson Tools is 5 hammers per hour, while
the marginal product of high school graduates is 4 hammers per hour
(regardless of the number of each type of worker employed).
a. What is the least-cost production method for producing 100
hammers in an eight-hour day?
| Hire one-third college graduates and two-thirds high school graduates. | |
| Hire only high school graduates. | |
| Hire two-thirds college graduates and one-third high school graduates. | |
| Hire half college graduates and half high school graduates. | |
| Hire only college graduates. |
b. What if the marginal product of high school graduates was
instead 2?
| Hire half college graduates and half high school graduates. | |
| Hire only college graduates. | |
| Hire two-thirds college graduates and one-third high school graduates. | |
| Hire one-third college graduates and two-thirds high school graduates. | |
| Hire only high school graduates. |
c. What is the critical difference in productivity (in percentage
terms) at which the type of worker hired changes?
When the marginal product of high school
graduates is percent of the marginal product of college
graduates.
Solutions
Expert Solution
Hourly wage rate for college graduates = $20
Hourly wage rate for school graduates = $10
Marginal Product per hour for college graduates = 5 hammers
Marginal Product per hour for school graduates = 4 hammers
a. What is the least-cost production method for producing 100 hammers in an eight-hour day?
| Hire one-third college graduates and two-thirds high school
graduates. |
|||||
|
Hourly MP A |
No. of workers B |
Hourly production C = A*B |
Hourly Wages Rate D |
Total hourly wages E |
|
| College Graduate | 5 | 1 | 5 | $ 20.00 | $ 20.00 |
| School Graduate | 4 | 2 | 8 | $ 10.00 | $ 20.00 |
| Total hourly production (F) | 13 | Total hourly wages (G) | $ 40.00 | ||
| Hours taken for 100 hammers H = (100/F) | 7.69 | Total cost of wages (G*H) | $ 307.69 | ||
| Hire only high school
graduates. |
|||||
|
Hourly MP A |
No. of workers B |
Hourly production C = A*B |
Hourly Wages Rate D |
Total hourly wages E |
|
| College Graduate | 0 | 0 | 0 | $ 20.00 | $ - |
| School Graduate | 4 | 1 | 4 | $ 10.00 | $ 10.00 |
| Total hourly production (F) | 4 | Total hourly wages (G) | $ 10.00 | ||
| Hours taken for 100 hammers H = (100/F) | 25.00 | Total cost of wages (G*H) | $ 250.00 | ||
| Hire two-thirds college graduates and one-third high school graduates. | |||||
|
Hourly MP A |
No. of workers B |
Hourly production C = A*B |
Hourly Wages Rate D |
Total hourly wages E |
|
| College Graduate | 5 | 2 | 10 | $ 20.00 | $ 40.00 |
| School Graduate | 4 | 1 | 4 | $ 10.00 | $ 10.00 |
| Total hourly production (F) | 14 | Total hourly wages (G) | $ 50.00 | ||
| Hours taken for 100 hammers H = (100/F) | 7.14 | Total cost of wages (G*H) | $ 357.14 | ||
| Hire half college graduates and half high school graduates. | |||||
|
Hourly MP A |
No. of workers B |
Hourly production C = A*B |
Hourly Wages Rate D |
Total hourly wages E |
|
| College Graduate | 5 | 1 | 5 | $ 20.00 | $ 20.00 |
| School Graduate | 4 | 1 | 4 | $ 10.00 | $ 10.00 |
| Total hourly production (F) | 9 | Total hourly wages (G) | $ 30.00 | ||
| Hours taken for 100 hammers H = (100/F) | 11.11 | Total cost of wages (G*H) | $ 333.33 | ||
| Hire only college graduates. | |||||
|
Hourly MP A |
No. of workers B |
Hourly production C = A*B |
Hourly Wages Rate D |
Total hourly wages E |
|
| College Graduate | 5 | 1 | 5 | $ 20.00 | $ 20.00 |
| School Graduate | 4 | 0 | 0 | $ 10.00 | $ - |
| Total hourly production (F) | 5 | Total hourly wages (G) | $ 20.00 | ||
| Hours taken for 100 hammers H = (100/F) | 20.00 | Total cost of wages (G*H) | $ 400.00 | ||
Conclusion: 2nd choice i.e. Hiring only high school graduates is
the most cost efficient choice at $250 only. This must be
taken.
On the similar lines, next question (b) can also be solved. I wish
you to solve it yourself. I did the calculations at my end and
figured out the following:
| Hire half college graduates and half high school graduates. $428.57 | |
| Hire only college graduates. $ 400 | |
| Hire two-thirds college graduates and one-third high school graduates. $416.67 | |
| Hire one-third college graduates and two-thirds high school graduates. $444.44 | |
| Hire only high school graduates. $500 | |
IF you also want calculations for question b., these are below:
|
Hourly MP A |
No. of workers B |
Hourly production C = A*B |
Hourly Wages Rate D |
Total hourly wages E |
|
| College Graduate | 5 | 1 | 5 | $ 20.00 | $ 20.00 |
| School Graduate | 2 | 1 | 2 | $ 10.00 | $ 10.00 |
| Total hourly production (F) | 7 | Total hourly wages (G) | $ 30.00 | ||
| Hours taken for 100 hammers H = (100/F) | 14.29 | Total cost of wages (G*H) | $ 428.57 | ||
|
Hourly MP A |
No. of workers B |
Hourly production C = A*B |
Hourly Wages Rate D |
Total hourly wages E |
|
| College Graduate | 5 | 1 | 5 | $ 20.00 | $ 20.00 |
| School Graduate | 2 | 0 | 0 | $ 10.00 | $ - |
| Total hourly production (F) | 5 | Total hourly wages (G) | $ 20.00 | ||
| Hours taken for 100 hammers H = (100/F) | 20.00 | Total cost of wages (G*H) | $ 400.00 | ||
|
Hourly MP A |
No. of workers B |
Hourly production C = A*B |
Hourly Wages Rate D |
Total hourly wages E |
|
| College Graduate | 5 | 2 | 10 | $ 20.00 | $ 40.00 |
| School Graduate | 2 | 1 | 2 | $ 10.00 | $ 10.00 |
| Total hourly production (F) | 12 | Total hourly wages (G) | $ 50.00 | ||
| Hours taken for 100 hammers H = (100/F) |
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