Answer:
Step-by-step explanation:
To determine the least-cost production method, we need to calculate the total cost of employing only college graduates and the total cost of employing only high school graduates and choose the one with the lowest cost.
Let's start with only college graduates:
Total hammers produced in 8 hours:
5 hammers per hour per college graduate * number of college graduates * 8 hours = 40 * number of college graduates
Total cost of employing only college graduates:
Total hours worked * wage rate = 8 * 25 * number of college graduates = 200 * number of college graduates
Now let's consider only high school graduates:
Total hammers produced in 8 hours:
4 hammers per hour per high school graduate * number of high school graduates * 8 hours = 32 * number of high school graduates
Total cost of employing only high school graduates:
Total hours worked * wage rate = 8 * 15 * number of high school graduates = 120 * number of high school graduates
To produce 100 hammers in 8 hours using the least-cost production method, we need to solve the following two equations:
40 * number of college graduates = 100
32 * number of high school graduates = 100
Solving for the number of college and high school graduates, we get:
number of college graduates = 2.5
number of high school graduates = 3.125
Since we can't hire fractional employees, we need to round up the number of college graduates to 3 and the number of high school graduates to 4. Therefore, the least-cost production method for producing 100 hammers in 8 hours is to hire 3 college graduates and 4 high school graduates.
If the marginal product of high school graduates were instead two hammers per hour, we would have:
Total hammers produced in 8 hours:
5 hammers per hour per college graduate * number of college graduates * 8 hours = 40 * number of college graduates
2 hammers per hour per high school graduate * number of high school graduates * 8 hours = 16 * number of high school graduates
Total cost of employing only college graduates:
Total hours worked * wage rate = 8 * 25 * number of college graduates = 200 * number of college graduates
Total cost of employing only high school graduates:
Total hours worked * wage rate = 8 * 15 * number of high school graduates = 120 * number of high school graduates
To produce 100 hammers in 8 hours using the least-cost production method, we need to solve the following two equations:
40 * number of college graduates = 100
16 * number of high school graduates = 100
Solving for the number of college and high school graduates, we get:
number of college graduates = 2.5
number of high school graduates = 6.25
Again, since we can't hire fractional employees, we need to round up the number of college graduates to 3 and the number of high school graduates to 7. Therefore, the least-cost production method for producing 100 hammers in 8 hours is to hire 3 college graduates and 7 high school graduates.
The critical difference in productivity at which the type of worker hired changes is when the marginal product of high school graduates is equal to the marginal product of college graduates. Let x be the critical difference in productivity:
5x = 4
x = 0.8
Therefore, if the marginal product of high school graduates is 80% or less than the marginal product of college graduates, it is more cost-effective to hire only college graduates. If the marginal product of high school graduates is more than 80% of the marginal product of college graduates, it is more cost