Assume that average product for six workers is fifteen. If the marginal product of the seventh worker is
eighteen, what is the average product of the seventh worker?
The total product for six workers is the average product multiplied by the number of workers, which is 15 * 6 = 90. When the seventh worker is added, the total product increases by the worker's marginal product, which is 90 + 18 = 108.
The average product for the seventh worker is the total product divided by the number of workers, which is 108 / 7 = 15.43.
To find the average product of the seventh worker, we need to consider the total output and the number of workers.
Given:
The average product for six workers is fifteen. This means that the total output produced by six workers is 15 units per worker.
Now, let's calculate the total output produced by the six workers:
Total Output = Average Product * Number of Workers
Total Output = 15 * 6
Total Output = 90 units
If the marginal product of the seventh worker is eighteen, it means that the additional output produced by the seventh worker is 18 units.
To find the new average product per worker with the addition of the seventh worker, we need to calculate the new total output and divide it by the total number of workers.
New Total Output = Total Output by Six Workers + Additional Output by the Seventh Worker
New Total Output = 90 + 18
New Total Output = 108 units
Since there are now seven workers, the new average product per worker is:
Average Product = New Total Output / Number of Workers
Average Product = 108 / 7
Average Product ≈ 15.43 (rounded to two decimal places)
Therefore, the average product of the seventh worker is approximately 15.43 units.
To find the average product of the seventh worker, we first need to understand what average product and marginal product mean.
Average product (AP) is the total output produced by a certain number of workers divided by the number of workers. It gives us the average contribution of each worker to the total output.
Marginal product (MP) is the additional output produced by adding one more worker to the existing workforce. It tells us how much the total output increases when one more worker is added.
Given that the average product for six workers is fifteen (AP = 15) and the marginal product of the seventh worker is eighteen (MP = 18), we can use the following formula to calculate the average product of the seventh worker:
Average Product (AP) = Total Product (TP) / Number of Workers (N)
We know that AP = 15 for six workers, so TP (Total Product) for six workers would be:
TP = AP × N
TP = 15 × 6
TP = 90
Now, to find the average product of the seventh worker, we add the marginal product of the seventh worker (MP = 18) to the total product for six workers (TP = 90). Then we divide this sum by the total number of workers (N = 7):
AP7 = (TP + MP) / N
AP7 = (90 + 18) / 7
AP7 ≈ 15.43
Therefore, the average product of the seventh worker is approximately 15.43 units.