The following table shows the number of calculators that can be assembled per week by various numbers of workers.If the price per calculator in a perfectly competitive product market is $8,how many workers would the firm employ if the weekly wage rate is $800?

Question

Quizplus · Accepted Answer

To determine the optimal number of workers to employ, we need to calculate the marginal product of labor (MPL) and the marginal revenue product of labor (MRP) for each level of labor.

MPL is the amount of output produced by one additional unit of labor. We can find this by taking the difference in output between two different levels of labor:

MPL = ∆output / ∆labor

For example, from 0 to 1 workers, the output increases from 0 to 60, so the MPL of the first worker is:

MPL = (60 - 0) / (1 - 0) = 60

Similarly, we can calculate the MPL for each level of labor:

MPL of 1 worker = 60 
MPL of 2 workers = 100 - 60 = 40 
MPL of 3 workers = 120 - 100 = 20 
MPL of 4 workers = 130 - 120 = 10

Next, we need to calculate the MRP, which is the additional revenue generated by one additional unit of labor:

MRP = MPL x Price

In this case, the price is $8 per calculator.

MRP of 1 worker = 60 x 8 = $480 
MRP of 2 workers = 40 x 8 = $320 
MRP of 3 workers = 20 x 8 = $160 
MRP of 4 workers = 10 x 8 = $80

Finally, we need to compare the MRP to the wage rate of $800 per week.

If MRP > wage rate, the firm should hire more workers. 
If MRP < wage rate, the firm should hire fewer workers. 
If MRP = wage rate, the firm is indifferent between hiring more or fewer workers.

Using this rule, we can see that:

- With 1 worker, MRP = $480 < $800, so the firm should not hire only one worker. 
- With 2 workers, MRP = $320 < $800, so the firm should not hire two workers. 
- With 3 workers, MRP = $160 < $800, so the firm should not hire three workers. 
- With 4 workers, MRP = $80 < $800, so the firm should not hire four workers.

Therefore, the optimal choice is to hire 3 workers.

The Following Table Shows the Number of Calculators That Can