Use the table to determine how many workers the firm will employ when the cost per good is $6

Question

, and the wage rate is $25
.

Labor Input (Workers) Total Product Marginal Product of Labor
Marginal Revenue Product of Labor (per hour)

Marginal Cost of Labor (per hour)
0 0 - - -
1 7 7 $42
$25
2 16 9 $54
$25
3 24 8 $48
$25
4 28 4 $24
$25
5 30 2 $12
$25

(1 point)
Responses

three workers
three workers

four workers
four workers

two workers
two workers

five workers
five workers
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Answer 1

To determine how many workers the firm will employ when the cost per good is $6 and the wage rate is $25, we first need to find the Marginal Revenue Product of Labor (MRP) which is derived from the Marginal Product of Labor (MPL) and the price of the good.

The MRP can be calculated as: \[ \text{MRP} = \text{MPL} \times \text{Price per Good} \]

Given that the price per good is $6, we can compute the MRP for each level of labor input:

1. For 1 worker:

   • MRP = 7 (MPL) × $6 = $42

2. For 2 workers:

   • MRP = 9 (MPL) × $6 = $54

3. For 3 workers:

   • MRP = 8 (MPL) × $6 = $48

4. For 4 workers:

   • MRP = 4 (MPL) × $6 = $24

5. For 5 workers:

   • MRP = 2 (MPL) × $6 = $12

Next, we compare the Marginal Revenue Product of Labor (MRP) to the Marginal Cost of Labor (MCL), which is the wage rate of $25.

We want to find the number of workers where the MRP is at least equal to the MCL ($25):

• 1 worker: MRP = $42 (greater than $25)
• 2 workers: MRP = $54 (greater than $25)
• 3 workers: MRP = $48 (greater than $25)
• 4 workers: MRP = $24 (less than $25)
• 5 workers: MRP = $12 (less than $25)

The firm will hire workers as long as MRP is greater than or equal to MCL. Therefore, it will employ workers up to 3:

The firm will employ three workers.