Value of Marginal Product
Labor
Marginal Product of Labor
Price of Product
VMPL
1
10
$4
2
8
$4
3
7
$4
4
5
$4
5
3
$4
6
1
$4
Calculate the VMPL at each level of labor
- If the Firm operates in a Perfectly Competitive Labor Market where the going market wage is $12, what is the profit maximizing level of employment?
Marginal Revenue Product
Calculate the Marginal Revenue Product to Derive the Demand for labor in this imperfectly competitive market
of Workers (L)
1
2
3
4
MPL
4
3
2
1
Marginal Revenue
$40
$35
$20
$15
MRPL
The Correct Answer and Explanation is :
1. Calculate the VMPL (Value of Marginal Product of Labor)
The VMPL (Value of the Marginal Product of Labor) is calculated by multiplying the Marginal Product of Labor (MPL) by the Price of the Product.
Given the following data:
- Price of Product = $4
The formula is: VMPL=MPL×Price of Product\text{VMPL} = \text{MPL} \times \text{Price of Product}
We can now calculate the VMPL for each level of labor.
| Labor (L) | MPL | Price of Product | VMPL (MPL * Price) |
|---|---|---|---|
| 1 | 10 | $4 | $40 |
| 2 | 8 | $4 | $32 |
| 3 | 7 | $4 | $28 |
| 4 | 5 | $4 | $20 |
| 5 | 3 | $4 | $12 |
| 6 | 1 | $4 | $4 |
2. Profit Maximizing Level of Employment
In a perfectly competitive labor market, a firm hires labor up to the point where the wage rate equals the Marginal Revenue Product of Labor (MRPL). Here, we are told that the market wage rate is $12.
From the VMPL calculations, we can compare the wage rate ($12) with the VMPL to determine the profit-maximizing level of employment:
- At L = 1, VMPL = $40 (greater than $12, so firm hires 1 worker).
- At L = 2, VMPL = $32 (greater than $12, so firm hires 2 workers).
- At L = 3, VMPL = $28 (greater than $12, so firm hires 3 workers).
- At L = 4, VMPL = $20 (greater than $12, so firm hires 4 workers).
- At L = 5, VMPL = $12 (equal to $12, so firm hires 5 workers).
- At L = 6, VMPL = $4 (less than $12, so firm does not hire 6 workers).
Thus, the profit-maximizing level of employment is 5 workers, as the VMPL at L=5 equals the market wage rate, and employing more workers would lead to the VMPL being less than the wage rate.
3. Calculate the Marginal Revenue Product (MRPL)
The Marginal Revenue Product of Labor (MRPL) is calculated by multiplying the MPL by the Marginal Revenue (MR). Here’s the calculation for each level of employment:
| # of Workers (L) | MPL | Marginal Revenue (MR) | MRPL (MPL * MR) |
|---|---|---|---|
| 1 | 4 | $40 | $160 |
| 2 | 3 | $35 | $105 |
| 3 | 2 | $20 | $40 |
| 4 | 1 | $15 | $15 |
The MRPL reflects the additional revenue generated by hiring one more worker. In this case, the MRPL shows the firm’s demand curve for labor in this imperfectly competitive market.
Explanation
In a perfectly competitive labor market, firms hire workers until the VMPL (which is equal to the MRPL in this case) equals the wage rate. The profit-maximizing level of employment is where the VMPL = Wage Rate. In this case, the firm hires 5 workers because the VMPL at L=5 equals the wage rate of $12. If the firm hired more than 5 workers, the VMPL would be less than the wage rate, meaning that the cost of hiring additional workers exceeds the revenue generated by them, reducing overall profits.
In an imperfectly competitive market, the firm sets its demand for labor based on the Marginal Revenue Product of Labor (MRPL). The MRPL decreases as more workers are hired due to diminishing marginal returns, as seen in the table where the MRPL decreases as the number of workers increases. This decrease in MRPL reflects the reduced additional revenue each worker generates as the firm scales up production. The firm would hire workers up to the point where the MRPL equals the wage rate, ensuring that labor costs are aligned with the additional revenue generated from employing each worker.