Assume that the following holds for a firm: Output 20 29 37 44 50 Labor Wage 5 1I234S 5 Assume amount of capital is constant. (A) Calculate the marginal product of labor for each level of labor use. (B) Assume the price of the output is $5 per unit. Assume the firm is in a perfectly competitive output and input market. Calculate the VMP and MRP of labor. (C) Assume the wage rate is $30. How many units of labor does this firm hire? 10 15 20 25 4 Assume now that the firm is a monopsony and is still perfectly competitive in the output market. The supply curve the firm faces is as follows: Labor 1 2 3 4 45 5 (D) Given the above data, how many workers does the monopsonist hire? (E) What wage does the monopsonist pay each worker? (F) Show all of the above using two graphs, one for the perfectly competitive firm (input) and one for the monopsonist.
The Correct Answer and Explanation is :
To solve this, let’s break down each part step by step:
(A) Marginal Product of Labor (MPL)
The marginal product of labor is the change in output resulting from the addition of one more unit of labor. This can be calculated by taking the difference in output at each labor level.
Output at Labor 0, 1, 2, 3, 4, 5:
Output: 20, 29, 37, 44, 50
Labor: 0, 1, 2, 3, 4, 5
We can calculate MPL as follows:
- From 0 to 1 labor: MPL = 29 – 20 = 9
- From 1 to 2 labor: MPL = 37 – 29 = 8
- From 2 to 3 labor: MPL = 44 – 37 = 7
- From 3 to 4 labor: MPL = 50 – 44 = 6
So, the marginal product of labor is:
MPL = 9, 8, 7, 6 (for labor units 1 to 4).
(B) Value of Marginal Product (VMP) and Marginal Revenue Product (MRP)
Given the price of the output is $5, the value of the marginal product (VMP) is the MPL multiplied by the price of the output.
[ VMP = MPL \times P ]
- For labor 1: VMP = 9 × 5 = 45
- For labor 2: VMP = 8 × 5 = 40
- For labor 3: VMP = 7 × 5 = 35
- For labor 4: VMP = 6 × 5 = 30
The marginal revenue product (MRP) in perfect competition is equal to the VMP because the firm takes the price of the output as given, so:
MRP = VMP.
Thus, the MRP is:
MRP = 45, 40, 35, 30.
(C) Firm’s Labor Hire at Wage Rate $30
In a perfectly competitive labor market, the firm will hire workers as long as the wage is less than or equal to the MRP. Given that the wage rate is $30, we compare it to the MRP.
- At 1 unit of labor: MRP = 45 (greater than 30, so hire)
- At 2 units of labor: MRP = 40 (greater than 30, so hire)
- At 3 units of labor: MRP = 35 (greater than 30, so hire)
- At 4 units of labor: MRP = 30 (equal to 30, so hire)
The firm will hire 4 units of labor.
(D) Monopsony Labor Hire
In a monopsony, the firm is the only buyer of labor. The supply curve it faces is upward sloping, meaning the firm has to offer higher wages to hire more labor. We assume the wage is determined where the marginal cost of labor (MCL) equals the MRP. The supply curve for labor is:
Labor: 1, 2, 3, 4, 5
Wage: 10, 12, 15, 18, 20
To calculate the marginal cost of labor (MCL), we compute the change in total labor cost as more labor is hired:
- MCL from 1 to 2 = 12 – 10 = 2
- MCL from 2 to 3 = 15 – 12 = 3
- MCL from 3 to 4 = 18 – 15 = 3
- MCL from 4 to 5 = 20 – 18 = 2
Now, compare MCL with the MRP to find the quantity of labor hired:
- At 1 unit: MRP = 45, MCL = 10 (hire)
- At 2 units: MRP = 40, MCL = 12 (hire)
- At 3 units: MRP = 35, MCL = 15 (hire)
- At 4 units: MRP = 30, MCL = 18 (hire)
The monopsonist will hire 3 units of labor.
(E) Wage Paid by Monopsonist
In a monopsony, the firm will pay the wage corresponding to the labor it hires. Since the monopsonist hires 3 units of labor, the wage paid will be the wage for 3 workers, which is $15.
(F) Graphs for Perfectly Competitive Firm and Monopsonist
In the graphs:
- Perfectly competitive market: The labor supply curve is horizontal, and the firm hires labor until MRP equals the wage. The wage is constant.
- Monopsonist: The labor supply curve is upward sloping, and the firm hires labor where MCL equals MRP, resulting in a lower quantity of labor hired and a lower wage paid compared to the perfectly competitive case.
These graphs would show the following:
- The perfectly competitive firm hires labor at a wage of $30 and 4 units of labor.
- The monopsonist hires 3 units of labor at a wage of $15.