2. In the table below, assume a monopsonist has the marginal-revenue-product schedule for a particular type of labor given in columns 1 and 2 and that the supply schedule for labor is that given in columns 1 and 3.
(1) (2) (3) (4) (5)
Number of MRP Wage Total Marginal
labor units of labor rate labor cost labor cost
0
1 $18 $ 6 $_____ $_____
2 16 7 _____ _____
3 14 8 _____ _____
4 12 9 _____ _____
5 10 10 _____ _____
6 8 11 _____ _____
7 6 12 _____ _____
8 4 13 _____ _____
(a) Compute the firm’s total labor costs at each level of employment and the marginal labor cost of each unit of labor, and enter these figures in columns 4 and 5. 8 points
(b) How many units of labor will the firm hire? What will be the wage rate? I point
(c) If this firm hired labor in a competitive labor market, what would be the wage rate and number of workers hired? 1 point
I would be so thankful for any help possible!
(a) To compute the total labor costs, we will multiply the number of labor units (column 1) by the wage rate (column 3) and fill in the values in column 4. To calculate the marginal labor cost, we will find the difference between the total labor costs at each level of employment and fill in the values in column 5. Here's the completed table:
(1) (2) (3) (4) (5)
Number of MRP Wage Total Marginal
labor units of labor rate labor cost labor cost
0
1 $18 $6 $6 $6
2 16 7 $14 $8
3 14 8 $24 $10
4 12 9 $36 $12
5 10 10 $50 $14
6 8 11 $66 $16
7 6 12 $84 $18
8 4 13 $104 $20
(b) The firm will hire labor units until the marginal labor cost (MLC) is equal to or greater than the marginal revenue product (MRP). In this case, the firm will hire 4 units of labor because, at this level, MRP ($12) is equal to MLC ($12). The wage rate at this level of employment will be $9.
(c) In a competitive labor market, the wage rate equals the MRP. In this case, the MRP for hiring four units of labor is $12 (column 2). So, in a competitive labor market, the firm would still hire 4 units of labor, but the wage rate would be $12 instead of $9.
To compute the firm's total labor costs at each level of employment and the marginal labor cost of each unit of labor, we can use the given marginal-revenue-product (MRP) schedule and supply schedule for labor.
(a) To calculate the total labor costs, we multiply the number of labor units by the wage rate in column 3. The marginal labor cost can be obtained by subtracting the previous total labor cost from the current total labor cost.
The completed table would look like this:
(1) (2) (3) (4) (5)
Number of MRP Wage Total Marginal
labor units of labor rate labor cost labor cost
0
1 $18 $6 $6 N/A
2 $16 $7 $14 $8
3 $14 $8 $24 $10
4 $12 $9 $36 $12
5 $10 $10 $50 $14
6 $8 $11 $66 $16
7 $6 $12 $84 $18
8 $4 $13 $104 $20
(b) To determine how many units of labor the firm will hire and the wage rate, we look at the marginal-revenue-product (MRP) and the wage rate columns. The firm will hire labor until the MRP is equal to or less than the wage rate. In this case, once the MRP drops below $13 (the wage rate), the firm will stop hiring. Therefore, the firm will hire 7 units of labor and the wage rate will be $12.
(c) If this firm hired labor in a competitive labor market, the wage rate and number of workers hired would be determined by the intersection of the competitive supply and demand for labor. Since the supply schedule for labor is not provided, we cannot determine the exact wage rate and number of workers hired in a competitive labor market.
To compute the firm's total labor costs at each level of employment and the marginal labor cost of each unit of labor, we need to use the given data in columns 1 and 2.
(a) Filling in column 4 (Total labor cost) and column 5 (Marginal labor cost):
- For the first row:
- Number of labor units: 0
- MRP (Marginal Revenue Product): Not given
- Wage rate: $6
- Total labor cost: 0 * $6 = $0
- Marginal labor cost: Not applicable (since there are no labor units)
- For the second row:
- Number of labor units: 1
- MRP: $18
- Wage rate: $6
- Total labor cost: 1 * $6 = $6
- Marginal labor cost: $18 - $0 (since there were no labor units before) = $18
You can continue filling in the remaining rows by following the same process.
(b) To determine how many units of labor the firm will hire and the wage rate, look for the level of employment where the marginal labor cost equals the wage rate. In other words, find the row where the value in column 5 matches the value in column 3.
From the given data, we can see that when the wage rate is $7, the marginal labor cost is also $7 in the second row. So, the firm will hire 2 units of labor and the wage rate will be $7.
(c) If the firm hired labor in a competitive labor market, the wage rate and number of workers hired would be determined by the intersection of the labor supply and labor demand curves. Since the labor demand curve is not given, we cannot determine the exact wage rate and number of workers hired in a competitive market.