Chapter 15, Problem 3P

Sub part (a):

To determine

The monopsony market.

Explanation of Solution

The total labor cost can be calculated by using the following formula.

$\text{Total labor cost}=\text{Number of labor}\times \text{Wage per person}$ (1)

Substitute the respective value in the equation (1) to calculate the total labor cost at one unit of labor.

$\begin{array}{c}\text{Total labor cost}=\text{1}\times \text{3}\\ =\text{3}\end{array}$

The total labor cost is $3.

The marginal resource cost can be calculated by using the following formula.

$\text{Marginal resource cost}=\frac{{\text{Total labor cost}}_{\text{Present}}-{\text{Total labor cost}}_{\text{Previous}}}{{\text{Total labor}}_{\text{Present}}-{\text{Total labor}}_{\text{Previous}}}$ (2)

Substitute the respective values in the equation (2) to calculate the marginal resource cost at one unit of labor.

$\begin{array}{c}\text{Marginal resource cost}=\frac{3-0}{1-0}\\ =\frac{3}{1}\\ =3\end{array}$

The marginal resource cost is $3.

Table -1 shows the value of the total labor cost and the marginal resources cost that are obtained by using the equation (1) and (2).

Table -1

Units of labor	Wage rate	Total labor cost	Marginal resources cost
0	-	0
1	6	6	6
2	9	18	12
3	12	36	18
4	15	60	24
5	18	90	30
6	21	120	36

The total revenue can be calculated by using the following formula.

The $\text{Total revenue}=\text{Price}\times \text{Total product}$ (3)

Substitute the respective value in the equation (3) to calculate the total revenue at one unit of labor.

$\begin{array}{c}\text{Total revenue}=\text{2}\times \text{17}\\ =34\end{array}$

The total revenue is $34.

The marginal product can be calculated by using the following formula.

$\text{Marginal product}=\frac{{\text{Total product}}_{\text{Present}}-{\text{Total product}}_{\text{Previous}}}{{\text{Total labor}}_{\text{Present}}-{\text{Total labor}}_{\text{Previous}}}$ (4)

Substitute the respective values in the equation (4) to calculate the marginal resource cost at one unit of labor.

$\begin{array}{c}\text{Marginal product}=\frac{17-0}{1-0}\\ =\frac{17}{1}\\ =17\end{array}$

The marginal product is $17.

The marginal revenue product can be calculated by using the following formula.

The $\text{Marginal revenue product}=\text{Price}\times \text{Marginal product}$ (5)

Substitute the respective values in the equation (5) to calculate the marginal revenue product.

$\begin{array}{c}\text{Marginal revenue product}=2\times \text{17}\\ =34\end{array}$

The marginal revenue product is $34.

Table -2 shows the value of the total revenue, the marginal revenue product and the marginal product that is obtained by using the equation (3), (4) and (5).

Table -2

Units of labor	Total product	Marginal product	Product price	Total revenue	Marginal revenue product
0	0		2	0
1	17	17	2	34	34
2	31	14	2	62	28
3	43	12	2	86	24
4	53	10	2	106	20
5	60	7	2	120	14
6	65	5	2	130	10

Graph -1 shows the firms labor supply and the marginal resources cost.7

In graph -1, the horizontal axis measures the units of labor and the vertical axis represents the wage rate. The discrete nature of problem requires that the (MRP) marginal revenue product should be equal or greater than the marginal resources cost. This marginal revenue cost curve lies above the labor supply because the employing of the next worker needs a higher wage in the market and will have to pay a higher wage for all the workers.

Economics Concept Introduction

Concept introduction:

Monopsony: The monopsony market refers to a market which consists of a single buyer who hires a particular type of labor. The workers provide labor to this type of market that has a limited employment opportunity as they need to acquire new skills to be hired. The firm is the wage marker.

Subpart (b):

To determine

How many workers should the firm employ.

Answer to Problem 3P

The firm should employ 3 workers.

Explanation of Solution

When the marginal revenue product for this worker is greater than the marginal cost, then the firm should employ the workers. From the table, the firm should employ three workers. For the first worker, the marginal revenue product is $34 and the marginal revenue cost is $6. Thus, the firm should employ the first worker. For the second worker, the marginal revenue product is $28 and the marginal revenue cost is $12. So, the firm should employ the second worker. For the third worker, the marginal revenue product is $24 and the marginal revenue cost is $18. So the firm should employ the third worker. But for the fourth worker, the marginal revenue product is $20 and the marginal revenue cost is $24. So, the firm should not employ the forth worker.

Subpart (c):

To determine

What happens to the monopolist employment and equilibrium wage rate.

Explanation of Solution

In this, the monopolist employment decreases by 2 units and the equilibrium wage rate is $2 which is less than the competitive wage.