Chapter 3, Problem 3NP

(a)

To determine

MPN for each level of employment.

Explanation of Solution

The marginal product of labor (MPN) is an additional output produced by an additional unit of labor.

It can be calculated using the following formula:

  $\text{Marginal product of labor = }\frac{\text{Change in production output}}{\text{Change in labor input}}$

The table (1) below shows the MPN for each level of employment.

TABLE-1:

Number of workers (N)	Number of widgets produced (Y)	Marginal product of labor (MPN)
0	0
1	8	8
2	15	7
3	21	6
4	26	5
5	30	4
6	33	3

(b)

To determine

The number of workers hired by the firm at given various levels of nominal wage.

Explanation of Solution

The equilibrium level of employment for a firm occurs when the nominal wage equals the marginal revenue product of labor. The marginal revenue product of labor is equal to the marginal product of labor times the price of the goods.

It is given that the price of the widget produced by the firm is equal to $5/unit.

Mathematically, the equilibrium condition of the level of employment can be expressed as follows:

  $\begin{array}{l}\text{MRPL=W }\left(1\right)\\ \text{MPN}\times \text{P=W }\end{array}$

Here,

MRPL is marginal revenue product of labor

MPN is a marginal product of labor

W is a nominal wage

P is the price of the good

The table (2) below shows the MRPL when the price is equal to $5/unit.

TABLE-2:

Number of workers (N)	Number of widgets produced (Y)	Marginal product of labor (MPN)	Marginal revenue product of labor (MRPL)
0	0
1	8	8	40
2	15	7	35
3	21	6	30
4	26	5	25
5	30	4	20
6	33	3	15

Now, according to employment equilibrium condition (1), when

1. Nominal wage is equal to $38, the firm will hire 1 worker.
2. Nominal wage is equal to $27, the firm will hire 3workers.
3. Nominal wage is equal to $22, the firm will hire 4 workers.

As a firm hires labor up to the point where nominal wage equals the marginal revenue product of labor.

(c)

To determine

Graphical relationship between a firm’s labor demand and nominal wage. And the firm’s labor demand curve.

Explanation of Solution

Figure (1) below shows the graphical relationship between a firm’s labor demand and nominal wage.

  

The graph in figure (1) is different from the labor demand curve because the labor demand curve plots the value of real wage equal to marginal product against the demand for labor.

Real wage is equal to the nominal wage divided by the price level. Thus, at nominal wage $38, $27, $22 and price $5, the value of real wage is equal to $7.6, $5.4, and $4.4, respectively.

As in real terms, the firm hires a number of workers up to a point where the real wage is equal to the marginal product of labor. Thus, according to the table (1), at,

1. Real wage equal to $7.6, the firm will hire 2 workers
2. Real wage equal to $5.4, the firm will hire 4 workers
3. Real wage equal to $4.4, the firm will hire 5 workers

The figure (2) below shows the firm’s labor demand curve. It depicts the graphical relationship between the real wage and labor demand.

  

(d)

To determine

Firm’s labor demand and production level at a fixed nominal wage of $38 and price $10/unit.

Explanation of Solution

The table (3) below shows the MRPL when the price is equal to $10/unit.

TABLE-3:

Number of workers (N)	Number of widgets produced (Y)	Marginal product of labor (MPN)	Marginal revenue product of labor (MRPL)
0	0
1	8	8	80
2	15	7	70
3	21	6	60
4	26	5	50
5	30	4	40
6	33	3	30

According to the employment equilibrium condition (1), at a fixed nominal wage $38, the firm will hire 5 workers. As beyond this level of workers, the marginal revenue product of labor (MRPL) falls below the nominal wage $38.

Thus, at fixed nominal wage $38 and increased price level from $5 to $10, the firm hires a greater number of workers compared to 1 worker found in part (b) and produces higher level of output equal to 30 units compared to 8 units found in part (b).

(e)

To determine

Effect on labor demand and production when there is an introduction of new technology.

Explanation of Solution

At fixed nominal wage $38 and price $5/unit, the firm was hiring 1 worker and production level was equal to 8 units. Now, it is given that the introduction of new technology doubles the number of units produced by the same number of workers.

When output doubles, then MPN double. This further doubles MRPL, as the MRPL rises to80. This is equal to MRPL in part (d), where the price was doubled from $5/unit to $10/unit.

Thus, the firm will hire the same number of workers equal to 5, as in part (d). It is just the production level that doubles from 30 units to 60 units due to the introduction of new technology.

(f)

To determine

Relationship between answers in part (d) and part (e).

Explanation of Solution

Since the marginal revenue product of labor (MRPL) is equal to the marginal product of labor (MPN) times the price (P) of the good, thus, any change in either P or MPN, will lead to an equivalent change in MRPL. And the equilibrium level of employment for a firm occurs when the nominal wage equals the marginal revenue product of labor.

This implies that the numbers of workers hired will remain the same in both the cases, i.e., when either P doubles as in part (d) or MPN doubles as in part (e).