Chapter 19, Problem 12P

To determine

Concept Introduction

Marginal Product of Labor (MPL): This refers to the additional unit of output produced when an additional unit of labor is employed in the current labor force.

The formula to calculate the marginal product of labor is:

Where,

• is the change in quantity.
  
• is the change in labor.
  

Value of Marginal Product of Labor (VMPL): This refers to the value of an additional unit of output produced when an additional unit of labor is employed in the current labor force.

The formula to calculate the value of marginal product of labor is:

Where,

• MPL is the marginal product of labor.
• P is the price.

Explanation of Solution

a. Calculation of MPL and VMPL.

Given,
Price of pizza is $2.
Hourly wage rate is $10.

Quantity of Labor(Workers)	Quantity of Pizza
0	0
1	9
2	15
3	19
4	22
5	24

In order to maximize the profit, the pizza parlor should employ that number of workers at which the value of the marginal product of labor is more than or equal to the wage rate of $10.

The below table shows the calculation of MPL and VMPL:

Quantity of Labor(Workers)	Change in Quantity of Labor(Workers)(A)	Quantity of Pizza	Change in Quantity of Pizza(B)	MPL(C)	VMPL($)
0	-	0	-	-	-
1	1	9	9	9	18
2	1	15	6	6	12
3	1	19	4	4	8
4	1	22	3	3	6
5	1	24	2	2	4

Conclusion:

Thus, the MPL and VMPL per worker is calculated in the table.

b. Graph to show the value of marginal product of labor curve.

The below graph shows the VMPL curve:

Fig 1

• In the above graph, VMPL curve shows the value of marginal product of labor which is downward sloping.

• The VMPL is more than or equal to the wage rate of $10 at the level where the number of workers employed is 2.

• Hence, two workers should be employed. If the third worker is employed, the VMPL falls below the wage rate at $8.

Conclusion:

Thus, two workers should be employed.

c. The price of pizza increases to $4.

The below table shows the calculation of MPL and VMPL:

Quantity of Labor(Workers)	Change in Quantity of Labor(Workers)(A)	Quantity of Pizza	Change in Quantity of Pizza(B)	MPL(C)	VMPL($)
0	-	0	-	-	-
1	1	9	9	9	36
2	1	15	6	6	24
3	1	19	4	4	16
4	1	22	3	3	12
5	1	24	2	2	8

The below graph shows the VMPL curve:

Fig 2

• In the above graph, VMPL₂curve shows the value of marginal product of labor which is downward sloping.

• The VMPL is more than or equal to the wage rate of $10 at the level where the number of workers employed is 4.

• Hence, 4 workers should be employed. If the fifth worker is employed, the VMPL falls below the wage rate at $8.

Conclusion:

Thus, four workers should be employed.

d. MPL and VMPL after the purchase of a new oven.

In order to maximize the profit, the pizza parlor should employ that number of workers at which the value of marginal product of labor is more than or equal to the wage rate of $10.

The below table shows the calculation of MPL and VMPL:

Quantity of Labor(Workers)	Change in Quantity of Labor(Workers)(A)	Quantity of Pizza	Change in Quantity of Pizza(B)	MPL(C)	VMPL($)
0	-	0	-	-	-
1	1	18	18	18	36
2	1	30	12	12	24
3	1	38	8	8	16
4	1	44	6	6	12
5	1	48	4	4	8

Conclusion:

Thus, the MPL and VMPL per worker is calculated in the table.

e. Graph to show the value of marginal product of labor curve.

The below graph shows the VMPL curve:

Fig 3

• In the above graph, VMPL₃curve shows the value of marginal product of labor which is downward sloping.

• The VMPL is more than or equal to the wage rate of $10 at the level where the number of workers employed is 4.

• Hence, 4 workers should be employed. If the fifth worker is employed, the VMPL falls below the wage rate at $8.

• Therefore, Ms. Patty should employ more workers as the technology gets better.

Conclusion:

Thus, four workers should be employed.