Chapter 14, Problem 1SCQ

Table 14.10 shows levels of employment (Labor), the marginal product at each of those levels, and the price at which the film can sell output in the perfectly competitive market where it operates.

1. What is the value of the marginal product at each level of labor?
2. If the firm operates in a perfectly competitive labor market where the going market wage is $\$\text{12}$, what is the film’s profit maximizing level of employment?

To determine

(a)

Based on the table, value of the marginal product at each level of labor is to be determined.

Explanation of Solution

Labor	Marginal Product of Labor	Price of the Product (in $)	Value of Marginal product of Labor
1	10	4	40
2	8	4	32
3	7	4	28
4	5	4	20
5	3	4	12
6	1	4	4

Economics Concept Introduction

A perfectly competitive labor market is a market in which the firm can hire all the labor at the market wage level. To maximize the profits, the firms in the perfectly competitive labor market will hire the labor where wage is equal to the value of marginal product of labor.

$\begin{array}{l}{\text{Wage}}_{\text{Market}}\text{= VMP}\\ \text{Where,VMP}\text{=}\text{ Value of Marginal Prodcut of labor}\end{array}$

The value of marginal product of labor is the value of output produced by each labor. It can be calculated using the following formula:

$\begin{array}{l}{\text{VMP}}_{\text{L}}{\text{= MP}}_{\text{L}}\text{×P}\\ {\text{where, VMP}}_{\text{L}}\text{= Value of Marginal Product of Labor}\\ {\text{MP}}_{\text{L}}\text{=Marginal product of Labor}\\ \text{P = Price of the product}\end{array}$

The marginal product of labor is the net addition to the total product when an additional labor unit is employed. It can be calculated by using the following formula:

$\begin{array}{l}{\text{MP}}_{\text{L}}{\text{= TP}}_{\text{n}}{\text{-TP}}_{\text{n-1}}\\ {\text{MP}}_{\text{L}}\text{= Marginal Product of labor}\\ \text{TP = Total Product}\end{array}$

To determine

(b)

The firm’s profit maximizing employment level is to be determined.

Explanation of Solution

As per the table shown below:

The value of marginal product of labor is calculated in part a.

Labor	Marginal Product of Labor	Price of the Product (in $)	Value of Marginal product of Labor
1	10	4	40
2	8	4	32
3	7	4	28
4	5	4	20
5	3	4	12
6	1	4	4

The profit maximizing perfectly competitive firm will hire 5 units of labor as the value of marginal product of labor is equal to market wage rate.

Economics Concept Introduction

A perfectly competitive labor market is a market in which the firm can hire all the labor at the market wage level. To maximize the profits, the firms in the perfectly competitive labor market will hire the labor where wage is equal to the value of marginal product of labor.

$\begin{array}{l}{\text{Wage}}_{\text{Market}}\text{= VMP}\\ \text{Where,VMP}\text{=}\text{ Value of Marginal Prodcut of labor}\end{array}$

The value of marginal product of labor is the value of output produced by each labor. It can be calculated using the following formula:

$\begin{array}{l}{\text{VMP}}_{\text{L}}{\text{= MP}}_{\text{L}}\text{×P}\\ {\text{where, VMP}}_{\text{L}}\text{= Value of Marginal Product of Labor}\\ {\text{MP}}_{\text{L}}\text{=Marginal product of Labor}\\ \text{P = Price of the product}\end{array}$

The marginal product of labor is the net addition to the total product when an additional labor unit is employed. It can be calculated by using the following formula:

$\begin{array}{l}{\text{MP}}_{\text{L}}{\text{= TP}}_{\text{n}}{\text{-TP}}_{\text{n-1}}\\ {\text{MP}}_{\text{L}}\text{= Marginal Product of labor}\\ \text{TP = Total Product}\end{array}$