Chapter 2, Problem 22P

A

Summary Introduction

Interpretation: Find out the productivity of both the companies and determine the company with higher productivity.

Concept Introduction: The production contribution of the total labor is represented by Labor Productivity.

Answer to Problem 22P

Through the calculations, we can infer that the productivity of the company A is 2.08 miles per hour, and that of the company B is 2.4 miles per hour. Hence, we can conclude that the Company B is higher productive of the two.

Explanation of Solution

Given Information: The ratio that relates output with the combined set of inputs involved is called as Multifactor Productivity.

Productivity of the companyA can be calculated using the below formula:

  $\begin{array}{l}\text{Productivity = }\frac{\text{Number of miles repaved}}{\text{Number of workers }\times \text{ Number of Days}}\\ =\frac{50\text{ miles }\times \text{ 2 lane road}}{6\text{ emplotees }\times \text{ 8 days}}\\ =\frac{100\text{ miles}}{48\text{ labor hours}}\\ =\text{2}\text{.08 miles per hour}\end{array}$

Thus, the productivity of the labor can be calculated as 17 poles per hour.

Productivity of the company B can be calculated using the below formula:

  $\begin{array}{l}\text{Productivity = }\frac{\text{Number of miles repaved}}{\text{Number of workers }\times \text{ Number of Days}}\\ =\frac{30\text{ miles }\times \text{ 4 lane road}}{\text{5 emplotees }\times \text{ 10 days}}\\ =\frac{120\text{ miles}}{\text{50 labor hours}}\\ =\text{2}\text{.4 miles per hour}\end{array}$

Thus, the productivity of the labor can be calculated as 2.4 miles per hour.

By observing the above derived results, we can see that the company B is more productive than the company A.

B

Summary Introduction

Interpretation: Find out the productivity of both the companies and determine the company with higher productivity, with the new assumptions.

Concept Introduction: The production contribution of the total labor is represented by Labor Productivity.

Answer to Problem 22P

Through the calculations, we can see that the labor productivity of the company A is more than that of the company B.

Explanation of Solution

Productivity of the labor can be calculated using the below formula:

  $\begin{array}{l}\text{Total Labor Cost for company A = Labor cost per hour }\times \text{ Total Labor Hours}\\ \text{=\$15}\times \text{(6 employees}\times \text{8 days}\times \text{8 hours)}\\ \text{=\$15}\times \text{384 hours}\\ \text{=\$5,760}\end{array}$

Thus, the total labor cost is $5,760.

With the derived labor cost for company A, Multifactor productivity can be computed,

  $\begin{array}{l}\text{Multifactor Productivity = }\frac{\text{Production}}{\text{Labor Cost + Material Cost}}\\ =\frac{\text{50 miles }\times \text{ 2 lane road}}{\$5,760+\$7000+\$12000}\\ =\frac{100\text{ miles}}{\$24,760}\\ =0.004039\text{ miles per dollar}\end{array}$

Now, we shall look at the labor productivity of the company B:

  $\begin{array}{l}\text{Total Labor Cost of Company B = Labor Cost per hour }\times \text{ Total Labor Hours}\\ \text{=\$15}\times \text{(5 employees}\times 10\text{ days}\times \text{8 hours)}\\ \text{=\$15}\times \text{400 hours}\\ \text{=\$6,000}\end{array}$

With the derived labor cost for company B, Multifactor productivity can be computed,

  $\begin{array}{l}\text{Multifactor Productivity = }\frac{\text{Production}}{\text{Labor Cost + Material Cost}}\\ =\frac{\text{30 miles }\times \text{ 4 lane road}}{\$6,000+\$9000+\$15000}\\ =\frac{120\text{ miles}}{\$30,000}\\ =0.004\text{ miles per dollar}\end{array}$

Thus, the company A is more productive than the company B.

C

Summary Introduction

Interpretation: Find out the productivity of both the companies and determine the company with higher productivity, with the new assumptions.

Concept Introduction: The production contribution of the total labor is represented by Labor Productivity.

Answer to Problem 22P

Through the calculations, we can see that the labor productivity of the company B is more than that of the company A.

Explanation of Solution

Productivity of the labor can be calculated using the below formula:

  $\begin{array}{l}\text{Total Labor Cost for company A = Labor cost per hour }\times \text{ Total Labor Hours}\\ \text{=\$35}\times \text{(6 employees}\times \text{8 days}\times \text{8 hours)}\\ \text{=\$35}\times \text{384 hours}\\ \text{=\$13,440}\end{array}$

Thus, the total labor cost is $13,440.

With the derived labor cost for company A, Multifactor productivity can be computed,

  $\begin{array}{l}\text{Multifactor Productivity = }\frac{\text{Production}}{\text{Labor Cost + Material Cost}}\\ =\frac{\text{50 miles }\times \text{ 2 lane road}}{\$13,440+\$7000+\$12000}\\ =\frac{100\text{ miles}}{\$32,440}\\ =0.003083\text{ miles per dollar}\end{array}$

Now, we shall look at the labor productivity of the company B:

  $\begin{array}{l}\text{Total Labor Cost of Company B = Labor Cost per hour }\times \text{ Total Labor Hours}\\ \text{=\$35}\times \text{(5 employees}\times 10\text{ days}\times \text{8 hours)}\\ \text{=\$35}\times \text{400 hours}\\ \text{=\$14,000}\end{array}$

With the derived labor cost for company B, Multifactor productivity can be computed,

  $\begin{array}{l}\text{Multifactor Productivity = }\frac{\text{Production}}{\text{Labor Cost + Material Cost}}\\ =\frac{\text{30 miles }\times \text{ 4 lane road}}{\$14,000+\$9000+\$15000}\\ =\frac{120\text{ miles}}{\$38,000}\\ =0.003158\text{ miles per dollar}\end{array}$

Thus, the company B is more productive than the company A.

D

Summary Introduction

Interpretation: Provide a conclusion with regard to the differences in the productivity with the changes in the labor costs.

Concept Introduction: The production contribution of the total labor is represented by Labor Productivity.

Answer to Problem 22P

From the point of view of person X, the deriving differ.

Explanation of Solution

In spite of the productivity stays higher for company B, the equipment and material costs are higher. On the other hand, when the labor cost is $15 per hour, Company A is more productive. At a labor cost of $35 per hour, company B is more productive.