Chapter 1, Problem 8P

a)

Summary Introduction

To determine: The labor productivity per labor hour of Company LF.

Introduction: Labor productivity is the valuation of economic growth in a nation. Labor production measures the amount of products produced within an hour;it especially evaluates labor productivity, that is, the amount of real gross domestic product (GDP) produced by a labor hour.

Answer to Problem 8P

The labor productivity of Company LF is 2.5 tires per hour.

Explanation of Solution

Given information:

Company LF is manufacturing 1,000 tires per day with 400 labor hours per day.

Formulae to calculate labor productivity:

$\text{Labor productivity}=\frac{\text{Total tiers produced}}{\text{Total Labor hours}}$

Calculate labor productivity:

The labor productivity is calculated by dividing the total output by the total input.

$\begin{array}{c}\text{Labor productivity}=\frac{1,000\text{tires}}{400\text{hours}}\\ =2.5\text{tires}\text{per}\text{hour}\end{array}$

Therefore, the labor productivity of Company LF is 2.5 tires per hour.

b)

Summary Introduction

To determine: Multifactor productivity of Company LF.

Introduction: Multifactor productivity is an evaluation of economic performance that compares the amount of products and services produced to the amount of combined input used to produce those products and services.

Answer to Problem 8P

The multifactor productivity of Company LF is 0.025tiers per dollar.

Explanation of Solution

Given information:

Company LFproduces 1,000 tiers per day with 400 labor hours at the cost of $12.50 per hour. Raw materials of 20,000 pounds per day were used at the cost of $1 per pound. Energy cost is $5,000 per day and capital cost is $10,000 per day.

Formula:

$\text{Multifactor productivity}=\frac{\text{Total goods produced}}{\left[\begin{array}{l}\left(\text{Labor hours}\times \text{Cost per hour}\right)+\left(\text{Raw materials used}\times \text{Cost }\right)+\\ \text{Energy cost}+\text{Capital cost}\end{array}\right]}$

Calculate multifactor productivity:

The multifactor productivity is calculated by dividing the total goods producedwith the total values of resources used to produce the total goods.

$\begin{array}{c}\text{Multifactor productivity}=\frac{\text{Total goods produced}}{\left[\begin{array}{l}\left(\text{Labor hours}\times \text{Cost per hour}\right)+\left(\text{Raw materials used}\times \text{Cost }\right)+\\ \text{Energy cost}+\text{Capital cost}\end{array}\right]}\\ =\frac{1,000\text{tires}}{\left[\begin{array}{l}\left(400\text{ hours}\times \text{\$12}\text{.50per}\text{hour}\right)+\left(20,000\times \text{\$1}\text{per gallon}\right)+\\ \$5,000+\$10,000\end{array}\right]}\\ =\frac{1,000\text{tires}}{\$40,000}\\ =0.025\text{tires}\text{per}\text{dollar}\end{array}$

Therefore, the multifactor productivity of Company LF is 0.025 tires per dollar.

c)

Summary Introduction

To determine: The percentage change in multifactor productivity if the company reduces the energy bill by $1,000 per day.

Answer to Problem 8P

The percentage change in multifactor productivity is 2.56%.

Explanation of Solution

First, calculate the change in multifactor productivity.

Given information:

The energy cost is reduced by $1,000 per day.

Formula:

$\begin{array}{l}\text{Multifactor}\\ \text{productivity}\end{array}\}=\left[\frac{\text{Total goods produced}}{\begin{array}{l}\left(\text{Labor hours}\times \text{cost per hour}\right)+\\ \left(\text{Raw materials}\times \text{cost}\right)+\text{Energy}+\text{Capital}\end{array}}\right]-\left(\begin{array}{l}\text{Initial multifactor}\\ \text{productivity}\end{array}\right)$

The change in multifactor productivity is calculated by dividing the total goods producedwith the total values of resources used to produce the total goods. The initial multifactor productivity must be subtracted from the change in multifactor productivity value.

$\begin{array}{c}\begin{array}{l}\text{Multifactor}\\ \text{productivity}\end{array}\}=\left[\frac{\text{Total goods produced}}{\begin{array}{l}\left(\text{Labor hours}\times \text{cost per hour}\right)+\\ \left(\text{Raw materials}\times \text{cost}\right)+\text{Energy}+\text{Capital}\end{array}}\right]-\left(\begin{array}{l}\text{Initial multifactor}\\ \text{productivity}\end{array}\right)\\ =\left[\frac{1,000\text{tires}}{\left[\begin{array}{l}\left(400\text{ hours}\times \text{\$12}\text{.50}\right)+\\ \left(20,000\times \text{\$1}\right)+\$4,000+\$10,000\end{array}\right]}-0.025\right]\\ =\frac{1,000\text{tires}}{\$39,000}-0.025\end{array}$

$\begin{array}{c}=0.02564-\text{0}\text{.025}\\ \text{=0}\text{.00064}\text{tires per dollar}\end{array}$

Hence, the change in multifactor productivity is 0.00064 tires per dollar.

Calculate the percentage change in multifactor productivity:

Formula:

$\text{Percentage change}=\frac{\text{Change in multifactor}\text{productivity}}{\text{Intital multifactor}\text{productivity}}\times 100$

Calculate percentage change:

The percentage change in productivity is calculated by dividing the change in productivity units with initial productivity.

$\begin{array}{c}\text{Multifactor productivity}=\frac{\text{Inital}\text{multifactor productivity}}{\text{Change in multifactor productivity value}}\times 100\\ =\frac{0.00064}{0.025}\times 100\\ =0.0256\times 100\\ =2.56\%\end{array}$

Therefore, the percentage change in productivity is 2.56%.