Chapter 1, Problem 17P

a)

Summary Introduction

To determine: The multifactor productivity for last year.

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

Answer to Problem 17P

Hence, the multifactor productivity for last year is 0.8533.

Explanation of Solution

Given information:

The given information is as follows:

	Last year	This year
Production (dozen)	1,500	1,500
Labor (hours)	350	325
Capital investment ($)	15,000	18,000
Energy (BTU)	3,000	2,700

Labor cost is given as $8 per hour, capital is 0.83% per month of investment, and energy is $0.60 per BTU.

Formulae to determine the multifactor productivity:

$\begin{array}{c}\text{Multifactor productivity}=\frac{\text{Total output}}{\text{Total input}}\\ =\frac{\text{Output units}}{\left(\begin{array}{l}\text{Labor hours}\times \\ \text{Cost per hour}\end{array}\right)+\left(\begin{array}{l}\text{Capital investment}+\\ \text{Interest on capital}\end{array}\right)+\left(\begin{array}{l}\text{Energy}\times \\ \text{Rate}\end{array}\right)}\end{array}$

Determine the multifactor productivity for last year:

It is calculated by dividing the output units and the value attained by adding the multiple of labor hours and cost per hours, sum of capital investment and interest on capital, and multiple of energy and rate.

$\begin{array}{c}\text{Multifactor productivity}=\frac{\text{Output units}}{\left(\begin{array}{l}\text{Labor hours}\times \\ \text{Cost per hour}\end{array}\right)+\left(\begin{array}{l}\text{Capital investment}+\\ \text{Interest on capital}\end{array}\right)+\left(\begin{array}{l}\text{Energy}\times \\ \text{Rate}\end{array}\right)}\\ =\frac{\left(1,500\times 12\right)}{\left(350\times 8\right)+\left(15,000+\left(15,000\times 0.83\%\times 12\right)\right)+\left(3,000\times \$0.60\right)}\\ =\frac{18,000}{2,800+\left(15,000+1,494\right)+1,800}\end{array}$

$\begin{array}{c}=\frac{18,000}{2,800+16,494+1,800}\\ =\frac{18,000}{21,094}\\ =0.8533\end{array}$

Hence, the multifactor productivity for last year is 0.8533.

b)

Summary Introduction

To determine: The multifactor productivity for the current year.

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

Answer to Problem 17P

Hence, the multifactor productivity for this year is 0.7496.

Explanation of Solution

Given information:

The given information is as follows:

	Last year	This year
Production (dozen)	1,500	1,500
Labor (hours)	350	325
Capital investment ($)	15,000	18,000
Energy (BTU)	3,000	2,700

Labor cost is given as $8 per hour, capital is 0.83% per month of investment, and energy is $0.60 per BTU.

Formulae to determine the multifactor productivity:

$\begin{array}{c}\text{Multifactor productivity}=\frac{\text{Total output}}{\text{Total input}}\\ =\frac{\text{Output units}}{\left(\begin{array}{l}\text{Labor hours}\times \\ \text{Cost per hour}\end{array}\right)+\left(\begin{array}{l}\text{Capital investment}+\\ \text{Interest on capital}\end{array}\right)+\left(\begin{array}{l}\text{Energy}\times \\ \text{Rate}\end{array}\right)}\end{array}$

Determine the multifactor productivity for this year:

It is calculated by dividing the output units and the value attained by adding the multiple of labor hours and cost per hours, sum of capital investment and interest on capital, and multiple of energy and rate.

$\begin{array}{c}\text{Multifactor productivity}=\frac{\text{Output units}}{\left(\begin{array}{l}\text{Labor hours}\times \\ \text{Cost per hour}\end{array}\right)+\left(\begin{array}{l}\text{Capital investment}+\\ \text{Interest on capital}\end{array}\right)+\left(\begin{array}{l}\text{Energy}\times \\ \text{Rate}\end{array}\right)}\\ =\frac{\left(1,500\times 12\right)}{\left(325\times 8\right)+\left(18,000+\left(18,000\times 0.83\%\times 12\right)\right)+\left(2,700\times \$0.60\right)}\\ =\frac{18,000}{2,600+\left(18,000+1,792.8\right)+1,620}\end{array}$

$\begin{array}{c}=\frac{18,000}{2,600+19,792.8+1,620}\\ =\frac{18,000}{24,012.8}\\ =0.7496\end{array}$

Hence, the multifactor productivity for this year is 0.7496.

c)

Summary Introduction

To determine: The percentage change in productivity for the monthly average last year versus the monthly average this year.

Introduction: Productivity is a measure of the effectiveness of an individual, systems, machinery and other equipment that are used in converting inputs into outputs. In all organizations, productivity is an important determinant to know cost efficiency.

Answer to Problem 17P

Hence, the percent change in multifactor productivity last year versus this year is -11.764.

Explanation of Solution

Given information:

The given information is as follows:

	Last year	This year
Production (dozen)	1,500	1,500
Labor (hours)	350	325
Capital investment ($)	15,000	18,000
Energy (BTU)	3,000	2,700

Labor cost is given as $8 per hour, capital is 0.83% per month of investment, and energy is $0.60 per BTU.

Formulae to calculate the percentage change on multifactor basis:

$\begin{array}{l}\text{Percentage change}\\ \text{on multifactor basis}\end{array}\}=\frac{\left(\begin{array}{l}\text{Multifactor productivity this year}-\\ \text{Multifactor productivity last year}\end{array}\right)}{\text{Multifactor productivity last year}}\times 100$

Calculate the percentage change on multifactor basis:

It is calculated by the dividing the value attained by subtracting the multifactor productivity last year from last year from this year and the multifactor productivity last year.

$\begin{array}{c}\begin{array}{l}\text{Percentage change}\\ \text{on multifactor basis}\end{array}\}=\frac{\left(\begin{array}{l}\text{Multifactor productivity this year}-\\ \text{Multifactor productivity last year}\end{array}\right)}{\text{Multifactor productivity last year}}\times 100\\ =\frac{0.7496-0.8533}{0.8533}\times 100\\ =\frac{-0.1037}{0.8533}\times 100\\ =-12.15\end{array}$

Hence, the percentage change on multifactor basis is -12.15%.