Chapter 2, Problem 4P

a)

Summary Introduction

To compute: The labor productivity under each system.

Introduction: Labor productivity is the measure of productivity of a worker during a period of time. It the ratio of total output to the total productivity hours.

Answer to Problem 4P

Labor productivity prior to buying new equipment is 16 carts/worker/hour and after buying new equipment is 21 carts/worker/hour.

Explanation of Solution

Given information:

Prior to buying new equipment:

$\begin{array}{c}\text{Number}\text{of}\text{worker}=\text{5}\\ \text{Number}\text{of}\text{carts}\text{produced}=\text{80}\text{carts}\text{per}\text{hour}\\ \text{Worker}\text{wages}=\text{\$10/hour}\\ \text{Machine}\text{cost}=\text{\$40/hour}\end{array}$

After buying new equipment:

After buying new equipment, one worker is transferred to another department, equipment cost is increased by $10/hour and output increased by four carts/hour.

Formula:

$\text{Labor}\text{productivity}=\frac{\text{Number}\text{of}\text{carts}}{\text{Number}\text{of}\text{workers}}$

Calculation of Labor productivity:

Prior to buying new equipment:

$\begin{array}{c}\text{Labor}\text{productivity}=\frac{\text{80}}{\text{5}}\\ =16\text{carts/worker/hour}\end{array}$

Labor productivity prior to buying new equipment is calculated by dividing number of carts of 80 with the number of workers 5 which yields 16 carts/worker/hour

After buying new equipment:

$\begin{array}{c}\text{Labor}\text{productivity}=\frac{\text{80}+\text{4}}{\text{5}-\text{1}}\\ =21\text{carts/worker/hour}\end{array}$

Labor productivity after buying new equipment is calculated by dividing number of carts of 84 with the number of workers 4which yields 21 carts/worker/hour.

Hence, labor productivity before buying new equipment is 16 carts/worker/hour and after buying new equipment is 21 carts/worker/hour.

b)

Summary Introduction

To compute: The multifactor productivity.

Introduction: Multifactor productivity is also referred as total factor productivity. It is the measure of economic performance by comparing the amount of goods and services produced to the total input used to produce the output.

Answer to Problem 4P

Multifactor productivity prior to buying new equipment is 0.89 carts/dollar and after buying new equipment is 0.93 carts/dollar.

Explanation of Solution

Given information:

Prior to buying new equipment:

$\begin{array}{c}\text{Number}\text{of}\text{worker}=\text{5}\\ \text{Number}\text{of}\text{carts}\text{produced}=\text{80}\text{carts}\text{per}\text{hour}\\ \text{Worker}\text{wages}=\text{\$10/hour}\\ \text{Machine}\text{cost}=\text{\$40/hour}\end{array}$

After buying new equipment:

After buying new equipment, one worker is transferred to another department, equipment cost is increased by $10/hour and output increased by four carts/hour.

Formula:

$\begin{array}{c}\text{Multifactor}\text{Productivity}=\frac{\text{Output}}{\text{Total}\text{cost}}\\ \text{Total}\text{cost}=\text{Labor}\text{cost}+\text{Equipment}\text{cost}\end{array}$

Calculation of Multifactor productivity:

Prior to buying new equipment:

$\begin{array}{c}\text{Laborcost}=5\times 10\text{/hour}\\ =\$50\text{/hour}\\ \text{Equipment cost}=\text{\$40/hour}\end{array}$

$\begin{array}{c}\text{Multifactor}\text{productivity}=\frac{80\text{carts}}{\$50+\$40}\\ =0.89\text{carts/dollar}\end{array}$

Labor cost is calculated by multiplying number of workers (5) with 10/ hours which gives 50/hour.

Multifactor productivity is calculated by dividing output of 80 carts with the total cost of $90 ($50+$40) which yields 0.89 carts/dollar.

After buying new equipment:

$\begin{array}{c}\text{Laborcost}=4\times 10\text{/hour}\\ =\$40\text{/hour}\\ \text{Equipment cost}=\text{\$40/hour}+\text{\$10/hour}\\ =\text{\$50/hour}\end{array}$

$\begin{array}{c}\text{Multifactor}\text{productivity}=\frac{84\text{carts}}{\$40+\$50}\\ =0.93\text{carts/dollar}\end{array}$

Labor cost is calculated by multiplying number of workers (4) with 10/ hours which gives 40/hour.

Multifactor productivity is calculated by dividing output of 84 carts with the total cost of $90 ($40+$50) which yields 0.93 carts/dollar.

Hence, multifactor productivity prior to buying new equipment is 0.89 carts/dollar and after buying new equipment is 0.93 carts/dollar.

c)

Summary Introduction

To determine: The changes in productivity and comment the best one.

Introduction: Productivity is the measure of performance of a person, machine or an organization. It is computed by dividing the average output per period by the total cost incurred or resources used in the process.

Answer to Problem 4P

Labor productivity growth is 31.25% and multifactor productivity growth is 4.49%.

Explanation of Solution

Given information:

Prior to buying new equipment:

$\begin{array}{c}\text{Number}\text{of}\text{worker}=\text{5}\\ \text{Number}\text{of}\text{carts}\text{produced}=\text{80}\text{carts}\text{per}\text{hour}\\ \text{Worker}\text{wages}=\text{\$10/hour}\\ \text{Machine}\text{cost}=\text{\$40/hour}\end{array}$

After buying new equipment:

After buying new equipment, one worker is transferred to another department, equipment cost is increased by $10/hour and output increased by four carts/hour.

Formula:

$\text{Productivity}\text{growth}=\frac{\text{Current}\text{productivity}-\text{Previous}\text{productivity}}{\text{Previous}\text{productivity}}$

Labor productivity growth:

$\begin{array}{c}\text{Labor}\text{Productivity}\text{growth}=\frac{\text{21}-\text{16}}{\text{16}}\times 100\\ =31.25\%\end{array}$

The labor productivity growth is calculated by dividing the difference of 21 and 16 with 16 which gives 31.25%

Multifactor productivity growth:

$\begin{array}{c}\text{MFP}\text{growth}=\frac{0.93-0.89}{0.89}\times 100\\ =4.49\%\end{array}$

Multifactor productivity growth is calculated by dividing the difference of 0.93 and 0.89 with 0.89 which gives 4.49%.

Hence, labor productivity growth is 31.25% and multifactor productivity growth is 4.49%.