Chapter 7, Problem 2.3P

To determine

Bundle price indexation and inflation.

Explanation of Solution

The bundle price in 2016 can be calculated as follows:

$\begin{array}{c}{\text{Bundle price}}_{\text{2016}}=\left[\begin{array}{l}\left({\text{Price}}_{\text{X}}\times {\text{Quantity}}_{\text{X}}\right)\\ +\left({\text{Price}}_{\text{Y}}\times {\text{Quantity}}_{\text{Y}}\right)\\ +\left({\text{Price}}_{\text{Z}}\times {\text{Quantity}}_{\text{Z}}\right)\end{array}\right]\\ =\left[\begin{array}{l}\left(\text{2}\times \text{50}\right)+\left(\text{3}\times \text{125}\right)\\ +\left(0.75\times \text{100}\right)\end{array}\right]\\ =100+375+75\\ =550\end{array}$

The bundle price in 2016 is $550.

Index in 2016 is calculated as follows:

$\begin{array}{c}\text{Index in 2016 = }\frac{{\text{Bundle price}}_{\text{2016}}}{{\text{Bundle price}}_{\text{2016}}}\times 100\\ =\frac{550}{550}\times 100\\ =100\end{array}$

The index in 2016 is 100.

The bundle price in 2017 can be calculated as follows:

$\begin{array}{c}{\text{Bundle price}}_{\text{2017}}=\left[\begin{array}{l}\left({\text{Price}}_{\text{X}}\times {\text{Quantity}}_{\text{X}}\right)\\ +\left({\text{Price}}_{\text{Y}}\times {\text{Quantity}}_{\text{Y}}\right)\\ +\left({\text{Price}}_{\text{Z}}\times {\text{Quantity}}_{\text{Z}}\right)\end{array}\right]\\ =\left[\begin{array}{l}\left(\text{1}\text{.5}\times \text{50}\right)+\left(\text{3}\times \text{125}\right)\\ +\left(1.25\times \text{100}\right)\end{array}\right]\\ =75+375+125\\ =575\end{array}$

The bundle price in 2017 is $575.

Index in 2017 is calculated as follows:

$\begin{array}{c}\text{Index in 2017 = }\frac{{\text{Bundle price}}_{\text{2017}}}{{\text{Bundle price}}_{\text{2016}}}\times 100\\ =\frac{575}{550}\times 100\\ =104.5\end{array}$

The index in 2017 is 104.5.

The bundle price in 2018 can be calculated as follows:

$\begin{array}{c}{\text{Bundle price}}_{\text{2018}}=\left[\begin{array}{l}\left({\text{Price}}_{\text{X}}\times {\text{Quantity}}_{\text{X}}\right)\\ +\left({\text{Price}}_{\text{Y}}\times {\text{Quantity}}_{\text{Y}}\right)\\ +\left({\text{Price}}_{\text{Z}}\times {\text{Quantity}}_{\text{Z}}\right)\end{array}\right]\\ =\left[\begin{array}{l}\left(\text{2}\times \text{50}\right)+\left(\text{2}\text{.5}\times \text{125}\right)\\ +\left(1.5\times \text{100}\right)\end{array}\right]\\ =100+312.50+150\\ =562.50\end{array}$

The bundle price in 2018 is $562.50.

Index in 2018 is calculated as follows:

$\begin{array}{c}\text{Index in 2018 = }\frac{{\text{Bundle price}}_{\text{2018}}}{{\text{Bundle price}}_{\text{2016}}}\times 100\\ =\frac{562.5}{550}\times 100\\ =102.3\end{array}$

The index in 2018 is 102.3.

The percentage change in index between 2016 and 2017 is calculated as follows:

$\begin{array}{c}\text{Percentage change= }\frac{{\text{Index}}_{\text{2017}}-{\text{Index}}_{\text{2016}}}{{\text{Index}}_{\text{2016}}}\times 100\\ =\frac{104.5-100}{100}\times 100\\ =4.5\%\end{array}$

The percentage change in index between 2016 and 2017 is 4.5%.

The percentage change in index between 2017 and 2018 is calculated as follows:

$\begin{array}{c}\text{Percentage change= }\frac{{\text{Index}}_{\text{2018}}-{\text{Index}}_{\text{2017}}}{{\text{Index}}_{\text{2017}}}\times 100\\ =\frac{102.3-104.5}{104.5}\times 100\\ =-\frac{220}{104.5}\\ =-2.1\%\end{array}$

The percentage change in index between 2017 and 2018 is -2.1%.

There was no inflation between 2017 and 2018 as there was a decrease in the price level between 2017 and 2018.

Economics Concept Introduction

Inflation: Inflation is the situation of abnormal price hike in the economy which leads to the situation of too much money chasing too few goods.