Chapter 16, Problem 3PA

Subpart (a):

To determine

Measuring percentage change in price, CPI and Inflation rate.

Explanation of Solution

The percentage change in price of the good is calculated by using the following formula:

$\text{Percentage change in price =}\frac{{\text{Price}}_{\text{Present year}}-{\text{Price}}_{\text{Previous year}}}{{\text{Price}}_{\text{Previous year}}}\times 100$ (1)

Substitute respective values in equation (1) to calculate the percentage price change for the tennis ball.

$\begin{array}{c}{\text{Percentage change in price}}_{\text{Tennis ball}}=\frac{2-2}{2}\times 100\\ =0\%\end{array}$

The percentage change in price for Tennis ball is 0.

Substitute respective values in equation (1) to calculate the percentage price change for the golf ball.

$\begin{array}{c}{\text{Percentage change in price}}_{\text{Golf ball}}=\frac{6-4}{4}\times 100\\ =50\%\end{array}$

The percentage change in price for golf ball is 0.

Substitute respective values in equation (1) to calculate the percentage price change for the galorade.

The percentage change in price of golf balls is 50%.

$\begin{array}{c}{\text{Percentage change in price}}_{\text{Gatorade}}=\frac{2-1}{1}\times 100\\ =100\%\end{array}$

The percentage change in price of bottle of gatorade is 100%.

Economics Concept Introduction

Concept Introduction:

Consumer Price index (CPI): It is a measure that examines the changes in price levels of a basket of consumer goods and services which includes food and energy prices.

Inflation rate: It is a measure of the percentage change in the price index from the preceding period.

Subpart (b):

To determine

Measuring percentage change in price, CPI and Inflation rate.

Explanation of Solution

The base year is 2017. The consumer price index (CPI) can be calculated by using the following formula.

$\text{CPI =}\frac{\left(\begin{array}{l}\left(\begin{array}{l}{\text{Present price}}_{\text{1}}\\ \times {\text{Quantity}}_1\end{array}\right)+\left(\begin{array}{l}{\text{Present price}}_{\text{2}}\\ \times {\text{Quantity}}_{\text{2}}\end{array}\right)\\ +\mathrm{...}+\left(\begin{array}{l}{\text{Present price}}_{\text{n}}\\ \times {\text{Quantity}}_{\text{n}}\end{array}\right)\end{array}\right)}{\left(\begin{array}{l}\left(\begin{array}{l}{\text{Base year price}}_{\text{1}}\\ \times {\text{Quantity}}_{\text{1}}\end{array}\right)+\left(\begin{array}{l}{\text{Base year price}}_{\text{2}}\\ \times {\text{Quantity}}_{\text{2}}\end{array}\right)\\ +\mathrm{...}+\left(\begin{array}{l}{\text{Base year price}}_{\text{n}}\\ \times {\text{Quantity}}_{\text{n}}\end{array}\right)\end{array}\right)}\times 100$ (1)

Substitute the respective values in equation (1) to calculate the CPI for the year 2017.

$\begin{array}{c}{\text{CPI}}_{\text{2017}}=\frac{\left(2\times 100\right)+\left(4\times 100\right)+\left(1\times 200\right)}{\left(2\times 100\right)+\left(4\times 100\right)+\left(1\times 200\right)}\times 100\\ =\frac{200+400+200}{200+400+200}\times 100\\ =\frac{800}{800}\times 100\\ =100\end{array}$

CPI in the year 2017 is 100.

Substitute the respective values in equation (1) to calculate the CPI for the year 2018.

$\begin{array}{c}{\text{CPI}}_{\text{2018}}=\frac{\left(2\times 100\right)+\left(6\times 100\right)+\left(2\times 200\right)}{\left(2\times 100\right)+\left(4\times 100\right)+\left(1\times 200\right)}\times 100\\ =\frac{200+600+400}{200+400+200}\times 100\\ =\frac{1,200}{800}\times 100\\ =150\end{array}$

CPI in the year 2018 is 150.

The overall change in price using CPI is calculated as follows:

$\begin{array}{c}\text{Overall percentage change in price =}\frac{{\text{CPI}}_{\text{Present}}-{\text{CPI}}_{\text{Previous}}}{{\text{CPI}}_{\text{Previous}}}\times 100\\ =\frac{150-100}{100}\times 100\\ =50\%\end{array}$

Thus, the overall change in price is 50%.

Economics Concept Introduction

Concept Introduction:

Consumer Price index (CPI): It is a measure that examines the changes in price levels of a basket of consumer goods and services which includes food and energy prices.

Inflation rate: It is a measure of the percentage change in the price index from the preceding period.

Subpart (c):

To determine

Measuring percentage change in price, CPI and Inflation rate.

Explanation of Solution

When the bottle of Gatorade increased in size from 2017 to2018, its value would be greater than before. As a result, this would lower the estimation of inflation rate.

Economics Concept Introduction

Concept Introduction:

Consumer Price index (CPI): It is a measure that examines the changes in price levels of a basket of consumer goods and services which includes food and energy prices.

Inflation rate: It is a measure of the percentage change in the price index from the preceding period.

Subpart (d):

To determine

Measuring percentage change in price, CPI and Inflation rate.

Explanation of Solution

More flavors enhance consumers’ well-being which would result in change in quality and thus would lower the estimate of the inflation rate.

Economics Concept Introduction

Concept Introduction:

Consumer Price index (CPI): It is a measure that examines the changes in price levels of a basket of consumer goods and services which includes food and energy prices.

Inflation rate: It is a measure of the percentage change in the price index from the preceding period.