Chapter 22, Problem 9P

To determine

a.

Percentage change in the price of an English textbook from year 2014 to 2016.

Introduction: Gross domestic product (GDP) refers to the gross money value or gross market value of all the finished goods and the services produced by the normal resident and non resident people of the country that is within that particular within the borders of the country in an accounting year.

Explanation of Solution

Formula to calculate percentage change in price,

    $\text{Percentage Change in Price}=\frac{\left(\begin{array}{l}\text{Price of English Textbook in 2016}\\ -\text{Price of English Textbook in 2014}\end{array}\right)}{\text{Price of English Textbook in 2014}}\times 100\%$

Substitute, $114 for price of English textbook in 2016 and $100 for price of English textbook in 2014:

$\begin{array}{l}\text{Percentage Change in Price}=\frac{\left(\$114-\$100\right)}{\$100}\times 100\%\\ =14\%\end{array}$

Thus, percentage change in the price of an English textbook from year 2014 to 2016 is 14%.

To determine

b.

Percentage change in the price of a Math textbook from year 2014 to 2016.

Explanation of Solution

Formula to calculate percentage change in price,

    $\text{Percentage Change in Price}=\frac{\left(\begin{array}{l}\text{Price of English Textbook in 2016}\\ -\text{Price of English Textbook in 2014}\end{array}\right)}{\text{Price of English Textbook in 2014}}\times 100\%$

Substitute, $148 for price of Math textbook in 2016 and $140 for price of Math textbook in 2014:

$\begin{array}{l}\text{Percentage Change in Price}=\frac{\left(\$148-\$140\right)}{\$140}\times 100\%\\ =5.7\%\end{array}$

Thus, percentage change in the price of an Math textbook from year 2014 to 2016 is 5.7%.

To determine

c.

Percentage change in the price of Economics textbook from year 2014 to 2016.

Explanation of Solution

Formula to calculate percentage change in price,

    $\text{Percentage Change in Price}=\frac{\left(\begin{array}{l}\text{Price of English Textbook in 2016}\\ -\text{Price of English Textbook in 2014}\end{array}\right)}{\text{Price of English Textbook in 2014}}\times 100\%$

Substitute, $200 for price of Economics textbook in 2016 and $160 for price of English textbook in 2014:

$\begin{array}{l}\text{Percentage Change in Price}=\frac{\left(\$200-\$160\right)}{\$160}\times 100\%\\ =25\%\end{array}$

Thus, percentage change in the price of Economics textbook from year 2014 to 2016 is 25%.

To determine

d.

Price index.

Explanation of Solution

Given,

In the given case the average student purchases three English, two Math and four Economics textbooks.

Formula to calculate price index:

$\text{Price Index}=\frac{\text{Total Cost of Book for Current Year}}{\text{Total Cost of Book for Base Year}}\times 100$          (I)

2014:

Given:

2014:

Price of English textbook is $100.

Price of Math textbook is $140.

Price of Economics textbook is $160.

2015:

Price of English textbook is $110.

Price of Math textbook is $144.

Price of Economics textbook is $180.

Calculation of total cost for 2014:

$\begin{array}{l}\text{Total Cost of Book for 2014}=\left(3\times \$100\right)+\left(2\times \$140\right)+\left(4\times \$160\right)\\ =\$300+\$280+\$640\\ =\$1220\end{array}$

Calculation of total cost for 2015:

$\begin{array}{l}\text{Total Cost of Book for 2014}=\left(3\times \$110\right)+\left(2\times \$144\right)+\left(4\times \$180\right)\\ =\$330+\$288+\$720\\ =\$1338\end{array}$

Substitute $1220 for total cost of book for current year and $1338 for total cost of book for base year in formula (I):

$\begin{array}{l}\text{Price Index}=\frac{\$1220}{\$1338}\times 100\\ \text{ =91}\text{.18}\end{array}$

2015:

Given:

2015:

Price of English textbook is $110.

Price of Math textbook is $144.

Price of Economics textbook is $180.

Calculation of total cost for 2015:

$\begin{array}{l}\text{Total Cost of Book for 2013}=\left(3\times \$110\right)+\left(2\times \$144\right)+\left(4\times \$180\right)\\ =\$330+\$288+\$720\\ =\$1338\end{array}$

Substitute $1338 for total cost of book for current year and $1338 for total cost of book for base year in formula (I):

$\begin{array}{l}\text{Price Index}=\frac{\$1338}{\$1338}\times 100\\ \text{ =100}\end{array}$

2016:

Given:

2015:

Price of English textbook is $110.

Price of Math textbook is $144.

Price of Economics textbook is $180.

2016:

Price of English textbook is $114.

Price of Math textbook is $148.

Price of Economics textbook is $200.

Calculation of total cost for 2014:

$\begin{array}{l}\text{Total Cost of Book for 2016}=\left(3\times \$114\right)+\left(2\times \$148\right)+\left(4\times \$200\right)\\ =\$342+\$296+\$800\\ =\$1438\end{array}$

Calculation of total cost for 2015:

$\begin{array}{l}\text{Total Cost of Book for 2013}=\left(3\times \$110\right)+\left(2\times \$144\right)+\left(4\times \$180\right)\\ =\$330+\$288+\$720\\ =\$1338\end{array}$

Substitute $1438 for total cost of book for current year and $1338 for total cost of book for base year in formula (I):

$\begin{array}{l}\text{Price Index}=\frac{\$1438}{\$1338}\times 100\\ \text{ =107}\text{.47}\end{array}$

Thus, price index for 2014 is 91.18, for 2015 is 100 and for 2016 is 107.47.

To determine

e.

Percentage change in price index from 2014 to 2016.

Explanation of Solution

Formula to calculate percentage change in price index:

    $\text{Percentage Change in Price}=\frac{\left(\begin{array}{l}\text{Price of English Textbook in 2016}\\ -\text{Price of English Textbook in 2014}\end{array}\right)}{\text{Price of English Textbook in 2014}}\times 100\%$

Substitute 107.47 for price index in year 2016 and 91.18 for price index in year 2014:

$\begin{array}{l}\text{Percentage change in price index}=\frac{107.47-91.18}{91.18}\times 100\%\\ =17.86\%\end{array}$

Thus, percentage change in price index from 2014 to 2016 is 17.86%.