Chapter 16, Problem 5PA

Subpart (a):

To determine

Measuring percentage change in price using CPI and GDP deflator.

Explanation of Solution

Cost of market for the basket can be calculated by using the following formula.

$\text{Cost of Market basket}=\left(\begin{array}{l}\left({\text{Price}}_1\times {\text{Quantity}}_1\right)+\left({\text{Price}}_2\times {\text{Quantity}}_2\right)\\ +\mathrm{...}+\left({\text{Price}}_{\text{n}}\times {\text{Quantity}}_{\text{n}}\right)\end{array}\right)$ (1)

Substitute the respective values in Equation (2) to calculate the cost of market basket in the year 2014:

$\begin{array}{c}{\text{Cost of the market basket}}_{2014}=1\times 40+3\times 10\\ =70\end{array}$

Cost of market basket for the year 2014 is $70.

Substitute the respective values in Equation (2) to calculate the cost of market basket in the year 2015:

$\begin{array}{c}{\text{Cost of the market basket}}_{2015}=1\times 60+3\times 12\\ =96\end{array}$

Cost of market basket for the year 2015 is $96.

CPI can be calculated by using the following formula:

$\text{CPI =}\frac{\text{Cost of Market basket in current year}}{\text{Price of basket in the base year}}\times 100$ (2)

Substitute the respective values in Equation (2) to calculate the CPI in the year 2014:

$\begin{array}{c}{\text{CPI}}_{\text{2014}}=\frac{70}{70}\times 100\\ =100\end{array}$

CPI in the year 2014 is 100.

Substitute the respective values in Equation (2) to calculate the CPI in the year 2015:

$\begin{array}{c}{\text{CPI}}_{\text{2015}}=\frac{96}{70}\times 100\\ =137.14\end{array}$

CPI in the year 2015 is 137.14.

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

$\begin{array}{c}\text{Overall percentage change in price =}\frac{{\text{CPI}}_{\text{Present}}-{\text{CPI}}_{\text{Previous}}}{{\text{CPI}}_{\text{Previous}}}\times 100\\ =\frac{137.14-100}{100}\times 100\\ =37.14\%\end{array}$

Thus the overall change in price is 37.14% which is the inflation rate for 2015 computed using CPI. Thus the inflation rate for 2015 is 37.14%.

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 for the present time from the base year.

Inflation rate: Inflation rate refers to the rate of change in the price level.

GDP deflator: Gross Domestic Product (GDP) deflator is the measure of inflation.

Real GDP: Real GDP refers to the market value of all final goods and services produced in an economy during an accounting year, and measured in constant prices.

Nominal GDP: Nominal GDP refers to the market value of all final goods and services produced in an economy during an accounting year, measured in current prices.

Subpart (b):

To determine

Measuring percentage change in price using CPI and GDP deflator.

Explanation of Solution

The Nominal GDP can be calculated by using the following formula:

$\text{Nominal GDP}=\left(\begin{array}{l}{\text{Present price}}_{\text{1}}\\ \times {\text{Quantity}}_1\end{array}\right)+\left(\begin{array}{l}{\text{Present price}}_{\text{1}}\\ \times {\text{Quantity}}_{\text{2}}\end{array}\right)+\mathrm{...}+\left(\begin{array}{l}{\text{Present price}}_{\text{n}}\\ \times {\text{Quantity}}_{\text{n}}\end{array}\right)$ (3)

Substitute the respective values in Equation (3) to calculate the nominal GDP in the year 2014:

$\begin{array}{c}{\text{Nominal GDP}}_{2014}=\left(10\times 40\right)+\left(30\times 10\right)\\ =700\end{array}$

Nominal GDP in the year 2014 is $700.

Substitute the respective values in Equation (3) to calculate the nominal GDP in the year 2015:

$\begin{array}{c}{\text{Nominal GDP}}_{2015}=\left(12\times 60\right)+\left(50\times 12\right)\\ =1,320\end{array}$

Nominal GDP in the year 2015 is $1,320.

The real GDP can be calculated by using the following formula:

$\text{Real GDP}=\left(\begin{array}{l}{\text{Base year price}}_{\text{1}}\\ \times {\text{Quantity}}_1\end{array}\right)+\left(\begin{array}{l}{\text{Base year price}}_{\text{1}}\\ \times {\text{Quantity}}_{\text{2}}\end{array}\right)+\mathrm{...}+\left(\begin{array}{l}{\text{Base year price}}_{\text{n}}\\ \times {\text{Quantity}}_{\text{n}}\end{array}\right)$ (4)

Substitute the respective values in Equation (4) to calculate the real GDP in the year 2014:

$\begin{array}{c}{\text{Real GDP}}_{2014}=10\times 40+30\times 10\\ =700\end{array}$

Real GDP in the year 2014 is $700.

Substitute the respective values in Equation (4) to calculate the real GDP in the year 2015:

$\begin{array}{c}{\text{Real GDP}}_{2015}=12\times 40+50\times 10\\ =980\end{array}$

Real GDP in the year 2015 is $980.

GDP deflator can be calculated by using the following formula:

$\text{GDP deflator =}\frac{\text{Nominal GDP}}{\text{Real GDP}}\times 100$ (5)

Substitute the respective values in equation (5) to calculate the GDP deflator in year 2014:

$\begin{array}{c}{\text{GDP deflator}}_{\text{2014}}=\frac{700}{700}\times 100\\ =100\end{array}$

GDP deflator in the year 2014 is 100.

Substitute the respective values in equation (5) to calculate the GDP deflator in year 2015:

$\begin{array}{c}{\text{GDP deflator}}_{\text{2015}}=\frac{1320}{980}\times 100\\ =134.69\end{array}$

GDP deflator in the year 2015 is 134.69.

Using 2014 as base year, the GDP deflator for 2014 is calculated as 100 and for 2015 is 134.69.

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

$\begin{array}{c}{\text{Inflation rate }}_{2015}\text{=}\frac{{\text{GDP deflator}}_{\text{Present}}-{\text{GDP deflator}}_{\text{Previous}}}{{\text{GDP deflator}}_{\text{Previous}}}\times 100\\ =\frac{134.69-100}{100}\times 100\\ =34.69\%\end{array}$

Thus the inflation rate for 2015 computed using GDP inflator is 34.69%.

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 for the present time from the base year.

Inflation rate: Inflation rate refers to the rate of change in the price level.

GDP deflator: Gross Domestic Product (GDP) deflator is the measure of inflation.

Real GDP: Real GDP refers to the market value of all final goods and services produced in an economy during an accounting year, and measured in constant prices.

Nominal GDP: Nominal GDP refers to the market value of all final goods and services produced in an economy during an accounting year, measured in current prices.

Subpart (c):

To determine

Measuring percentage change in price using CPI and GDP deflator.

Explanation of Solution

No, the inflation rate is not the same. It is calculated as 37.14% using CPI whereas it is found to be 34.69% when computed using GDP deflator. This is because, the rate of inflation computed by the CPI holds the basket of goods and services constant; and on the other hand, the GDP deflator allows it to change and holds the prices constant.

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 for the present time from the base year.

Inflation rate: Inflation rate refers to the rate of change in the price level.

GDP deflator: Gross Domestic Product (GDP) deflator is the measure of inflation.

Real GDP: Real GDP refers to the market value of all final goods and services produced in an economy during an accounting year, and measured in constant prices.

Nominal GDP: Nominal GDP refers to the market value of all final goods and services produced in an economy during an accounting year, measured in current prices.