Chapter 2, Problem 7PA

(a)

To determine

Calculation of nominal GDP, real GDP, GDP deflator, and CPI.

Explanation of Solution

Given information:

Price of hot dog in 2010 is $2.

Quantity of hot dog in 2010 is 200 units.

Price of hamburgers in 2010 is $3.

Quantity of hamburgers in 2010 is 200 units.

Price of hot dog in 2018 is $4.

Quantity of hot dog in 2010 is 250 units.

Price of hamburgers in 2010 is $4.

Quantity of hamburgers in 2010 is 500 units.

Calculation:

The general formula for calculating nominal GDP is given as follows:

$\text{Nominal GDP}=\left(\begin{array}{l}\left({\text{Price}}_{\text{Good X}}\times {\text{Quantity}}_{\text{Good X}}\right)+\\ \left({\text{Price}}_{\text{Good Y}}\times {\text{Quantity}}_{\text{Good Y}}\right)\end{array}\right)$ (1)

Substitute the respective values in Equation (1) to calculate the nominal GDP in 2010.

$\begin{array}{c}{\text{Nominal GDP}}_{2010}=\left(2\times 200\right)+\left(3\times 200\right)\\ =400+600\\ =1,000\end{array}$

Nominal GDP in 2010 is $1,000.

Using the same Equation (1), the calculation of nominal GDP in 2018 is shown below:

$\begin{array}{c}{\text{Nominal GDP}}_{2018}=\left(4\times 250\right)+\left(4\times 500\right)\\ =1,000+2,000\\ =3,000\end{array}$

Nominal GDP in 2018 is $3,000.

The real GDP is calculated on the basis of base year price. Here, the base year is 2010. The formula for calculating real GDP is shown as follows:

$\text{Real GDP}=\left(\begin{array}{l}\left({\text{Base year price}}_{\text{Good X}}\times {\text{Quantity}}_{\text{Good X}}\right)+\\ \left({\text{Base year price}}_{\text{Good Y}}\times {\text{Quantity}}_{\text{Good Y}}\right)\end{array}\right)$ (2)

Substitute the respective values in Equation (2) to calculate the real GDP in 2010.

$\begin{array}{r}{\text{Real GDP}}_{2010}=\left(2\times 200\right)+\left(3\times 200\right)\\ =100+600\\ =1,000\end{array}$

Real GDP in 2010 is $1,000.

Using the same Equation (2), the calculation of real GDP in 2018 is shown below:

$\begin{array}{r}{\text{Real GDP}}_{2018}=\left(2\times 250\right)+\left(3\times 500\right)\\ =500+1,500\\ =2,000\end{array}$

Real GDP in 2018 is $2000.

The general formula for calculating GDP deflator is given below:

$\text{GDP deflator}=\left(\frac{\text{Nominal GDP}}{\text{Real GDP}}\right)$ (3)

Substitute the respective values in Equation (3) to calculate the GDP deflator in 2010.

$\begin{array}{c}{\text{GDP deflator}}_{2010}=\left(\frac{1,000}{1,000}\right)\\ =1\end{array}$

GDP deflator in 2010 is 1.

Using the same Equation (3), the calculation of GDP deflator in 2018 is shown below:

$\begin{array}{c}{\text{GDP deflator}}_{2018}=\left(\frac{3,000}{2,000}\right)\\ =1.5\end{array}$

GDP deflator in 2018 is 1.5.

The CPI in 2010 is equal to 1, thus, the calculation of CPI (Consumer Price Index) in 2018 is shown below:

$\begin{array}{c}{\text{CPI}}_{2018}=\left(\frac{\left({\text{Price}}_{\text{Hot dogs}}^{2018}\times {\text{Quantity}}_{\text{Hot dogs}}^{2010}\right)+\left({\text{Price}}_{\text{Burgers}}^{2018}\times {\text{Quantity}}_{\text{Burgers}}^{2010}\right)}{\left({\text{Price}}_{\text{Hot dogs}}^{2010}\times {\text{Quantity}}_{\text{Hot dogs}}^{2010}\right)+\left(\left({\text{Price}}_{\text{Burgers}}^{2010}\times {\text{Quantity}}_{\text{Burgers}}^{2010}\right)\right)}\right)\\ =\left(\frac{\left(4\times 200\right)+\left(4\times 200\right)}{\left(2\times 200\right)+\left(3\times 200\right)}\right)\\ =\left(\frac{1,600}{1,000}\right)\\ =1.6\end{array}$

CPI (Consumer Price Index) in 2018 is 1.6.

Economics Concept Introduction

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

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

(b)

To determine

Compare the answers by the Laspeyres and Paasche price indexes.

Explanation of Solution

A GDP (gross domestic product) deflator is a Paasche index, the reason is, it has changing basket of goods. On the other hand, the consumer price index is a Laspeyres index, because, it has fixed basket of goods.