Chapter 6, Problem 15QP

(a)

To determine

The consumer price index in Snowland for each year.

Explanation of Solution

The consumer price index is calculated by using the following formula:

$\text{CPI}\text{=}\frac{\text{Total cost in the Current year}}{\text{Total cost in the Base year}}\times 100$ (1)

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

Total cost in the year 1(base year) is $26,

              $\begin{array}{l}\text{CPI}\text{=}\frac{26}{26}\times 100\\ =100\end{array}$

Thus, CPI for year 1 is 100.

The cost increased to $29 in year 2. Then, substitute the respective values in Equation (1) to calculate the CPI for year 2.

$\begin{array}{l}\text{CPI}\text{=}\frac{29}{26}\times 100\\ =111.54\end{array}$

Thus, CPI for year 2 is 111.54.

The total cost in year 3 is $30.20. Then, substitute the respective values in Equation (1) to calculate the CPI for year 3.

               $\begin{array}{l}\text{CPI}\text{=}\frac{30.20}{26}\times 100\\ =116.15\end{array}$

Thus, CPI for year 3 is 116.15.

The total cost in year 4 is $30.5. Then, substitute the respective values in Equation (1) to calculate the CPI for year 4.

                 $\begin{array}{l}\text{CPI}\text{=}\frac{30.5}{26}\times 100\\ =117.30\end{array}$

Thus, CPI for year 4 is 117.30.

Economics Concept Introduction

Consumer Price index (CPI): Consumer price index is a measure that examines the changes in price levels of a basket of consumer goods and services for the present time from base year.

(b)

To determine

The rate of inflation in year 2, year 3, and year 4.

Explanation of Solution

The rate of inflation is calculated using Equation (2):

$\text{Rate of inflation}=\frac{{\text{CPI}}_{\text{Current year}}-{\text{CPI}}_{\text{Previous year}}}{{\text{CPI}}_{\text{Previous year}}}\times 100$ (2)

In case 1, the consumer price index for this year is 111.54 and the consumer price index for the previous year is . Thus, the rate of inflation in the economy can be calculated using these values and substituting them in Equation (2) is as follows:

$\begin{array}{c}\text{Rate of inflation}=\frac{\text{111}\text{.54}-\text{100}}{\text{100}}\times 100\\ =11.54\end{array}$

Thus, the rate of inflation in year 2 is 11.54 percent.

In case 2, the consumer price index for year 3 is 116.15, and the consumer price index for the previous year is 111.54. Thus, the rate of inflation in the economy can be calculated by using these values and substituting them in Equation (2) as follows:

$\begin{array}{c}\text{Rate of inflation}=\frac{\text{116}\text{.15}-\text{111}\text{.54}}{\text{111}\text{.54}}\times 100\\ =\frac{4.61}{111.54}\times 100\\ =4.1\end{array}$

Thus, the rate of inflation in year 3 is 4.1 percent.

In case 3, the consumer price index for year 4 is 117.30, and the consumer price index for the previous year is 116.54. Thus, the rate of inflation in the economy can be calculated using these values and substituting them in Equation (2) as follows:

$\begin{array}{c}\text{Rate of inflation}=\frac{\text{117}\text{.30}-\text{116}\text{.15}}{\text{116}\text{.15}}\times 100\\ =\frac{1.15}{116.15}\times 100\\ =1\end{array}$

Thus, the rate of inflation in year 4 is 1 percent.

Economics Concept Introduction

 Inflation rate: Inflation rate refers to the percentage change in the price level from the preceding period.

(c)

To determine

The real GDP in each of the four years.

Explanation of Solution

The consumer price index for year 1 is 100, and the corresponding nominal GDP is $5 billion. Thus, the real GDP can be calculated by using these values and substituting them in Equation (3) as follows:

$\begin{array}{c}\text{Real GDP}=\frac{\text{Nominal GDP}}{\text{CPI}}\times 100\mathrm{.......}(3)\\ =\frac{5}{100}\times 100\\ =5\end{array}$

Thus, the real GDP in year 1 is $5 billion.

The consumer price index for year 2 is 111.54, and the corresponding nominal GDP is $5.6 billion. Thus, the real GDP can be calculated by using these values and substituting them in Equation (3) as follows:

$\begin{array}{c}\\ \text{Real GDP}=\frac{5.6}{111.54}\times 100\\ =0.502\times 100\\ =5.02\end{array}$

Thus, the real GDP in year 2 is $5.02 billion.

The consumer price index for year 3 is 116.15, and the corresponding nominal GDP is $6.1 billion. Thus, the real GDP can be calculated by using these values and substituting them in Equation (3) as follows:

$\begin{array}{c}\\ \text{Real GDP}=\frac{6.1}{116.15}\times 100\\ =0.0525\times 100\\ =5.25\end{array}$

Thus, the real GDP in year 3 is $5.25 billion.

The consumer price index for year 4 is 117.30, and the corresponding nominal GDP is $6.5 billion. Thus, the real GDP can be calculated by using these values and substituting them in Equation (3) as follows:

$\begin{array}{c}\\ \text{Real GDP}=\frac{6.5}{117.30}\times 100\\ =0.0554\times 100\\ =5.54\end{array}$

Thus, the real GDP in year 4 is $5.54 billion.

Economics Concept Introduction

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

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.

(d)

To determine

The percentage increase in nominal GDP as a result of inflation from the year 1 to 4.

Explanation of Solution

There is a 30 percentage increase in the nominal GDP from the year 1 to 4.

$\begin{array}{c}\\ \text{Percentage change in Nominal GDP}=\frac{6.5-5}{5}\times 100\\ =30\end{array}$

For 17.3 percentage change in the price level:

$\begin{array}{c}\\ \text{Percentage change in Price}=\frac{117.30-100}{100}\times 100\\ =17.3\end{array}$

Therefore, the inflation represented as follows: $\frac{17.3}{30}\times 100=57.67$

Thus, the inflation represents a 57.67% of rise in nominal GDP.