Chapter 3R, Problem 3FRQ

a)

To determine

The question requires us to calculate the price index.

Answer to Problem 3FRQ

The price index for year 1 is 50, and for year 2 is 100.

Explanation of Solution

The formula for the price index is:

  $\text{Price}\text{index=}\frac{\text{Price}\text{of}\text{good}\text{in}\text{current}\text{year}}{\text{Price}\text{of}\text{good}\text{in}\text{base}\text{year}}\text{×100}$

Given,

Price of goods in year 1 = $400

Price of goods in the base year (year 2 is the base year) = $800

  $\begin{array}{c}\text{Price}\text{index}\text{for}\text{year}\text{1=}\frac{\text{Price}\text{of}\text{good}\text{in}\text{current}\text{year}}{\text{Price}\text{of}\text{good}\text{in}\text{base}\text{year}}\text{×100}\\ =\frac{\$400}{\$800}\times 100\\ =50\end{array}$

  $\begin{array}{c}\text{Price}\text{index}\text{for}\text{year}\text{2=}\frac{\text{Price}\text{of}\text{good}\text{in}\text{year}\text{1}}{\text{Price}\text{of}\text{good}\text{in}\text{base}\text{year}}\text{×100}\\ =\frac{\$800}{\$800}\times 100\\ =100\end{array}$

The price index for year 1 is 50, and for year 2 is 100.

b)

To determine

The question requires us to calculate the inflation rate.

Answer to Problem 3FRQ

Inflation rate between year 1 and year 2 is 100 percent.

Explanation of Solution

The inflation rate formula in terms of price index is:

  $\text{Inflation}\text{}\text{rate=}\frac{\text{Price}\text{index}\text{in}\text{year}\text{2-Price}\text{index}\text{in}\text{year}\text{1}}{\text{Price}\text{index}\text{in}\text{year}\text{1}}\text{×100}$

From part 1,

Price index in year 1 = 50

Price index in year 2 = 100

Insert these values in the inflation formula:

  $\begin{array}{c}\text{Inflation}\text{}\text{rate=}\frac{\text{Price}\text{index}\text{in}\text{year}\text{2-Price}\text{index}\text{in}\text{year}\text{1}}{\text{Price}\text{index}\text{in}\text{year}\text{1}}\text{×100}\\ =\frac{100-50}{50}\times 100\\ =100\end{array}$

The inflation rate between year 1 and year 2 is 100 percent.

c)

To determine

The question requires us to determine the years in which the economy experienced deflation.

Answer to Problem 3FRQ

Between years 3 and 4, the economy is experiencing deflation in the market.

Explanation of Solution

Given,

Price in year 3 = $1000

Price in year 4 = $800

Rate of inflation between year 3 and year 4 is:

  $\begin{array}{c}\text{Inflation}\text{}\text{rate=}\frac{\text{Price}\text{in}\text{year}\text{4-Price}\text{in}\text{year}\text{3}}{\text{Price}\text{in}\text{year}\text{3}}\text{×100}\\ =\frac{800-1000}{1000}\times 100\\ =-20\end{array}$

Between years 3 and 4, the economy is experiencing a negative inflation rate which represents deflation in the market.

d)

To determine

The question requires us to determine the years in which the economy experienced disinflation.

Answer to Problem 3FRQ

Between years 2 and 3, the economy is experiencing disinflation.

Explanation of Solution

Given,

Price in year 2 = $800

Price in year 3 = $1000

Rate of inflation between year 2 and year 3 is:

  $\begin{array}{c}\text{Inflation}\text{}\text{rate=}\frac{\text{Price}\text{in}\text{year}\text{3-Price}\text{in}\text{year}\text{2}}{\text{Price}\text{in}\text{year}\text{2}}\text{×100}\\ =\frac{1000-800}{800}\times 100\\ =25\end{array}$

Between years 2 and 3, the economy is experiencing a falling inflation rate which represents disinflation in the market.