Chapter 15, Problem 1CYU

To determine

The question requires us to determine the consumer price indexes in the pre-frost and post-frost periods when the composition of the market basket changes.

Explanation of Solution

Given,

New basket consists of 100 oranges, 50 grapefruit, and 200 lemons.

Cost of the basket in the pre-frost period

  $\begin{array}{l}=\left(100\times \$0.20\right)+\left(50\times \$0.60\right)+\left(200\times \$0.25\right)\\ =\$20+\$30+\$50\\ =\$100\end{array}$

Cost of the basket in the post-frost period

  $\begin{array}{l}=\left(100\times \$0.40\right)+\left(50\times \$1\right)+\left(200\times \$0.45\right)\\ =\$40+\$50+\$90\\ =\$180\end{array}$

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,

Cost or price of the basket in the pre-frost period = $100

Cost of the basket in the post-frost period (year 2 is the base year) = $180

  $\begin{array}{c}\text{Price}\text{index in pre-frost=}\frac{\text{Price}\text{of}\text{good}\text{in}\text{current}\text{year}}{\text{Price}\text{of}\text{good}\text{in}\text{base}\text{year}}\text{×100}\\ =\frac{\$100}{\$180}\times 100\\ =55.55\end{array}$

  $\begin{array}{c}\text{Price}\text{index in post-frost=}\frac{\text{Price}\text{of}\text{good}\text{in}\text{current}\text{year}}{\text{Price}\text{of}\text{good}\text{in}\text{base}\text{year}}\text{×100}\\ =\frac{\$180}{\$180}\times 100\\ =100\end{array}$

The price index in the pre-frost period is 55.55, and in the post-frost period is 100.

A change in the composition of the market basket will change the value of CPI because in the market basket price of different goods are different. So, a change in the composition of quantities will change the price of the basket.

In the given example, when the composition of the market basket changes, the price index of the basket rises from 54 to 55.55.