Problems and Applications Q2 The residents of Vegopia spend all of their income on cauliflower, broccoli, and carrots. In 2020, they spend a total of $250 for 100 heads of cauliflower, $100 for 50 bunches of broccoli, and $250 for 500 carrots. In 2021, they spend a total of $210 for 60 heads of cauliflower, $180 for 90 bunches of broccoli, and $270 for 450 carrots.
Complete the following table by calculating the price of one unit of each vegetable in each year.
Year Cauliflower Broccoli Carrots
2020
2021
Using 2020 as the base year, the CPI for 2020 is , and the CPI for 2021 is .
The inflation rate in 2021 is
using the CPI.

Vegopia

Consumer Price Index

1. Using 2020 as the base year, the CPI for 2020 is 100, and the CPI for 2021 is 122.

2. The inflation rate in 2021 is 22%  using the CPI.

Explanation:

a) Data and Calculations:

In 2020:

Amount spent for 100 heads of cauliflower = $250, each $2.50

Amount spent for 50 bunches of broccoli = $100, each  $2.00

Amount spent for 500 carrots = $250, each $0.50

In 2021:

Amount spent for 60 heads of cauliflower = $210, each $3.50

Amount spent for 90 bunches of broccoli = $180, each $2.00

Amount spent for 450 carrots = $270, each $0.60

Year     Cauliflower  Broccoli  Carrots  Basket

2020         $2.50      $2.00    $0.50     $5.00

2021          $3.50      $2.00    $0.60     $6.10

Change     $1.00       $0.00    $0.10      $1.10

CPI index = $1.10/$5.00 + 1  * 100 = 122

Inflation rate = 122 - 100 = 22%

b) The Consumer Price Index (CPI) of Vegopia measures the weighted average of prices of a basket of consumer goods and services in Vegopia, such as transportation, food, and medical care.  It averages the price changes for each item in the predetermined basket of goods.  The changes in the CPI assess the price changes associated with the cost of living.  As one of the most frequently used statistics, the CPI is used to identify periods of inflation or deflation in Vegopia.