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QUESTION:

Use the following table to answer the question. The table shows the prices and the quantities consumed in Vegetarian Country. Suppose the base year is 2020. Also, suppose that 2020 is the year the typical consumption basket was determined, so the quantities consumed in 2020 are the only quantities needed to calculate the CPI in each year.

YearPrice of CarrotsQuantity of CarrotsPrice of CeleryQuantity of Celery
2020$2.00100$1.00100
2021  2.50  90  0.90120
2022  2.75105  1.00130

Suppose the base year is changed in the table from 2020 to 2022. Also, suppose that the typical consumption basket was now determined in 2022 (now use the 2022 consumption basket). What is the new value of the CPI in 2021?


ANSWER:

Step 1: Calculate the cost of the basket in the base year (2022)

  • Price of Carrots in 2022 = $2.75
  • Price of Celery in 2022 = $1.00
  • Quantity of Carrots in 2022 = 105
  • Quantity of Celery in 2022 = 130

Cost of Basket in 2022=(2.75×105)+(1.00×130)=288.75+130=418.75\text{Cost of Basket in 2022} = (2.75 \times 105) + (1.00 \times 130) = 288.75 + 130 = 418.75

Step 2: Calculate the cost of the basket in 2021 using 2022 quantities

  • Price of Carrots in 2021 = $2.50
  • Price of Celery in 2021 = $0.90
  • Quantity of Carrots in 2022 = 105
  • Quantity of Celery in 2022 = 130

Cost of Basket in 2021=(2.50×105)+(0.90×130)=262.50+117=379.50\text{Cost of Basket in 2021} = (2.50 \times 105) + (0.90 \times 130) = 262.50 + 117 = 379.50

Step 3: Calculate the CPI for 2021

CPI in 2021=(379.50418.75)×100≈90.6\text{CPI in 2021} = \left( \frac{379.50}{418.75} \right) \times 100 \approx 90.6

Final Answer:

The new value of the CPI in 2021 is a. 90.6.


Posted by Cleveland on September 9, 2024
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