Question

i. QUESTION THRee Consider the below information which reflects the changes in prices and quantities of each individual good in hypothetical economy. PRICES ii. ITEM Cotton Clothes Soft drinks QUANTITIES ITEM Cotton Clothes Required Soft drinks 2021 Tsh. 10 Tsh. 20 Tsh. 30 2021 200 400 600 2022 Tsh. 20 Tsh. 24 Tsh. 50 2022 250 450 650 2023 Tsh.14 Tsh.26 Tsh.48 2023 300 500 700 Compute the Consumer Price INDEX for year 2021, 2022 and 2023 using a base year. Determine the percentage increase of inflation from 2022 to 2023. ​

Answer 1

To compute the Consumer Price Index (CPI) for the given years, we will use 2021 as the base year. The CPI measures the average price changes of a basket of goods and services over time.

Step 1: Calculate the total expenditure for each year using the base year prices:

2021: (Tsh.10 * 200) + (Tsh.20 * 400) + (Tsh.30 * 600) = Tsh.20,000 + Tsh.80,000 + Tsh.180,000 = Tsh.280,000

2022: (Tsh.10 * 250) + (Tsh.20 * 450) + (Tsh.30 * 650) = Tsh.25,000 + Tsh.90,000 + Tsh.195,000 = Tsh.310,000

2023: (Tsh.10 * 300) + (Tsh.20 * 500) + (Tsh.30 * 700) = Tsh.30,000 + Tsh.100,000 + Tsh.210,000 = Tsh.340,000

Step 2: Calculate the CPI for each year using the formula:

CPI = (Total expenditure in the given year / Total expenditure in the base year) * 100

CPI for 2021 = (Tsh.280,000 / Tsh.280,000) * 100 = 100

CPI for 2022 = (Tsh.310,000 / Tsh.280,000) * 100 = 110.71

CPI for 2023 = (Tsh.340,000 / Tsh.280,000) * 100 = 121.43

Step 3: Calculate the percentage increase of inflation from 2022 to 2023:

Percentage increase = ((CPI in 2023 - CPI in 2022) / CPI in 2022) * 100

Percentage increase = ((121.43 - 110.71) / 110.71) * 100 ≈ 9.68%

Therefore, the Consumer Price Index for 2021, 2022, and 2023 using 2021 as the base year is 100, 110.71, and 121.43, respectively. The percentage increase of inflation from 2022 to 2023 is approximately 9.68%.