Which of the following statements is/are correct? 1. A price index captures the change in the average price of a constant basket of commodities. 2. If the price index takes values 100, 110 and 121 in three consecutive years respectively, then the inflation rates in the 2nd and 3rd years are 10% and 21% respectively. Select the correct answer using the code given below.
1 only
Understanding Price Indices and Inflation Rates
This question asks us to evaluate two specific statements about price indices and calculate associated inflation rates. We need to determine which statement(s) accurately reflect economic principles and calculations.
Statement 1 Analysis: The Role of a Price Index
The first statement suggests that a price index measures changes in the average price of a constant basket of commodities. Let's break this down:
- Price Index: This is a statistical tool used to measure the average change in prices for a group of goods or services over time. Examples include the Consumer Price Index (CPI).
- Constant Basket of Commodities: To accurately track price changes, economists use a fixed list (basket) of goods and services whose quantities and types remain unchanged. This ensures that the measured price changes are due solely to price fluctuations, not alterations in what is being measured.
- Conclusion: Statement 1 correctly defines the fundamental purpose and methodology of a price index. Therefore, statement 1 is correct.
Statement 2 Analysis: Calculating Inflation Rates
The second statement presents a scenario with consecutive price index values and asserts specific inflation rates.
Given Price Index Values:
- Year 1: \(I_1 = 100\)
- Year 2: \(I_2 = 110\)
- Year 3: \(I_3 = 121\)
Inflation Rate Calculation (2nd Year)
The inflation rate between Year 1 and Year 2 is calculated as the percentage change in the price index:
Inflation Rate (Year 2) = \( \frac{I_2 - I_1}{I_1} \times 100\% \)
Substituting the values:
Inflation Rate (Year 2) = \( \frac{110 - 100}{100} \times 100\% = \frac{10}{100} \times 100\% = 10\% \)
The statement correctly identifies the inflation rate for the 2nd year as 10%.
Inflation Rate Calculation (3rd Year)
The inflation rate between Year 2 and Year 3 is calculated similarly:
Inflation Rate (Year 3) = \( \frac{I_3 - I_2}{I_2} \times 100\% \)
Substituting the values:
Inflation Rate (Year 3) = \( \frac{121 - 110}{110} \times 100\% = \frac{11}{110} \times 100\% = \frac{1}{10} \times 100\% = 10\% \)
The statement claims the inflation rate for the 3rd year is 21%. Our calculation shows it is 10%. Therefore, the second part of statement 2 is incorrect.
Conclusion: Since only the inflation rate for the 2nd year (10%) is correctly stated, and the rate for the 3rd year is incorrectly stated (as 21% instead of 10%), statement 2 as a whole is incorrect.
Final Summary
Reviewing both statements:
- Statement 1 is correct as it accurately defines a price index.
- Statement 2 is incorrect because the calculated inflation rate for the 3rd year (10%) does not match the rate claimed in the statement (21%).
Therefore, only statement 1 is correct.
Choosing the Correct Option
We need to select the option that reflects our findings. Since only statement 1 is correct, the correct choice is the one indicating "1 only".
The correct option is 1. 1 only.
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