Composite Price Index Formula

Laspeyres Composite Price Index:

\[ CPI = \frac{\sum (p_t \times q_b)}{\sum (p_b \times q_b)} \times 100 \]

Composite Price Index (CPI):

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1. What is the Composite Price Index?

The Composite Price Index (CPI), specifically the Laspeyres index, measures the average change in prices over time for a fixed basket of goods and services using base period quantities as weights.

2. How Does the Calculator Work?

The calculator uses the Laspeyres Composite Price Index formula:

\[ CPI = \frac{\sum (p_t \times q_b)}{\sum (p_b \times q_b)} \times 100 \]

Where:

\( p_t \) — Current period prices
\( q_b \) — Base period quantities
\( p_b \) — Base period prices
\( \sum \) — Summation across all items in the basket

Explanation: The formula compares the cost of purchasing the base period basket of goods at current prices versus base period prices, providing a measure of price inflation.

3. Importance of CPI Calculation

Details: The Composite Price Index is crucial for measuring inflation, adjusting wages and pensions, formulating economic policy, and making international price comparisons.

4. Using the Calculator

Tips: Enter comma-separated values for current prices, base quantities, and base prices. Ensure all three arrays have the same number of elements representing the same items in the same order.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between Laspeyres and Paasche index?
A: Laspeyres uses base period quantities as weights, while Paasche uses current period quantities. Laspeyres tends to overstate inflation while Paasche understates it.

Q2: What does a CPI value of 120 mean?
A: A CPI of 120 indicates that prices have increased by 20% compared to the base period (when CPI was 100).

Q3: Why use base period quantities as weights?
A: Base period quantities reflect consumption patterns at the time of comparison and provide a consistent framework for measuring pure price changes.

Q4: What are common applications of CPI?
A: Inflation measurement, cost-of-living adjustments, economic policy formulation, and real value calculations in financial analysis.

Q5: What are limitations of the Laspeyres index?
A: It doesn't account for substitution effects, quality changes, or new products, which can lead to upward bias in inflation measurement.