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Index Numbers in Economics
1. Introduction
📌 Index numbers are statistical measures that track changes in variables over time.
- Used to measure inflation, cost of living, stock prices, and economic growth.
- Expresses relative changes as percentages, making comparisons easy.
✔ Example: The Consumer Price Index (CPI) measures inflation by tracking the price level of consumer goods over time.
2. Types of Index Numbers
🔹 (1) Price Index Numbers
✔ Measures changes in the price level of goods and services over time.
✔ Examples:
- Consumer Price Index (CPI) – Measures the cost of living.
- Wholesale Price Index (WPI) – Measures wholesale market price changes.
🔹 (2) Quantity Index Numbers
✔ Tracks changes in the physical quantity of goods produced or sold.
✔ Example: Industrial Production Index (IPI), which measures manufacturing output.
🔹 (3) Value Index Numbers
✔ Measures total value changes (Price × Quantity).
✔ Example: GDP Deflator, which adjusts nominal GDP for inflation.
📌 Formula: Value Index=∑P1Q1∑P0Q0×100\text{Value Index} = \frac{\sum P_1 Q_1}{\sum P_0 Q_0} \times 100
where:
- P1,Q1P_1, Q_1 = Price and quantity in the current year.
- P0,Q0P_0, Q_0 = Price and quantity in the base year.
3. Methods of Constructing Index Numbers
🔹 (1) Simple Aggregative Method
✔ Compares total prices of a group of items in different years.
📌 Formula: PI=∑P1∑P0×100P_I = \frac{\sum P_1}{\sum P_0} \times 100
✔ Example: If the total price of goods in 2025 is ₹1200 and in the base year (2020) was ₹1000, PI=12001000×100=120P_I = \frac{1200}{1000} \times 100 = 120
✔ Interpretation: Prices have increased by 20% since 2020.
🔹 (2) Simple Average of Price Relatives Method
✔ Calculates price changes of individual goods and takes their average.
📌 Formula: PI=∑P1P0×100NP_I = \frac{\sum \frac{P_1}{P_0} \times 100}{N}
✔ Example: If rice price rose from ₹20 to ₹25 and wheat from ₹30 to ₹33, Price=2520×100=125,Pwheat=3330×100=110P_{\text{rice}} = \frac{25}{20} \times 100 = 125, \quad P_{\text{wheat}} = \frac{33}{30} \times 100 = 110 PI=125+1102=117.5P_I = \frac{125 + 110}{2} = 117.5
✔ Interpretation: Average price increase of 17.5%.
🔹 (3) Weighted Index Numbers
✔ Gives importance to items based on their significance.
(i) Laspeyres’ Index (Base Year Weights)
📌 Formula: PL=∑P1Q0∑P0Q0×100P_L = \frac{\sum P_1 Q_0}{\sum P_0 Q_0} \times 100
✔ Uses base year quantities as weights.
✔ Pros: Simple to calculate.
✔ Cons: Overestimates price changes if consumption patterns change.
(ii) Paasche’s Index (Current Year Weights)
📌 Formula: PP=∑P1Q1∑P0Q1×100P_P = \frac{\sum P_1 Q_1}{\sum P_0 Q_1} \times 100
✔ Uses current year quantities as weights.
✔ Pros: Adjusts for changing consumption.
✔ Cons: Harder to compute due to varying weights.
(iii) Fisher’s Ideal Index
📌 Formula: PF=PL×PPP_F = \sqrt{P_L \times P_P}
✔ Geometric mean of Laspeyres and Paasche indices.
✔ Most accurate as it balances both weightings.
4. Special Types of Index Numbers
🔹 (1) Consumer Price Index (CPI)
✔ Measures changes in the cost of living for consumers.
✔ Used to calculate inflation and adjust salaries.
✔ Formula: CPI=∑P1Q0∑P0Q0×100CPI = \frac{\sum P_1 Q_0}{\sum P_0 Q_0} \times 100
✔ Example: If the CPI in 2020 was 100 and in 2025 it is 120, inflation is 20%.
🔹 (2) Wholesale Price Index (WPI)
✔ Measures price changes at the wholesale level before they reach consumers.
✔ Used by policymakers to track inflation trends.
🔹 (3) GDP Deflator
✔ Measures overall inflation in an economy.
✔ Formula: GDP Deflator=Nominal GDPReal GDP×100\text{GDP Deflator} = \frac{\text{Nominal GDP}}{\text{Real GDP}} \times 100
✔ Example: If nominal GDP = ₹200 trillion and real GDP = ₹180 trillion, GDP Deflator=200180×100=111.1\text{GDP Deflator} = \frac{200}{180} \times 100 = 111.1
✔ Interpretation: Prices have increased by 11.1% since the base year.
5. Uses and Importance of Index Numbers
✔ Inflation Measurement – Used in setting interest rates and wages.
✔ Cost of Living Adjustments – Helps adjust pensions and salaries.
✔ Stock Market Analysis – Stock indices like NIFTY, SENSEX, S&P 500 track stock performance.
✔ Economic Policy Making – Used by governments to decide monetary and fiscal policies.
6. Limitations of Index Numbers
❌ Choice of Base Year – A bad base year can give misleading results.
❌ Changes in Consumption Patterns – People’s spending habits change over time.
❌ Quality Changes Not Considered – A product may improve, but index numbers don’t always reflect quality changes.
❌ Substitution Bias – Consumers switch to cheaper alternatives when prices rise, which indices may not capture.
7. Conclusion
✔ Index numbers are essential in economics to measure price changes, inflation, and economic trends.
✔ CPI, WPI, and GDP Deflator are widely used indicators.
✔ Weighted index numbers like Laspeyres, Paasche, and Fisher’s provide better accuracy.
✔ Despite limitations, index numbers remain a key tool for economic analysis and policymaking.