01 · Explore
Introduction to Index Numbers
An index number is a statistical device designed to measure changes in the magnitude of a group of related variables over time or between different situations.
In economics, we often need to summarize how a group of items changes. For instance, if a worker's salary rises from Rs 1,000 in 1982 to Rs 12,000 today, we cannot immediately say their standard of living has risen twelvefold without knowing how the prices of goods they buy have changed. Index numbers provide a single numerical measure to represent these complex shifts.
Conventionally, index numbers are expressed as percentages. We compare a 'current period' to a 'base period'. The base period is assigned a value of 100. If the index for a later year is 250, it indicates the value is two and a half times that of the base period. This allows for easy comparison across different categories like persons, schools, or hospitals.
There are two primary types: Price Index Numbers, which measure changes in the cost of goods, and Quantity Index Numbers, which measure changes in the physical volume of production, construction, or employment. While price indices are more common, production indices are vital indicators of economic output.
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Question
If the price index for the year 2023 is 150 with 2015 as the base year, what does this indicate about price changes?
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02 · Explore
The Simple Aggregative Method
The simplest way to construct a price index is to sum the prices of all commodities in the current period and divide them by the sum of prices in the base period.
The formula for a simple aggregative price index is P01 = (ΣP1 / ΣP0) × 100, where P1 represents current prices and P0 represents base period prices. This method treats every commodity as having equal importance, which is its primary limitation.
In reality, consumers spend more on certain items, like food, than on others. A simple aggregative index fails to reflect this because it is unweighted. Furthermore, it is sensitive to the units of measurement used for different prices.
Calculating Simple Aggregative Index
P01 = (4 + 6 + 5 + 3) / (2 + 5 + 4 + 2) × 100
Summing current prices (4, 6, 5, 3) gives 18. Summing base prices (2, 5, 4, 2) gives 13. The index is (18/13) × 100 = 138.46, which is approximately 138.5 as shown in the source. This indicates a 38.5% price rise.
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Why is the simple aggregative method considered of limited use in economics?
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03 · Explore
Weighted Aggregative Methods: Laspeyre and Paasche
Weighted indices account for the relative importance of different items by using quantities as weights.
To construct a weighted index, we calculate the worth of a specific 'basket' of goods. The two most famous methods differ in which period's quantities they use as weights. Laspeyre’s Price Index uses base period quantities (q0) as weights. It answers: 'If we bought the same basket as the base year, how much more would it cost today?'
Paasche’s Price Index uses current period quantities (q1) as weights. It answers: 'If we consumed today's basket in the base year, how much would we have spent then compared to now?' Because consumption patterns change over time, these two methods often yield different results.
| Method | Formula | Weight Used |
|---|---|---|
| Laspeyre’s Index | P01 = (ΣP1q0 / ΣP0q0) × 100 | Base Period Quantities (q0) |
| Paasche’s Index | P01 = (ΣP1q1 / ΣP0q1) × 100 | Current Period Quantities (q1) |
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Which index uses current period quantities as weights?
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04 · Explore
Method of Averaging Relatives
This method calculates the price relative for each commodity individually before averaging them.
A price relative is the ratio of the current price to the base price, expressed as a percentage: (P1/P0) × 100. In the unweighted version, we sum these relatives and divide by the number of commodities (n).
The weighted version, known as the weighted arithmetic mean of price relatives, is more common. Here, weights (W) are usually the percentage of total expenditure spent on that item in the base period. The formula is P01 = Σ(W × R) / ΣW, where R is the price relative.
Weighted Price Relative Calculation
P01 = (40 × 200 + 30 × 120 + 20 × 125 + 10 × 150) / 100
Summing the products of weights and relatives (8000 + 3600 + 2500 + 1500) gives 15600. Dividing by the total weight (100) results in an index of 156.
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What is a 'price relative'?
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05 · Explore
Consumer Price Index (CPI)
The Consumer Price Index, or Cost of Living Index, measures the average change in retail prices paid by specific consumer groups.
CPI is vital for understanding how inflation affects households. For example, if the CPI for industrial workers (base 2001=100) was 277 in December 2014, it means a basket costing Rs 100 in 2001 would cost Rs 277 in 2014. This necessitates upward adjustments in wages, often called Dearness Allowance.
In India, various CPIs are maintained for different groups, such as Industrial Workers, Agricultural Labourers, and Rural Labourers. The Reserve Bank of India (RBI) currently uses the All-India Combined Consumer Price Index (base 2012=100) as its primary measure of inflation. The weights in this index are based on the Consumer Expenditure Survey (CES) of 2011-12.
| Major Group (CPI Combined) | Weight (%) |
|---|---|
| Food and beverages | 45.86 |
| Pan, tobacco and intoxicants | 2.38 |
| Clothing & footwear | 6.53 |
| Housing | 10.07 |
| Fuel & light | 6.84 |
| Miscellaneous | 28.32 |
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Which group has the highest weight in the All-India Combined CPI (2014-15 data)?
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06 · Explore
Wholesale Price Index (WPI)
The WPI measures changes in the prices of goods traded at the wholesale level.
Unlike the CPI, the WPI does not refer to a specific consumer category and excludes services like repairs or barber charges. It is often used to measure 'Headline Inflation'. In India, the WPI (base 2011-12=100) categorizes goods into three main groups: Primary Articles, Fuel and Power, and Manufactured Products.
Manufactured products carry the highest weight (64.23%). Economists also track 'Core Inflation', which excludes volatile food and fuel prices from the WPI to understand underlying price trends. The WPI is useful for deflating economic aggregates like National Income to remove the effect of price changes.
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What is the main difference between CPI and WPI?
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07 · Explore
Index of Industrial Production (IIP)
The IIP is a quantity index that measures the physical volume of production in the industrial sector.
The IIP (base 2011-12=100) is calculated as a weighted arithmetic mean of quantity relatives using Laspeyre’s formula. Weights are assigned based on the 'value added' by manufacture in the base year. The three main sectors are Mining (14.4%), Manufacturing (77.6%), and Electricity (8.0%).
A significant portion of the IIP (40.27%) is comprised of the 'Eight Core Industries': coal, crude oil, natural gas, refinery products, fertilizers, steel, cement, and electricity. The IIP is also reported based on the 'use' of products, such as Capital Goods, Consumer Durables, and Primary Goods.
IIP Sectoral Weights (2016-17 Source)
- 1
Manufacturing
The largest sector with a weight of 77.6%.
- 2
Mining
Accounts for 14.4% of the industrial production index.
- 3
Electricity
The smallest of the three main sectors at 8.0%.
The sectoral composition of the Index of Industrial Production shows the dominance of the manufacturing sector.
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What are the 'Eight Core Industries' in the context of IIP?
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08 · Explore
Sensex and Other Indices
Beyond price and production, indices are used to track stock markets and human development.
The Sensex (Bombay Stock Exchange Sensitive Index) is the benchmark index for the Indian stock market, with 1978-79 as its base. It tracks 30 stocks representing 13 sectors. A rising Sensex indicates investor confidence and expectations of better corporate earnings.
The Human Development Index (HDI) is another crucial measure used to compare the development levels of different countries, focusing on health, education, and standard of living rather than just economic output.
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What does a rising Sensex signify?
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09 · Explore
Economic Applications and Calculations
Index numbers are indispensable for policy-making, wage negotiations, and understanding the purchasing power of money.
One major use of the CPI is calculating the Purchasing Power of Money, which is the reciprocal of the price index (1/CPI). As prices rise, the value of a rupee falls. For example, if the CPI (base 1982=100) is 526 in 2005, a rupee is worth only 100/526 = 0.19 (19 paise) in 1982 terms.
Real Wages are calculated by dividing the money wage by the cost of living index and multiplying by 100. This shows the actual quantity of goods a worker can buy. To maintain the same standard of living when prices rise, the money wage must be increased by the same factor as the index.
Calculating Real Wage
Real Wage = (10,000 / 526) × 100 = 1,901
If a consumer earns Rs 10,000 in 2005 when the CPI is 526 (base 1982), their real wage in 1982 prices is Rs 1,901. The equivalent of a rupee is 100/526 = 0.19, meaning it is worth 19 paise in 1982 terms.
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How is the purchasing power of money related to the cost of living index?
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10 · Explore
Issues in Constructing Index Numbers
Constructing a reliable index requires careful selection of items, base years, and formulas.
The purpose of the index must be clear; for instance, a volume index is useless if a value index is needed. The items included must be representative of the group being studied. A rise in petrol prices affects a car owner significantly but may not directly impact a poor agricultural labourer.
The base year should be a 'normal' year, free from extreme events like wars or natural disasters. It should not be too far in the past, as consumption patterns change. For this reason, base years are updated periodically. Finally, the reliability of the data source is paramount, as poor data leads to misleading results.
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What are the characteristics of a good base year?
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