Index numbers | ISC Class 11 Economics Notes

This note covers index numbers in economics: the meaning and purpose of an index number, the difference between a simple (unweighted) and a weighted index, the construction of price index numbers by the aggregative method and by the method of averaging relatives, Laspeyre's, Paasche's and Fisher's methods, the Wholesale Price Index, the Consumer Price Index and the Index of Industrial Production, the problems involved in constructing a price index number, and the uses of index numbers in economic policy.

What is an index number?

An index number is a statistical device for measuring changes in the magnitude of a group of related variables.

It represents the general trend of diverging ratios from which it is calculated, and is a measure of the average change in a group of related variables over two different situations.

The comparison may be between like categories such as persons, schools or hospitals, or it may measure changes in the value of variables such as prices of a specified list of commodities, the volume of production in different sectors of an industry, the production of various agricultural crops or the cost of living.

Definition: Index number. A statistical device for measuring the average relative change in a group of related variables over two different periods, usually expressed as a percentage with the base period taken as 100.

Index numbers are conventionally expressed in terms of percentage. Of the two periods being compared, the period with which the comparison is made is known as the base period, and the period being studied is the current period.

The value in the base period is given the index number 100. An index number of any period is in proportion with it; thus an index number of 250 indicates that the value is two and a half times that of the base period.

A price index measures and permits comparison of the prices of certain goods. A quantity index measures the changes in the physical volume of production, construction or employment.

Though price index numbers are more widely used, a production index is also an important indicator of the level of output in the economy.

How is a simple (unweighted) index number constructed?

There are two methods of constructing an index number: the aggregative method, and the method of averaging relatives.

The simple aggregative index

In the simple aggregative index, the prices of all commodities in the current period are summed and expressed as a percentage of the sum of their prices in the base period.

Simple Aggregative Index = ΣP1/ΣP0 × 100, where P1 is the price of a commodity in the current period and P0 is its price in the base period, and Σ means "the sum of".

Worked example 1. Calculate the simple aggregative price index from the following base-period and current-period prices (in ₹) of four commodities: A, ₹2 to ₹4; B, ₹5 to ₹6; C, ₹4 to ₹5; D, ₹2 to ₹3.

Answer: ΣP0 = 2 + 5 + 4 + 2 = ₹13. ΣP1 = 4 + 6 + 5 + 3 = ₹18. Simple aggregative index = (18/13) × 100 = 138.5. Price is said to have risen by 38.5 per cent.

Why the simple aggregative index is of limited use

This index is of limited use because the units of measurement of the prices of various commodities are not the same, and because it is unweighted: the relative importance of items is not reflected, so all items are treated as having equal weight.

In reality, items purchased differ in order of importance; food items, for example, occupy a large proportion of expenditure, so an equal rise in the price of a heavily weighted item and a lightly weighted item will have different implications for the overall price index.

How is a weighted index number constructed?

An index number becomes a weighted index when the relative importance of items is taken into account.

To construct a weighted aggregative index, a well-specified basket of commodities is taken and its worth in each period is calculated; since the basket is fixed, any change in its total value is due to price change. Different methods use different baskets of quantities as weights.

Laspeyre's price index

Laspeyre's Price Index = Σ(P1q0)/Σ(P0q0) × 100, where q0 is the quantity of the commodity in the base period.

This method uses base-period quantities as weights, and answers the question: if the expenditure on the base-period basket of commodities was ₹100, how much should the expenditure on the same basket be in the current period?

Paasche's price index

Paasche's Price Index = Σ(P1q1)/Σ(P0q1) × 100, where q1 is the quantity of the commodity in the current period.

This method uses current-period quantities as weights, and answers the question: if the current-period basket had been consumed in the base period at an expenditure of ₹100, how much should the expenditure on that same basket be in the current period?

Worked example 2. Base-period price (P0) and quantity (q0), and current-period price (P1) and quantity (q1), for four commodities: A, P0 = ₹2, q0 = 10, P1 = ₹4, q1 = 5;

B, P0 = ₹5, q0 = 12, P1 = ₹6, q1 = 10; C, P0 = ₹4, q0 = 20, P1 = ₹5, q1 = 15; D, P0 = ₹2, q0 = 15, P1 = ₹3, q1 = 10. Calculate Laspeyre's and Paasche's price index.

Answer: For Laspeyre's: Σ(P1q0) = (4×10)+(6×12)+(5×20)+(3×15) = 40+72+100+45 = 257. Σ(P0q0) = (2×10)+(5×12)+(4×20)+(2×15) = 20+60+80+30 = 190. Laspeyre's index = (257/190) × 100 = 135.3.

For Paasche's: Σ(P1q1) = (4×5)+(6×10)+(5×15)+(3×10) = 20+60+75+30 = 185. Σ(P0q1) = (2×5)+(5×10)+(4×15)+(2×10) = 10+50+60+20 = 140. Paasche's index = (185/140) × 100 = 132.1.

Using base-period weights the price is said to have risen by 35.3 per cent; using current-period weights it is said to have risen by 32.1 per cent.

Fisher's price index

A third, widely known standard method is Fisher's Price Index, defined as the geometric mean of Laspeyre's and Paasche's indices: Fisher's Price Index = √(Laspeyre's × Paasche's). Because it combines base-period and current-period weights, it is often called the "ideal" index number.

Definition: Laspeyre's, Paasche's and Fisher's indices. Laspeyre's index weights prices by base-period quantities, Paasche's index weights prices by current-period quantities, and Fisher's index is the geometric mean of the two, combining both sets of weights.

Worked example 2A. Using the data of Worked example 2, calculate Fisher's price index.

Answer: Fisher's index = √[(Σ(P1q0)/Σ(P0q0)) × (Σ(P1q1)/Σ(P0q1))] × 100 = √[(257/190) × (185/140)] × 100 = √(1.3526 × 1.3214) × 100 = √1.7873 × 100 = 1.3369 × 100 = 133.7. Fisher's index lies between Laspeyre's (135.3) and Paasche's (132.1), as a geometric mean of the two always does, so the price rise is put at 33.7 per cent.

Price-weighted and quantity-weighted index numbers

A weighted index can be weighted in two ways, depending on what it measures. A price index compares prices, so it is weighted by quantities: Laspeyre's and Paasche's price indices use base-period quantities (q0) or current-period quantities (q1) as the weights of the prices.

A quantity index compares quantities, so it is weighted by prices (or by values): Laspeyre's quantity index, for example, is Σ(q1P0)/Σ(q0P0) × 100, where base-period prices are the weights of the quantities. The Index of Industrial Production is a quantity index of this kind, with weights based on value added.

A simple index uses no weights at all, so every commodity counts equally, whereas a weighted index, whether price weighted or quantity weighted, gives each item an importance that matches its share in spending or output.

What is the method of averaging relatives?

Simple price relatives

When there is only one commodity, the price index is simply the ratio of its current-period price to its base-period price, expressed as a percentage; this ratio is called the price relative. The method of averaging relatives takes the average of these relatives when there are many commodities.

Price Relative = P1/P0 × 100. The simple price-relatives index is the average of these relatives across n commodities, where n stands for the number of commodities.

Weighted price relatives

The weighted price relatives index is the weighted arithmetic mean of price relatives, where each commodity's weight (W) is usually determined by the proportion or percentage of expenditure on it in total expenditure during the base period.

These weights are, essentially, the value shares of different commodities in total expenditure. The base-period weight is generally preferred to the current-period weight because calculating the weight afresh every year is inconvenient, and weighted baskets of different periods are not strictly comparable.

Worked example 3. Four commodities have weights (in per cent of total expenditure) and price relatives as follows: A, weight 40, price relative 200 (base price ₹2, current price ₹4);

B, weight 30, price relative 120 (base price ₹5, current price ₹6); C, weight 20, price relative 125 (base price ₹4, current price ₹5); D, weight 10, price relative 150 (base price ₹2, current price ₹3). Calculate the weighted price relatives index.

Answer: ΣWR = (40×200) + (30×120) + (20×125) + (10×150) = 8,000 + 3,600 + 2,500 + 1,500 = 15,600. ΣW = 40+30+20+10 = 100. Weighted index = 15,600/100 = 156. The price index has risen by 56 per cent.

The weighted index is higher than the simple aggregative index because item A, which carries the highest weight, doubled in price.

What is the Consumer Price Index?

How is the CPI interpreted?

The Consumer Price Index (CPI), also known as the cost of living index, measures the average change in retail prices.

If the CPI for industrial workers (2001=100) is 277 in December 2014, this means that a worker who was spending ₹100 in 2001 on a typical basket of commodities would need ₹277 in December 2014 to buy an identical basket; it is not necessary that the basket is actually bought, only that the capability to buy it is maintained.

Worked example 4. Construct a consumer price index from the following data, where R = (P1/P0) × 100 is the price relative and W is the weight (per cent): Food, weight 35, base price ₹150, current price ₹145;

Fuel, weight 10, base price ₹25, current price ₹23; Cloth, weight 20, base price ₹75, current price ₹65; Rent, weight 15, base price ₹30, current price ₹30; Misc., weight 20, base price ₹40, current price ₹45.

Answer: R values: Food = (145/150)×100 = 96.67; Fuel = (23/25)×100 = 92.00; Cloth = (65/75)×100 = 86.67; Rent = (30/30)×100 = 100.00; Misc. = (45/40)×100 = 112.50. WR values: Food = 35×96.67 = 3,383.45; Fuel = 10×92.00 = 920.00;

Cloth = 20×86.67 = 1,733.40; Rent = 15×100.00 = 1,500.00; Misc. = 20×112.50 = 2,250.00. ΣWR = 9,786.85. ΣW = 100. CPI = 9,786.85/100 = 97.86. The cost of living has declined by 2.14 per cent.

An index larger than 100 indicates a higher cost of living, requiring an upward adjustment in wages and salaries equal to the amount by which the index exceeds 100; an index of 150 requires a 50 per cent upward adjustment.

The CPI basket in India

The index is now prepared with base 2012 = 100, using data of the Consumer Expenditure Survey of the National Sample Survey.

The Consumer Food Price Index (CFPI) is the same as the CPI for "Food and Beverages", except that it excludes alcoholic beverages and prepared meals, snacks and sweets.

Different CPI series in India

Government agencies in India prepare several consumer price indices for different categories of consumers, because the composition of consumption differs markedly between these groups, so a single common index would not represent their actual cost of living.

These include the Consumer Price Index Numbers for Industrial Workers, with base 2001=100, which stood at 278 in May 2017; the All-India Consumer Price Index Numbers for Agricultural Labourers, with base 1986-87=100, which stood at 872 in May 2017; and the All-India Consumer Price Index Numbers for Rural Labourers, with the same base, which stood at 878 in May 2017.

In addition, the All-India Rural Consumer Index (base 2012=100) stood at 133.3, the All-India Urban Consumer Price Index (base 2012=100) stood at 129.3, and the All-India Combined Consumer Price Index (base 2012=100) stood at 131.4, all in May 2017. These indices are also available at the state level, and the Reserve Bank of India uses the All-India Combined Consumer Price Index as its main measure of how consumer prices are changing.

What is the Wholesale Price Index?

How the WPI differs from the CPI

The Wholesale Price Index (WPI) indicates the change in the general price level. Unlike the CPI, it has no reference consumer category and does not include items relating to services, such as barber charges or repairing.

If the statement "WPI with 2004-05 as base is 253 in October 2014" is made, it means that the general price level has risen by 153 per cent during this period.

The WPI is now prepared with base 2011-12 = 100 and uses only the prices of goods prevailing at the wholesale level.

The WPI basket

Data on wholesale prices are usually available quickly.

Headline and core inflation

The "all commodities" inflation rate is often called headline inflation. The food index is made up of food articles from the primary articles group and food products from the manufactured products group.

Economists who focus instead on wholesale prices of manufactured goods other than food and fuel study core inflation, which makes up around 55 per cent of the total weight of the WPI.

What is the Index of Industrial Production?

How is the IIP calculated?

Unlike the CPI or WPI, the Index of Industrial Production (IIP) tries to measure quantities rather than prices.

With effect from April 2017 its base year was fixed at 2011-12 = 100; the base is changed fairly often because every year a large number of items either stop being manufactured or become inconsequential, while new items start being manufactured.

While price indices are weighted averages of price relatives, the IIP is a weighted arithmetic mean of quantity relatives, with weights allotted to various items in proportion to the value added by manufacture in the base year, using Laspeyre's formula: IIP = Σ(qi1 × Wi)/ΣWi × 100, where qi1 is the quantity relative for the current year with the base year for good i, and Wi is the weight allotted to good i.

Sectors covered in India

The IIP is available at the level of industrial sectors and sub-sectors, with mining, manufacturing and electricity as the main branches in India, and also according to the "use" of the product (for example primary goods, capital goods or consumer durables).

Sometimes the focus is on the Eight Core Industries, namely coal, crude oil, natural gas, refinery products, fertilisers, steel, cement and electricity, which together carry a combined weight of 40.27 per cent in the IIP.

What problems arise in constructing a price index number?

Four main issues

Several issues need to be kept in mind while constructing an index number. These are the choice of the base year, the coverage (number of commodities to be included), the choice of prices to use, and the choice of the method (formula) to be used.

1. Purpose of the index. One must be clear about the purpose of the index: calculating a volume index will be inappropriate when a value index is actually needed, and the items to be included must be as representative as possible of the group being studied.
2. Choice of the base year. Every index should have a base year, and this base year should be as normal as possible; years with extreme values should not be chosen. The base period should also not be too far in the past, because many items in an old consumption basket may have disappeared from the current one (for example, a comparison between 1993 and 2005 is more meaningful than one between 1960 and 2005), so the base year of any index number is routinely updated.
3. Coverage (number of commodities). The index must include enough commodities to represent what the group actually buys or produces, but not so many that collecting prices becomes slow and costly. The items chosen should be standard and easy to identify (for example a stated variety and grade of rice), and the list must be revised as consumption patterns change.
4. Choice of prices. It must be decided which prices to use (retail prices for a consumer price index, wholesale prices for a wholesale price index), from which markets or shops, and on which dates. Prices should be collected regularly from representative markets, and where the same good sells at different prices, for example a controlled ration-shop price and an open-market price, the price actually paid by the group being studied should be used.
5. Choice of the method (formula). The choice of formula depends on the nature of the question being studied; the only difference between Laspeyre's and Paasche's index is the weights used, so the choice between them affects the final result.
6. Choice of data source. There are many sources of data with differing degrees of reliability; data of poor reliability give misleading results, so due care must be taken in collecting data, and the most reliable source of secondary data should be used if primary data are not available.

Selecting items for different groups of consumers

In addition, items are not equally important for different groups of consumers when a consumer price index is constructed; for example, a rise in petrol price may not directly affect the living conditions of poor agricultural labourers, so the items included in any index have to be selected carefully for the group being studied.

What are the uses of index numbers?

Uses of the CPI and WPI in policy making

The WPI, CPI and IIP are widely used in policy making. The CPI, or cost of living index, is helpful in wage negotiation, the formulation of income policy, price policy, rent control, taxation and general economic policy formulation.

The WPI is used to eliminate the effect of changes in prices on aggregates such as national income and capital formation, and is widely used to measure the rate of inflation, which is a general and continuing increase in prices; if inflation becomes sufficiently large, money may lose its traditional function as a medium of exchange and as a unit of account, and its primary impact lies in lowering the value of money.

Uses in wages and investment decisions

The CPI is also used to calculate the purchasing power of money and the real wage. Purchasing Power = 1/Cost of Living Index, and Real Wage = Money Wage/CPI × 100.

Worked example 5. The CPI (1982=100) is 526 in January 2005. A consumer's money wage is ₹10,000. Calculate the purchasing power of a rupee in January 2005, and the real wage in terms of 1982 rupees.

Answer: Purchasing power of a rupee = 100/CPI = 100/526 = ₹0.19, so a rupee in January 2005 is worth 19 paise at 1982 prices. Real wage = (Money wage/CPI) × 100 = (10,000/526) × 100 = ₹1,901.

This means ₹1,901 in 1982 had the same purchasing power as ₹10,000 in January 2005.

The IIP gives a quantitative figure about the change in production in the industrial sector, and an agricultural production index provides a ready reckoner of the performance of the agricultural sector.

The Sensex, the short form of the Bombay Stock Exchange Sensitive Index with 1978-79 as base, is a useful guide for investors in India: if the Sensex is rising, investors are optimistic about the future performance of the economy and it is seen as an appropriate time for investment.

Widely used Indian index numbers, such as the WPI, CPI, Index Number of Yield of Principal Crops, IIP and Index of Foreign Trade, are available in official sources such as the Economic Survey.

Going beyond the syllabus

The Human Development Index (HDI) is another widely used index that measures the development of a country, combining indicators of income, education and life expectancy rather than prices or quantities alone.

The Sensex, which is the benchmark index for the Indian stock market, consists of 30 stocks representing 13 sectors of the economy, chosen from leading companies in their respective industries. When the Sensex rises, it indicates that the market is doing well, that investors expect better earnings from the listed companies, and that there is growing confidence in the basic health of the economy; a falling Sensex has the opposite meaning and can erode investors' wealth considerably.

These two indices show that the idea of an index number extends well beyond prices and quantities of goods: the same statistical technique of combining many changing variables into one summary figure, with a chosen base, is used across economics, development studies and financial markets.

How are index numbers used in the Indian economy?

In India, several official index numbers are published regularly, and each one illustrates a different use of the general method described above.

Consumer price index series in India

For example, the Consumer Price Index Numbers for Industrial Workers (base 2001=100) stood at 278 in May 2017, while the All-India Consumer Price Index Numbers for Agricultural Labourers (base 1986-87=100) stood at 872 and the All-India Consumer Price Index Numbers for Rural Labourers (same base) stood at 878, both also in May 2017.

These three series are different because the basket of goods and services consumed by an industrial worker, an agricultural labourer and a rural labourer differs; a single common index would not represent the actual cost of living of each group accurately.

WPI and IIP in India

The Wholesale Price Index, with base 2011-12=100, stood at 112.8 in May 2017; this is an example of how a general price index is tracked for the whole of India without reference to any one consumer group.

The Index of Industrial Production for India is published separately for mining (weight 14.4 per cent), manufacturing (weight 77.6 per cent) and electricity (weight 8.0 per cent), so that changes in India's industrial output can be studied sector by sector as well as for the economy as a whole.

Sensex as an example of an index number

The Sensex, the Bombay Stock Exchange Sensitive Index with 1978-79 as base, is a further Indian example of the same statistical idea applied to share prices rather than to a basket of goods: it is the benchmark index for the Indian stock market, consisting of 30 stocks representing 13 sectors of the economy, and a rise in the Sensex is read as a sign of growing investor confidence in India's economic health.

Taken together, India's CPI series, the WPI, the IIP and the Sensex show how the same index-number technique is applied across the Indian economy, from the cost of living of specific groups of Indian workers to the general price level and the performance of Indian industry and the Indian stock market.

Glossary

• Index number — a statistical device measuring the average relative change in a group of related variables between two periods, expressed as a percentage with the base period as 100.
• Base period — the period with which comparison is made, given an index value of 100.
• Current period — the period being compared with the base period in an index number.
• Price index — an index measuring and permitting comparison of the prices of a specified basket of goods.
• Quantity index — an index measuring changes in the physical volume of production, construction or employment.
• Simple aggregative index — an unweighted index found by dividing the sum of current-period prices by the sum of base-period prices.
• Weighted aggregative index — an index that takes the relative importance (quantity weight) of each item into account.
• Price relative — the ratio of a commodity's current-period price to its base-period price, expressed as a percentage.
• Laspeyre's index — a weighted price index using base-period quantities as weights.
• Paasche's index — a weighted price index using current-period quantities as weights.
• Fisher's index — the geometric mean of Laspeyre's and Paasche's indices, combining base- and current-period weights.
• Consumer Price Index — an index, also called the cost of living index, measuring the average change in retail prices paid by consumers.
• Wholesale Price Index — an index measuring the general price level at the wholesale stage, with no reference consumer category.
• Index of Industrial Production — a quantity index measuring changes in the physical volume of industrial output.

Common errors and misconceptions

• Misconception: an index number of 150 means the value has grown 150 times. Correct: it means the current value is one and a half times the base-period value, that is, a rise of 50 per cent.
• Misconception: a simple index and a weighted index must give the same result. Correct: they usually differ, because a weighted index reflects the relative importance of each item through its quantity or expenditure weight.
• Misconception: Laspeyre's and Paasche's indices use the same weights. Correct: Laspeyre's index uses base-period quantities as weights, while Paasche's index uses current-period quantities as weights.
• Misconception: the CPI and the WPI measure the same thing. Correct: the CPI measures retail prices faced by a defined group of consumers, while the WPI measures the general wholesale price level with no reference consumer category.
• Misconception: any convenient year can be chosen as the base year. Correct: the base year should be a normal year, free of extreme values, and not too far in the past.
• Misconception: the Index of Industrial Production measures price changes in industry. Correct: the IIP is a quantity index measuring changes in the physical volume of industrial output, using Laspeyre's formula applied to quantity relatives.
• Misconception: a price index shows exactly how much each commodity's price has changed. Correct: a price index is a single summary measure of the average change across many commodities, whose individual price changes may differ widely.

Exam-style questions with model answers

Q1. State the meaning of an index number. [1 mark]

1. An index number is a statistical device for measuring changes in the magnitude of a group of related variables, expressed conventionally as a percentage, with the base period given the value 100.

Q2. Distinguish between a price index and a quantity index. [2 marks]

1. A price index measures and permits comparison of the prices of certain goods over two periods.
2. A quantity index measures changes in the physical volume of production, construction or employment, rather than prices.

Q3. The base-period and current-period prices (in ₹) of four commodities are: A, ₹2 to ₹4; B, ₹5 to ₹6; C, ₹4 to ₹5; D, ₹2 to ₹3. Calculate the simple aggregative price index and comment on the result. [4 marks]

1. ΣP0 = 2+5+4+2 = ₹13.
2. ΣP1 = 4+6+5+3 = ₹18.
3. Simple aggregative index = (ΣP1/ΣP0) × 100 = (18/13) × 100 = 138.5.
4. This means price has risen by 38.5 per cent on average, but the index is unweighted, so it does not reflect the relative importance of the four commodities and gives equal weight to each.

Q4. Explain the difference between Laspeyre's price index and Paasche's price index. [4 marks]

1. Laspeyre's index uses base-period quantities (q0) as weights for both the current- and base-period prices.
2. Paasche's index uses current-period quantities (q1) as weights for both the current- and base-period prices.
3. Laspeyre's index answers how much it would cost, at current prices, to buy the base-period basket, while Paasche's index answers how much it would cost, at current prices, to buy the current-period basket.
4. Because quantities consumed usually change between the two periods, the two methods give different numerical values of the index for the same data.

Q5. Weights (W, per cent) and base-period and current-period prices (in ₹) of five items used for a cost of living index are: Food, weight 35, ₹150 to ₹145; Fuel, weight 10, ₹25 to ₹23; Cloth, weight 20, ₹75 to ₹65; Rent, weight 15, ₹30 to ₹30; Misc., weight 20, ₹40 to ₹45. Calculate the consumer price index. [4 marks]

1. Price relative R = (P1/P0) × 100 for each item: Food 96.67, Fuel 92.00, Cloth 86.67, Rent 100.00, Misc. 112.50.
2. WR for each item: Food 3,383.45, Fuel 920.00, Cloth 1,733.40, Rent 1,500.00, Misc. 2,250.00.
3. ΣWR = 9,786.85 and ΣW = 100.
4. CPI = ΣWR/ΣW = 9,786.85/100 = 97.86, which means the cost of living has fallen by 2.14 per cent.

Q6. Explain the problems involved in constructing a price index number. [6 marks]

1. The purpose of the index must be clear, since a volume index would be inappropriate where a value index is required.
2. The items included must be as representative as possible, because the items that matter differ between groups of consumers, so a rise in one price may not affect all groups equally.
3. The base year must be chosen carefully: it should be a normal year, free of extreme values, and not too far in the past, since items in an old consumption basket may have disappeared from current use.
4. The number of commodities to be included (the coverage) must be decided so that the basket reflects the relevant group's consumption or production.
5. The choice of prices to be used (for example retail or wholesale prices) must suit the purpose of the index.
6. The choice of method or formula matters, since Laspeyre's and Paasche's indices differ only in the weights used and can give different results for the same data; the reliability of the data source used must also be checked carefully.

Q7. Explain six uses of index numbers in economic policy. [6 marks]

1. The consumer price index helps in wage negotiation, and in formulating income policy, price policy, rent control and taxation policy.
2. The wholesale price index is used to eliminate the effect of price changes on aggregates such as national income and capital formation.
3. The wholesale price index is widely used to measure the rate of inflation, since a general and continuing rise in prices lowers the value of money.
4. The consumer price index is used to calculate the purchasing power of money and the real wage of workers, so that salaries can be adjusted to maintain a given standard of living.
5. The index of industrial production gives a quantitative measure of the change in output of the industrial sector.
6. The Sensex acts as a guide for investors: a rising Sensex signals growing confidence in the economy and is taken as an appropriate time for investment.

Key takeaways

• An index number measures the average relative change in a group of related variables, with the base period set at 100.
• A simple aggregative index treats all commodities as equally important and is of limited use for this reason.
• A weighted index reflects the relative importance of items through quantity or expenditure weights.
• Laspeyre's index uses base-period quantities as weights, Paasche's index uses current-period quantities, and Fisher's index is their geometric mean.
• The method of averaging relatives finds the (weighted) average of price relatives rather than aggregating prices directly.
• The Consumer Price Index measures the average change in retail prices paid by a defined group of consumers.
• The Wholesale Price Index measures the general wholesale price level and has no reference consumer category.
• The Index of Industrial Production is a quantity index built on Laspeyre's formula applied to quantity relatives.
• Constructing a price index number requires careful choice of purpose, base year, coverage, prices and method.
• Index numbers are used in wage negotiation, inflation measurement, capital formation estimates and investment decisions.

Test yourself

What value is conventionally given to the base period in an index number?

The base period is conventionally given an index value of 100, against which the current period's index is compared.

Why is the simple aggregative price index called unweighted?

Because it treats all commodities as equally important, ignoring differences in the quantities consumed or the relative importance of each item.

Which quantities are used as weights in Laspeyre's price index?

Laspeyre's price index uses base-period quantities (q0) as weights for both base-period and current-period prices.

Which quantities are used as weights in Paasche's price index?

Paasche's price index uses current-period quantities (q1) as weights for both base-period and current-period prices.

How is Fisher's price index calculated from Laspeyre's and Paasche's indices?

Fisher's price index is the geometric mean of Laspeyre's and Paasche's indices: the square root of their product.

What does the Wholesale Price Index measure, and how does it differ from the CPI?

The WPI measures the general price level at the wholesale stage with no reference consumer category, while the CPI measures retail prices for a defined group of consumers.

What does the Index of Industrial Production measure?

It measures changes in the physical quantity of industrial output, using a weighted arithmetic mean of quantity relatives based on Laspeyre's formula.

Why should the base year of an index number not be too far in the past?

Because many items in an old consumption or production basket may have disappeared from current use, making the comparison less meaningful.