Price index

Topic: Inflation and Index Numbers: CPI, WPI, IIP and the Deflator · NCERT: Class 11, Ch 7 "Index Numbers"

Meaning

A price index is an index number that measures the average change in the prices of a chosen set of goods and services between two periods (or two places), with the base period set at 100.

• General (weighted) formula: Price index = Σp₁q / Σp₀q × 100. The same basket of quantities (q) is priced at current prices (p₁) and at base prices (p₀).
• Laspeyres form (base-period basket): Σp₁q₀ / Σp₀q₀ × 100.

It matters because thousands of prices move in different directions, and a price index sums them all up in one number. That number is used to measure inflation, to turn money values into real values, and to revise wages. It is the most widely used type of index number.

Explanation

How a price index works

• Base period: the period we compare against. Its index value is always 100.
• Current period: the period being compared with the base.
• Reading the number:
• An index of 250 means prices are 2.5 times the base level, a rise of 150%.

• An index of 90 means prices have fallen 10% from the base.

• It is really a percentage, but the "%" sign is left out.

• Price relative (the index for one good) = (p₁/p₀) × 100. If a good's price goes from ₹2 to ₹4, its price relative is 200, meaning the price has doubled.

Main methods of building a price index (Class 11 data)

Data: four goods A–D with base prices (2, 5, 4, 2), current prices (4, 6, 5, 3), base quantities (10, 12, 20, 15), current quantities (5, 10, 15, 10) and base-period weights (40, 30, 20, 10).

• Simple aggregative index = ΣP₁/ΣP₀ × 100
• 18/13 × 100 = 138.5

• Weakness: it adds prices quoted in different units (per kg, per litre), and it is unweighted, so salt counts as much as food.

• Laspeyres index (base-period quantities) = Σp₁q₀/Σp₀q₀ × 100

• Σp₁q₀ = 257 and Σp₀q₀ = 190 (NCERT wrongly prints the denominator as 100).
• Index = 257/190 × 100 = 135.3
• Meaning: a basket that cost ₹100 in the base year now costs ₹135.3.

• Official statisticians like it because base quantities are collected only once. After that, only prices need to be collected each month.

• Paasche index (current-period quantities) = Σp₁q₁/Σp₀q₁ × 100

• 185/140 × 100 = 132.1

• Drawback: quantity data are needed every period, which is costly, and the basket changes every period.

• Fisher's ideal index (beyond NCERT) = √(Laspeyres × Paasche) = √(135.3 × 132.1) ≈ 133.7. It lies between the two.

• Simple average of price relatives = (1/n) Σ(p₁/p₀) × 100
• ¼ × (2 + 1.2 + 1.25 + 1.5) × 100 = 149 (148.75 rounded).

• Relatives have no unit, so the "per kg vs per litre" problem goes away.

• Weighted index of price relatives = ΣWR/ΣW (W = weight, usually the base-period expenditure share; R = price relative)

• (40×200 + 30×120 + 20×125 + 10×150)/100 = 15,600/100 = 156
• It is higher than 149 because good A has the biggest weight (40) and its price doubled.
• If W is the actual base expenditure (p₀q₀), this method gives exactly the Laspeyres index.

Why different formulas give different answers: substitution bias

• Substitution bias: when one good becomes dear, people switch to cheaper goods.
• Laspeyres overstates the rise in the cost of living.
• It keeps the old basket.

• So it gives too much weight to goods that have become costly.

• Paasche understates the rise.

• It uses the new basket.

• That basket has already shifted towards goods that stayed cheap.

• In our data: Laspeyres 135.3 > Fisher 133.7 > Paasche 132.1.

• A geometric mean of price relatives (the Jevons index) gives a lower figure than a simple average. This partly allows for shoppers moving to cheaper varieties.

Uses: inflation and deflating

• Inflation rate (%) = (Iₜ − Iₜ₋₁₂) / Iₜ₋₁₂ × 100. Iₜ is the index for month t, and Iₜ₋₁₂ is the index for the same month last year [3].
• Deflating means dividing a money value by a price index to get its real value.
• A worker's pay rises from ₹1,000 (1982) to ₹12,000 today, which is 12 times more rupees.
• If the price index rose from 100 to 600 (an illustrative figure), the real wage = 12,000 ÷ (600/100) = ₹2,000 at 1982 prices.
• So the worker is only 2 times better off, not 12 times.

In India

• CPI (Consumer Price Index, retail prices paid by households) — MoSPI, Rural/Urban/Combined:
• Base revised from 2012 = 100 to 2024 = 100, released on 12 February 2026 [2].
• Weighted items rose from 299 to 358 [2][3].
• Weights come from HCES 2023-24 (Household Consumption Expenditure Survey) [3].
• Elementary indices (the lowest-level index, built from price quotes for one item) use the Jevons geometric mean. Higher levels use the Young / Modified Laspeyres index [3].
• Share of Food & Beverages fell from 45.86% (CPI 2012) to 36.75% (CPI 2024) [3].
• CPI inflation was 2.75% in January 2026 (provisional): rural 2.73%, urban 2.77% [2].

• The RBI targets CPI inflation in its monetary policy.

• CPI-IW (CPI for Industrial Workers) — Labour Bureau:

• Base moved from 2001 = 100 to 2016 = 100 in 2020, with a linking factor of 2.88 [7].

• Main use: revising dearness allowance (DA, the extra pay given to cover price rises).

• WPI (Wholesale Price Index, prices in bulk trade) — Office of the Economic Adviser, DPIIT:

• Base revised from 2011-12 to 2022-23, released on 15 June 2026 together with new Producer Price Indices (PPIs) [4][5].

• Items rose from 697 to 957. It is compiled with the Laspeyres formula [4][5].

• GDP deflator: a Paasche-type price index used to turn nominal GDP into real GDP.

Don't confuse with

• Quantity index: it measures changes in physical volume (production, employment), not prices. IIP is a quantity index [6], not a price index.
• Price relative: this is the price index for one good (p₁/p₀ × 100). A price index averages many goods.
• Inflation rate: the index level (e.g. 135.3) compares with the base year. The inflation rate is the % change in the index over a period, usually year on year.
• GDP deflator vs CPI: the deflator is Paasche-type, covers all domestic output and excludes imports. CPI is Laspeyres-type (fixed basket), covers only household purchases and includes imported consumer goods.

Prelims Hooks

• Base period value is always 100. An index of 250 means 2.5 times the base, i.e. a 150% rise.
• Laspeyres = Σp₁q₀/Σp₀q₀ (overstates inflation). Paasche = Σp₁q₁/Σp₀q₁ (understates inflation). Fisher = √(L × P).
• A weighted average of price relatives with base expenditure-share weights gives the Laspeyres index.
• WPI is compiled by the Office of the Economic Adviser, DPIIT, not MoSPI. New base 2022-23, 957 items [4][5].
• CPI (2024 = 100): Jevons for elementary indices, Young / Modified Laspeyres at higher levels [3].
• Trap: in the new CPI, the weight reference period (HCES 2023-24) differs from the index reference period (2024 = 100) [3].

Mains Points

• The formula choice affects people's incomes.
• Fixed-basket (Laspeyres-type) indices can overstate the cost of living because of substitution bias.
• This matters because CPI drives the RBI's inflation target, and CPI-IW drives DA, wages and pensions.

• Regular base revision and Jevons elementary indices in CPI 2024 reduce this bias [3].

• Old weights distort policy.

• With a food weight of 45.86% (CPI 2012), vegetable price shocks could push up headline inflation and sway RBI decisions [3].

• The 2024 weight of 36.75%, from HCES 2023-24, matches what households buy today more closely [3].

• Limits of price indices.

• Quality changes are hard to measure, because a price rise may partly reflect a better product.
• New goods enter only when the base is revised.
• Free public services are left out [3], and prices differ across rural areas, towns and regions.
• So read the headline index together with its sub-indices and with other data.

Related concepts

• Index number
• Quantity index
• Simple aggregative price index
• Weighted index
• Weighted aggregative price index
• Laspeyres price index
• Paasche price index
• Price relative
• Method of averaging relatives
• Weighted index of price relatives

Read more

• Index numbers: meaning and construction