Index Numbers

The full picture

Imagine your family's monthly grocery bill was ₹5,000 in 2020 and is ₹7,000 today. Prices went up, but by exactly how much? A single rupee figure doesn't tell the full story because you may be buying slightly different things now. An index number solves this: it condenses the average price change of a whole basket of goods into one easy number, always anchored to a chosen starting point called the base year. The base year is assigned the value 100 by definition, so if the index reads 140 today, prices are 40 per cent higher than in the base year — no matter what the actual rupee amounts are.

The simplest index number is a price relative: (Price in current year ÷ Price in base year) × 100. If a litre of coconut oil cost ₹120 in 2020 and costs ₹168 today, the price relative is (168 ÷ 120) × 100 = 140. But a single item isn't enough — we need a composite index that covers many items at once. The unweighted (simple aggregate) index just adds all current prices and divides by all base prices. That treats a ₹10 matchbox and a ₹10,000 smartphone as equally important, which is clearly wrong. Weighted index numbers fix this by giving each item a weight based on how important it is to spending or production.

The two most important weighted index formulae for your exam are the Laspeyres index and the Paasche index. The Laspeyres index uses base-year quantities as weights: it answers the question 'What does the original basket cost today?' You multiply every current price by the base-year quantity purchased, sum those up, then divide by the base-year total cost, and multiply by 100. The Paasche index uses current-year quantities: it reflects today's spending habits. In practice, base-year data is easier to collect (you only survey households once), so Laspeyres is used more widely — including in India's Consumer Price Index (CPI). Paasche is theoretically more current but needs fresh household surveys every period.

You already meet index numbers in daily life without realising it. When All India Radio or a news app says 'retail inflation is 5.4 per cent', that figure is calculated from India's CPI — a weighted price index covering food, fuel, clothing, housing, and services. The weights reflect how a typical Indian household spends its money (food alone has about a 45 per cent weight). Kerala's own cost-of-living experience can differ from the national CPI because Keralites spend a larger share on fish, coconut oil, and education. Beyond prices, index numbers also track production (the Index of Industrial Production, IIP, measures factory output) and share markets (the Nifty 50 index tracks 50 large company share prices).

Two issues trip students up in problems. First, the choice of base year matters: a base year with abnormally low prices will make every future index look high, exaggerating inflation. That is why India periodically updates its base years — the WPI base shifted to 2011-12 and the CPI to 2012 to better reflect modern spending patterns. When the base year changes, old and new series must be 'spliced' (mathematically linked) so long-run comparisons remain valid. Second, Laspeyres tends to overstate inflation and Paasche tends to understate it. This happens because when prices rise, consumers switch away from now-expensive goods — Laspeyres ignores that switch (it still uses the old basket), so it overstates the cost increase.

To summarise the key formula chain: Simple price relative = (Pn ÷ P0) × 100. Laspeyres index = [Σ(Pn × Q0) ÷ Σ(P0 × Q0)] × 100. Paasche index = [Σ(Pn × Qn) ÷ Σ(P0 × Qn)] × 100. In these symbols, P0 and Q0 are base-year price and quantity; Pn and Qn are current-year price and quantity. Always write the formula before substituting numbers in board exam answers — it earns you method marks even if you make an arithmetic slip.

An Indian example

Meena runs a small canteen near a Plus Two college in Thrissur. In January 2020 she tracked her daily supplies: a 5-kg bag of rice (₹200), a litre of coconut oil (₹120), a dozen eggs (₹60), and a bundle of vegetables (₹80) — total ₹460. By January 2024 the same supplies cost ₹300, ₹168, ₹90, and ₹130 respectively — total ₹688. Using a simple Laspeyres approach (treating 2020 quantities as weights), her food-cost index is (688 ÷ 460) × 100 = 149.6. That single number tells the story: Meena's ingredient costs rose nearly 50 per cent in four years. She now knows she needs to either raise prices or find cheaper suppliers — and she can quote this index to her bank manager when she applies for a small-business loan, because an index is far more persuasive than a vague 'costs have gone up a lot'.

Common misconceptions to watch for

• Wrong belief: 'An index number of 180 means the price is ₹180.' Correction: Index numbers measure relative change, not absolute rupee values. An index of 180 with base year = 100 means prices are 80 per cent higher than in the base year; the actual rupee price depends on what the item cost in the base year.
• Wrong belief: 'Laspeyres and Paasche indices give the same answer — they're just two names for the same formula.' Correction: They differ in the quantities used as weights. Laspeyres uses base-year quantities and typically overstates inflation; Paasche uses current-year quantities and typically understates it. You will get different numerical answers from the same price data, and your exam may specifically ask you to distinguish them.
• Wrong belief: 'Changing the base year changes actual inflation.' Correction: Shifting the base year is only a mathematical re-scaling — the same real price change now appears as a different index value because the starting point moved. Actual inflation in the economy does not change; only the number on the index changes, which is why old and new series must be spliced before comparing across a base-year shift.