Index Numbers: Meaning, Types and Construction Method

An index number measures how a quantity changes over time relative to a chosen base period, which is set to 100. If a price index rises from 100 to 126, prices are up 26% since the base year. Index numbers compress the messy reality of thousands of changing prices into one readable trend.

This matters because index numbers run the economy's dashboard: inflation is the Consumer Price Index in motion, salaries and pensions are adjusted using them, and stock market indices tell investors the market's mood at a glance. Understanding how they are built protects you from misreading every economic headline.

Key Concepts

• Base year: the reference period assigned the value 100. All comparisons are "relative to base".
• Simple vs weighted indices: simple indices average price relatives equally; weighted indices give important items more influence via quantities.
• Laspeyres index: uses base-year quantities as weights — answers "what would the old basket cost today?"
• Paasche index: uses current-year quantities as weights — answers "what does today's basket cost versus then?"
• Fisher's ideal index: the geometric mean of Laspeyres and Paasche, √(L × P), balancing both perspectives.
• CPI and WPI: the Consumer Price Index tracks retail prices households pay; the Wholesale Price Index tracks bulk/business prices.

Formulas

• Laspeyres: P₀₁ = (Σ p₁q₀ / Σ p₀q₀) × 100, where p₀, q₀ are base-year prices and quantities, p₁ current prices.
• Paasche: P₀₁ = (Σ p₁q₁ / Σ p₀q₁) × 100, using current-year quantities q₁ as weights.
• Fisher: F = √(Laspeyres × Paasche).
• Inflation rate: ((Index this year − Index last year) / Index last year) × 100.

Assumptions and limits: the basket of goods is fixed and representative, quality is unchanged, and the base year is a "normal" year — none of which holds perfectly in practice.

Worked Example

Two goods. Base year: prices ₹10 and ₹20, quantities 5 and 4. Current year: prices ₹12 and ₹26, quantities 6 and 5. Compute the Laspeyres price index.

1. Base-year basket cost (then): 10 × 5 + 20 × 4 = 50 + 80 = 130.
2. Base-year basket cost (now): 12 × 5 + 26 × 4 = 60 + 104 = 164.
3. Index: (164 / 130) × 100 = 1.2615 × 100 = 126.15.
4. Interpretation: prices rose about 26.15% since the base year for this basket.
5. Paasche for contrast: (12×6 + 26×5)/(10×6 + 20×5) × 100 = (72+130)/(60+100) × 100 = 202/160 × 100 = 126.25 — nearly identical here.

Common Misconceptions

• An index is not an absolute price level. "CPI = 126" is meaningless alone — it only says prices are 26% above the base year.
• The base year choice matters. Rebasing to a boom year versus a recession year changes every growth story built on the index.
• Quality change is invisible to indices. If a phone costs the same but is twice as good, a fixed-basket index records zero change — a known upward bias in inflation measures.

Real-World Applications

• Inflation tracking: central banks set interest rates watching the CPI.
• Wage contracts: dearness allowance for government employees is linked to the CPI.
• Stock markets: indices like the Nifty 50 and Sensex are weighted index numbers of share prices.
• Business planning: firms deflate nominal sales by a price index to see real volume growth.

Index numbers turn "prices went up" into "prices went up 26.15% since 2020" — precise, comparable, and actionable. Laspeyres, Paasche, and Fisher are just three honest ways to weight the basket, and knowing which one a headline uses tells you how much to trust it.