Chapter Overview
🧭Your visual roadmap through the chapter
Index Numbers
Base periods, price/quantity/value indices
Unweighted & Weighted Indices
Simple, Laspeyre, Paasche & Fisher methods
Inflation, Purchasing Power & Wages
CPI, inflation rate, real vs nominal values
Index numbers are statistical devices used to measure changes in price, quantity or value over time, relative to a chosen base period.
Indices (like the CPI) drive real-world decisions on inflation, wages, purchasing power and government economic policy.
Construct simple, Laspeyre, Paasche and Fisher indices; calculate CPI, inflation rate, purchasing power, and real vs nominal wages/GDP.
Key Definitions
📘Source-based terminology, exam-ready
Index Number
A statistical device used to express the relationship between quantitative variables, often as a measure of fluctuation in the economy.
Key word: relative measure
Base Period
The reference period (usually given a value of 100 or 1,000) against which all other periods are compared.
Key word: reference = 100
Price / Quantity / Value Index
Price: change in price of goods/services. Quantity: change in volume. Value: change in total value (price × quantity).
Key word: price, volume, or both
Unweighted vs Weighted Index
Unweighted: equal importance to each item. Weighted: relative importance/significance of each item is factored in.
Key word: equal vs relative importance
Consumer Price Index (CPI)
Measures the cost of a "typical" consumer basket of goods/services at a point in time, compared to the base year.
Key word: cost of living
Inflation / Deflation
Inflation: general increase in prices (money buys less). Deflation: general decrease in prices (money buys more).
Key word: prices up/down
Purchasing Power
The reciprocal of the CPI (×100); the real value of money given current prices. Inversely related to the CPI.
Key word: 1/CPI × 100
Nominal vs Real Wages
Nominal (money) wage: amount earned in current rupees, ignoring inflation. Real wage: what that money can actually buy after inflation.
Key word: earned vs buying power
Core Concept
🎯Explained in exam-oriented language
CONCEPT → Index Numbers
MEANING
A base value (usually 100) against which every other period's value is compared.
PURPOSE
Judge past changes and forecast future values for price, quantity or value.
APPLICATION
CPI, stock market indices, GDP deflators, wage/salary adjustments.
CONCEPT → Weighting (Laspeyre vs Paasche)
MEANING
Different items matter differently; weighting reflects each item's real importance in the basket.
PURPOSE
Avoid distortion from treating all items as equally significant.
APPLICATION
Laspeyre uses base-year quantities; Paasche uses current-year quantities as weights.
Key Rules & Principles
📏Every source rule, exam-ready
RULE 1 Selecting the base period
Should not be too far in the past
Should reflect stability within the variables (free from abnormalities like earthquakes, lockouts)
RULE 4 Laspeyre vs Paasche bias
Laspeyre tends to OVERSTATE inflation (ignores consumers buying less of items that got pricier)
Paasche tends to UNDERSTATE inflation (biased to cheaper substitute items)
Laspeyre needs less new data each year, so it's used more in practice
RULE 2 Fixed base vs Chain base method
Fixed base: one base year stays unchanged throughout
Chain base: base period moves year to year; results are "link relatives", later converted back to a fixed base to give the chain index
RULE 5 Fisher's ideal index
Fisher index = geometric mean of the Laspeyre and Paasche indices
Balances both indices' baskets (base period AND current period)
RULE 3 Rebasing an index
Divide the existing index number in each year by the index number of the new base year, then ×100
Rebasing never changes the underlying story — only how it's expressed
RULE 6 CPI, inflation & purchasing power links
CPI rises → inflation; CPI falls → deflation
Purchasing power is inversely proportional to the CPI
GDP deflator (Nominal GDP÷Real GDP) is a broader measure of inflation than CPI
Formula Zone — Simple (Unweighted) Indices
🧮Every formula supported by the source text
SIMPLE PRICE INDEX & SIMPLE QUANTITY INDEX
p0/q0=base period price/quantity, p1/q1=current period. For a single item only.
SIMPLE AGGREGATE PRICE INDEX
Sum of current-period prices ÷ sum of base-period prices, for a group of items. Ignores relative importance of items.
AVERAGE OF PRICE RELATIVES
K=number of commodities. Changes in measuring units do not affect this index's value.
Composite Price Index — the two families
Unweighted: Simple Aggregative Method; Average of Relatives Method.
Weighted: Weighted Aggregative Method (Laspeyre/Paasche/Fisher); Average of Weighted Relatives Method.
Formula Zone — Weighted Price Indices
🧮Every formula supported by the source text
LASPEYRE PRICE INDEX
Σ(p1×q0) ÷ Σ(p0×q0) × 100
Uses BASE year quantities (q0) as weights. The usual/default weighted price index.
PAASCHE PRICE INDEX
Σ(p1×q1) ÷ Σ(p0×q1) × 100
Uses CURRENT year quantities (q1) as weights — must be recollected every year.
FISHER PRICE INDEX (IDEAL INDEX)
The geometric mean of the Laspeyre and Paasche price indices.
AVERAGE OF WEIGHTED RELATIVES
P=price relative (p1/p0×100), w=weight assigned, Pw=P×w for each item.
Formula Zone — Quantity Indices
🧮Every formula supported by the source text
LASPEYRE QUANTITY INDEX
Σ(p0×q1) ÷ Σ(p0×q0) × 100
Uses BASE year price levels (p0) as weights.
PAASCHE QUANTITY INDEX
Σ(p1×q1) ÷ Σ(p1×q0) × 100
Uses CURRENT price levels (p1) as weights.
FISHER QUANTITY INDEX (IDEAL INDEX)
The geometric mean of the Laspeyre and Paasche quantity indices.
CHAIN INDEX
Link Relative = (value in current period ÷ value in previous period)×100. Used to monitor and forecast trends.
Formula Zone — Cpi, Inflation, Purchasing Power & Wages
🧮Every formula supported by the source text
CONSUMER PRICE INDEX (CPI)
Other methods: Family Budget Method (ΣPw/w); Expenditure Method (Σ(p1q0)/Σ(p0q0)×100).
INFLATION RATE
CPI rising = inflation; CPI falling = deflation.
PURCHASING POWER
Inversely related to the CPI — as CPI rises, purchasing power falls.
REAL GDP & GDP DEFLATOR
GDP deflator is a broader measure of inflation than the CPI.
REAL WAGE EQUIVALENCE
Used to find the equivalent (inflation-adjusted) wage needed in the current period, e.g. for a dearness allowance.
Calculation Roadmap
🗺️General path for any index question
1· Read Question
Identify base & current period data
2· Identify Index Type
Simple, Laspeyre, Paasche, Fisher, CPI...?
3· Select Formula
Match weights (q0 or q1; p0 or p1)
4· Substitute
Put known values into the formula
5· Calculate & Interpret
Solve, state % change, final answer
Step-by-step Methods
🪜Kept separate — do not mix methods
METHOD A · Simple/Aggregate Price Index
- 1Identify base-period and current-period prices
- 2Single item: divide current by base, ×100
- 3Multiple items (unweighted): sum current prices, sum base prices, divide, ×100
- 4State the % change from the index value
METHOD D · Chain Index
- 1Calculate each year's link relative vs the PREVIOUS year
- 2Year 1's chain index = its relative index (base = 100)
- 3Each subsequent chain index = (this year's relative × last year's chain index)÷100
- 4Continue year by year to build the full chain series
METHOD B · Laspeyre / Paasche Index
- 1Tabulate p0, q0, p1, q1 for every item
- 2Laspeyre: compute p1×q0 and p0×q0 columns
- 3Paasche: compute p1×q1 and p0×q1 columns instead
- 4Sum each column, divide, ×100
METHOD E · CPI & Inflation Rate
- 1Total the basket's cost in the base year and in each other year
- 2CPI = (current basket cost ÷ base basket cost)×100 for each year
- 3Inflation rate = (CPI2−CPI1)÷CPI1 ×100 between any two years
- 4Positive = inflation; negative = deflation
METHOD C · Fisher Index
- 1Calculate the Laspeyre index for the same data
- 2Calculate the Paasche index for the same data
- 3Multiply the two index values together
- 4Take the square root for the Fisher (ideal) index
METHOD F · Purchasing Power / Real Wage / Real GDP
- 1Purchasing power: substitute the CPI into PP=(1/CPI)×100
- 2Real wage: solve Wagebase/CPIbase=Wagecurrent/CPIcurrent for the unknown
- 3Real GDP: multiply current-year quantities by BASE-year prices
- 4GDP deflator = Nominal GDP÷Real GDP; convert to an index/% for inflation
Different Cases / Scenarios
🔀Recognise what's given, pick the right index
IF only one item/commodity is involved
→ USE a simple price/quantity index
IF multiple items, all treated as equally important
→ USE the simple aggregative or average of relatives method
IF weights are BASE-year quantities
→ USE the Laspeyre index
IF weights are CURRENT-year quantities
→ USE the Paasche index
IF asked for the "ideal" index balancing both periods
→ USE the Fisher index (√Laspeyre×Paasche)
IF the base period should move forward each year
→ USE the chain base method
IF measuring a household's cost of living over time
→ USE the CPI
IF asked what money can actually buy, or a wage's real value
→ USE purchasing power or the real wage formula
Comparison Tables
⚖️Don't confuse these!
| Laspeyre Index | Paasche Index | Fisher Index | |
|---|---|---|---|
| Quantity weights used | Base year (q0) | Current year (q1) | Both (geometric mean) |
| Inflation bias | Tends to overstate | Tends to understate | Balances both biases |
| Data needed each year | Only new prices | New prices AND new quantities | Both indices' full data |
| Used in practice | Most common (less data needed) | Less common | Considered the "ideal" but data-heavy |
| Fixed Base Method | Chain Base Method | |
|---|---|---|
| Base period | One year, unchanged throughout | Moves year to year (previous year is base) |
| Result | Direct index number | "Link relatives", converted to a chain index |
| Nominal Value | Real Value | |
|---|---|---|
| Wages | Money actually earned (current Rs.) | What that money can actually buy after inflation |
| GDP | Current-year prices × current-year quantities | Base-year prices × current-year quantities |
Worked Calculation Logic
✍️Method students must reproduce in the exam
LASPEYRE PRICE INDEX: GIVEN → FORMULA → SUBSTITUTION → ANSWER
A basket of 4 materials: Σ(p0×q0)=21.0, Σ(p1×q0)=25.0.
GIVEN: Σ(p1q0)=25.0, Σ(p0q0)=21.0
FORMULA: Laspeyre = Σ(p1q0)÷Σ(p0q0)×100
SUBSTITUTION: = 25.0÷21.0×100
ANSWER: Laspeyre index = 119.04 → prices have risen 19.04%
PURCHASING POWER: GIVEN → FORMULA → SUBSTITUTION → ANSWER
The CPI in a given year is 140 (base year = 100). Find the purchasing power of the rupee.
GIVEN: CPI = 140
FORMULA: PP = (1÷CPI)×100
SUBSTITUTION: PP = (1÷140)×100
ANSWER: PP = 0.71 → the rupee now buys only 71% of what it did in the base year
REAL WAGE / DEARNESS ALLOWANCE: GIVEN → FORMULA → SUBSTITUTION → ANSWER
In 1980 an employee's wage was Rs. 1,200 when CPI was 180. CPI rose to 220 in 1982. Find the wage needed to keep the employee's purchasing power unchanged.
GIVEN: Wage1980=1,200, CPI1980=180, CPI1982=220
FORMULA: Wage1980÷CPI1980 = Wage1982÷CPI1982
SUBSTITUTION: Wage1982 = 1,200×220÷180 = 1,467
ANSWER: Additional dearness allowance = 1,467−1,200 = Rs. 267
INFLATION RATE: GIVEN → FORMULA → SUBSTITUTION → ANSWER
CPI was 120.18 in one year and 112.79 the next. Find the rate of inflation/deflation.
GIVEN: CPI1=120.18, CPI2=112.79
FORMULA: Inflation Rate = [(CPI2−CPI1)÷CPI1]×100
SUBSTITUTION: = [(112.79−120.18)÷120.18]×100
ANSWER: −6.15% → this is deflation (prices fell)
Exam Question Patterns
📝Simple index calculation — single item, or unweighted aggregate
Laspeyre/Paasche/Fisher — construct and compare weighted indices
Chain index — building a series year by year
CPI & inflation rate — direct calculation and interpretation
Purchasing power / real wage / real GDP — adjusting for inflation
Conceptual — uses/limitations of index numbers, base period selection
Exam Traps
⚠️⚠ WATCH OUT
- ✗ Laspeyre vs Paasche mix-up — check whether q0 (base) or q1 (current) weights are used.
- ✗ Forgetting the ×100 at the end of an index calculation.
- ✗ CPI vs purchasing power direction — they move inversely; don't apply the wrong formula.
- ✗ Nominal vs real confusion — always check whether inflation has been removed.
- ✗ Chain index errors — using the WRONG previous year's chain index in the next link.
Quick Decision Tree
🌳Chapter 9 in 60 Seconds
⚡Simple index: p1/p0×100
Laspeyre: Σ(p1q0)/Σ(p0q0)×100
Paasche: Σ(p1q1)/Σ(p0q1)×100
Fisher: √(Laspeyre×Paasche)
CPI: current basket/base basket×100
Inflation: (CPI2−CPI1)/CPI1×100 PP = (1/CPI)×100
Trap: Laspeyre overstates, Paasche understates inflation
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