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Index Numbers

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Chapter Notes

Overview
This chapter introduces index numbers as a statistical device for measuring relative changes in a group of related variables, such as prices, quantities, or production. It exists in the syllabus to equip students with the tools to understand and calculate widely used indices like the Consumer Price Index (CPI), Wholesale Price Index (WPI), and Index of Industrial Production (IIP). The one big idea a student must walk away with is that an index number summarizes the average change in a set of variables over time, expressed as a percentage relative to a base period, and is indispensable for economic policy-making and everyday decision-making.
Key Concepts (22)
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.
e.g. The Consumer Price Index (CPI) measures the average change in retail prices of a fixed basket of goods and services consumed by a specific group, like industrial workers.
Base Period
The period with which the comparison is to be made is known as the base period. The value in the base period is given the index number 100.
e.g. If we want to compare prices in 2005 with prices in 1990, then 1990 is the base period and its index number is set to 100.
Price Index Number
Price index numbers measure and permit comparison of the prices of certain goods.
e.g. The Wholesale Price Index (WPI) measures the change in the general price level at the wholesale level.
Quantity Index Number
Quantity index numbers measure the changes in the physical volume of production, construction or employment.
e.g. The Index of Industrial Production (IIP) measures changes in the physical volume of production in the industrial sector.
Simple Aggregative Price Index
A price index computed by the aggregative method using the formula P01 = (ΣP1 / ΣP0) × 100, where P1 and P0 are prices in the current and base periods respectively.
e.g. Using data from Example 1, the simple aggregative price index is (4+6+5+3)/(2+5+4+2) × 100 = 138.5, indicating a 38.5% rise in prices.
Weighted Aggregative Price Index
An index number that takes into account the relative importance of items by using weights, typically quantities. The formula is P01 = (ΣP1q0 / ΣP0q0) × 100 for Laspeyre's index.
e.g. In Example 2, the weighted aggregative price index using base period quantities is (4×10 + 6×12 + 5×20 + 3×15) / (2×10 + 5×12 + 4×20 + 2×15) × 100 = 135.3.
Laspeyre's Price Index
A weighted aggregative price index using base period quantities as weights. Formula: P01 = (ΣP1q0 / ΣP0q0) × 100.
e.g. In Example 2, Laspeyre's index is 135.3, meaning the expenditure on the base period basket has risen by 35.3% due to price rise.
Paasche's Price Index
A weighted aggregative price index using current period quantities as weights. Formula: P01 = (ΣP1q1 / ΣP0q1) × 100.
e.g. In Example 2, Paasche's index is 132.1, indicating a price rise of 32.1% using current period weights.
Method of Averaging Relatives (Unweighted)
A method of constructing an index number by taking the arithmetic mean of price relatives. Formula: P01 = (1/n) × Σ(P1/P0 × 100).
e.g. Using data from Example 1, the unweighted price index is (1/4) × (200 + 120 + 125 + 150) = 149, indicating a 49% rise.
Weighted Index of Price Relatives
The weighted arithmetic mean of price relatives, where weights are determined by the proportion of expenditure on items. Formula: P01 = (ΣW × (P1/P0 × 100)) / ΣW.
e.g. In Example 3, the weighted price index is (40×200 + 30×120 + 20×125 + 10×150) / 100 = 156, a 56% rise.
Consumer Price Index (CPI)
Also known as the cost of living index, CPI measures the average change in retail prices of a fixed basket of goods and services consumed by a specific group of consumers.
e.g. If CPI for industrial workers (2001=100) is 277 in December 2014, it means a worker spending Rs 100 in 2001 needs Rs 277 in 2014 to buy the same basket.
Wholesale Price Index (WPI)
An index that indicates the change in the general price level at the wholesale level. It does not have any reference consumer category and includes only prices of goods, not services.
e.g. WPI with 2004-05 as base is 253 in October 2014, meaning the general price level has risen by 153% during this period.
Index of Industrial Production (IIP)
A quantity index that measures changes in the physical volume of production in the industrial sector. It is a weighted arithmetic mean of quantity relatives using Laspeyre's formula.
e.g. IIP with base 2011-12 = 100, with sectors like Mining (14.4% weight), Manufacturing (77.6%), and Electricity (8.0%).
Human Development Index (HDI)
An index widely used to know the development of a country, based on indicators like life expectancy, education, and per capita income.
e.g. HDI is used to rank countries based on their level of human development.
SENSEX
The short form of Bombay Stock Exchange Sensitive Index with 1978–79 as base. It is the benchmark index for the Indian stock market, consisting of 30 stocks representing 13 sectors.
e.g. If Sensex rises, it indicates that the market is doing well and investors expect better earnings from companies.
Price Relative
The ratio (P1/P0) × 100, also referred to as the price relative of the commodity.
e.g. For commodity A in Example 1, price relative = (4/2) × 100 = 200.
Inflation
A general and continuing increase in prices. It is often measured using the Wholesale Price Index (WPI) or Consumer Price Index (CPI).
e.g. The weekly inflation rate is given by ((X_t - X_{t-1}) / X_{t-1}) × 100, where X_t and X_{t-1} refer to WPI for consecutive weeks.
Purchasing Power of Money
The amount of goods and services that can be bought with a unit of money. It is inversely related to the cost of living index: Purchasing power of money = 1 / Cost of living index.
e.g. If CPI (1982=100) is 526 in January 2005, the purchasing power of Rs 1 in 2005 is Rs 100/526 = Rs 0.19, i.e., 19 paise in 1982 terms.
Real Wage
The wage adjusted for changes in the price level, calculated as: Real wage = (Money wage / Cost of living index) × 100.
e.g. If money wage is Rs 10,000 and CPI is 526, real wage = (10,000 / 526) × 100 = Rs 1,901 in 1982 terms.
Headline Inflation
The 'All Commodities Inflation Rate' based on the Wholesale Price Index (WPI), often referred to as headline inflation.
e.g. The WPI 'All Commodities' group has a weight of 100% and its inflation rate is called headline inflation.
Core Inflation
Inflation measured by focusing on wholesale prices in manufactured goods, excluding food articles and fuel. It makes up around 55% of the total weight of the WPI.
e.g. Economists study core inflation to understand underlying price trends excluding volatile food and energy prices.
Consumer Food Price Index (CFPI)
Same as the Consumer Price Index for 'Food and Beverages' except it does not include alcoholic beverages and prepared meals, snacks, sweets, etc.
e.g. CFPI is used to track food price inflation specifically.
Formulas & Equations (10)
P01 = (ΣP1 / ΣP0) × 100
Reads as: P zero one equals sum of P1 divided by sum of P0, multiplied by 100
Variables: P01 = simple aggregative price index; ΣP1 = sum of prices of commodities in the current period; ΣP0 = sum of prices of commodities in the base period
Use when: Use when constructing a simple aggregative price index without considering weights.
⚠ Students forget to multiply by 100, or they use the formula for weighted index without weights.
P01 = (ΣP1q0 / ΣP0q0) × 100
Reads as: P zero one equals sum of P1 times q0 divided by sum of P0 times q0, multiplied by 100
Variables: P01 = Laspeyre's price index; P1 = current period price; P0 = base period price; q0 = base period quantity
Use when: Use when constructing a weighted aggregative price index using base period quantities as weights (Laspeyre's index).
⚠ Students confuse q0 with q1, or forget to multiply by 100.
P01 = (ΣP1q1 / ΣP0q1) × 100
Reads as: P zero one equals sum of P1 times q1 divided by sum of P0 times q1, multiplied by 100
Variables: P01 = Paasche's price index; P1 = current period price; P0 = base period price; q1 = current period quantity
Use when: Use when constructing a weighted aggregative price index using current period quantities as weights (Paasche's index).
⚠ Students mix up Laspeyre's and Paasche's formulas, especially which quantities to use as weights.
P01 = (1/n) × Σ(P1/P0 × 100)
Reads as: P zero one equals one over n times the sum of P1 over P0 times 100
Variables: P01 = unweighted price index using method of averaging relatives; n = number of commodities; P1 = current period price; P0 = base period price
Use when: Use when constructing an unweighted price index by averaging price relatives.
⚠ Students forget to multiply each price relative by 100 before averaging, or they use weighted formula without weights.
P01 = (ΣW × (P1/P0 × 100)) / ΣW
Reads as: P zero one equals sum of W times P1 over P0 times 100, divided by sum of W
Variables: P01 = weighted price index of relatives; W = weight (e.g., percentage of expenditure); P1 = current period price; P0 = base period price
Use when: Use when constructing a weighted price index using price relatives and weights based on expenditure shares.
⚠ Students forget to multiply the price relative by 100 before weighting, or they use incorrect weights.
CPI = (ΣWR) / ΣW
Reads as: CPI equals sum of W times R divided by sum of W
Variables: CPI = Consumer Price Index; W = weight in percentage; R = price relative (P1/P0 × 100)
Use when: Use when constructing a consumer price index from given weights and price relatives.
⚠ Students forget that R = (P1/P0) × 100, not just P1/P0.
IIP01 = (Σ(q_i1 / q_i0) × W_i) / ΣW_i × 100
Reads as: IIP zero one equals sum of quantity relative times weight divided by sum of weight, multiplied by 100
Variables: IIP01 = Index of Industrial Production; q_i1 = quantity in current year; q_i0 = quantity in base year; W_i = weight allotted to good i
Use when: Use when calculating the Index of Industrial Production using Laspeyre's formula with quantity relatives.
⚠ Students forget to multiply by 100, or they use price relatives instead of quantity relatives.
Inflation rate = ((X_t - X_{t-1}) / X_{t-1}) × 100
Reads as: Inflation rate equals X_t minus X_{t-1} divided by X_{t-1}, multiplied by 100
Variables: X_t = WPI for the tth week; X_{t-1} = WPI for the (t-1)th week
Use when: Use when calculating the weekly inflation rate using WPI data.
⚠ Students forget to multiply by 100, or they use CPI instead of WPI when the formula specifies WPI.
Purchasing power of money = 1 / Cost of living index
Reads as: Purchasing power of money equals 1 divided by cost of living index
Variables: Cost of living index = CPI or similar index
Use when: Use when calculating how much a unit of currency is worth in terms of base period purchasing power.
⚠ Students forget that the result is a fraction and needs to be interpreted as a proportion of the base period value.
Real wage = (Money wage / Cost of living index) × 100
Reads as: Real wage equals money wage divided by cost of living index, multiplied by 100
Variables: Money wage = current salary; Cost of living index = CPI or similar index
Use when: Use when calculating the real value of a wage adjusted for inflation.
⚠ Students forget to multiply by 100, or they divide the cost of living index by money wage instead.
How It Works
Construction of a Simple Aggregative Price Index
  1. Step 1: Select the commodities and collect their prices in the base period (P0) and current period (P1).
  2. Step 2: Sum the prices of all commodities for the base period (ΣP0) and for the current period (ΣP1).
  3. Step 3: Apply the formula P01 = (ΣP1 / ΣP0) × 100.
  4. Step 4: Interpret the result — a value greater than 100 indicates a price rise, less than 100 indicates a price fall.
💡 This method is unweighted and treats all commodities equally, which is a limitation because it ignores the relative importance of items.
Construction of a Weighted Aggregative Price Index (Laspeyre's Index)
  1. Step 1: Select commodities and collect base period prices (P0), base period quantities (q0), and current period prices (P1).
  2. Step 2: Calculate ΣP1q0 by multiplying each current price by its base period quantity and summing.
  3. Step 3: Calculate ΣP0q0 by multiplying each base price by its base period quantity and summing.
  4. Step 4: Apply the formula P01 = (ΣP1q0 / ΣP0q0) × 100.
  5. Step 5: Interpret — it answers: if expenditure on base period basket was Rs 100, how much is it now?
💡 Laspeyre's index uses base period quantities as weights, so it does not account for changes in consumption patterns.
Construction of a Weighted Aggregative Price Index (Paasche's Index)
  1. Step 1: Select commodities and collect base period prices (P0), current period prices (P1), and current period quantities (q1).
  2. Step 2: Calculate ΣP1q1 by multiplying each current price by its current period quantity and summing.
  3. Step 3: Calculate ΣP0q1 by multiplying each base price by its current period quantity and summing.
  4. Step 4: Apply the formula P01 = (ΣP1q1 / ΣP0q1) × 100.
  5. Step 5: Interpret — it answers: if current period basket was bought in base period, what would it cost now?
💡 Paasche's index uses current period quantities as weights, so it reflects current consumption patterns but requires data on current quantities, which is harder to obtain.
Construction of an Index Using the Method of Averaging Relatives (Unweighted)
  1. Step 1: For each commodity, calculate the price relative: (P1/P0) × 100.
  2. Step 2: Sum all the price relatives.
  3. Step 3: Divide the sum by the number of commodities (n).
  4. Step 4: The result is the unweighted price index.
💡 This method gives equal importance to each commodity, regardless of its economic significance.
Construction of a Weighted Index of Price Relatives
  1. Step 1: For each commodity, calculate the price relative: (P1/P0) × 100.
  2. Step 2: Multiply each price relative by its weight (W), where weights are typically expenditure shares in the base period.
  3. Step 3: Sum the weighted price relatives (ΣW × (P1/P0 × 100)).
  4. Step 4: Divide by the sum of weights (ΣW).
  5. Step 5: The result is the weighted price index.
💡 Weights must sum to 100 if using percentages, or to the total expenditure if using absolute values.
Construction of a Consumer Price Index (CPI)
  1. Step 1: Select a basket of goods and services representative of the consumption pattern of a specific group (e.g., industrial workers).
  2. Step 2: Assign weights to each item based on the proportion of total expenditure on that item.
  3. Step 3: Collect base period prices and current period prices for all items.
  4. Step 4: Calculate price relatives for each item: R = (P1/P0) × 100.
  5. Step 5: Multiply each price relative by its weight: WR.
  6. Step 6: Sum all WR values and divide by the sum of weights: CPI = ΣWR / ΣW.
  7. Step 7: Interpret — if CPI > 100, cost of living has risen; if CPI < 100, it has fallen.
💡 CPI is also called the cost of living index and is used for wage negotiations and inflation measurement.
Calculation of Real Wage and Purchasing Power of Money
  1. Step 1: Obtain the Consumer Price Index (CPI) for the current period.
  2. Step 2: To find purchasing power of money: Purchasing power = 1 / CPI (as a decimal). For example, if CPI = 526, purchasing power of Re 1 = 1/5.26 = Rs 0.19 in base year terms.
  3. Step 3: To find real wage: Real wage = (Money wage / CPI) × 100.
  4. Step 4: Interpret — real wage tells you the equivalent wage in base period purchasing power.
💡 A higher CPI means lower purchasing power of money and lower real wage for a given money wage.
Exam Traps — Don't Make These Mistakes
⚠ Confusing Laspeyre's and Paasche's formulas
✗ Students write P01 = (ΣP1q1 / ΣP0q0) × 100 or mix up the quantities, using q1 in Laspeyre's and q0 in Paasche's.
→ Laspeyre's uses base period quantities (q0) as weights, while Paasche's uses current period quantities (q1). Using the wrong quantities gives an incorrect index.
✓ For Laspeyre's: P01 = (ΣP1q0 / ΣP0q0) × 100. For Paasche's: P01 = (ΣP1q1 / ΣP0q1) × 100.
⚠ Forgetting to multiply by 100 in index number formulas
✗ Students write P01 = ΣP1 / ΣP0 without multiplying by 100, giving a decimal instead of a percentage.
→ Index numbers are conventionally expressed in terms of percentage, with the base period value set to 100. Omitting the multiplication by 100 gives a ratio, not an index number.
✓ Always write P01 = (ΣP1 / ΣP0) × 100, and similarly for all index formulas.
⚠ Misinterpreting the meaning of CPI and WPI
✗ Students write that CPI measures wholesale prices or that WPI measures retail prices for a specific consumer group.
→ CPI measures retail prices for a specific consumer group (e.g., industrial workers), while WPI measures wholesale prices and does not have a reference consumer category.
✓ CPI measures changes in retail prices for a specific basket of goods consumed by a particular group. WPI measures changes in the general price level at the wholesale level, including only goods, not services.
⚠ Using price relatives without multiplying by 100 in weighted index
✗ Students use P1/P0 directly in the weighted index formula without multiplying by 100, e.g., P01 = (ΣW × (P1/P0)) / ΣW.
→ The price relative is defined as (P1/P0) × 100. Using P1/P0 gives a decimal, not the correct index number.
✓ Use P01 = (ΣW × (P1/P0 × 100)) / ΣW.
⚠ Confusing price index with quantity index
✗ Students use price data to calculate a quantity index, or use quantity data to calculate a price index, without understanding the purpose.
→ Price index measures changes in prices, while quantity index measures changes in physical volume. The formulas differ: price index uses prices, quantity index uses quantities (or quantity relatives).
✓ For price index, use prices and appropriate weights. For quantity index like IIP, use quantity relatives: IIP01 = (Σ(q_i1/q_i0) × W_i) / ΣW_i × 100.
⚠ Assuming all index numbers are comparable across different base years
✗ Students directly compare index numbers with different base years, e.g., comparing CPI with base 1982=100 to CPI with base 2012=100.
→ Index numbers with different base years are not directly comparable because the base period values, baskets of goods, and weights may differ. The base year is routinely updated.
✓ To compare, convert all indices to a common base year using the formula: New index = (Old index / Old base year index) × New base year index value.
Compare & Contrast
Weights used in the formula
Laspeyre's Price Index
Paasche's Price Index
Laspeyre's index uses base period quantities (q0) as weights, while Paasche's index uses current period quantities (q1) as weights.
Level of prices measured
Consumer Price Index (CPI)
Wholesale Price Index (WPI)
CPI measures changes in retail prices for a specific consumer group (e.g., industrial workers), while WPI measures changes in the general price level at the wholesale level and does not have a reference consumer category.
What is being measured
Price Index
Quantity Index
A price index measures changes in the prices of goods or services over time, while a quantity index measures changes in the physical volume of production, construction, or employment.
Consideration of relative importance
Simple Aggregative Price Index
Weighted Aggregative Price Index
A simple aggregative index treats all commodities as equally important (unweighted), while a weighted aggregative index assigns weights to reflect the relative importance of each commodity.
Exam Focus
Marks pattern: This chapter typically appears with 2 MCQs (1 mark each), 1 short answer question (3 marks) on formula or interpretation, and 1 long answer question (5 marks) involving calculation of an index number or comparison of indices.
Most asked: Calculation and interpretation of Laspeyre's and Paasche's price indices · Construction and use of Consumer Price Index (CPI) · Difference between price index and quantity index · Uses of index numbers in economic policy (inflation, real wage, purchasing power) · Issues in construction of index numbers (choice of base period, selection of items, choice of formula)
Don't skip: Numerical problems on calculating Laspeyre's, Paasche's, and weighted price relatives index; Questions on the meaning and interpretation of CPI and WPI; Application of index numbers to calculate real wage and purchasing power of money
One-Line Revision (read aloud before the exam)
  1. An index number is a statistical device for measuring relative changes in a group of related variables, expressed as a percentage with the base period set to 100.
  2. The base period is the period with which comparison is made, and it should be as normal as possible and not too far in the past.
  3. Price index numbers measure changes in prices, while quantity index numbers measure changes in physical volume of production or employment.
  4. Simple aggregative price index is calculated as (ΣP1 / ΣP0) × 100, but it is unweighted and of limited use.
  5. Laspeyre's price index uses base period quantities as weights: P01 = (ΣP1q0 / ΣP0q0) × 100.
  6. Paasche's price index uses current period quantities as weights: P01 = (ΣP1q1 / ΣP0q1) × 100.
  7. The method of averaging relatives calculates the average of price relatives: P01 = (1/n) × Σ(P1/P0 × 100).
  8. Weighted index of price relatives uses expenditure shares as weights: P01 = (ΣW × (P1/P0 × 100)) / ΣW.
  9. Consumer Price Index (CPI) measures changes in retail prices for a specific consumer group and is also called the cost of living index.
  10. Wholesale Price Index (WPI) measures changes in the general price level at the wholesale level and includes only goods, not services.
  11. Index of Industrial Production (IIP) is a quantity index measuring changes in industrial output using Laspeyre's formula with quantity relatives.
  12. SENSEX is the benchmark index of the Bombay Stock Exchange, consisting of 30 stocks representing 13 sectors, with base 1978-79.
  13. Inflation is a general and continuing increase in prices, often measured using WPI or CPI.
  14. Purchasing power of money = 1 / Cost of living index; as CPI rises, purchasing power falls.
  15. Real wage = (Money wage / Cost of living index) × 100; it shows the actual purchasing power of a wage.
  16. Key issues in constructing an index number include: clear purpose, selection of representative items, choice of a normal base year, choice of formula, and reliability of data.
  17. Index numbers are indispensable in economic policy making, including wage negotiation, inflation measurement, and investment decisions.

MCQs — 10 Questions with Answers

Q1. An index number of 200 means:

  • A. The value has doubled from the base period ✓
  • B. There is a 200% increase from base period
  • C. The value is 200 rupees
  • D. The base period value is 200

Answer: A — An index of 200 means the current value is 2 times (100% increase) the base value of 100.

Q2. Why is the simple aggregative price index considered of limited use?

  • A. It cannot measure inflation
  • B. It treats all commodities with equal weight despite different importance levels ✓
  • C. It requires more data than weighted indices
  • D. It only works for prices, not quantities

Answer: B — Simple aggregative index ignores relative importance of items; food price rise affects common people more than luxury items, but the method counts both equally.

Q3. In a weighted aggregative price index, weights are typically:

  • A. Always equal to 1
  • B. Prices of commodities
  • C. Quantities consumed or produced ✓
  • D. Fixed numerical values like 2, 3, 4

Answer: C — In weighted aggregative indices, weights represent quantities (q₀ for Laspeyre's or q₁ for Paasche's) to reflect importance of each item.

Q4. If base period expenditure was Rs 100 and current period index is 120, the current period expenditure on the same basket is:

  • A. Rs 100
  • B. Rs 120 ✓
  • C. Rs 20
  • D. Cannot be determined

Answer: B — Index of 120 means current value is 120% of base, so if base was Rs 100, current is 100 × 1.20 = Rs 120.

Q5. Laspeyre's price index uses _______ as weights, while Paasche's uses _______:

  • A. Current period quantities; base period quantities
  • B. Base period quantities; current period quantities ✓
  • C. Prices; quantities
  • D. Fixed weights; variable weights

Answer: B — Laspeyre's = (ΣP₁q₀)/(ΣP₀q₀) × 100 uses base weights; Paasche's = (ΣP₁q₁)/(ΣP₀q₁) × 100 uses current weights.

Q6. A worker's salary rose from Rs 1,000 in 1982 to Rs 12,000 today. His standard of living has increased 12 times because:

  • A. Nominal salary increased 12 times
  • B. The purchasing power may not have increased 12 times due to inflation ✓
  • C. Real wage must equal nominal wage
  • D. Inflation index is always 100

Answer: B — Nominal salary rose 12× but inflation (measured by price index) means goods cost much more; real purchasing power increase depends on cost of living index.

Q7. Which statement is INCORRECT regarding index numbers?

  • A. Base period always has index value of 100
  • B. Price index measures changes in inflation only, not quality changes ✓
  • C. Weighted indices are more realistic than unweighted indices
  • D. Paasche's index uses current period quantities as weights

Answer: B — Price index measures price changes but cannot measure quality changes; it assumes constant quality, which is a limitation.

Q8. Given: Base period prices = Rs 100, Current period prices = Rs 135. If base period quantities are 10 units each for 2 items, the weighted aggregative index is: (Assume prices per item remain proportional)

  • A. 135 ✓
  • B. 100
  • C. 120
  • D. Cannot be determined without exact item prices

Answer: A — Weighted aggregative = (ΣP₁q₀)/(ΣP₀q₀) × 100 = (135 × quantity)/(100 × quantity) × 100 = 135; the ratio of total prices gives the index regardless of specific quantities when proportions are equal.

Q9. The Sensex crossing 8,000 points indicates: (Assertion-Reason style)

  • A. Stock prices increased by 8,000% from base
  • B. The index value reached 8,000, showing value change from a base period benchmark ✓
  • C. Investors earned Rs 8,000 crores
  • D. Total stock value is exactly Rs 8,000

Answer: B — Sensex is an index number tracking 30 major company stocks; reaching 8,000 points means current index value is 8,000 from a defined base period (not percentage or rupee amount).

Q10. In India, if the CPI (Consumer Price Index) increased from 120 to 135 over one year, and a worker wants same purchasing power, his nominal salary should increase by approximately:

  • A. 12.5% ✓
  • B. 15%
  • C. 20%
  • D. 25%

Answer: A — CPI increased by (135-120)/120 × 100 = 12.5%; to maintain same purchasing power (real wage), nominal salary must rise by same percentage as inflation rate.

Flashcards

What is an index number?

A statistical device for measuring average changes in a group of related variables over two different situations, expressed as a percentage with base period = 100.

Why is simple aggregative price index of limited use?

It treats all commodities with equal importance regardless of their share in total expenditure, and ignores different units of measurement.

What is the formula for weighted aggregative price index using base period quantities?

P₀₁ = (ΣP₁q₀)/(ΣP₀q₀) × 100, also known as Laspeyre's price index.

How do you interpret an index number of 135?

The value has increased by 35% compared to the base period, or is 1.35 times the base value.

What is Laspeyre's price index and what question does it answer?

It uses base period quantities as weights; it answers if spending on the base period basket was Rs 100, how much should be spent in current period.

What is Paasche's price index?

A weighted aggregative price index using current period quantities as weights to show changing expenditure on current period basket.

Why do Laspeyre's and Paasche's indices give different values for the same data?

They use different period quantities as weights; Laspeyre's uses fixed base quantities while Paasche's uses changing current quantities.

How does an index number differ from a simple percentage change?

An index number measures average change across multiple related items, while percentage change applies to a single item only.

What does a price index number measure in the economy?

It measures and permits comparison of prices of specified goods, helping determine inflation and cost of living changes.

In India, how is the Sensex related to index numbers?

The Sensex is a stock market index number tracking changes in value of top 30 companies, with changes measured as points from a base value.

Important Board Questions

Define index number and give one example relevant to the Indian economy. [2 marks]

Define as statistical measure of average change with base = 100; example could be WPI, CPI, agricultural production index, or Sensex with brief context.

Calculate the weighted aggregative price index using Laspeyre's method from the following data: Commodity | Base Price (P₀) | Base Quantity (q₀) | Current Price (P₁) A | 10 | 5 | 12 B | 8 | 3 | 10 C | 6 | 4 | 7 Interpret the result. [5 marks]

Use formula P₀₁ = (ΣP₁q₀)/(ΣP₀q₀) × 100; calculate numerator = 12×5 + 10×3 + 7×4 = 118; denominator = 10×5 + 8×3 + 6×4 = 98; then interpret as percentage change.

Explain why a weighted aggregative price index is more useful than a simple aggregative price index in measuring inflation in India. Discuss the difference between Laspeyre's and Paasche's indices, and state which one is more commonly used and why. [6 marks]

Argument 1: Unweighted treats all items equally despite different consumption importance (food vs luxury); weighted reflects actual spending patterns. Argument 2: Laspeyre's (fixed base basket) easier to compute and understand, used in India's CPI; Paasche's reflects current consumption but needs frequent data updates; explain trade-offs between practicality and accuracy.

Assertion-Reason Questions for Index Numbers

Q1. Assertion (A):

An index number is conventionally expressed as a percentage with the base period assigned a value of 100.

Reason (R):

This convention allows all time periods to be directly comparable as proportional changes from the base period, making interpretation intuitive.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both the assertion and reason are true, and the reason correctly explains why this convention is used. The base of 100 makes it easy to interpret any index value as a percentage change directly.

Q2. Assertion (A):

A simple aggregative price index is limited in its usefulness for measuring overall price changes in an economy.

Reason (R):

It treats all commodities with equal weight regardless of their importance in household expenditure or production.

Answer: A — Both A and R are true, and R is the correct explanation of A — Both statements are true and the reason is the correct explanation. Food items with high expenditure share and luxury items with low share should not have equal impact on an inflation index. The reason directly supports the assertion.

Q3. Assertion (A):

Laspeyre's price index and Paasche's price index always give identical results for the same period comparison.

Reason (R):

Both indices use different quantity weights, leading to different values that measure different economic questions.

Answer: D — A is false but R is true — The assertion is false—as shown in Example 2, Laspeyre's gave 135.3 while Paasche's gave 132.1 for the same data. The reason is true and explains why they differ, but since the assertion is false, the answer is D.

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Case-Based Questions (CBQ) for Index Numbers

Case Study:

The Central Bureau of Health Intelligence constructs a Cost of Living Index for urban households in Delhi. In 2025, the index is based on a basket of goods comprising food, housing, and transport. The table below shows the weights and price relatives for 2025 with 2024 as base: Food (weight 50, price relative 120), Housing (weight 30, price relative 110), Transport (weight 20, price relative 105).

Q1. Using the given data, what is the weighted average of price relatives for the Cost of Living Index in 2025?

  • A. 112.5
  • B. 115.0
  • C. 116.5 ✓
  • D. 118.0

Answer: C

Q2. If the price relative for food had been 130 instead of 120, by how many points would the overall Cost of Living Index increase?

  • A. 5.0 points ✓
  • B. 10.0 points
  • C. 15.0 points
  • D. 20.0 points

Answer: A

Q3. A researcher argues that this index understates the true cost of living for low-income households. Which of the following is the MOST valid reason for this argument?

  • A. The index uses fixed weights that may not reflect the consumption pattern of low-income households ✓
  • B. The index uses 2024 as base year, which is too recent
  • C. The index includes transport but excludes medical expenses
  • D. The price relatives are calculated using current year quantities

Answer: A

Q4. Which of the following is a LIMITATION of using a fixed-weight index like this Cost of Living Index over a long period?

  • A. It can only be calculated using geometric mean
  • B. It requires data on prices from multiple countries
  • C. It does not allow for substitution by consumers when relative prices change ✓
  • D. It automatically adjusts for changes in quality of goods

Answer: C

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