Index Numbers: Concepts, Construction, Tests and Uses Questions

Question 1

What is Paasche price index based on?

Accepted Answer

Paasche price index uses current year quantities (q1) as weights.

Question 2

Define index number.

Accepted Answer

An index number is a statistical measure that shows the relative change in a variable or group of variables over time (base period usually = 100).

Question 3

What is a base year?

Accepted Answer

Base year is the reference period against which changes are compared (index in base year is taken as 100).

Question 4

Define CPI.

Accepted Answer

CPI (Consumer Price Index) measures change in the cost of living of consumers by tracking prices of a fixed basket.

Question 5

What is Laspeyres price index based on?

Accepted Answer

Laspeyres price index uses base year quantities (q0) as weights.

Question 6

What is Fisher’s ideal index?

Accepted Answer

Fisher’s ideal index is the geometric mean of Laspeyres and Paasche indices: PF = √(PL×PP).

Question 7

Write any three uses of index numbers.

Accepted Answer

Uses of index numbers include:

1) Measuring inflation and cost of living (CPI).
2) Adjusting wages/DA and contracts.
3) Studying trends in sales/production and planning.

(Any three uses can be written.)

Question 8

Write any three types of index numbers.

Accepted Answer

Types of index numbers include:

1) Price index.
2) Quantity/volume index.
3) Value index.

(Any three types can be written.)

Question 9

Differentiate between Laspeyres and Paasche index (any three points).

Accepted Answer

Difference:

| Point | Laspeyres | Paasche |
|---|---|---|
| Weights | base quantities (q0) | current quantities (q1) |
| Tendency | may overstate inflation | may understate inflation |
| Data need | easier (base q) | harder (current q) |

(Any three points can be written.)

Question 10

Write any three steps in constructing CPI.

Accepted Answer

Steps in CPI construction:

1) Select representative basket and base year.
2) Collect base and current prices and assign weights.
3) Compute weighted index and express with base = 100.

(Any three steps can be written.)

Question 11

Explain time reversal test and factor reversal test (any three points).

Accepted Answer

Tests of index numbers:

1) Time reversal test: P01 × P10 should equal 1.
2) Factor reversal test: P01 × Q01 should equal V01 (value index).
3) Fisher’s index is called ideal because it satisfies these tests.

(Any three points can be written.)

Question 12

Write any three limitations of index numbers.

Accepted Answer

Limitations of index numbers include:

1) Selection of items and weights may be subjective.
2) Quality changes and new products are hard to adjust.
3) Data errors and changing consumption patterns can distort index.

(Any three limitations can be written.)

Question 13

Explain index numbers and write important formulas using a table.

Accepted Answer

Index numbers are statistical measures that show relative change in a variable (or group of variables) over time, usually with the base period taken as 100. They are widely used to measure inflation, cost of living and trend changes in business and economics.

Important formulas for price index numbers:

| Index | Formula |
|---|---|
| Simple aggregative | (Σp1 / Σp0) × 100 |
| Simple average of relatives | [Σ(p1/p0 × 100)] / n |
| Laspeyres | [Σ(p1q0) / Σ(p0q0)] × 100 |
| Paasche | [Σ(p1q1) / Σ(p0q1)] × 100 |
| Fisher | √(PL × PP) |

Thus, formula selection depends on whether weights are used and whether base or current quantities are considered.

Question 14

Construct a simple price index using a mini example and interpret it.

Accepted Answer

A simple price index compares prices of a group of items in the current period with the base period.

**Example (Simple aggregative index):**

| Item | p0 | p1 |
|---|---:|---:|
| A | 10 | 12 |
| B | 20 | 25 |

Σp0 = 10 + 20 = 30
Σp1 = 12 + 25 = 37

Price index P01 = (Σp1/Σp0) × 100 = (37/30) × 100 = 123.33

Interpretation: The overall price level (for these items) increased by about 23.33% compared to the base period.

Thus, index numbers provide a quick summary of price changes over time.

Question 15

Explain Fisher’s ideal index and why it is called ideal. Include tests in your answer.

Accepted Answer

Fisher’s ideal index is a weighted index number that combines the advantages of Laspeyres and Paasche indices. It is defined as the geometric mean of Laspeyres (PL) and Paasche (PP) indices:

PF = √(PL × PP)

Why it is called “ideal”:

1) It uses both base year and current year quantities indirectly, reducing bias.
2) It satisfies important tests of adequacy:

- **Time reversal test:** P01 × P10 = 1
- **Factor reversal test:** P01 × Q01 = V01

Laspeyres uses base weights and may overstate price rise; Paasche uses current weights and may understate. Fisher balances both by taking geometric mean.

Therefore, Fisher’s index is called ideal because it is more reliable and satisfies the key tests, making it suitable for accurate index number construction.

Index Numbers: Concepts, Construction, Tests and Uses

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