Chapter 16: Index Number

Important Formulae for Index Number

Theoretical Questions on Index Number

Numerical Questions (Very Short)

Numerical Problems: Index Number Calculations

Index Number | Class 12 Economics Notes & Numerical Solutions

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Index Number Class 12 Economics Notes and Solutions

This comprehensive guide covers Index Number for Class 12 Economics. An Index Number is a statistical measure designed to show changes in a variable or group of related variables with respect to time, geographic location or other characteristics. Below, we provide detailed formulae, theoretical explanations, and step-by-step solutions for calculating Laspeyre’s and Paasche’s Price Index numbers.

Important Formulae for Index Number
Theoretical Questions on Index Number
Numerical Questions (Very Short)
Numerical Problems: Index Number Calculations
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1. Simple Aggregative Method

P₀₁ = Σp₁Σp₀ × 100

Where, Σp₁ = Total current year prices, Σp₀ = Total base year prices.

2. Simple Average of Price Relatives

P₀₁(AM) = ΣPn

P₀₁(GM) = Antilog Σ log Pn

3. Weighted Aggregative Method

a. Laspeyre’s Price Index (Base Year Weight):

P₀₁^La = Σp₁q₀Σp₀q₀ × 100

b. Paasche’s Price Index (Current Year Weight):

P₀₁^Pa = Σp₁q₁Σp₀q₁ × 100

4. Weighted Average of Price Relatives

P₀₁ = ΣWPΣW

1. What is index number? Explain different methods of constructing price index number. [5]

Meaning of Index Number: An index number is a statistical tool designed to measure the relative change in a variable or group of variables with respect to time, geographical location, or other characteristics.

Methods of Constructing Price Index Number:

Simple (Un-weighted) Price Index Number: All items are given equal importance.
- Simple Aggregative Method: The total sum of current year prices is divided by the total sum of base year prices.
- Simple Average of Price Relative Method: The average of the price relatives of individual items is taken.
Weighted Price Index Number: Items are assigned weights based on their importance.
- Weighted Aggregative Method: Includes Laspeyre’s (Base year quantity as weight) and Paasche’s (Current year quantity as weight) methods.
- Weighted Average of Price Relatives: Uses weights assigned to price relatives.

1. If the value of current year’s price index number of an economy is 150, what does it mean? [1]

If the current year’s price index number is 150 (P₀₁ = 150), it means that the price level has increased by 50% compared to the base year.

Σp₁q₁ = 247

Σp₀q₁ = 226

1. Find the Paasche’s price index number from the given data and interpret the result. [5]

P₀₁^Pa = 247226 × 100 = 109.29

Interpretation: The price level has risen by 9.29%.

2. Find the Laspeyre’s Price Index from the given data. [5]

Goods	p₀	q₀	p₁	q₁	p₀q₀	p₁q₀
A	10	15	20	15	150	300
B	12	18	13	17	216	234
C	15	15	18	20	225	270
D	8	9	12	13	72	108
Total					Σp₀q₀ = 663	Σp₁q₀ = 912

P₀₁^La = 912663 × 100 = 137.56

Interpretation: The price level has increased by 37.56%.

3. Calculate price index number by using Paasche’s method. [5]

P₀₁^Pa = 524388 × 100 = 135.05

Result: The Index Number is 135.05.

4. Construct Laspeyre’s price Index number from the following table. [5]

Item	p₀	q₀	p₁	q₁	p₀q₀	p₁q₀
A	5	60	12	50	300	720
B	4	40	10	45	160	400
C	3	20	8	30	60	160
D	2	50	7	40	100	350
Total					620	1630

P₀₁^La = 1630620 × 100 = 262.90

5. Find the Paasche price index number. [5]

P₀₁^Pa = 427256 × 100 = 166.79

6. Find the Laspeyre’s Price Index. [5]

P₀₁^La = 275186 × 100 = 147.85

7. Construct price index number using Laspeyre’s method. [5]

Item	p₀	q₀	p₁	q₁	p₀q₀	p₁q₀
A	10	80	15	100	800	1200
B	4	150	4	200	600	600
C	6	120	10	130	720	1200
D	20	70	25	40	1400	1750
Total					3520	4750

P₀₁^La = 47503520 × 100 = 134.94

8. Find the index number using Paasche method. [5]

Item	p₀	q₀	p₁	q₁	p₁q₁	p₀q₁
A	8	20	10	25	250	200
B	9	18	12	20	240	180
C	7	6	9	5	45	35
D	6	15	12	30	360	180
E	4	12	5	8	40	32
Total					935	627

P₀₁^Pa = 935627 × 100 = 149.12

9. Construct the index number by Laspeyre’s method. [5]

Item	p₀	q₀	p₁	q₁	p₀q₀	p₁q₀
Rice	20	100	28	160	2000	2800
Sugar	11	18	30	37	198	540
Salt	1	1	5	12	1	5
Milk	8	57	32	149	456	1824
Total					2655	5169

P₀₁^La = 51692655 × 100 = 194.69

10. Construct Paasche’s price index number. [5]

P₀₁^Pa = 383277 × 100 = 138.26

11. Construct Paasche’s price index number from the following table. [5]

Commodity	p₀	q₀	p₁	q₁	p₁q₁	p₀q₁
A	2	40	5	50	250	100
B	4	16	8	30	240	120
C	1	10	2	18	36	18
D	5	25	10	40	400	200
Total					926	438

P₀₁^Pa = 926438 × 100 = 211.41

12. Find the Paasche’s price index number from the given data. [5]

Type	p₀	q₀	p₁	q₁	p₁q₁	p₀q₁
A	10	10	12	15	180	150
B	12	15	15	19	285	228
C	8	8	10	12	120	96
D	4	22	6	25	150	100
Total					735	574

P₀₁^Pa = 735574 × 100 = 128.04

13. Find the price index using both Laspeyre’s and Paasche’s methods. [8]

Item	p₀	q₀	p₁	q₁	p₁q₀	p₀q₀	p₁q₁	p₀q₁
Rice	120	12	205	15	2460	1440	3075	1800
Wheat	100	12	202	21	2424	1200	4242	2100
Sugar	140	15	185	15	2775	2100	2775	2100
Pulses	160	18	180	28	3240	2880	5040	4480
Corn	185	30	209	15	6270	5550	3135	2775
Total					17169	13170	18267	13255