Index numbers

1. INDEX NUMBERS
PREVIOUS YEARS’ QUESTIONS

2. 2012
NO NUMERICALS

3. • Elaborate on the tests which help to determine the
adequacy of an index number formula.

4. 2011
NO THEORY

5. • Compute Laspeyre’s Paasche’s, Fisher’s and Marshall-
Edgeworth’s index numbers from the following data:
Item 1998 1999
Price Quantity Price Quantity
A 5 25 6 30
B 3 8 4 10
C 2 10 3 8
D 10 4 3 5

6. LASPEYRE’S METHOD
𝑃01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
× 100

7. PAASCHE’S METHOD
𝑃01 =
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
× 100

8. FISHER’S IDEAL INDEX NUMBER
𝑃01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
×
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
× 100

9. MARSHALL-EDGEWORTH METHOD
𝑃01 =
Σ𝑝1 𝑞0 + 𝑞1
Σ𝑝0 𝑞0 + 𝑞1
× 100 =
Σ𝑝1 𝑞0 + Σ𝑝1 𝑞1
Σ𝑝0 𝑞0 + Σ𝑝0 𝑞1
× 100

10. Item p0 q0 p1 q1 p1q0 p0q0 p1q1 p0q1
A 5 25 6 30 150 125 180 150
B 3 8 4 10 32 24 40 30
C 2 10 3 8 30 20 24 16
D 10 4 3 5 12 40 15 50
224 209 259 246

11. LASPEYRE’S METHOD
𝑃01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
× 100 =
224
209
× 100 = 107.177

12. PAASCHE’S METHOD
𝑃01 =
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
× 100 =
259
246
× 100 = 105.2846

13. FISHER’S IDEAL INDEX NUMBER
𝑃01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
×
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
× 100 =
224
209
×
259
246
× 100 = 1.1284 × 100
= 1.0623 × 100 = 106.23

14. MARSHALL-EDGEWORTH METHOD
𝑃01 =
Σ𝑝1 𝑞0 + Σ𝑝1 𝑞1
Σ𝑝0 𝑞0 + Σ𝑝0 𝑞1
× 100 =
224 + 259
209 + 246
× 100 =
483
455
× 100
= 106.1538

15. 2011
MMTU
NO NUMERICALS

16. • Distinguish between chain base and fixed base indices.
• What are factor reversal and time reversal tests? Explain.
• What are the uses of index numbers?

17. 2010
NO QUESTIONS

18. 2009
NO THEORY

19. • Calculate price index numbers for the year 2001 with 1991
as the base year from the following data using:
1. Laspeyre’s index
2. Paasche’s index
3. Fisher’s index.
Commodity Unit 1991 2001
Price Value Quantity Consumed Value
A kg 10 1500 160 1760
B kg 12 1080 100 1300
C Metre 15 900 60 960
D Packets 9 450 40 480

20. LASPEYRE’S METHOD
𝑃01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
× 100

21. PAASCHE’S METHOD
𝑃01 =
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
× 100

22. FISHER’S IDEAL INDEX NUMBER
𝑃01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
×
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
× 100

23. Commodity p0 p0q0 q1 p1q1
A 10 1500 160 1760
B 12 1080 100 1300
C 15 900 60 960
D 9 450 40 480

24. Commodity p0 q0 p1 q1 p1q0 p0q0 p1q1 p0q1
A 10 150 11 160 1650 1500 1760 1600
B 12 90 13 100 1170 1080 1300 1200
C 15 60 16 60 960 900 960 900
D 9 50 12 40 600 450 480 360
4380 3930 4500 4060

25. LASPEYRE’S METHOD
𝑃01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
× 100 =
4380
3930
× 100 = 111.4504

26. PAASCHE’S METHOD
𝑃01 =
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
× 100 =
4500
4060
× 100 = 110.8374

27. FISHER’S IDEAL INDEX NUMBER
𝑃01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
×
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
× 100 =
4380
3930
×
4500
4060
× 100
= 1.2353 × 100 = 1.1114 × 100 = 111.14

28. 2008
NO THEORY
NUMERICAL ASKED FOR THE FIRST TIME

29. • Construct Fisher’s ideal index from the following data and
show that it satisfies time reversal and factor reversal tests.
Commodity 2006 2007
Price Value Price Value
A 10 100 12 144
B 15 75 20 120
C 8 80 10 110
D 20 60 25 50
E 50 500 60 540

30. FISHER’S IDEAL INDEX NUMBER
𝑃01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
×
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
× 100

31. TIME REVERSAL TEST
𝑃01 × 𝑃10 = 1

32. FACTOR REVERSAL TEST
𝑃01 × 𝑄01 = 𝑉01

33. Commodity 2006 2007
Price Value Price Value
A 10 100 12 144
B 15 75 20 120
C 8 80 10 110
D 20 60 25 50
E 50 500 60 540

34. Commodity p0 v0 p1 v1
A 10 100 12 144
B 15 75 20 120
C 8 80 10 110
D 20 60 25 50
E 50 500 60 540

35. Commodity p0 p0q0 p1 p1q1
A 10 100 12 144
B 15 75 20 120
C 8 80 10 110
D 20 60 25 50
E 50 500 60 540

36. Commodity p0 q0 p1 q1 p1q0 p0q0 p1q1 p0q1
A 10 12 100 144
B 15 20 75 120
C 8 10 80 110
D 20 25 60 50
E 50 60 500 540

37. Commodity p0 q0 p1 q1 p1q0 p0q0 p1q1 p0q1
A 10 10 12 12 120 100 144 120
B 15 5 20 6 100 75 120 90
C 8 10 10 11 100 80 110 88
D 20 3 25 2 75 60 50 40
E 50 10 60 9 600 500 540 450
995 815 964 788

38. FISHER’S IDEAL INDEX NUMBER
𝑃01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
×
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
× 100 =
995
815
×
964
788
× 100 = 1.4935 × 100
= 1.2221 × 100 = 122.21

39. TIME REVERSAL TEST
𝑃01 × 𝑃10 = 1
𝑃01 × 𝑃10 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
×
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
×
Σ𝑝0 𝑞1
Σ𝑝1 𝑞1
×
Σ𝑝0 𝑞0
Σ𝑝1 𝑞0
=
995
815
×
964
788
×
788
964
×
815
995
= 1
𝑃𝑟𝑜𝑜𝑣𝑒𝑑

40. FACTOR REVERSAL TEST
𝑃01 × 𝑄01 = 𝑉01
𝑃𝑟𝑜𝑜𝑓:
𝑃01 × 𝑄01 =
Σ𝑝1 𝑞0
Σ𝑝0 𝑞0
×
Σ𝑝1 𝑞1
Σ𝑝0 𝑞1
×
Σ𝑞1 𝑝0
Σ𝑞0 𝑝0
×
Σ𝑞1 𝑝1
Σ𝑞0 𝑝1
=
995
815
×
964
788
×
788
815
×
964
995
=
964 2
815 2
=
964
815
=
Σ𝑝1 𝑞1
Σ𝑝0 𝑞0
= 𝑉01
𝑃𝑟𝑜𝑜𝑣𝑒𝑑

41. 2007
NO NUMERICALS

42. • Index number and its uses.

43. 2006
NO NUMERICALS

44. • Distinguish between time reversal and factor reversal tests.

45. 2005
NO NUMERICALS

46. • Distinguish between Laspeyre’s and Paasche’s index
number formulae.
• Cost of living index number.

47. 2004
NO NUMERICALS

48. • Index number and its construction.

49. 2003
INDEX NUMBERS INTRODUCED IN THE SYLLABUS FOR THE FIRST TIME IN 2004