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1. INDEXNUMBERS

2. INTRODUCTION
• An index number measures the relative change in price,
quantity, value, or some other item of interest from one time
period to another.
• A simple index number measures the relative change in one or
more than one variable.

3. WHAT IS AN INDEX
NUMBER

4. DEFINITION
• “Index numbers are quantitative measures of
growth of prices, production, inventory and other
quantities of economic interest.”
•
-Ronold

5. CHARACTERISTICS OF INDEX
NUMBERS
Index numbers are specialised averages.
Index numbers measure the change in the level of a
phenomenon.
Index numbers measure the effect of changes over a period of
time.

6. USES OF INDEX NUMBERS
o A Barometer :-
Index numbers serve as a barometer for measuring the value
of money. With the help of index number we can easily make
a comparison in the value of money in different years.
o Importance For The Govt. :-
The change in the value of money has a direct effect on the
public. So Govt. adopts the fiscal and monetary policy
according the results of index numbers.
o Throws Light On Economic Condition :-
Index numbers are very helpful in comparing the economic
conditions of a particular group at two different periods.

7. Continued…
• Consumption Standard :-
It is easy to ascertain the true consumption standard of a class
in a locality we can compute the consumption index number.
• Fixation of Wages :-
The money wages can be revised according the proportionate
change in the cost of living. The cost of living index number
guides the Govt. and the executives for the fixation and
revision of wages.
• Importance For The Producer :-
Price index number indicates the producer that he should
expand the production or he should reduce the production. If
price level is rising it means profit rate is high.

8. Continued…
• Analysis Of Industry :-
If we want to judge the prospects of manufacturing concern the
investment index number can be constructed, to know the net
yield of the industrial sector.
• Comparison Of Developed and Under Developed Countries :-
International price index number can be used for comparing the
general level of prices in the developed and under developed
countries.
• Efficiency Of Labour :-
To check the efficiency and per capita out put of the labour can be
shown by index number. Promotion and salary can be also
considered keeping in view the index number.
• Measures To remove Inequality Of Income :-
Index number of whole sale prices also indicate about the regional
disparity. So different measures can be taken for the proper
distribution of wealth and stabilizing of prices.

9. PROBLEMS RELATED TO INDEX
NUMBERS
• Choice of the base period.
• Choice of an average.
• Choice of index.
• Selection of commodities.
• Data collection.

10. METHODS OF CONSTRUCTING INDEX
NUMBERS

11. SIMPLE AGGREGATIVE METHOD
It consists in expressing the aggregate price of all commodities in the
current year as a percentage of the aggregate price in the base year.
P01= Index number of the current year.
= Total of the current year’s price of all commodities.
= Total of the base year’s price of all commodities.
100
0
1
01 



p
p
P
1
p
0
p

12. EXAMPLE:-
Fromthedatagivenbelowconstructtheindexnumberfor
theyear2007onthebaseyear2008inRajasthanstate.
COMMODITIES UNITS
PRICE (Rs)
2007
PRICE (Rs)
2008
Sugar Quintal 2200 3200
Milk Quintal 18 20
Oil Liter 68 71
Wheat Quintal 900 1000
Clothing Meter 50 60

13. Solution:-
COMMODITIES UNITS
PRICE (Rs)
2007
PRICE (Rs)
2008
Sugar Quintal 2200 3200
Milk Quintal 18 20
Oil Litre 68 71
Wheat Quintal 900 1000
Clothing Meter 50 60
3236
0 
 p 4351
1 
 p
Index Number for 2008-
45
.
134
100
3236
4351
100
0
1
01 






p
p
P
It means the prize in 2008 were 34.45% higher than the previous year.

14. SIMPLEAVERAGE OF RELATIVESMETHOD.
• The current year price is expressed as a price relative of the
base year price. These price relatives are then averaged to get
the index number. The average used could be arithmetic mean,
geometric mean or even median.
N
p
p
P
 









100
0
1
01
Where N is Numbers Of items.

15. Example-
From the data given below construct the index number for
the year 2008 taking 2007 as by using arithmetic mean.
Commodities Price (2007) Price (2008)
P 6 10
Q 12 2
R 4 6
S 10 12
T 8 12

16. Solution-
Index number using arithmetic mean-
Commodities Price (2007) Price (2008) Price Relative
P 6 10 166.7
Q 12 2 16.67
R 4 6 150.0
S 10 12 120.0
T 8 12 150.0
100
0
1

p
p
 







100
0
1
p
p
=603.37
63
.
120
5
37
.
603
100
0
1
01 












N
p
p
P
1
p
0
p

17. Weighted index numbers
These are those index numbers in which rational weights are
assigned to various chains in an explicit fashion.
(A) Weighted aggregative index numbers-
These index numbers are the simple aggregative type with the
fundamental difference that weights are assigned to the various
items included in the index.
 Fisher’s ideal method.
 Laspeyres method.
 Paasche method.
 Kelly’s method.

18. Laspeyres Method-
This method was devised by Laspeyres in 1871. In this method
the weights are determined by quantities in the base.
100
0
0
0
1
01 



q
p
q
p
p
Paasche’s Method.
This method was devised by a German statistician Paasche
in 1874. The weights of current year are used as base year
in constructing the Paasche’s Index number.
100
1
0
1
1
01 



q
p
q
p
p

19. Fisher’s Ideal Index.
Fisher’s deal index number is the geometric mean of the
Laspeyre’s and Paasche’s index numbers.



 

1
0
1
1
0
0
0
1
01
q
p
q
p
q
p
q
p
P 100


20. Kelly’s Method.
Kelly thinks that a ratio of aggregates with selected weights (not
necessarily of base year or current year) gives the base index
number.
100
0
1
01 



q
p
q
p
p
q refers to the quantities of the year which is selected as the base.
It may be any year, either base year or current year.

21. Example-
Given below are the price quantity data,with price quoted in Rs.
per kg and production in qtls.
Find- (1) Laspeyers Index (2) Paasche’s Index (3)Fisher Ideal
Index.
ITEMS PRICE(P0) PRODUCTION(q0) PRICE(P1) PRODUCTION(q1)
BEEF 15 500 20 600
MUTTON 18 590 23 640
CHICKEN 22 450 24 500
2002 2007

22. Solution-
ITEMS PRICE PRODUCTI
ON
PRICE PRODUCT
ION
BEEF 15 500 20 600 10000 7500 12000 9000
MUTTON 18 590 23 640 13570 10620 14720 11520
CHICKEN
22 450 24 500 10800 9900 12000 11000
TOTAL 34370 28020 38720 31520
 
0
p  
0
q  
1
q
 
1
p
 
0
1q
p  
0
0q
p  
1
1q
p  
1
0q
p

23. Solution-



 

1
0
1
1
0
0
0
1
01
q
p
q
p
q
p
q
p
P
66
.
122
100
28020
34370
100
0
0
0
1
01 






q
p
q
p
p
2. Paasche’s Index :
84
.
122
100
31520
38720
100
1
0
1
1
01 






q
p
q
p
p
3. Fisher Ideal Index
100
 69
.
122
100
31520
38720
28020
34370




1.Laspeyres index:

24. Chain index numbers
When this method is used the comparisons are not made with a
fixed base, rather the base changes from year to year. For
example, for 2007,2006 will be the base; for 2006, 2005 will be
the same and so on.
Chain index for current year-
100
year
previous
of
index
Chain
year
current
of
relative
link
Average 


25. Example-
• From the data given below construct an index number by
chain base method.
Price of a commodity from 2006 to 2008.
YEAR PRICE
2006 50
2007 60
2008 65

26. solution-
YEAR PRICE LINK RELATIVE CHAIN INDEX
(BASE 2006)
2006 50 100 100
2007 60
2008 65
120
100
50
60


108
100
60
65


120
100
100
120


60
.
129
100
120
108



27. Example:
• Construct Index Numbers by chain base method from the
following data of wholesale prices.
• Year: 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
• Prices 75 50 65 60 72 70 69 75 84 80

28. Solution:
YEAR PRICE LINK RELATIVE CHAIN INDEX
(BASE 1991)
1991 75 100 100
1992 50 66.6666 66.6666
1993 65 130 86.6665
1994 60 92.3076 79.9997
1995 72 120 95.9996
1996 70 97.2222 93.3329
1997 69 98.5714 91.9995
1998 75 108.6956 99.3594
1999 84 112 111.2825
2000 80 95.2380 105.9832