INDEX NUMBERS
Presented by: Rashmi Ranjan Malla
Introduction Uses of index numbers Understand the difference between a weighted
and an unweighted index. Construct and interpret a Laspeyres price index. Construct and interpret a Paasche price index. Construct and interpret a value index. Explain how the Consumer Price Index is
constructed and interpreted.
CONTENTS
An index number measures the value of a variable relative to its value during a base period (the percent change from a base period)
Index Number = (Value / Base Value) x 100
Price index numbersQuantity index numbersValue index numbersSpecial purpose index number
Classification of Index Numbers
They can be grouped into two heads:a)Unweighted indecesb)Weighted indeces
Methods of constructing Index Numbers
.
Unweighted Weighted
Simple Aggregativ
e
Simple Average or Relatives
Weighted Aggregativ
e
Weighted Average of Relatives
o Measurement of change in the price levelo Useful to governmento Knowledge of change in standard of livingo Information regarding foreign tradeo Index numbers can also be used to study the
relative changes on the basis of geographical locations or some other characteristics
Advantages or Uses OF INDEX NUMBERS
Unweighted Index Numbers
1000
1
01 P
PP
1P
0P
Commodity Price in 2008 ( Rs.) Price in 2009 ( Rs.)
A 50 70
B 40 60
C 80 90
D 110 120
E 20 20
Illustration: From the following data construct an index for 2009 taking 2008 as base.
Solution:
1000
1
01 P
PP
It means that as compared to 2008,in 2009 there is net increase in the prices of commodities included in the index to the extent of 20%
Under this method ,the price relatives for each commodity are calculated and average is found out.
*Simple Average of Price relative Method:
N
PP
P
1000
1
01
Where N is the number of items from which the index number is constructed.
When geometric mean is used the formula would be
N
PP
P
100log
log0
1
01
Commodity Price in 2007( Rs.) Pice in 2008 (Rs.)
A 50 70
B 40 60
C 80 90
D 110 120
E 20 20
Illustration:From the following data ,construct an index for 2008 taking 2009 as base by the average of relatives method using arithmetic mean
Commodity Price in 2007( Rs.)
Pice in 2008 (Rs.)
Price Relatives
A 50 70 140.0
B 40 60 150.0
C 80 90 112.5
D 110 120 109.1
E 20 20 100.0
Solution:
P
0P 1P 1000
1 P
P
32.122
1000
1
01
N
PP
P
6.6111000
1
P
P
An index number in which the component items are weighted according to some system of weights reflecting their relative importance. In one sense nearly all index numbers are weighted by implication; for example, an index number of prices amalgamates prices per unit of quantity and the size of these units may vary from one commodity to another in such a way as to constitute weighting.
Weighted Index Numbers
1) Weighted Aggregative Indices2) Weighted Average of Relatives
Weighted Index Numbers are of two types
These indices are similar to simple aggregative type with the fundamental difference that weights are assigned explicitly to the various items included in the index. Various methods of constructing Weighted Aggregative Indices are:
Laspeyres Method Paasche’s Method Drobish & Bowley’s Method Fisher’s Ideal Method Marshall Edge worth Method Walsh Method Kelly’s Method.
Weighted Aggregative Indices
In this method ,base year quantity are taken as weights. The formula for constructing the index is:
Price in current year Price in base year Quantity in the base year
Laspeyres Method
1P
0P0q
Where,
10000
0101
qp
qpp
Paasche’s Index
1q
01P 10010
11
qp
qp
Steps for constructing the paasches index are same as those taken in constructing laspayre’s index with only difference that the price of each commodity in each year is multiplied by the quantity of that commodity in the current year rather than by the quantity in the base year.
This method is the simple arithemetic mean of Laspcyre’s and Paasche’s indices.
The formula for constructing Bowley-Drobish index is:
Bowley Drobish Method
1002
10
11
00
01
qp
qp
qp
qp01P =
01P2
PL
Where, L=Laspeyre’s index P=Paasche’s index
Prof. Irving fisher has given a number of formulae for constructing index number .This mehod is the geometric mean of Laspeyre’s and Passche’s indices.The formula for constructing the index is:
Fisher’s Ideal Index
10010
11
0
01
qp
qp
qp
qp
o
01P =
In this method also both the current as well as base year price and quantities are considered. The formula for constructing the index is:
Marshall-Edgeworth Method
1001000
1101
qpqp
qpqp01P =
Truman L.kelly has suggested the following formulla for constructing index number :
Kelly’s Method
1000
1
qp
qp01P =
Commodity Price Quantity Price Quantity
A 2 10 4 16
B 5 10 6 5
C 4 14 5 10
D 2 19 2 13
Illustration:From the data given below ,construct index number of prices for 2008 with 2002 as base ,using Laspeyres MethodPaasche’s MethodDrobish & Bowley’s MethodFisher’s Ideal MethodMarshall Edge worth MethodWalsh MethodKelly’s Method.
Commodity
A 2 8 4 6 32 16 24 12
B 5 10 6 5 60 50 30 25
C 4 14 5 10 70 56 50 40
D 2 19 2 13 38 38 26 26
=200
=160
=130
= 103
Solution:
0P 0q 1P 1q0P 0q 0P
1q 1q1P 1P0q
1P 0q 1P 1q0P 1q
0P 0q
01P 1000
01
qp
qp
o
01P 1002
10
11
00
01
qp
qp
qp
qp
125100160
200
21.126100103
130
4. Fisher Ideal Index
1002
10
11
00
01
qp
qp
qp
qp
01P
10010
11
0
01
qp
qp
qp
qp
o01P
6.1251002
103130
160200
6.126100100578.1100102
130
160
200
5. Marshall-Edgeworth Index
1001000
1101
qpqp
qpqp01P
47.125100103160
130200
Quantity or volume index numbers
Price indices measures changes in the price level of certain commodities .On the other hand quantity or volume index numbers measures the changes in the physical volume of goods produced ,distributed or consumed .These indices are important indicators of the level of output in the economy or in part of it If a quantity index number is prepared by using the laspeyers method it would be :
10000
01
01
pq
pqQ
.
When Paasche’s formula is used
When fisher formula is used
10010
11
01
pq
pqQ
10010
11
10
01
01
pq
pq
pq
pqQ
Value index numbers
Value means price times quantity .Thus a value V is the sum of the value of a given year divided by sum of the values for the base year. The formula, therefore is:
Where V= Value index
10000
11
qp
qpV
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.
Average link relative of current year Chain index for previous year = 100
The chain index numbers
S.P GUPTAB.M AGARWALK.K KHANNA
REFRENCES:
THANK YOU
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