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:

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