Index numbers

Index Numbers
By Poona jangid
11th ‘B’

Understand the
meaning of the term
index numbers
Apprecia
te its
limitatio
n
Calculate an
index number
Become
familiar
with the
use of
some
widely
used index
numbers

Content:
• Index numbers- meaning
• Features of index numbers
• Advantages of index numbers
• Problems in construction of index numbers
• Limitation of index number
• Methods of construction of index numbers
• Some important index numbers
• Uses of different types of index numbers
• Inflation and index numbers
• Conclusion
(List of formula’s used in construction of index
numbers)

Index numbers: meaning
• An index number is a statistical device for
measuring relative changes in magnitude of a
group of related variables over time
• Index numbers are expressed in terms of
percentage
• Of the two periods, the period with which the
comparison is to be made is known as the base
period.
• Index number for base period is always taken as
100.
• Therefore the study of index numbers helps us
to know percentage change in the values of
different variables over a period of time with
reference to the base year

Features or characteristics of
index numbers
• Index numbers are used for comparison of such
variables which have different units
Index numbers are
specialised averages
• Index numbers measures the relative (percentage)
changes in the variables over a period of time. They
are expressed in percentage.
Index numbers are
measures of relative
changes
• Index numbers are used to measure changes in
magnitude of certain phenomenon which are
not capable of direct measurement.
They measure changes
in composite and
complex phenomenon
• They are constructed to make comparison over different time
periods with reference some base year. Index numbers
measure changes and compare economic conditions of
different business units, different places in relation to some
base year
Basis of
comparison

Advantages of index numbers
Useful to
assess
exports
and
imports
Helpful in
formulatio
n of
policies
Helpful in
measuring
inflation
and
defiation
Helpful in
knowing the
changes in
standard of
living
Useful to
businessme
n. Important
device of
business
world
Useful to
government
in studying
changes in
trend.

Problems in construction of index numbers

• Sources of collection of data is decided this is done to
ensure the reliability of data which is to ensure that
data is reliable and comparable
Selection of
sources of
data
• We require unbiased price quotations so that adequate
accuracy can be maintained.
• To ensure uniformity two methods of quoting should be
adopted- money prices (prices quoted is per unit commodity)
and quantity prices ( prices are quoted per unit of money)
Price quotations
• Index numbers are specialised averages. We need to
select from various averaged. Median and mode can’t
be used because of their limitations.
• We need to select arithmetic mean or geometric mean.
Selection of an
average

Selection of system of weighing
• It refers to assigning relative importance to different
items included in the construction of index numbers
• Their are two types of indices weighted and. unweighted
. Weighted all commodities are given equal Importance
• Unweighted include quantity weights ( commodities are
given importance according to the amount of quantity)
and value weight ( importance is given according to
amount of expenditure (P * Q)
Selection of appropriate formula
• Selection of formulae from laspeyre’s method,
paasche’s method, fisher’s method etc
• We can’t depend on one formulae and
selection depends upon type and purpose of
index numbers

Limitations of index numbers
• Limitedcoverage- indexnumbersarebasedonsample
items.
• Qualitativechangesareignored
• Ignoreschangesin theconsumptionpattern
• Limitedapplicability
• Misleadingresults-indexnumbersmaynot beperfect
it wrongbaseyearhasbeentaken,wrongformulaeor
wrongweightageis takenetc
• Basedonaverages

Methods of constructing index
numbers
Unweighted or
simple index
numbers
Simple
aggregative
method
Simple averages
of price relative
method
Weighted index
numbers
Weighted
averages of
prices relative
method
Weighted
aggregative
method
Methods of constructing index numbers

Unweighted (simple) index numbers
• In this method all items of the series are
given equal importance. Index numbers
are constructed in two methods
1. Simple aggregative method
2. Simple average of price relative method

Simple aggregative method
• This method is also known as actual price method. It is
simple to construct.
• In this method aggregate price of commodities in
current year ( ) are divided by the aggregate price
of these commodities in the base year( ) and
expressed in percentage
symbolically
P 1 - price index of current year
-sum of prices of commodities of current year
- sum of prices of commodities of base year

Example:
• Construct index numbers for 2008 taking 2000 as the base
year
Solution -
Commodities A B C D E
Prices in 2000 16 40 35 9 2
Prices in 2008 20 60 70 18 1.50
Commodi
ties
Prices in
2000 (P0)
Prices in
2008(P1)
A 16 20
B 40 60
C 35 70
D 9 18
E 2 1.50
total 102 169.5
169.5
102
= 100X
= 166.18

Simple average of price relative method
• In this method first price relative of current year is calculated. A Price
relative is the price for current year expressed as percentageof the
period of base year.
• Symbolically
or
P1- prices of current year P0- prices of base year
N- number of commodities
R or - price relative

Example:
• Construct index numbers for following data using average of relative
price method
Commodities P Q R S T
Prices in 1998 40 28 12.5 10 30
Prices in 2004 50 35 15 20 90
Solution:
commodities Prices
in 1998
Prices in
2004
Price
relative (PR)
P 40 5 125
Q 28 35 125
R 12.5 15 120
S 10 20 200
T 30 90 300
Total 120.5 210 870
210
120.5
5
= X 100 = 174
Or
870
5
= = 174

In the construction all the
items of the series are
assigned rational weights in
an explicit manner. Weights
are assigned to various items
to reflect their relatives
importance in the series.
Weights in index numbers
are constructed by the
following methods
Weighted index numbers

Weighted aggregative method
 In this method weights are
assigned to various items.
Weighted aggregate of the
prices are calculated instead
of simple aggregates
 Various techniques are used
for assigning weights to items-
• On the basis of quantities of
the base year or
current year or
current and base year
Weighted
aggregativ
e method
Laspeyre’s
method
Fisher’s
method
Paasche’s
method

Laspeyre’s method
• This method was introduced by Mr. Laspeyre in 1871. in
this method weights are represented by the quantities
of the commodities in the base year.
• Formulae is
- prices of current year
- prices of base year
-Quantities of base year
- sum total of the product of prices of current year ( )
and quantities of the base year( )
- sum total of the product of prices of base year ( ) and
quantities of base year ( )

Example:
• Construct index numbers for following using Laspeyre’ method
Commodities 1997 2008
prices quantity prices quantity
A 20 4 40 6
B 50 3 60 5
C 40 5 50 10
D 20 10 40 20

com
modit
ies
1997 2008
pric
es
quantit
y
price
s
Quantit
y
A 20 4 40 6 160 80
B 50 3 60 5 180 150
C 40 5 50 10 250 200
D 20 10 40 20 400 200
Total 990 630
Solution
= 990
630 X 100
= 157.26

Paasche’s method
• This method was introduced by Mr.Paasche in.1874 in this
method weights are represented by the quantities of the
commodities in their current year.
• Formulae
-Prices of current year
-prices of base year
-Quantities of the current year
- sum of total of the product of price of the current year ( )
and quantities of the current year ( )
- sum of total of the product of price of base year ( ) and
quantities of the current year ( )

Fisher’s method-
• This method was introduced by Prof.Irving fisher. This
method combines the techniques of both Laspeyre’s
method and paasche’s method.
• In other words in fisher’s method weights are represented
by quantities of both base and current year.
• Formulae
-Prices of current year
-prices of base year
-Quantities of the current year
- Quantities of base year
L- Laspeyre’s method and
P- paasche’s method

Example:
• Construct index numbers for following
Commodities Base year 1998 Current year 2009
prices quantities prices quantities
A 2 100 3 100
B 8 200 10 50
C 10 300 15 100
D 6 400 10 50

Solution
Commo
dities
1998 2009
price
s
quantit
y
price
s
quantit
y
A 2 100 3 100 300 200 300 200
B 8 200 10 50 2000 1600 500 400
C 10 300 15 100 4500 3000 1500 1000
D 6 400 10 50 4000 2400 500 300
Total 10800 7200 2800 1900

Weighted average of price relative method
• In this method, the price relatives of current year are
calculated on the basis of base year prices. Since it is
weighted method, we need to calculate weights and find
the products of weights and price relatives and then
average is calculated.
We need to calculate weights (if not given)
W=
R or PR =

Example:
• Construct index number for given data
Commodity A B C D E
Quantity (units)
in 1998
2 3 5 2 1
Price in 1998 50 40 40 100 160
Price in 2005 70 60 50 140 160

Solution:
commodit
y
Quantity
in 1998
Price in
1998
Price in
2005
Weights
W=
R= RW
A 2 50 70 100 140 14000
B 3 40 60 120 150 18000
C 5 40 50 200 125 25000
D 2 100 140 200 140 28000
E 1 160 160 160 100 16000
780 101000
101000
780
= = 129.49

Some important index numbers
• The following index numbers have been regularly
published by the govt and
used for determining various
policy measures
Importan
t index
numbers
Consume
r price
index
Sensex
Agricultur
al
productio
n index
Industrial
productio
n index
Wholesale
price
index

Consumer price index
• Consumer price index (CPI) also known
as the cost of living index, measures the
average change in the retail prices. The CPI for
industrial workers is increasingly considered the
appropriate indicator of general inflation, which
shows the most accurate impact of price rise on
the cost of living of common people.
• The main groups of consumers for whom the
consumer price index numbers have been
calculated in India are:
1. The industrial workers
2. The urban non-manual workers and
3. The agricultural labourers

Need to prepare CPI ?
• We need to prepare CPI because
1. General index numbers fail to highlight the effect of
increase or decrease in prices of various goods on
cost of living of people
2. Different classes of consumers, consume different
commodities that too in different proportions
CPI reflects the effect of increase or decrease of
prices in the cost of living of different classes
of people in a society.

Construction of CPI
The following steps are observed to construct consumer price
index
• Selection of class of consumer- consumers should be classified
into various classes e.g., industrial labour, teachers etc
• Enquiry about the family budget- we select a sample of adequate
number representative families from the selected group and
following information is collected
(I)Commodities consumed (II)quantity of these commodities
(III)prices of these commodities
(IV)total expenditure incurred by consumers
• Information about prices- the retail prices of selected goods and
services should be gathered from the area to which these
consumers belong.
• Assigning weightage- weightage to different items must be given
according to their relative importance

Methods of construction
Their are two methods to construct CPI
Aggregative
expenditure method
• This method gives
importance to quantities of
the base year. We need to
find aggregate expenditure
of base year and current
year
• In simple word we use
Laspeyre’s method
• Formulae-
Family budget method
• This method gives
importance to price relatives
the current year price id
divided by base years and
multiplied by 100. this is
done for each commodity
Then weights are calculated
• Formulae- R=

Example:
• Construct CPI using both aggregative expenditure
and family budget method
Commodity Base year Current year
Prices Quantity Prices Quantity
A 2 10 4 5
B 5 12 6 10
C 4 20 5 15
D 2 15 3 10

Solution:
• Aggregative expenditure method
Commodity Base year Current year
Prices quantity Prices Quantity
A 2 10 4 5 40 20
B 5 12 6 10 72 60
C 4 20 5 15 100 80
D 2 15 3 10 45 30
total 257 190
257
190
= =X 100 135.26

Solution:
commodi
ty
Base year Current year Weights
W=
R= RW
prices quantit
y
price
s
Quantit
y
A 2 10 4 5 20 200 4000
B 5 12 6 10 60 120 7200
C 4 20 5 15 80 125 10000
D 2 15 3 10 30 150 4500
190 25700
25700
190
= = 135.26

Importance of CPI
• The CPI is used to determine the purchasing power of
money and real wages
• It helps to formulate govt.policy
• If the prices of certain essential commodities increase
due to shortage the govt may decided to provide
them through faire price shops or rationing
• Consumer price index also used to analyse the market
of specific commodities

Difficulties in construction of CPI
• As different sections of society have different
standards of living becomes difficult to have one CPI
for different classes of people
• Every family household has different budget set because
proportion of expenditure incurred on given basket of
goods varies from one family to other. The reasons is that
the habits, tastes and preference of consumers keep
changing
• Retail prices being used to construct CPI also fails to truly
express the results because retail prices of commodities are
not fixed they keep on changing whenever their is change in
supply and demand
• Sample of consumers selected to construct index numbers
may fail to truly represent the class if sample is not done
carefully

Whole sale price index
• The whole sale price index numbers indicates the change in
general price level . Unlike CPI, it does not have any reference
consumercategory. It does include itemspertaining to services like
barber charges, repairing etc.
• the commodityweights in WPI are determined by the estimates of the
commodity value of domestic production and value of imports
inclusive of import duty during the base year.
• It is available on weekly basis. Commodity are broadly classified into
three categories- (I) primary articles, (II)fuel, power, light &
lubricants (III) manufactured products

Uses of wholesale price index
• The index number is helpful in forecasting the demand and
supply conditions of the commodities in the economy. If
there is increase in wholesale price index, it means the
demand of commodities is more than their supply.
• It helps us to understand monetary and real value of macro
aggregates. Monetary value is based on prices of the current
year and real value is based on prices of the base year.
• The WPI is used to calculate the rate of inflation in the
country.
The weekly inflation rate is given by
= whole sale price index for tth week
= whole sale price index for(t -1)th week

Example:
• If wholesale price index for week 1 = 800 and
for week 2= 880 calculate weekly rate of
inflation
• Solution: Rate of inflation=
here t=880 and t-1=800
880-800
800
X 100 = 80
800
X 100 = 10%

Industrial production index
• The index number of industrial production measures
changes in the level of industrial changes in the
level of industrial production comprisng many
industries. It include production of public and private
sector.
• It is weighted average of quantity relatives
• Formula,
- quantity production in current year
- quantity production in base year
W- weights

Purpose of construction
• This is designed to measure the increase or decrease
min output of some industries
• It is a quantity index which measure changes in the quantity
index which measures changes in the quantity of production
• Data of industrial production are collected under the
following categories: (I) mining and quarrying industries –
coal, aluminium, petroleum etc.
(II)mechanical industries- ships, aeroplanes etc
(III)textile industries- woollen cotton silk etc.
(IV)metallurgical industries- iron and steel, rolling mills etc.
(V)miscellaneous- glass, washing powder, chemical etc.
• The data for above are collected monthly, quarterly or yearly
• We use quantity relative method for construction

Example:
• Construct index number of industrial production for
the following
Industries Mining Textiles Cement Iron and
steel
Output (base
year)
125 80 40 60
Output
(current
year)
250 120 50 180
Weights 30 40 20 10

Solution:
Industries Base year
quantity
Current
year
quantity
Weights
W
quantity relative
w
Mining 125 250 30 200 6000
Textile 80 120 40 150 6000
Cement 40 50 20 125 2500
Iron and
steel
60 180 10 300 3000
100 17500
17500
100
= = 175

Agriculture production index
• Index numbers of agricultural production
is a weighted average of quantity
relatives
• Its base period is triennium ending 1981-
82
• In 2003-04 the index number of
agricultural production was 179.5 it
means that agricultural production has
increased by 79.5% over the average of
three years 1979-80, 1980-81 and 1981-
82
• Food grains have a weight of 62.92% in

Sensex
 Sensex is an index numbers representing the
movement in share price of major companies
listed in the Bombay stock exchange.
 It is one number that represents whole share
markets.
 The movement of Sensex tells us about
prices of shares of listed companies with
Bombay stock exchange
• if the Sensex goes up it means that prices of
the stock of most of the companies under
BSE Sensex have gone up
• If Sensex goes down it means that prices of
the stock of companies under BSE have gone

Other useful index numbers
1. Human development index-
• this index measures literacy, life expectancy,
attainment of education and per capita GDP
for different countries.
• This index number measures human
development which helps to compare human
development in different countries to
determine whether the country is developed or
underdeveloped.

Producer price index
• Producer price index numbers measures price
changes from the producer’s perspective.
• It uses only basic price including taxes, trade
margins, and transport costs.
• A working group on revision of whole sale price
index (1933-34 = 100) is inter alia examining the
feasibility of switching over from WPI to a PPI in
India as in many countries.

Inflation and index numbers
• Inflation refers to general rise in price level.
Inflation is the persistent rise in prices.
• If the inflation is not controlled money will not able
to perform its function as a unit of value or medium
of exchange. Inflation lowers the value of money
that is purchasing power of money goes down.
• The WPI is widely used to measure the rate of
inflation. This index has capability to measure the
price fluctuations of all commodities in a
comprehensive way.
• Real income of wages =
present wages
present price index
X 100

Example:
• Calculate real wages if present wages are Rs.340
and current price index is Rs.250
Solution:
Real income of wages =
340
250
680
5
present wages
present price index
X
100
100=
= = 136
X

Important formula’s
• Unweighted (simple) index numbers
1. Simple aggregative method
2. Simple average of price relative method
• Weighted index numbers
o Weighted aggregative method
1. Laspeyre’s method
2. Paasche’s method

3. Fisher’s method
o Weighted average of price relative method
 Construction of CPI
I. Aggregative expenditure method
II. Family budget method
 Wholesale price index
 Industrial production index
 Real income of wages =
Important formula’s
present wages
present price index X 100

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