2. 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
3. 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
comparis
on
4. Advantages of index numbers
Useful
to
assess
exports
and
imports
Helpful
in
formulati
o n of
policies
Helpful
in
measuri
ng
inflation
and
defiation
Helpful in
knowing
the
changes in
standard of
living
Useful to
business
me
n.
Importan
t device
of
busine
ss
world
Useful to
governmen
t in
studying
changes in
trend.
5. Limitations of index numbers
• Limited coverage- index numbers are based
on sample items.
• Qualitative changes are ignored
• Ignores changes in the consumption pattern
• Limited applicability
• Misleading results- index numbers may not
be perfect it wrong base year has been
taken, wrong formulae or wrong weight age
is taken etc
• Based on averages
7. 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
8. Simple aggregative method
P 1 - price index of current year
-sum of prices of commodities of current
year
- sum of prices of commodities of base
• 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
9. 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
X
100
102
=
166.18
10. 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 percentage of the
period of base year.
• Symbolically
or
P0- prices of base
year
P1- prices of current
year N- number of
commodities R or -
price relative
11. 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
Solutio
n:
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
5
= 120.5
X
100
=
174
O
r
5
=
870 =
174
12. 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
13. 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
• On the basis of
quantities of current
year or
• On the basis of
quantities of current
and base year
Weighte
d
aggregat
iv e
method
Laspeyr
e’s
method
Fisher
’s
metho
d
Paasche
’s
method
14. Laspeyre’s method
• This method was introduced by Mr. Laspeyre in
1871.
i
n 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( )
15. 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
16. com
modi
t ies
1997 2008
pri
c
es
quanti
t y
pric
e s
Quanti
t 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
17. 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 ( )
18. 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
19. Example:
• Construct index numbers for
following
Commoditie
s
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
20. Solution
Comm
o
dities
1998 2009
pric
e s
quanti
t y
pric
e s
quanti
t 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
21. 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.
R or PR =
We need to calculate weights (if not
given) W=
22. 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
24. Some important index numbers
• The following index numbers have been
regularly published by the govt and
used for determining
various
policy measures
Importa
n t
index
number
s
Consu
me r
price
index
Sens
ex
Agricult
ur al
producti
o n
index
Industri
al
producti
o n
index
Wholesal
e price
index
25. 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 commonpeople.
• 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
26. 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.
27. 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
28. 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=
29. Example:
• ConstructCPI 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
30. 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
=
135.2
6
31. Solution:
commodi
ty
Base year Current year Weights
W=
R= RW
prices quanti
t y
pric
e s
Quanti
t 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
2570
019
0
= =
135.2
6
32. 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
33. 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
34. Whole sale price index
• Thewholesalepriceindexnumbersindicatesthechangein
generalpricelevel.UnlikeCPI,itdoesnothaveanyreference
consumercategory.Itdoesincludeitemspertainingtoserviceslike
barbercharges,repairingetc.
• thecommodityweightsinW
P
Iaredeterminedbytheestimatesofthe
commodityvalueofdomesticproductionandvalueofimports
inclusiveofimportdutyduringthebaseyear
.
• Itisavailableonweeklybasis.Commodityarebroadlyclassifiedinto
threecategories-(I)primaryarticles, (II)fuel,power
,light&
lubricants (III)manufacturedproducts
35. Uses of wholesale price index
• The index numberis helpful in forecasting the demandand supplyconditions
ofthe commoditiesin the economy.If there is increase in wholesale price index,
it meansthe demandofcommoditiesis morethan their supply.
• It helps us to understand monetary and real value ofmacro aggregates.
Monetary value is based onprices ofthe currentyear and real value is based on
prices ofthe base year.
• The WPI is used to calculate the rate ofinflation 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
36. 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
80
0
X 100 =
10%
37. 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
38. 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,
39. 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
(curren
t year)
250 120 50 180
Weights 30 40 20 10
41. 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
42. 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
43. 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.
44. P
r
oducerpriceindex
• 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.
45. 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.
present wages
• Real income of wages = present price
index
X 10
0
46. Example:
• Calculate real wages if present wages are
Rs.340 and current price index is Rs.250
Solution:
Real income of
wages =
34
0
25
0
X
10
0
10
0
=
=
680
=
5
13
6
present wages
X
present price index
47. 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
48. 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 10
0
