Based On the types of Index Numbers. Prepared By Siddhant Kumar Behera. Ravenshaw University Student Of IMBA-FM.

2. 20-2

3. 
A price index measures the changes in prices from a
selected base period to another period.

EXAMPLE: Price index is widely applied in various
economic and business policy formation and decision
making.It is used to measure cost of living of
teachers,farmers and weavers.It is also used to
construct price index of securities in securities markets.

4. 
A quantity index measures the changes in quantity
consumed from the base period to another period.

EXAMPLE: Federal Reserve Board indexes of quantity
output.

5. 
A special-purpose index combines and weights a
heterogeneous group of series to arrive at an overall
index showing the change in business activity from the
base period to the present.

EXAMPLE: Profits or sales or production,Price index of
stock markets or productivity index

6. 
A value index measures the change in the value of one or
more items from the base period to the given period. The
values for the base period and the given periods are found by
PxQ. Where p = price and q = quantity

EXAMPLE: the index of department store sales,agricultural
production,export,industrial production.

7. 
A value index measures changes in both the price and quantities involved.

A value index, such as the index of department store sales, needs
the original base-year prices, the original base year quantities, the presentyear prices, and the present year quantities for its construction.

Its formula is:
V =
∑p q
∑p q
t
t
0
0
(100) =
$10,600
(100) = 117.8
$9,000

8. 

The consumer price index (CPI) / cost of living
index is a measure of the overall cost of the goods and
services bought by a typical consumer.
It is used to monitor changes in the cost of living over
time.

9. The inflation rate is calculated as follows:
Inflation Rate in Year2 =
CPI in Year 2 - CPI in Year 1
× 100
CPI in Year 1

10. 5%
6%
6% 5% 5%
Housing
Food/Beverages
Transportation
40%
17%
16%
Medical Care
Apparel
Recreation
Other
Education and
communication

11. 
An aggregate index is used to measure the rate of
change from a base period for a group of items
Aggregate
Price Indexes
Unweighted/
Simple
aggregate
price index
Weighted
aggregate price
indexes
Paasche Index
Laspeyres Index

12. 
A simple price index tracks the price
of a single commodity
 The formal definition is:
Simple aggregate index =
∑p
∑p
n
× 100
o
Where
Σpn = the sum of the prices in the current period
Σpo = the sum of the prices in the base period
20-12

13. Automobile Expenses:
Monthly Amounts ($):
Index
Year
Lease payment
Fuel
Repair
Total
(2001=100)
2001
260
45
40
345
100.0
2002
280
60
40
380
110.1
2003
305
55
45
405
117.4
2004
310
50
50
410
118.8
I2004

∑P
=
∑P
410
× 100 =
(100) = 118.8
345
2001
2004
Unweighted total expenses were 18.8%
higher in 2004 than in 2001

14. 
Airplane ticket prices from 1995 to 2003:
Index
Year
Price
(base year
= 2000)
1995
272
85.0
1996
288
90.0
1997
295
92.2
1998
311
97.2
1999
322
100.6
2000
320
100.0
2001
348
108.8
2002
366
114.4
2003
384
120.0
I1996
P1996
288
=
× 100 =
(100 ) = 90
P2000
320
Base Year:
P2000
320
I2000 =
× 100 =
(100 ) = 100
P2000
320
I2003
P2003
384
=
× 100 =
(100 ) = 120
P2000
320

15. I2000

Prices in 1996 were 90% of
base year prices
P2000
320
=
× 100 =
(100 ) = 100
P2000
320

Prices in 2000 were 100% of
base year prices (by definition,
since 2000 is the base year)

I1996
P1996
288
=
× 100 =
(100 ) = 90
P2000
320
Prices in 2003 were 120% of
base year prices
I2003 =
P2003
384
× 100 =
(100 ) = 120
P2000
320

16. Unweighted aggregate price index formula:

n
(
IUt ) =
Pi( t )
∑
i=1
n
∑P
i=1
(
IUt )
n
× 100
t = time period
n = total number of items
= unweighted price index at time t
∑P
i=1
(0)
i
i = item
(t)
i
= sum of the prices for the group of items at time t
n
Pi( 0 )
∑
i=1
= sum of the prices for the group of items in time period 0

17. Weighted index no. Consists of –

Laspeyres index


20-17
The Laspeyres index is also known as the average
of weighted relative prices
In this case, the weights used are the quantities
of each item bought in the base period

18. 
The formula is:
∑p q
Laspeyres index =
∑p q
n o
× 100
o o
Where:
qo = the quantity bought (or sold) in the base period
pn = price in current period
po = price in base period
20-18

19. The 1990 party
Drink
The 2000 party
Unit price
Quantity
Unit price
Quantity
po
qo
pn
qn
wine
2.50
25
3
30
beer
4.50
10
6.00
8
soft drinks 0.60
10
0.84
15
pnqo = (3 x 25) + (6 x 10) + (0.84 x 10) = 143.4
poqo = (2.5 x 25) + (4.5 x 10) + (0.6 x 10) = 113.5
So, Laspeyre's price index =
(143.4/113.5) x 100 = 126.3
20-19

20. Laspeyres Index
Requires quantity data from only the base period.
This allows a more meaningful comparison over
time.

21. Laspeyres index assumes that the same amount of each
item is bought every year.
If I bought a radio one year, the index assumes I
bought one the next year.
If I bought 35 kg of oranges in Po, the index assumes I
bought the same amount every year, when in reality if
the price went up, one might buy less.
Does not reflect changes in buying patterns
over time. Also, it may overweight goods
whose prices increase.

22. 
Paasche index



The Paasche index uses the consumption in the
current period
It measures the change in the cost of purchasing
items, in terms of quantities relating to the current
period
The formal definition of the Paasche index is:
pnqn
Paasche index =
× 100
poqn
∑
∑
Where:
pn = the price in the current period
po = the price in the base period
qn = the quantity bought (or sold) in the current period
20-22

23. ∑ pq
P=
∑pq
t t
0 t
$811.60
(100) =
(100) = 135.64
$598.36

24. Paasche Index
Because it uses quantities from the current period, it
reflects current buying habits.

25. Paasche Index
It requires quantity data for the current year.
Because different quantities are used each year, it is
impossible to attribute changes in the index to
changes in price alone.
It tends to overweight the goods whose prices have
declined.
It requires the prices to be recomputed each year.

26. 
Fisher’s ideal index
 Fisher’s ideal index is the geometric mean of the Laspeyres
and Paasche indexes
 The formal definition is:
Fisher' s index =
( Laspeyres index )( Paasche index )
∑p q ∑p q
∑p q ∑p q
20-26
n o
n n
o o
=
o n
× 100

27. i) Index numbers are economic barometers. They
measure the level of business and economic activities
and are therefore helpful in gauging the economic
status of the country.
(ii) Index numbers measure the relative change in a
variable or a group of related variable(s) under study.
(iii) Consumer price indices are useful in measuring the
purchasing
power
of
money,
thereby
used
in
compensating the employees in the form of increase of
allowances.

28. 20-28

29. 20-29