Types Of Index Numbers

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 present-
year prices, and the present year quantities for its construction.
Its formula is:
8.117)100(
000,9$
600,10$
)100(
00
===
å
å
qp
qp
V
tt

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:
100
1 Year in CPI
1 Year in CPI - 2 Year in CPI
Year2in Rate Inflation ´=

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

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:
Where
Sp
n
= the sum of the prices in the current period
Sp
o
= the sum of the prices in the base period
100
p
p
indexaggregateSimple
o
n
´=
å
å
20-12

13. Unweighted total expenses were 18.8%
higher in 2004 than in 2001
Automobile Expenses:
Monthly Amounts ($):
YearLease payment Fuel RepairTotal
Index
(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
118.8(100)
345
410
100
P
P
I
2001
2004
2004 ==´=
å
å

14. Airplane ticket prices from 1995 to 2003:
90)100(
320
288
100
P
P
I
2000
1996
1996 ==´=
Year Price
Index
(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
100)100(
320
320
100
P
P
I
2000
2000
2000 ==´=
120)100(
320
384
100
P
P
I
2000
2003
2003
==´=
Base Year:

15. Prices in 1996 were 90% of
base year prices
Prices in 2000 were 100% of
base year prices (by definition,
since 2000 is the base year)
Prices in 2003 were 120% of
base year prices
90)100(
320
288
100
P
P
I
2000
1996
1996 ==´=
100)100(
320
320
100
P
P
I
2000
2000
2000 ==´=
120)100(
320
384
100
P
P
I
2000
2003
2003
==´=

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

17. 20-17
Weighted index no. Consists of –
Laspeyres index
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:
Where:
q
o = the quantity bought (or sold) in the base period
p
n = price in current period
p
o = price in base period
100index Laspeyres ´=
å
å
oo
on
qp
qp
20-18

19. 20-19
The 1990 party The 2000 party
Drink Unit priceQuantity Unit priceQuantity
p
o
q
o
p
n
q
n
wine 2.50 25 3 30
beer 4.50 10 6.00 8
soft drinks 0.60 10 0.84 15
p
o
q
o
= (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

p
n
q
o
= (3 x 25) + (6 x 10) + (0.84 x 10) = 143.4

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 P
o
, 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:
Where:
p
n
= the price in the current period
p
o
= the price in the base period
q
n
= the quantity bought (or sold) in the current period
100
qp
qp
indexPaasche
no
nn
´=
å
å
20-22

23. 64.135)100(
36.598$
60.811$
)100(
0
===
å
å
t
tt
qp
qp
P

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:
( )( )
100
qpqp
qpqp
indexPaascheindexLaspeyresindexsFisher'
nooo
nnon
´=
=
åå
åå
20-26

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