Transcript INDEX NUMBERS

INDEX NUMBERS
Definition of Index Number
A summary measure that states a
relative comparison between groups
of related items
 Price Relative or Percentage Relative
 A Number used to measure how
much somthing has changed from
one time period to another

Simple Price Relative Index
An index which describes a
single item or commodity in
a given period versus the
base period
Simple Price Index
Pn
IP =
Po
.
100
Example of Simple Price Index
Suppose the price of one pound of a
certain brand of coffee was $2.00 in
1990, $3.22 in 1995 and $6.04 in 1997.
What are the price indicies of the
three figures, with 1990 as the base
(written, 1990 = 100)?
YEAR
PRICE INDICES
(1990 = 100)
1990
 $2.00 

 100  100
 $2.00 
1995
 $3.22 

 100  161
 $2.00 
1997
 $6.04 

 100  302
 $2.00 
pn
I
po
$2.00
$3.22
$6.04
Quantity Index
Q
I   100
Qo
n
Q
Value Index
PQ
n
n
I
 100
PQ
o o
V
Unweighted
Aggregate Price Index
(Summarizes a groups of items or commodities)
I
P
 n
P
 o
 100
C o m m o d ity
P rice
1995(p o )
1997(p n )
M ilk (p in t)
Ro u n d S te a k(lb )
F lo u r,w h e a t (lb )
Eg g s, G ra d e A la rg e (d o z e n )
Unweighted Aggregate
Price Index:
19.6
188.5
19.9
77.0
305.0
21.4
189.5
16.9
81.5
309.3
pn

I
 100
 po
21.4  189 .5  16.9  81.5
309 .3
I
100 
 101
19.6  188 .5  19.9  77.0
305 .0
C o m m o d ity
P rice
1995(p o )
1997(p n )
M ilk (p in t) quart
156.8
Ro u n d S te a k(lb )
F lo u r,w h e a t (lb )
Eg g s, G ra d e A la rg e (d o z e n )
442.2
Unweighted Aggregate
Price Index:
19.6
188.5
19.9
77.0
305.0
171.2
459.1
21.4
189.5
16.9
81.5
309.3
pn

I
 100
 po
171 .2  189 .5  16.9  81.5
I
 100  134 ..16
156 .8  88.5  19.9  77.0
101=134.16
Dow Jones Industrial Average
(DJIA)
30
DJIA 
P
n 1
n
Divisor
Where:
Pn = the price of stock n
Divisor = the special DJIA divisor
Unweighted Average of Price
Relatives Index
I

P
 100
P
k
n
o
Price
1995(po) 1997(pn)
Commodity
Milk (quart)
Round Steak(lb)
Flour,wheat (lb)
Eggs, GradeA large (dozen)
I

156.8
188.5
19.9
77.0
305.0
171.2
189.5
16.9
81.5
309.3
pn/po
1.09
1.01
0.85
1.06
4.01
Pn
 100
Po
k
(109
.  101
.  0.85  106
. )  100 4.01(100)
I

 100.25
4
4
Weighted Aggregate Price
Index
 Takes
prices and quantities
(weights) into consideration
 Laspeyres Index
 Paasche Index
 Fixed-Weight AggregatePrice
Index
Laspeyres Index
 Quantities
are from the base
period
 Reflects changes in prices alone
 Tends to overestimate price
 Ignores changes in consumption
 Easiest to calculate
 Consumer Price Index-modified
Laspeyres Index
PQ

I
 100
PQ
n
o
o
o
1990
p 90
Re frige ra tor 335
Ra nge
425
Toa ste r
18
TV
390
Laspeyres Index=
q 90
2
3
22
12
1996
p90q90
670
1275
396
4680
7021
p 96
444
588
25
440
q 96
12
18
58
29
PQ

I 
 100
PQ
96
90
90
90
8482
I
 100  120 .8
7021
p96q90
888
1764
550
5280
8482
Paasche Index
Quantities are from the given period
 Reflects changes in production or
consumption
 Tend to underestimate price change
 Weights have to be revised each time
period
 Can be costly and time consuming

Paasche Index
PQ

I
 100
PQ
n
n
o
n
1990
p 90
Re frige ra tor 335
Ra nge
425
Toa ste r
18
TV
390
Paasche Index=
q 90
2
3
22
12
1996
p90q96
4020
7650
1044
11310
24024
p 96
444
588
25
440
q 96
12
18
58
29
PQ

I 
 100
PQ
96
90
96
96
30122
 100  125 .4
I 
24024
p96q96
5328
10584
1450
12760
30122
Fixed-Weight Aggregate
Price Index
Weights are from one or more
representative periods
 Bureau of Labor Statistics revises
weights every 10 years
 Producer Price Index
 Government agencies indicies are
publishes in series (impractical to
use Paasche)

Fixed-Weight Aggregate
Price Index
PQ

I
 100
PQ
n
a
o
a
Weighted Arithmetic Mean of
Price Relatives Index
Pn


(
w
(
))
 Po 100
I
w
Where w = paqa
Standard and Poor’s (S&P) 500
Index


  N i Pi 
i 1


S&P 
10
 O.V . 




500
Where:
O.V. = original valuation in 1941- 43
Ni
= number of shares outstanding for Firm I
Pi
= price of shares for Firm i
Consumer Price Index
Fixed-weight aggregate price
index
(modified Laspeyres)
Consumer Price Index
Measures average changes in prices of
a fixed “market basket”of goods and
services usually bought by urban wage
earners and clerical workers from one
time period to another
 Published monthly by Bureau of Labor
Statistics
 400 goods and services

Uses of CPI



Economic Indicator
Escalator
Deflator for real wages
 Process called deflating
money wages
 Price index - deflator
 Deflated dollar value = constant dollar
Real Wages
Real Wages98 =
Current Wage98
X 100
Consumer Price Index98
CPI1987 = 100
$30,853
$27,159 .33 
100
113 .6
Purchasing Power of Dollar
1
$=
X 100
CPI
1
$.82 =
X 100
122
$0.18 decrease in purchasing power of $
% age Increase or Decrease
Current Wage - Past Wage
X 100
Past Wage
30000 - 20000
20000
X 100 = 50%
Median
Family
Income
CPI1987=100
Real Income
1990
$20,000
105.5
$18,957.35
1998
$30,000
130.5
$22,988.51
50%
increase
23.7%
increase
21.3%
increase
Median
Shift Base
Family
Income CPI1987=100 CPI1990=100 Real Income
1990
$20,000
105.5
100
$20,000
1998
$30,000
130.5
123.7
$24,252.22
50%
increase
23.7%
23.7%
increase increase
21.3%
increase