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

P

P 100n

o

.IP =

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)?

1990

1995

1997

$2.

$2.

00

00100 100

$3.

$2.

22

00100 161

$6.

$2.

04

00100 302

PRICE INDICESYEAR (1990 = 100)

$2.00$3.22$6.04

$2.00$3.22$6.04

Ip

p n

o

Quantity Index

IQ

Q 100

Q

n

o

Value Index

IPQ

PQ 100n n

oo

V

Unweighted Aggregate Price Index

(Summarizes a groups of items or commodities)

IP

P

100n

o

Price

Commodity 1995(po) 1997(pn)Milk (pint) 19.6 21.4Round Steak(lb) 188.5 189.5Flour,wheat (lb) 19.9 16.9Eggs, GradeA large (dozen) 77.0 81.5

305.0 309.3

Unweighted Aggregate Price Index:

Unweighted Aggregate Price Index:

Ip

p

100n

o

1010.305

3.309100

0.779.195.1886.19

5.819.165.1894.21

I

Price

Commodity 1995(po) 1997(pn)Milk (pint) 19.6 21.4Round Steak(lb) 188.5 189.5Flour,wheat (lb) 19.9 16.9Eggs, GradeA large (dozen) 77.0 81.5

305.0 309.3

156.8 171.2quart

442.2 459.1

Unweighted Aggregate Price Index:

Unweighted Aggregate Price Index:

Ip

p

100n

o

16.1341000.779.195.888.156

5.819.165.1892.171

I

101=134.16

.

Dow Jones Industrial Average(DJIA)

Divisor

PDJIA n

n

30

1

Where:

Pn = the price of stock n

Divisor = the special DJIA divisor

Unweighted Average of Price Relatives Index

I

P

Pk

100n

o

PriceCommodity 1995(po) 1997(pn) pn/po

Milk (quart) 156.8 171.2 1.09Round Steak(lb) 188.5 189.5 1.01Flour,wheat (lb) 19.9 16.9 0.85Eggs, GradeA large (dozen) 77.0 81.5 1.06

305.0 309.3 4.01

I

P

Pk

100n

o

I

( . . . . ) . ( )

.109 101 085 106 100

4

4 01 100

4100 25

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

IP Q

P Q

100n o

o o

1990 1996p90 q90 p96 q96

Refrigerator 335 2 444 12Range 425 3 588 18Toaster 18 22 25 58TV 390 12 440 29

Laspeyres Index= IP Q

P Q

10096 90

9090

p96q90

8881764550

52808482

p90q90

670127539646807021

8.1201007021

8482I

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

IP Q

P Q

100n n

o n

1990 1996p90 q90 p96 q96

Refrigerator 335 2 444 12Range 425 3 588 18Toaster 18 22 25 58TV 390 12 440 29

IP Q

P Q

100Paasche Index=96 96

9690

p96q96

53281058414501276030122

p90q96

402076501044

1131024024

I 30122

24024100 125 4.

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

IP Q

P Q

100n a

ao

Weighted Arithmetic Mean of Price Relatives Index

Where w = paqa

w

PP

wI

100))(( n

o

Standard and Poor’s (S&P) 500 Index

10..

&

500

1

VO

PNPS i

ii

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

CPI1987 = 100

Real Wages98 =Current Wage98

Consumer Price Index98

X 100

1006.113

853,30$33.159,27$

Purchasing Power of Dollar

$.82 = 1

122X 100

$ = 1

CPIX 100

$0.18 decrease in purchasing power of $

% age Increase or Decrease

Current Wage - Past Wage

Past WageX 100

30000 - 20000

20000X 100 = 50%

Median Family Income CPI1987=100 Real Income

1990

1998

$20,000

$30,000

105.5

130.5

$18,957.35

$22,988.51

50% increase

23.7% increase

21.3% increase

Median Family Income

1990

1998

$20,000

$30,000

50% increase

CPI1987=100

105.5

130.5

23.7% increase

Real Income

$20,000

$24,252.22

21.3% increase

100

123.7

Shift Base

CPI1990=100

23.7% increase