INDEX NUMBERS

Index Numbers Definition Unweighted and Weighted Index

Numbers ( Simple Index Numbers, Laspeyre’s,

Paasche’s Index, Fisher’s “Ideal” Index) CPI ( Consumer Price Index ) Issues in using Index Numbers

DefinitionAn index number describes how collected data (statistics) changes over time. They are often used for comparison between price, quantity and value between different time periods.

It provides a summary of information in a simple form and it is widely used by government bodies, for economic policy and business information.

caseA cup of coffee in a particular café cost $10 in 1995. In 2002, an identical cup of coffee cost $15. How has the price changed between 1995 and 2002?1995 Base period $102002 Given period $15

1501001015

15010010

15

PgPb %50

Index number=

Unweighted Index Numbers

Simple Index Simple Composite (aggregate) Index Simple Average Index

Unweighted Index Numbers

Simple Index Numbers Simple Price Index Simple Quantity Index Composite (aggregate) Index Simple Average Index

Unweighted Index Numbers

Simple Index Simple Composite (aggregate) Index Simple Composite (aggregate) Price Index Simple Composite (aggregate) Quantity Index Simple Average Index

Unweighted Index Numbers

Simple Index Simple Composite (aggregate) Index Simple Average Index Simple Average Price Index Simple Average Quantity Index

Unweighted Index Numbers

Simple Index Simple Price Index Simple Quantity Index Simple Composite (Aggregate) Index Simple Composite (Aggregate) Price Index Simple Composite (Aggregate) Quantity Index Simple Average Index Simple Average Price Index Simple Average Quantity Index

1. Simple Index

Simple Price Index

Simple Quantity Index

100Pb

Pg

100Qb

Qg

2007 (Base year) 2009 (Given year)

Price Quantity Price Quantity

Racquets $120 420 $160 480

Court Hire

$15 2,300 $15 2,500

Shoes $120 390 $100 270

100Pb

Pg

A. What is the simple price index for Racquets?

33.133100120

160

The price of racquets increased by 33.33% from 2007 to 2009.

2007 (Base year) 2009 (Given year)

Price Quantity Price Quantity

Racquets $120 420 $160 480

Court Hire

$15 2,300 $15 2,500

Shoes $120 390 $100 270

100Qb

Qg

B. What is the simple quantity index for Shoes?

23.69100390

270

2. Simple Composite (Aggregate) Index

Simple Aggregate Price Index

Simple Aggregate Quantity Index

100Pb

Pg

100Qb

Qg

2007 (Base year) 2009 (Given year)

Price Quantity Price Quantity

Racquets $120 420 $160 480

Court Hire

$15 2,300 $15 2,500

Shoes $120 390 $100 270A. What is the simple aggregate price

index?

84.10710012015120

10015160

100Pb

Pg

The total price of the selected items increased by 7.84% from 2007 to 2009.

2007 (Base year) 2009 (Given year)

Price Quantity Price Quantity

Racquets $120 420 $160 480

Court Hire

$15 2,300 $15 2,500

Shoes $120 390 $100 270B. What is the simple aggregate quantity

index?

100Qb

Qg

50.104100

390300,2420

7022,500804

3. Simple Average Index

Simple Average Price Index

Simple Average Quantity Indexn

100PbPg

n

100QbQg

2007 (Base year) 2009 (Given year)

Price Quantity Price Quantity

Racquets $120 420 $160 480

Court Hire

$15 2,300 $15 2,500

Shoes $120 390 $100 270A. What is the simple average price index?

56.1053

100120100

1001515

100120160

n

100PbPg

The price of the selected items,

on average, increased by 7.84% from 2007 to 2009.

2007 (Base year) 2009 (Given year)

Price Quantity Price Quantity

Racquets $120 420 $160 480

Court Hire

$15 2,300 $15 2,500

Shoes $120 390 $100 270B. What is the simple average quantity index?

n

100QbQg

40.973

100390270

100300,2

2,500100

420480

Weighted Index Numbers

Laspeyre’s Index Paasche’s Index Fisher’s “Ideal” Index

Laspeyere’s Index

100Qb)(Pb

Qb)(Pg

100Qb)(Pb

Qg)(Pb

2007 (Base year) 2009 (Given year)

Price Quantity Price Quantity

Racquets $120 420 $160 480

Court Hire

$15 2,300 $15 2,500

Shoes $120 390 $100 270

100Qb)(Pb

Qb)(Pg

100)390120()300,215()420120(

)390100()300,215()420160(

83.106

Paasche’s Index

100Qg)(Pb

Qg)(Pg

100Qb)(Pg

Qg)(Pg

2007 (Base year) 2009 (Given year)

Price Quantity Price Quantity

Racquets $120 420 $160 480

Court Hire

$15 2,300 $15 2,500

Shoes $120 390 $100 270

100)270120()500,215()480120(

)270100()500,215()480160(

82.110

100Qg)(Pb

Qg)(Pg

Fisher’s “Ideal” Index

LaspeyrePaasche

2007 (Base year) 2009 (Given year)

Price Quantity Price Quantity

Racquets $120 420 $160 480

Court Hire

$15 2,300 $15 2,500

Shoes $120 390 $100 270LaspeyrePaasche

81.10882.10183.061

Laspeyere’s Index

100Qb)(Pb

Qb)(Pg

Paasche’s Index

100Qg)(Pb

Qg)(Pg

Fisher’s Index

LaspeyrePaasche

Consumer Price Index (CPI)

It examines the changes in the price of groups of goods and services referred to as “the basket”.

100, 1, 2,...,i ig b

i ib b

P QCPI i n

P Q

Calculation Calculate new CPI after shifting base

year to 2006. Using new CPI convert rental for 2009 to real prices.

Year CPI Salary Revised CPI

2005 160.1 2,000

2006 167.8 2,500 100.00

2007 183.5 3,520 109.36

2008 200.2 4,600 119.31

2009 350.4 5,000 208.82

36.109 100167.8

183.5

100

Current CPINew CPI

Base Year Old CPI

CalculationYear CPI Salary Revised

CPI

2005 160.1 2,000

2006 167.8 2,500 100.00

2007 183.5 3,520 109.36

2008 200.2 4,600 119.31

2009 350.4 5,000 208.82

Re 100

Actual Valueal Value

CPI

$5,000100 $2,394.41

208.82

CalculationYear CPI Salary Revised

CPI

2005 160.1 2,000

2006 167.8 2,500 100.00

2007 183.5 3,520 109.36

2008 193.2 4,600 119.31

2009 203.4 5,000 208.82

$2,500 208.82$5,220.5

100

Re

100

al Value CPIActual Value

Issues in Using Index Numbers

Choice of Formula Choice of “Basket” Choice of Price Choice of Base year