Definition Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s...

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INDEX NUMBERS

Transcript of Definition Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s...

Page 1: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

INDEX NUMBERS

Page 2: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 3: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.
Page 4: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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.

Page 5: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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=

Page 6: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

Unweighted Index Numbers

Simple Index Simple Composite (aggregate) Index Simple Average Index

Page 7: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

Unweighted Index Numbers

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

Page 8: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

Unweighted Index Numbers

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

Page 9: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

Unweighted Index Numbers

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

Page 10: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 11: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

1. Simple Index

Simple Price Index

Simple Quantity Index

100Pb

Pg

100Qb

Qg

Page 12: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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.

Page 13: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 14: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

2. Simple Composite (Aggregate) Index

Simple Aggregate Price Index

Simple Aggregate Quantity Index

100Pb

Pg

100Qb

Qg

Page 15: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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.

Page 16: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 17: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

3. Simple Average Index

Simple Average Price Index

Simple Average Quantity Indexn

100PbPg

n

100QbQg

Page 18: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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.

Page 19: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 20: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

Weighted Index Numbers

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

Page 21: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

Laspeyere’s Index

100Qb)(Pb

Qb)(Pg

100Qb)(Pb

Qg)(Pb

Page 22: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 23: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

Paasche’s Index

100Qg)(Pb

Qg)(Pg

100Qb)(Pg

Qg)(Pg

Page 24: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 25: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

Fisher’s “Ideal” Index

LaspeyrePaasche

Page 26: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 27: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

Laspeyere’s Index

100Qb)(Pb

Qb)(Pg

Paasche’s Index

100Qg)(Pb

Qg)(Pg

Fisher’s Index

LaspeyrePaasche

Page 28: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 29: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 30: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 31: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

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

Page 32: Definition  Unweighted and Weighted Index Numbers ( Simple Index Numbers, Laspeyre’s, Paasche’s Index, Fisher’s “Ideal” Index)  CPI ( Consumer Price.

Issues in Using Index Numbers

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