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Index

Number

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Index Numbers

A SimpleIndex Numbermeasures the relative change injust one variable.

An

Index Numberexpresses the relative

change in price,quantity, or value

compared to a base

period.

36-Month CPI 2000-2002

0

1

2

3

4

1 3 5 7 9 11 13 15 17 19 21 23 25 27 2 9 31 33 35

Month beginning 1/1/2002

CPI

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Stock 1997

Price

1997

Shares

2002

Price

2002

Shares

NWS $1 30 $2 50

NPC $5 15 $4 30

GAC $6 40 $6 20

Mr. X owns

stock in three

companies.

Given is theprice per share

at the end of

1997 and 2002

for the threestocks and the

quantities he

owned in 1997

and 2002.

Simple indexes using 1997 as

base year (1997=100)Price

($2/$1)(100)=200

($4/$5)(100)=80

($6/$6)(100)=100

Share(50/30)(100)=167

(30/15)(100)=200

(20/40)(100)=50

Example 1

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Why Convert Data to Indexes?

CPI

Easier tocomprehendthan actual

numbers(percentchange)

Whycompute

indexes?

Facilitatecomparison ofunlike series

Provide convenientways to express thechange in the totalof a heterogeneousgroup of items

Indexes

Bread $0.89

Car $18,000

Dress $200

Surgery $400,000

$345,651,289,560

or 10%?

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Types of Index Numbers

Indexes: Four classifications

Price

Quantity

Value

Special purpose

Measures the changes

in prices from a

selected base period

to another period.

Measures the changes in

quantity consumed fromthe base period to

another period.

Measures the change in the

value of one or more itemsfrom the base period to the

given period (PxQ).

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.

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Construction of Index Numbers

where

po the base period price

ptthe price at the selected

or given period.

Simple Price Index

From Example 1 a simple

aggregate price index for

the three stocks

0.100

)100(6$5$1$

6$5$2$

)100(0

p

pK t

P

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Two methods of

computing theprice index

Weighted index Considers both the price andthe quantities of items

Laspeyres method

Paasche method wherept is the current price

p0 is the price in the base period

q0 is the quantity consumed in the base

period

Laspeyres Weighted Price Index

Uses the base period quantities as

weights

Upward bias

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Construction of Index Numbers

Paasche Weighted Price Index, P

Present year weights

substituted for the originalbase period weights

Downward bias

where

qt is the current quantity consumedp0 is the price in the base period

pt is the current price.

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Fishers ideal index = (Laspeyres index)(Paasches index)

Balances the negativeeffects of the

Laspeyres and

Paasches indices.

The geometricmean of Laspeyres

and Paasche

indexes

Fishers Ideal Index

Fishers Ideal Index

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Value Index

Both the price and quantity change

from the base period to the given period

Reflects changes in both price and quantity

Value Index

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Exercise: Compute the CPI

Basket contains 20 pizzas and 10 compact discs.

prices:

pizza CDs

2002 $10 $15

2003 $11 $15

2004 $12 $16

2005 $13 $15

For each year, compute

the cost of the basket

the CPI (use 2002 as

the base year)

the inflation rate from

the preceding year

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Cost of Inflation

basket CPI rate

2002 n.a.2003

2004

2005

Answers:

Exercise: Compute the CPI

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Cost of Inflation

basket CPI rate

2002 $350 100.0 n.a.2003 370 105.7 5.7%

2004 400 114.3 8.1%

2005 410 117.1 2.5%

Answers:

Exercise: Compute the CPI

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Consumer Price Index

Usefulness of CPI

It allows consumers to

determine the effect ofprice increases on their

purchasing power.

It is a

yardstick for

revising

wages,pensions, and

other

payments.

It is an economicindicator of the

rate of inflation.

It computesreal income:

real income

= money

income/CPI

(100)

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Mr. X owns

stock in three

companies.

Shown below is

the price per

share at the endof 1997 and

2002 for the

three stocks and

the quantities heowned in 1997

and 2002.

Stock 1997

Price

1997

Shares

2002

Price

2002

Shares

NWS $1 30 $2 50

NPC $5 15 $4 30

GAC $6 40 $6 20

Laspeyres Weighted Price Index, P

35.104)100(345$

360$

)100()40(6$)15(5$)30(1$

)40(6$)15(4$)30(2$

)100(Kp00

0

qp

qpt

Example: Solution

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Example 1 continued

25.106)100(320$

340$

)100()20(6$)30(5$)50(1$

)20(6$)30(4$)50(2$

)100(0

t

tt

qp

qpKp

F= (104.35)(106.25)=105.3

Paasche Weighted Price Index, P

Fishers Ideal Index

55.98)100(345$340$

)100()40(6$)15(5$)30(1$

)20(6$)30(4$)50(2$

)100(00

qpqpK tt

Value Index

Example: Solution

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Prices (Rs. per kg/lit.) Quantities produces (millions of

kg/lit.)

2000 2005 2010 2000 2005 2010

Milk 3.95 3.89 4.13 9675 9717 10436

Butter 61.5 62.2 59.7 117.7 115.5 115.5Cheese 34.8 35.4 38.9 77.93 74.39 82.79

Calculate Laspeyre and Paasche price Index for2010 with 2000 as base.

Practice Exercise

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Prices (Rs.) Quantities (units)

2005 2010 2005 2010

Wheat 200 220 20 12

Rice 300 340 30 36

Cloth 10 8 100 60

Calculate Fishers price Index for 2010 with

2005 as base.

Practice Exercise