Slides by John Loucks St. Edward’s University

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Slides by

JohnLoucks

St. Edward’sUniversity



Chapter 17 Index Numbers

Price Relatives Aggregate Price Indexes Computing an Aggregate Price

Index from Price Relatives Some Important Price Indexes

Deflating a Series by Price Indexes Price Indexes: Other Considerations Quantity Indexes



Price Relatives

Price relative in period =Price in period Base period price

( )tt

100Price relative in period =Price in period Base period price

( )tt

100

A base period is a given starting point in time.

A price relative expresses the unit price in each period as a percentage of the unit price in the base period.

A price relative shows how the current price per unit for a given item compares to a base period price per unit for the same item.

Price relatives are helpful in understanding and interpreting changing economic and business conditions over time.



Price Relatives

Television 11,469 23,904Newspaper $14,794 $29,412

1998 2008

The prices Besco paid for newspaper and

television ads in 1998 and 2008 are shown below.

Using 1998 as the base year, compute a 2008 price

index for newspaper and television ad prices.

Example: Besco Products



Price Relatives

2008

29,412(100) 199

14,794I

Television advertising cost increased at a greater rate.

Newspaper Television

2008

23,904(100) 208

11,469I



An aggregate price index is developed for the specific purpose of measuring the combined change of a group of items.

Aggregate Price Indexes

IPPt

it

i

0100( )I

PPt

it

i

0100( )

wherePit = unit price for item i in period tPi 0 = unit price for item i in the base period

An unweighted aggregate price index in period t,denoted by It , is given by



Letting Qi = quantity for item i, the weighted aggregate price index in period t is given by

IP QP Qt

it i

i i

0100( )I

P QP Qt

it i

i i

0100( )


where the sums are over all items in the group

With a weighted aggregate index each item in the group is weighted according to its importance, which typically is the quantity of usage.




When the weights are based on period t usage, the index is a Paasche index.

When the fixed quantity weights are determined from the base-year usage, the index is called a Laspeyres index.




Data on energy consumption and expenditures

by sector for the city of Rockdale are given on the

next slide. Construct an aggregate price index for

energy expenditures in 2008 using 1990 as the base

year.

Example: City of Rockdale




Transport. 15,293 20,262 2.32 6.16

Industrial 21,287 17,832 .79 5.13

Commercial 5,416 6,015 1.97 11.32

Residential 9,473 8,804$2.12 $10.92

Sector 1990 2008 1990 2008

Quantity (BTU) Unit Price ($/BTU)




Unweighted Aggregate Price Index


2008

10.92 11.32 5.13 6.16(100) 466

2.12 1.97 .79 2.32I




Weighted Aggregate Index (Laspeyres Method)


2008

10.92(9,473) 6.16(15,293)(100) 443

2.12(9,473) 2.32(15,293)I

2008

10.92(8,804) 6.16(20,262)(100) 415

2.12(8,804) 2.32(20,262)I

The Paasche value being less than theLaspeyres indicates usage has increased

faster in the lower-priced sectors.

Weighted Aggregate Index (Paasche Method)




Dina wants an index that measures the change inthe overall cost of her lawn care. Price and quantity data for her annual lawn expenses are listed on the next slide.

Example: Annual Cost of Lawn Care Dina Evers is pleased with her lovely lawn,

but sheis concern about the increasing cost of maintaining it. The cost includes mowing, fertilizing, watering, andmore.




ItemQuantity(Units)

MowingLeaf RemovalWatering (1000s

gal.)FertilizingSprinkler Repair

32 340 2 1

Unit Price ($)2004 2008

57.00

56.00

1.83

56.00

109.00

79.00

71.00

2.78

67.00

128.00

Example: Annual Cost of Lawn Care




Unweighted

0

(100)itt

i

PI

P

where: Pit = unit price for item i in period t Pi 0 = unit price for item i in the base period

Unweighted aggregate price index in period t is:

. . . . .( )

. . . . .

2008

7900 7100 278 6700 12800100 124

5700 5600 183 5600 10900I

A 24%increase

in annuallawn care

expenses

A 24%increase

in annuallawn care

expenses




Weighted aggregate price index in period t is:

0

(100)it it

i i

P QI

P Q

. ( ) . ( ) . ( ) . ( ) . ( )( )

. ( ) . ( ) . ( ) . ( ) . ( )

2008

7900 32 7100 3 278 40 6700 2 12800 1100 136

5700 32 5600 3 183 40 5600 2 10900 1I

Weighted (Fixed Quantity)

where: Qi = quantity for item i

Note that Qi

does not have a

second subscriptfor a time

period.

A 36% increase inannual lawn care

expenses

A 36% increase inannual lawn care

expenses




Weighted (Base-Period Quantity)

A variable-quantity

index

Special caseof the fixed

quantity index

( )it it

i i

P QI

P Q

0

0 0

100

( )it itt

i it

P QI

P Q 0

100

LaspeyresIndex

PaascheIndex

More widelyused than

thePaasche

index

Pro: Reflectscurrent

usage; Con: Weightsrequire

contin- ual updating

Weighted (Period t Quantity)




The 5-year increases in unit price ranged from a low of 17.4% for sprinkler repair to a high of 51.9% for water.

The 5-year increases in unit price ranged from a low of 17.4% for sprinkler repair to a high of 51.9% for water.


Item i

MowingLeaf RemovalWater (1000s gal.)FertilizingSprinkler Repair

Unit Price ($)2004 2008

57.00

56.00

1.83

56.00

109.00

79.00

71.00

2.78

67.00

128.00

Pi 0 Pi t

PriceRelative

(Pi t/Pi 0)100

138.6

126.8

151.9

119.6

117.4

79(100)

57



Item

PriceRelative

(Pit/Pi 0)100

MowingLeavesWater FertilizeSprinkle

r

BasePrice ($)

57.00

56.00

1.83

56.00

109.00

Qi

138.6

126.8

151.9

119.6

117.4

Pi 0

Quantity

32 340 2 1

Weightwi = Pi 0Qi

WeightedPrice Relative(Pit/Pi 0)(100)wi

1,824.0

168.0

73.2

112.0

109.0

252,806.40

21,302.40

11,119.08

13,395.20

12,796.60

Total 2,286.2 311,419.68( ), .

, .

0

100311 41968

1362 2862

iti

it

i

Pw

PI

w


This value is the same as the

one identified by the weighted

aggregate index computation.

This value is the same as the

one identified by the weighted

aggregate index computation.



• Its base period is 1982-1984 with an index of 100.

• Published monthly by the U.S. Bureau of Labor Statistics.

• Weighted aggregate price index with fixed weights derived from a usage survey.

• Based on 400 items including food, housing, clothing, transportation, and medical items.

• Primary measure of the cost of living in U.S.

Some Important Price Indexes

Consumer Price Index (CPI)



Year CPI Year CPI Year CPI Year CPI1977 60.6 1985 107.6 1993 144.5 2001 177.11978 65.2 1986 109.6 1994 148.2 2002 179.91979 72.6 1987 113.6 1995 152.4 2003 184.01980 82.4 1988 118.3 1996 156.9 2004 188.91981 90.9 1989 124.0 1997 160.5 2005 195.31982 96.5 1990 130.7 1998 163.0 2006 201.61983 99.6 1991 136.2 1999 166.6 2007 207.31984 103.9 1992 140.3 2000 172.2 2008 215.3

Consumer Price Index (CPI) Base 1982-1984 = 100.0

Note: For 1982 – 1984 that (96.5 + 99.6 + 103.9)/3 = 100.0




• Is a weighted average of price relatives using the Laspeyres method.

• Includes the output of manufacturing, agriculture, forestry, fishing, mining, gas and electricity, and public utilities.

• Covers raw, manufactured, and processed goods at each level of processing.

• Used as a leading indicator of the future trend of consumer prices and the cost of living.

• Measures the monthly changes in prices in primary markets in the U.S.

Producer Price Index (PPI)




• Another average is computed for 20 transportation stocks, and another for 15 utility stocks.

• The DJIA is not expressed as a percentage of base-year prices.

• The Dow Jones Industrial Average (DJIA) is based on common stock prices of 30 industrial firms.

• Indexes designed to show price trends and movements on the New York Stock Exchange.

Dow Jones Averages




3M Disney J.P.Morgan Chase

Alcoa DuPont Kraft Foods

American Express ExxonMobil McDonald's

At&T General Electric Merck

Bank of America General Motors Microsoft

Boeing Hewlett-Packard Pfizer

Caterpillar Home Depot Procter & Gamble

Chevron Corp. IBM United Technologies

Citigroup Intel Verizon

Coca-Cola Johnson & Johnson Wal-Mart Stores

Dow Jones Industrial Average (DJIA) 30 Companies

As of 04/2009




Deflating a Series by Price Indexes

Deflating actual hourly wages results in real wages or the purchasing power of wages.

In order to correctly interpret business activity over time when it is expressed in dollar amounts, we should adjust the data for the price-increase effect. Removing the price-increase effect from a time series is called deflating the series.



McNeer Cleaners, with 46 branch locations, has

had the total sales revenues shown on the nextslide for the last five years. Deflate the sales revenue

figures on the basis of 1982-1984 constant dollars. Is

the increase in sales due entirely to the price-increase

effect?

Example: McNeer Cleaners




Example: McNeer Cleaners


2008 11,690 215.3

2007 10,724 207.3

2006 9,830 201.6

2005 9,062 195.3

2004 8,446 188.9

Year Total Sales ($1000) CPI



Adjusting Revenue For the Price-Increase Effect

After adjusting, revenue is still increasing at anaverage rate of 5.0% per year.

2008 (11,690/215.3)(100) = 5,430 +5.02007 (10,724/207.3)(100) = 5,173 +6.1

2006 (9,830/201.6)(100) = 4,876 +5.12005 (9,062/195.3)(100) = 4,640 +3.82004 (8,446/188.9)(100) = 4,471

YearDeflated

Sales ($1000)Annual

Change (%)




Real S

ale

s R

even

ue

($1

00

0s)

Real S

ale

s R

even

ue

($1

00

0s)

2004 2005 2006 2007 20082004 2005 2006 2007 2008

A real sales

increase of

21.45% from 2004

to 200845004500

47504750

50005000

52505250

5500 5500

42504250

Year

4471

4640

5173

5430

4876




When the class of items is very large, arepresentative group (usually not a random

sample)must be used.The group of items in the aggregate index must

beperiodically reviewed and revised if it is not representative of the class of items in mind.

Selection of Items

Price Indexes: Other Considerations



For example, a CPI with a 1945 base period wouldbe difficult for most individuals to understand, dueto unfamiliarity with conditions in 1945.

Selection of a Base Period

The base period for most indexes isadjusted periodically to a more recentperiod of time.

As a rule, the base period should not be too far from the current period.

The CPI’s base periodwas changedto 1982-84

in 1988.




An increase in an item’s quality may or may notresult in a price increase . . . and a decrease inquality may or may not result in a price decrease.

Is a product that has undergone a major qualitychange the same product it was ?

A basic assumption of a price index is that pricesover time are identified for the same item.

Quality Changes




An index used to measure changes in quantity levels over time is called a quantity index.

A weighted aggregate quantity index is computedin much the same way as a weighted aggregateprice index.

A quantity relative shows how the current quantitylevel for a single item compares to a base periodquantity level for the same item.

Quantity Indexes

IQ wQ wt

it i

i i

0100( )I

Q wQ wt

it i

i i

0100( )



Example: Appliance Mart Appliance Mart reports the 1999 and 2008 sales forthree major kitchen appliances as shown below. Compute quantity relatives and use them to develop a weighted aggregate quantity index for 2008.Kitchen

Appliance

Sales Price(1999)

DishwasherRangeRefrigerato

r

Sales (Units)1999 2008

720

540

980

950

610

1110

$325

$450

$710

Quantity Indexes



KitchenApplianc

eDishwasherRangeRefrigerato

r

Sales (Units)1999 2008

720

540

980

950

610

1110

Quantity Relative

(950/720)100 = 131.9 (610/540)100 = 113.0(1110/980)100 = 113.3

Quantity in period Quantity relative in period = (100)

Base period quantityt

t

Quantity Indexes



Unweighted

itt

i

QI

Q 0

(100)

where: Qit = quantity for item i in period t Qi 0 = quantity for item i in the base period

Unweighted aggregate quantity index in period t is:

( )

2008

950 610 1110100 119

720 540 980I

Quantity Indexes



it it

i i

Q PI

Q P

0

0 0

(100)

Weighted (Base-Period Price)

( ) ( ) ( )( )

( ) ( ) ( )

2008

950 325 610 450 1110 710100 117

720 325 540 450 980 710I

where: Pi 0 = price for item i in the base period

Weighted aggregate quantity index in period t is:

Quantity Indexes



it it

i i

Q PI

Q P 0

(100)

Weighted (Fixed Price)

it itt

i it

Q PI

Q P 0

(100)

Weighted (Period t Price)

Note that Pi

does not have a

second subscriptfor a time

period.

Quantity Indexes



End of Chapter 17

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