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Elasticity

Hall and Lieberman, 3rd edition, Thomson South-Western, Chapter 4


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Overview

Elasticity calculation and interpretation

Difference between elastic, inelastic, and unitaryelasticdemand/supply

Prediction on revenue change in response to achange in price

Elasticity varies as one moves along a straight-linedemand curve

Determinants of price elasticity of demand/supply

Income elasticity

Cross price elasticity of demand


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Motivation to Study Elasticity The Problem with Rate Change

-- is not a good measure of pricesensitivity

Doesnt tell whether a change in price or a change inquantity demanded is a relatively large or relativelysmall change Relative means compared to value of price or quantity before

change

One extreme example: 100 more Big Mac purchased per week after every $1

decrease in Ames

100 more Ipod Nano purchased per week after every $1decrease in Ames

PQ (( /


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Elasticity - Concept Elasticity approach improves on the problems with rate of change

By comparing percentage change in quantity demanded with percentagechange in price

Price elasticity of demand ( ) for a good is percentage change inquantity demanded divided by percentage change in price

P%Q%

D

D ((

!L always be a negative number

Arc elasticity

Price elasticity of demand tells us percentage change in quantitydemanded caused by a 1% rise in price as we move alonga demandcurve from one point to another

LD


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Part 1: Price Elasticity of Demand

- Calculation

Base value for percentage changes in price or quantity is alwaysmidway between initial value and new value

Denominator

- Define the percentage change in price from any value P0 to any othervalue P1 as

2

)(

)(PriceinChange%

PPPP

01

01

!

Numerator:

When quantity demanded changes from Q0 to Q1,percentage change is calculated as

-

!

2

)_(emandedQuantityinhange

01

01

QQ

QQ


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Figure 1: Calculating Price Elasticity of Demand

-- laptop computer demand

Quantity ofLaptops

C

Price perLaptop

100,000 00,000 300,000 400,000 500,000 600,000

$3,500

3,000

,500

,000

1,500

1,000

B

A

D

D


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Calculating Price Elasticity of Demand

-- An Example Now lets calculate an elasticity of demand for laptop

computers using data in Figure 1 from point A to point B

%2.18or,182.0000,550

000,100

2

)000,600000,500(

)000,600000,500(Q% !

!

-

!(

Use percentage changes for price and quantity tocalculate price elasticity of demand ( )

%40.0or,400.0250,1$

500$

2

)000,1$500,1($

)000,1$500,1($P% !!

-

!(

46.0400.0

182.0D

!

!L

LD


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Price Elasticity of Demand

-- Categorize Goods Inelastic Demand

Price elasticity of demand between 0 and -1

1.0P%

Q%DemandInelastic (

(

|% Change in Quantity Demanded| < |% Change in Price|

Extreme Case: Perfectly Inelastic Demand Price elasticity of demand equal to 0


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Categorizing Goods by Elasticity Elastic Demand Price elasticity of demand with absolute value > 1

|% Change in Quantity Demanded| > |% Change in Price|

Extreme Case: Perfectly (infinitely) Elastic Demand Price elasticity of demand approaching minus infinity

Another Special Case: Unitary Elastic Demand Price elasticity of demand equal to -1

1P%

Q%

DemandElastic"

(

(


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Figure 3: Relationship between demand

slope and elasticityElasticityElasticity = |(1/slope)*(P/Q)|= |(1/slope)*(P/Q)|

Quantity

PRICE

Perfectly elastic

Perfectly inelastic

Relatively Inelastic Demand

Relatively Elastic Demand


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Figure 4(a): When does it pay to raise the price?

Price increases from P0 to P1 and quantitydemanded decreases from Q0 to Q1

Quantity

PRICE

Demand

P1

P0

Q1 Q0


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Figure 4(b): When does it pay to raise theprice? How about revenue change?

Quantity

PRICE

Demand

P1

P0

Q1 Q0

Change in total revenue =

P1Q1-P0Q0


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Figure 4(c): When does it pay to raise the

price? How much is the change in total revenue?

Quantity

PRICE

Demand

P1

P0

Q1 Q0

Change in total revenue =

P1Q1-P0Q0

Loss = P0*(Q0 - Q1)

= P0Q

Gain = Q1(P1 P0)

= Q1P


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When does it pay to raise the price?

SUPPOSE DEMAND IS INELASTIC SO THAT THE %CHANGE IN QUANTITY IS SMALLER THAN THE %CHANGE IN PRICE

LOSS GAIN

1( )

( )

D

Q PQ PEP Q P Q

Q P P Q

( y (! y ! ( ( y

( y

( y


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Elasticity & Straight-Line Demand Curves

Look at percentage change in P

Look at percentage change in Q

As we move upward and leftward by equal distances,

percentage change in quantity rises Percentage change in price falls

Elasticity of demand varies along a straight-line demandcurve

Demand becomes more elastic as we move upwardand leftward


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Figure 4: Elasticity and Straight-

Line Demand Curves

Quantity

Price

and since equal quantity decreases(horizontal arrows) are larger andlargerpercentage decreases . . .

Since equal dollar increases (verticalarrows) are smaller and smallerpercentage increases . . .

1

2

3

D

demand becomes more and moreelastic as we move leftward andupward along a straight-linedemand curve.


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0

4

6

8

10

0 10 0 30 40 50

PRICE

QUANTITY

1(1/ ) 5

DPE

slope Q

slope fixed

! y

! !

As P increases, Q falls,elasticity gets bigger

| ED | > 1

elastic

| ED | = 1

Unit elastic

| ED | < 1

inelastic

2525

55


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Small Summary

Inelastic

Demand

Unitary ElasticDemand

Elastic Demand

Definition |ED| 1

Total Revenue Same directionas price change

Does not changewith price

change

Oppositedirection

from price

Straight LineDemand Curve

Lowersegment

Middle point Upper segment


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What Affects Elasticity?

-- 1. Availability of Substitutes

Demand is more elastic

If close substitutes are easy to find and buyers

can cut back on purchases of the good inquestion

Demand is less elastic

If close substitutes are difficult to find andbuyers can not cut back on purchases of thegood in question


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-- 2. Narrowness ofMarket More narrowly we define a good, easier it

is to find substitutes

More elastic is demand for the good More broadly we define a good

Harder it is to find substitutes and the lesselastic is demand for the good

Different things are assumed constantwhen we use a narrow definitioncompared with a broader definition


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-- 3.Necessities vs. Luxuries

The more necessary we regard an item,the harder it is to find a substitute

Expect it to be less price elastic

The less necessary (luxurious) we regardan item, the easier it can be substituted

Expect it to be more price elastic

Example?


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-- 4. Time Horizon Short-run elasticity

Measured a short time after a price change

Long-run elasticity Measured a year or more after a price change

Usually easier to find substitutes for an item inthe long run than in the short run

Therefore, demand tends to be more elastic in thelong run than in the short run


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-- 5. Importance in the Buyers Budget

The more of their total budgets thathouseholds spend on an item

The more elastic is demand for that item

The less of their total budgets thathouseholds spend on an item

The less elastic is demand for that item


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Using Price Elasticity of Demand

-- (1) The War on Drugs Every year U.S. Government spends about $20

billion on efforts to restrict the supply of drugs

Figure 6(a) Market for heroin without government intervention

Figure 6(b)

Result of government efforts to restrict supply (current

policy) Figure 6(c)

Results of an effective policy of reducing demand


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Using Price Elasticity of Demand-- (2) Mass

Transit Elasticity studies show that long-run

demand for mass transit is inelastic

Therefore, a rise in fare would increase revenues Would also decrease ridership and require the city to

sacrifice other goals To provide low-income households with affordable

transportation

To manage traffic congestion by enough ridership

To limit air pollution in the city

most cities do not raise transit fares


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Source: ISU FACTBOOK

Figure 8 ISU Nonresident Enrollment and

Nonresident Tuition and Fees, 2002 & 2005

Year Tuition Freshmen Non Resident

2002 $12,083 1240 4255

2005 $15, 0 6 418

Change 3624 -264 -66

Mid point 138 5 1108 4222%change 0.261 -0.238 -0.016

Elasticity -0. 14 -0.060

%

%D

Q

E P

(

! (


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Part 2: Income Elasticity of Demand

Percentage change in quantity demandeddivided by the percentage change in income With all other influences on demand with the price of

the goodkept constant

Y%

Q%

IncomeinChange%

DemandedQuantityinchange%Y

(

(!

!L

Interpretation: percentage increase in quantitydemanded for each 1% rise in income


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Income Elasticity of Demand vs.

Price Elasticity of Demand Price elasticity measures sensitivity of demand toprice as we move alonga demand curve from one

point to another Income elasticity tells us relative shiftin demand

curveincrease in quantity demanded at a givenprice

While a price elasticity is virtually always negative,income elasticity can be positive or negative

Normal goods

Inferior goods


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Income Elasticity of Demand

Economic necessity Good with an income elasticity of demand between 0 and 1

Economic luxury Good with an income elasticity of demand greater than 1

An implication As income rises, proportion of income spent on economic

necessities will fall While proportion of income spent on economic luxuries will rise

But, it is important to remember that economicnecessities and luxuries are categorized by actualconsumer behavior Not by our judgment of a goods importance to human survival


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Figure 9 Some Income Elasticities

IncomeElasticity

IncomeElasticityGood or Service Good or Service

FreshFruit 1. Imports 2. 3

Computers 1. 1

Transatlantic Air Travel 1.40 Transportation 1.

College Education 0.55

Cigarettes 0.50 Recreation 1.0

Chicken 0.42 Clothing 1.02

Pork 0.34 Food 0.60 to 0.85

Fresh Vegetables 0.26

Tooth Extraction 0.13 to 0.4

Ground Beef

0.20Bread 0.42

Potatoes 0.81 Luxury (>1), Necessity (0


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Figure 10 Some Cross-Price Elasticities

Products Cross-Price Elasticity

Margarine with price of butter 1.53

Pepsi with price of Coke 0.80

Coke with price ofPepsi 0.61

Ground beef with price of beef table cuts 0.41Ground beef with price of poultry 0.24

Electricity with price of natural gas 0.20

Theater with price of all other lively arts 0.12

Entertainment with price of food 0. 2

Complements (-) vs Substitutes (+)

defined by sign of cross price elasticity


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Part 4: Price Elasticity of Supply

Percentage change in quantity of a goodsupplied that is caused by a 1% change in the

price of the good With all other influences on supply held constant

PriceinChange%

SuppliedQuantityinChange%S!L


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What Affects Price Elasticity of Supply?

Supply will tend to be more elastic whensuppliers can switch to producing alternategoods more easily

How easy? Depends on Nature of the good itself

Narrowness of the market definitionespecially geographicnarrowness

Time horizonlonger we wait after a price change, greaterthe supply response to a price change


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Price Elasticity of Supply

Extreme cases of supply elasticity

Perfectly inelastic supply curve is a vertical

line Many markets display almost completely inelastic

supply curves over very short periods of time

Perfectly elastic supply curve is a horizontal

line


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Figure 10: Extreme Cases of Supply

S

(a)

Quantity per Period

Priceper

Unit

P1

P2 S

(b)

Quantity per Period

Priceper

Unit

Perfectly InelasticSupply

Perfectly ElasticSupply

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