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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 changein quantity demanded with percentagechangein price
Price elasticity of demand ( ) for a good is percentage change in
quantity demanded divided by percentage change in price
P%Q%
D
D
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
D
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Part 1: Price Elasticity of Demand
- Calculation Base value for percentage changes in price or quantity is always
midway 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
)_(DemandedQuantityinChange%
01
01
QQ
QQ
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%
%
1
D
QQQ
E P PP
Q P
P Q
Pslope Q
(Own) Price Elasticity of Demand Or written as
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Figure 1: Calculating Price Elasticity of Demand-- laptop computer demand
Quantity ofLaptops
C
Price perLaptop
100,000 200,000 300,000 400,000 500,000 600,000
$3,500
3,000
2,500
2,000
1,500
1,000
B
A
D
D
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Calculating Price Elasticity of Demand
-- An Example Now lets calculate an elasticity of demand for laptop
computers using data in Figure 1 from point A to point B
%2.18or,182.0000,550
000,100
2
)000,600000,500(
)000,600000,500(
Q%
Use percentage changes for price and quantity tocalculate price elasticity of demand ( )
%40.0or,400.0250,1$
500$
2
)000,1$500,1($
)000,1$500,1($P%
46.0400.0
182.0D
D
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Price Elasticity of Demand
-- Categorize Goods Inelastic DemandPrice 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
1
P%
Q%DemandElastic
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Figure 2: Extreme Cases of Demand
D
Perfectly InelasticDemand
(a)
Quantity
Priceper
Unit
1
2
3
$4
20 40 60 80 100
(b)
D
Quantity20 40 60 80 100
1
2
3
$4
Priceper
Unit
Perfectly ElasticDemand
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Figure 3: Relationship between demand
slope and elasticityElasticity = |(1/slope)*(P/Q)|
Quantity
PRICE
Perfectly elastic
Perfectly inelastic
Relatively Inelastic Demand
Relatively Elastic Demand
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Elasticity and Total Revenue
Total revenue (TR) of all firms is defined as TR = P x Q
Rule: when two numbers are both changing, percentagechange in their product is (approximately) the sum oftheir individual percentage changes Applying this to total revenue
Example: assume demand is unitary elastic and Q risesby 10% % Change in TR = 10% + (-10%) = 0
PQTR %%%
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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 theprice?
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
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Figure 5 Effects of Price Changes on Expenditure
Where demand is: A price increase will: A price decrease will:
Inelastic ( | | 1) decrease expenditure increase expenditure
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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 andlarger percentagedecreases . . .
Since equal dollar increases (verticalarrows) are smaller and smallerpercentageincreases . . .
1
2
3
D
demand becomes more and moreelastic as we move leftward andupward along a straight-linedemand curve.
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0
2
4
6
8
10
0 10 20 30 40 50
PRICE
QUANTITY
1(1/ ) 5
DPE
slope Q
slope fixed
As P increases, Q falls,elasticity gets bigger
| ED | > 1
elastic
|ED |= 1
Unit elastic
|ED |< 1
inelastic
25
5
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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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What Affects Elasticity?
-- 2. Narrowness of Market More narrowly we define a good, easier it
is to find substitutes
More elastic is demand for the good More broadly we define a goodHarder it is to find substitutes and the less
elastic is demand for the good
Different things are assumed constantwhen we use a narrow definitioncompared with a broader definition
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What Affects Elasticity?
-- 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 regard
an item, the easier it can be substituted
Expect it to be more price elastic
Example?
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What Affects Elasticity?
-- 4. Time Horizon Short-run elasticity
Measured a short time after a price change
Long-run elasticityMeasured 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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What Affects Elasticity?
-- 5. Importance in the Buyers Budget The more of their total budgets that
households 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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Figure 6 Some Short-Run Price Elasticities ofDemand
Specific Brands Narrow Categories Broad Categories
Tide Detergent 2.79 Transatlantic Air Travel 1.30 Recreation 1.09
Tourism in Thailand 1.20
Pepsi 2.08 Ground Beef 1.02 Clothing 0.89
Coke 1.71 Pork 0.78 Food 0.67
Milk
0.54 Imports
0.58Cigarettes 0.45 Transportation0.56
Electricity 0.40 to 0.50
Beer 0.26
Eggs 0.26
Gasoline 0.20
Oil
0.15
inelastic
elastic
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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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Figure 7 The War on Drugs
Quantity
PriceperUnit
P1
Q1
D1
A A
S1
Quantity
PriceperUnit
Q1
D1
S1
Quantity
PriceperUnit
P1
Q1
S1
D1
(a) (b) (c)
A
P1
Q2
B
S2
P2
Q3
P3
D2
C
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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 tosacrifice 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 andNonresident Tuition and Fees, 2002 & 2005
Year Tuition Freshmen Non Resident
2002 $12,083 1240 4255
2005 $15,707 976 4189
Change 3624 -264 -66
Mid point 13895 1108 4222%change 0.261 -0.238 -0.016
Elasticity -0.914 -0.060
%
%D
QE
P
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Part 2: Income Elasticity of Demand
Percentage change in quantity demandeddivided by the percentage change in incomeWith all other influences on demand with the price of
the good kept constant
Y%
Q%
IncomeinChange%
DemandedQuantityinchange%Y
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 to
priceas we move alonga demand curve from onepoint to another
Income elasticity tells us relative shiftin demandcurveincrease 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
Income Elasticity IncomeElasticityGood or Service Good or Service
Fresh Fruit 1.99 Imports 2.73
Computers 1.71
Transatlantic Air Travel 1.40 Transportation 1.79
College Education 0.55Cigarettes 0.50 Recreation 1.07
Chicken 0.42 Clothing 1.02
Pork 0.34 Food 0.60 to 0.85
Fresh Vegetables 0.26
Tooth Extraction 0.13 to 0.47
Ground Beef
0.20Bread 0.42
Potatoes 0.81 Luxury (>1), Necessity (0
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Part 3: Cross-Price Elasticity of Demand
Cross-price elasticity of demand Percentage change in quantity demanded of one good (x)
caused by a 1% change in price of another good (z)
While all other influences on demand remain unchanged
z
x
PQ
%%
XZ
Sign of ? Substitutes (+)
Complements (-) Its size tells us how closely the two goods are related
A large absolute value for suggests that the two goodsare close substitutes or complements
xz
xz
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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 of Pepsi 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 0.72
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 goodWith all other influences on supply held constant
PriceinChange%
SuppliedQuantityinChange%S
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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 Elastic
Supply