Chapter 4 Elasticity

5/24/2018 Chapter 4 Elasticity

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Chapter 4A

Elasticity

Gary Payne, MBA

Sam Houston State University


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Elasticity

04

McGraw-Hill/IrwinCopyright 2012 by The McGraw-Hill Companies, Inc. All rights reserved.

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Student Learning Outcomes (SLO)

Calculate supply and demand elasticities, identify the

determinants of price elasticity of demand and supply, and

demonstrate the relationship between elasticity and total

revenue.

SLO 4


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4 Terms and Concepts

Price elasticity of demand

Midpoint formula

Elastic demand

Inelastic demand

Unit elasticity

Perfectly inelastic demand

Perfectly elastic demand

Total revenue (TR)

Total-revenue test

Price elasticity of supply

Market period

Short run

Long run

Cross elasticity of demand

Income elasticity of demand


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Elasticity

Why do buyers of some products respond to price increases by

substantially reducing their purchases while buyers of other

products respond by only slightly cutting back their purchases?

Why does the demand for some products rise a great deal when

household income increases while the demand for other productsrises just a little?

Elasticity lets us know the degree to which changes in prices and

incomes affect supply and demand.


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Elasticity

Examples:

In 1997, the Texas Department of Transportation (TDOT)

increased the price of vanity plates with the intention of

increasing the amount of money they received from the

sale of vanity plates.

According to the Law of Demand when the price goes up

the quantity demanded goes down. Hence, the TDOT was

expecting the quantity demanded to go down but less

than the increase in the price so that at the end the totalmoney they receive increases.


7/74Dr. Fidel Gonzalez (SHSU) 7

Elasticity

So what happened?

When the price of vanity plates increased the money received

by the TDOT decreased. In other words, the percentage

change in the price of vanity plates was less that the

percentage decrease in the quantity of vanity plates.

They could have benefited from a better understanding of the

elasticity concept!


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Price Elasticity of Demand

The law of demand tells us that, other things equal, consumers will

buy more of a product when its price declines and less when its

price increases. But how much more or less will they buy?

Price elasticity of demandmeasures the responsiveness

(sensitivity) of consumers to a price change. For some productsfor example, restaurant mealsconsumers are

highly responsive to price changes. Demand is relatively elasticor

elastic.

For other productsfor example toothpasteconsumers pay muchless attention to price changes. Substantial price changes cause only

small changes in the amount purchased. Demand is relatively

inelasticor simply inelastic.


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Price Elasticity (cont'd)

Price Elasticity of Demand (Ep)

Ep=Percentage change in quantity demanded

Percentage change in price


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Ep=1%

+10% =.1

Price Elasticity (cont'd)

Example

Price of oil increases 10%

Quantity demanded decreases 1%


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The Price Elasticity of Demand

Heads Up!

Do not confuse elasticity with slope

When computing elasticity at different points on a linear

demand curve, the slope is constant, but the value forelasticity will change


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The Price-Elasticity Coefficient and Formula

Economists measure the degree to which demand is price elastic or

inelastic with the coefficient Ed

__________________________

Percentage change in quantity

Demanded of product XEd =

Percentage change in price

Of product X


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Calculating Elasticity

To calculate the Ep, we compare percentage changes in

quantity demanded and price.

Change in QD / original QD

Change in P / original P

Arithmetic problemthe percentage change from 2 to 3 (50

percent) is not the same as the percentage change from 3 to 2

(33.3 percent).

So, we use average values


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ELASTICITY AND ITSAPPLICATION

14

Calculating Percentage Changes

P

Q

D

$250

8

B

$200

12

A

Demand for

your websites

Problem:

The standard method givesdifferent answers depending on

where you start.

From A to B,Prises 25%, Qfalls 33%,

elasticity = 33/25 = 1.33

From B to A,

Pfalls 20%, Qrises 50%,elasticity = 50/20 = 2.50


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Using Averages

An annoying problem arises in computing the price-elasticity

coefficient. A price change from, say, $4 to $5 along a demand

curve is a 25 percent increase, but the opposite price change from

$5 to $4 along the same curve is a 20 percent decrease. Elasticity should be the same whether price rises or falls.

Simplest solution to the problem is to use the midpoint formula

which averages the two prices and the two quantities.


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Price Elasticity Mid-Point Formula

Calculating Elasticity

Elasticity formula:

Change in QSum of quantities/2

Ep= Change inP

Sum of prices/2

or

in Q

(Q1+ Q2)/2Ep=

in P

(P1+ P2)/2


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17

Calculating Percentage Changes

Using the midpoint method, the % change

in Pequals

$250$200

$225x 100% = 22.2%

The % change in Qequals

128

10x 100% = 40.0%

The price elasticity of demand equals

40/22.2 = 1.8

.40 / .22 = 1.81 %


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Midpoint Formula

This class will use the midpoint formula for all future calculations

Ed = Change in quantity

Sum of quantities/2

Change in price

Sum of prices/2


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Elimination of Minus Sign

We know from the downsloping demand curve that price and

quantity demanded are inversely related. Thus, the price-elasticity

coefficient of demand Edwill always be a negative number.

Economists usually ignore the minus sign and simply present theabsolute value to avoid any ambiguity.

Interpretations of Ed

We can interpret the coefficient of price elasticity of demand asfollows


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Elastic Demand

Demand is elasticif a specific percentage change in price results in

a larger percentage change in quantity demanded. Edwill be

greater than 1

Ed =.04

.02

= 2


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21

D

Elastic demand

P

QQ1

P1

Q2

P2

Q rises more

than 10%

> 10%

10%> 1

Price elasticity

of demand

=% change in Q

% change in P=

P fallsby 10%

Consumers

price sensitivity:

Dcurve:

Elasticity:

relatively flat

relatively high

> 1

The more responsive buyers are to a change in price, theflatter the demand curve will be


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Inelastic Demand

If a specific percentage change in price produces a smaller

percentage change in quantity demanded, demand is inelastic.Ed

will be less than 1

Ed =.01

.02

= .5


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23

D

Inelastic demand

P

QQ1

P1

Q2

P2

Q rises less

than 10%

< 10%

10%< 1

Price elasticity

of demand

=% change in Q

% change in P=

P fallsby 10%

Consumers

price sensitivity:

Dcurve:

Elasticity:

relatively steep

relatively low

< 1

The less responsive buyers are to a change in price, the

steeper the demand curve will be


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Unit Elasticity

The case separating elastic and inelastic demands occurs where a

percentage change in price and the resulting percentage change in

quantity demanded are the same. Ed= 1

Ed =

.02

.02= 1


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25

D

Unit elastic demand

P

QQ1

P1

Q2

P2

Qrises by 10%

10%

10%

= 1Price elasticity

of demand

=% change in Q

% change in P=

P fallsby 10%

Consumers

price sensitivity:

Elasticity:

intermediate

1

Dcurve:

intermediate slope

Demand is unit elastic if quantity demanded changes by the same

percent as the price


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Summary of Price Elasticities of Demand

Polar Cases of Perfectly Elastic and Perfectly Inelastic Demand


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Interpretation of Elasticity of Demand

Ed> 1 demand is elasticEd= 1 demand is unit elasticEd< 1 demand is inelasticExtreme cases

Perfectly inelastic

Perfectly elastic

LO1 4-27


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Price Elasticity Ranges

Elastic demand

% change in Q> % change in P; Ep> 1

Unit-elastic

% change in Q= % change in P; Ep= 1

Inelastic demand

% change in Q< % change in P; Ep< 1


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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.91

010

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

170

180

190

200

Pricep

er

ride

Quantity of rides per day (in thousands)

Price Elasticities Along a Linear DemandCurve

eD= -.33

eD= -1.00

eD= -3.00


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30


Price elasticity

of demand

equals

P

Q

D

Q2

P2

P1

Q1

P risesby 10%

Q falls

by 15%

15%

10%= 1.5

Price elasticityof demand=

Percentage change in Qd

Percentage change in P

Example:


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Extreme Cases

Perfectly inelasticwhere a price change results in no change

whatsoever In the quantity demanded.Ed= 0

There is no response to a change in price.

Graphically, a line parallel to the vertical axis.

Example: insulin


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Extreme Cases

LO1

D1P


Perfectlyinelasticdemand(Ed = 0)

0

4-32


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33

Q1

P1

D


P

Q

P2

P fallsby 10%

Q changes

by 0%

0%

10%

= 0Price elasticity

of demand

=% change in Q

% change in P

=

Consumers

price sensitivity:

Dcurve:

Elasticity:

vertical

none

0


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Extreme Cases

Perfectly elastic

A small price reduction causes buyers to increase their purchases

from zero to all they can obtain. Ed = infinity

A line parallel to the horizontal axis.

Example: firms selling a commodity item in a purely competitive

market.

E t C


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Extreme Cases

LO1


P

D2

Perfectlyelasticdemand

(Ed = )

0

4-35


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36

D


P

Q

P1

Q1Pchanges

by 0%

Q changes

by any %

any %

0%

= infinity

Q2

P2=Consumers

price sensitivity:

Dcurve:

Elasticity:

infinity

horizontal

extreme

Price elasticity

of demand

=% change in Q

% change in P

=


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Summary of Price Elasticities of Demand


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The Total-Revenue Test

The importance of elasticity for firms relates to the effect of price

changes on total revenue and thus profits.

Total revenue (TR)is the total amount the seller receives from the

sale of a product in a particular time period; calculated bymultiplying the product price (P) by the quantity sold (Q).

TR = P X Q

Graphically, total revenue is represented by the P XQ rectangle lyingbelow a point on a demand curve. (area of the rectangle is found by

multiplying one side by the other).


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The Total-Revenue Test

If total revenue changes in the opposite direction from price,

demand is elastic.

If total revenue changes in the same direction as price, demand is

inelastic.

If total revenue does not change when price changes, demand is

unit-elastic.


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The Relationship Between Price Elasticity of Demand and Total

Revenues for Cellular Phone Service


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The Relationship Between Price Elasticity of Demand and Total

Revenues for Cellular Phone Service


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Elastic Demand

If demand is elastic, a decrease in price will increase total revenue.Even a lesser price is received per unit, enough additional units aresold to more than make up for the lower price.

The analysis is reversible: If demand is elastic, a price increase willreduce total revenue. The revenue gained on the higher-pricedunits will be more than offset by the revenue lost from the lowerquantity sold.

Other things equal, when price and total revenue move in oppositedirections, demand is elastic. Edis greater than 1 The percentagechange in quantity demanded is greater than the percentagechange in price.


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Consider ThisA Bit of a Stretch

For some products, a price change causes a substantial stretch of

quantity demanded. When this stretch in in percentage terms

exceeds the percentage change in price, demand is elastic.

For other products, quantity demanded stretches very little in

response to the price change. When this stretch in percentageterms in less than the percentage change in price, demand is

inelastic.

Elastic demand displays considerable quantity stretch

Inelastic demand displays relatively little quantity stretch


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Inelastic Demand

If demand is inelastic, a price decrease will reduce total revenue.The increase in sales will not fully offset the decline in revenue perunit, and total revenue will decline.

The loss in revenue from the lower unit price is larger than the gainin revenue from the accompanying increase in sales.

Price has fallen, and total revenue has also declined.

Conversely, if demand is inelastic, a price increase will increase total

revenue. Other things equal, when price and total revenue move inthe same direction, demand is inelastic. Edis less than 1 thepercentage change in quantity demanded is less than thepercentage change in price.


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Unit Elasticity

An increase or a decrease in price leaves total revenue unchanged.

The loss in revenue from a lower unit price is exactly offset by the

gain in revenue from the accompanying increase in sales.

Conversely, the gain in revenue from a higher unit price is exactlyoffset by the revenue loss associated with the accompanying

decline in the amount demanded.

Other things equal, when price changes and total revenue remainsconstant, demand is unit-elastic Edis 1 The percentage change in

quantity equals the percentage change in price.

Total Revenue Test


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Total Revenue Test

LO2

$3

2

1

0 10 20 30 40 Q

P

a

b

D1

Lower price and elastic demandBlue gain exceeds orange loss

4-46

Total Revenue Test


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Total Revenue Test

LO2

$4

3

2

1

0 10 20 Q

P

c

d

D2

Lower price and inelastic demand

Orange loss exceeds blue gain

4-47

Total Revenue Test


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Total Revenue Test

LO2

$3

2

1

0 10 20 30 Q

P

e

f

D3

Lower price and unit elastic demandBlue gain equals orange loss

4-48


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Price Elasticity along a Linear Demand Curve

Elasticity typically varies over different price ranges of the same

demand curve.

Demand is more price elastic toward the upper left than toward the

lower right. In the upper-left segment of the demand curve, the percentage

change in quantity is large because the original reference quantity is

small.

Similarly, the percentage change in price is small in that segment

because the original reference price is large.

The relatively large percentage change in price yields a large Ed, an

elastic demand.


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The reverse holds true for the lower-right segment of the demand

curve. Here the percentage change in quantity is small because the

original reference quantity is large; similarly, the percentage change

in price is large because the original reference price is small. The relatively small percentage change in quantity divided by the

relatively large percentage change in price results in a small Ed, an

inelastic demand.


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The slope of the demand curveits flatness or steepnessis not a

sound basis for judging elasticity. The catch is that the slope of the

curve is computed from absolutechanges in price and quantity,

while elasticity involves relativeorpercentagechanges in price andquantity.

Total Revenue Test


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Total Revenue Test

LO2

Price Elasticity of Demand for Movie Tickets as Measured by the ElasticityCoefficient and the Total-Revenue Test

(1)Total Quantity of

Tickets Demanded perWeek, Thousands

(2)Price per Ticket

(3)Elasticity

Coefficient(Ed)

(4)Total

Revenue(1) X (2)

(5)Total

RevenueTest

1 $8 $8,000

2 7 5.00 14,000 Elastic3 6 2.60 18,000 Elastic

4 5 1.57 20,000 Elastic

5 4 1.00 20,000 Unit Elastic

6 3 0.64 18,000 Inelastic

7 2 0.38 14,000 Inelastic

8 1 0.20 8,000 Inelastic

4-52

Elasticity and Total Revenue


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Elasticity and Total Revenue

LO2

0 1 2 3 4 5 6 7 8

0 1 2 3 4 5 6 7 8

Quantity Demanded

Quantity Demanded

Price

TotalRe

venue

(Thousands

ofDollars)

$20181614

1210

8642

$8

7

65

4

3

2

1

a

b

c

de

fg

h

ElasticE

d> 1Unit Elastic

Ed= 1

InelasticE

d< 1

D

TR

4-53


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Price Elasticity and the Total-Revenue Curve

The total revenue curve first slopes upward, then reaches a

maximum, and finally turns downward.

Lowering price in the elastic range of demand increases total

revenue. Conversely, increasing the price in that range reduces totalrevenue. Price and total revenue change in opposite directions,

confirming that demand is elastic.


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Price Elasticity and the Total-Revenue Curve

The $5 - $4 price range of the demand curve reflects unit elasticity.

When price decreases or increases, total revenue remains the

same. Price has changed and total revenue has remained constant,

confirming that demand is unit-elastic.

In the inelastic range of the demand curve, lowering the price

decreases total revenue. Raising the price boosts total revenue.

Price and total revenue move in the same direction, confirming that

demand is inelastic.

Summary of Price Elasticity of Demand


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Summary of Price Elasticity of Demand

LO2

Price Elasticity of Demand: A Summary

Absolute Valueof ElasticityCoefficient Demand Is: Description

Impact on Total Revenue of a:

Price Increase Price Decrease

Greater than 1(Ed > 1)

Elastic orrelatively

elastic

Qdchanges by alarger

percentage thandoes price

Total Revenuedecreases

Total Revenueincreases

Equal to 1(Ed= 1)

Unit or unitaryelastic

Qd changes bythe samepercentage asdoes price

Total revenueis unchanged

Total revenueis unchanged

Less than 1(Ed< 1)

Inelastic orrelativelyinelastic

Qdchanges by asmallerpercentage thandoes price

Total revenueincreases

Total revenuedecreases

4-56


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Determinants of Price Elasticity of Demand

Substitutability

Generally, the larger the number of substitute goods that are

available, the greater the price elasticity of demand.

The demand for Snickers candy bar is highly elastic.

Proportion of Income

Other things equal, the higher the price of a good relative to

consumers incomes, the greater the price elasticity of demand. A10 percent increase in the price of a house is significant. Price

elasticity tends to be high.


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Luxuries versus Necessities

In general, the more that a good is considered to be a luxury

rather than a necessity, the greater is the price elasticity of

demand. Vacation travel can easily be forgone.

Salt is highly inelastic


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Time

Generally, product demand is more elastic the longer the time

period under consideration. Consumers often need time to adjust

to changes in prices. In the short-run, demand for gasoline is more inelastic (Ed= .2)

than in the long-run (Ed= .7).



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LO1

Selected Price Elasticities of Demand

Product or Service

Price Elasticity

of Demand (Ed) Product or Service

Price Elasticity

of Demand (Ed)Newspapers .10 Milk .63

Electricity (household) .13 Household appliances .63

Bread .15 Liquor .70

MLB Tickets .23 Movies .87

Telephone Service .26 Beer .90

Cigarettes .25 Shoes .91

Sugar .30 Motor vehicles 1.14

Medical Care .31 Beef 1.27

Eggs .32 China, glassware 1.54

Legal Services .37 Residential land 1.60

Automobile repair .40 Restaurant meals 2.27

Clothing .49 Lamb and mutton 2.65

Gasoline .60 Fresh peas 2.834-60


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Applications of Price Elasticity of Demand

Excise Taxes

The government pays attention to elasticity of demand when it

selects goods and services on which to levy excise taxes.

Legislatures tend to seek out products that have inelasticdemandliquor, gasoline, cigaretteswhen levying excise taxes.


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ELASTICITY AND ITS

APPLICATION 62

Appendix


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Dr. Fidel Gonzalez (SHSU)


The Price Elasticity of Demand is given by the following formula:

Where Ed= elasticity of demand.

Remember that the Law of Demand says that price and quantity demanded move in

opposite directions. This means that if the percentage change in the price is positive (price

goes up) then the percentage change in the quantity demanded is negative (the quantity

demanded goes down). That is, the numerator will be negative and the denominator willbe positive, therefore the Ed will be negative. Notice that when the percentage change in

the price is negative the percentage change in the quantity will be positive and the Ed will

also be negative.

In other words, the Ed will always be negative because of the Law of Demand.

Percentage change in the Quantity Demanded

Percentage change in the PricedE

The price elasticity of demand tells us how much the quantity demanded changes when

the price changes. We are going to use percentage changes to measure the change in all

prices and quantities.


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Since Ed is always negative we are going to get rid of the negative sign and report Ed as a

positive number. This is achieved by using the absolute number concept. Remember from

you High School classes that any number can be converted into a positive one if we

place the absolute number operator around it ||.

For example, |-5| =5 and |5|=5 . Therefore, our new definition of Ed is the following:

Since, I do not want to write percentage change every time I write the formula for Ed I

will use the following expression for Ed

Percentage change in the Quantity DemandedPercentage change in the Price

dE

% QD% P

dE

where % means percentage change, QD is quantity demanded, and P is price.


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For example if the Price of Pepsi goes up by 5% and as a response the Quantity

Demanded goes down by 10% then the Price Elasticity of Demand for Pepsi is:

This has an interesting interpretation. Ed=2 indicates that the percentage change in the

quantity demanded is twice a big as the percentage change in the price. In other words,

the quantity demanded is very sensitive to changes in the price because in this case thequantity demanded changed more (in percentage terms) than the change in the price.

In general the elasticity can be interpreted as follows: the percentage change in the

Quantity Demanded is Ed times the percentage change in the Price.

In the example above Ed=2 so we concluded that QD is sensitive to changes in P. In general,

whenever the percentage change in the QD demand is greater than the percentage changein P we are going to say the demand is sensitive to changes in the price.

A sensitive demand is called Elastic, and insensitive demand is called Inelastic.

-10%2

5%dE


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Hence,

If Ed > 1 then Elastic since |%QD| >| %P| (sensitive demand, the Quantity Demandresponds more than proportional to changes in the Price)

If Ed < 1 then Inelastic since |%QD|


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Mid-point Formula and Ed:

When computing elasticities we need to obtain the percentage change in the price and the

percentage change in the quantity demanded. However, percentage changes are tricky

because their value depend on the original value.The formula to get a percentage change is the following

Final Value - Original Value

OriginalValuePercentage Change =

1 2For example consider P 10 and P =20. The percentage will be different depending on

whether the P goes from 10 to 20 or from 20 to 10

When the prices goes from 10 to 20:

20 - 10 10Percentage Change =

10

1 100%

10When the prices goes from 20 to 10:

10 - 20 10Percentage Change = 0.5 50%

20 20

Mid-point Formula and Ed:


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d po t o u a a d d:

This is a problem because it means that we will get different value of the Ed depending on

whether the price increases or decreases. Note that in both percentage changes the

absolute value of the numerator is 10. However, what changes is the value of the

denominator, in one case is 10 and in the other one is 20.

To solve this problem we are going to use the Mid-point formula. What this formula does is

to change the denominator of the percentage change formula.

Final Value - Original Value

Final Value + Original Value2

Mid-Point Formula Percentage Change =

A you can tell all we have done is to change the denominator of the percentage change to

the average of the original and final value (thats why it is called the mid-point formula, the

average is the midpoint). In our previous example:

10 - 20 10Mid-point Percentage Change = 0.67 67%

20 + 10 15

2

Notice that we will always get the value 67% (positive or negative) regardless if whether P

increase or decrease. FOR ALL OUR ELASTICITY CALCULATIONS WE WILL USE THE MID-

POINT FORMULA.


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Perfectly Inelastic Demand:

There are two extreme cases that we will consider. The first one is when the QD does not

change at all when the price changes. This is the case of goods that you must buy. For

example, a crack addict needs to buy crack regardless of the price. A person that needs alife-saving medicine they have to get it. In this case the demand is not sensitive at all to

price changes. We will call these cases: Perfectly Inelastic Demand

10

Price of crack

QD of crack

For the crack addict it does not matter if the prices is $100,

$500 or $1000; he always buys 10 units of crack. Hisdemand is then perfectly inelastic.

A perfectly inelastic demand is represented by a completely

vertical demand curve.

Question: What is the value of the Ed when the demand is

perfectly inelastic

100

500

1,000

D

Answer:

In this case the QD never changes so: % in QD = 0

Therefore,

0Ed= 0

% in P


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Perfectly Elastic Demand:

The other extreme cases is when the QD changes infinity the price changes just a little

but. This is the case of goods that you do not really need and that have plenty of perfect

substitutes. For example, blue and navy blue pens. If the price of blue pens increases youdo not buy any of them and instead buy only navy blue pens. We will call these cases:

Perfectly Elastic Demand

Price of blue pens

QD of blue pens

The consumer will only purchase pens at $20 or less. If the

price drops below $20 the consumer will purchase and

infinite amount of pens.

Question: What is the value of the Ed when the demand is

perfectly elastic

10

20

40

D

Answer:

In this case the change in QD is infinity so: % in QD =Therefore,

Ed=% in P


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Ed Along the Demand Curves

The Ed is not only different for demand curves with different slope, Ed also changes along

the demand curve.

In other words, we can look at two demand curves and figure out which demand curve is

more elastic by comparing slopes, but the specific value of Ed will change along each

individual demand.

Moreover, Ed > 1 for the top part of the demand curve, Ed=1 in the middle and Ed1

Ed=1

Ed


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Ed Along the Demand Curves

Question: Why is Ed>1 in the top part of the demand curve and Ed


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Income Elasticity of Demand

Where EI= income elasticity of demand.

Note that we are not using absolute value in the formula for EI. This is because in this case

the sign of EI matters. If EI >0 then we know that Income and QD move in the same

direction and the good is normal. If EI 1, this means that the percentage change in QD is less than the percentage

change in Income, these goods are considered luxuries.

Moreover EI < 1, this means that the percentage change in QD is greater than the

percentage change in Income, these goods are considered necessities.

Percentage change in the Quantity DemandedPercentage change in Income

IE

We are now going to consider the effect of income on the quantity demanded. The income

elasticity of demand is given by the following formula:


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Cross Price Elasticity of Demand

Where Ecp= cross-price elasticity of demand.

Note that we are not using absolute value in the formula for Ecp. This is because in this

case the sign of Ecp matters.

If Ecp >0 then we know that the price of good 1 and QD of good 2 move in the same

direction and the goods are substitutes.

If Ecp>0 then we know that the price of good 1 and QD of good 2 move in the opposite

direction and the goods are complements.

Percentage change in the Quantity Demanded of good 2

Percentage change in price of good 1cpE

We are now going to consider the effect of the price of another on the quantity demanded

of the good. This is the cross-price elasticity of demand is given by the following formula:

Chapter 4 Elasticity

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Transcript of Chapter 4 Elasticity