elasticity and its application - principles of...

ELASTICITY AND ITS APPLICATION J. Mao

Elasticity

¨  Until now, we’ve been talking about the direction in which quantities change. ¤  A downward-sloping demand: price é è quantity

demanded ê ¨  In real life it is quite important to know the

intensity of the change (how much) ¤  By how much will the demand for my product

decrease if I increase the price by 10%?

Elasticity

¨  Elasticity: a measure of the responsiveness of quantity demanded or quantity supplied to a change in one of their determinants

¨  Price elasticity of demand measures how much quantity demanded changes in response to a change in price.

Price elasticity of demand

1

© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

EconomicsPrinciples of

N. Gregory Mankiw

Elasticity and its Application

Seventh Edition

CHAPTER

ͷ

Wojciech�Ge

rson

�(183

1Ͳ19

01)

Modified�by�Joseph�TaoͲyi Wang

In this chapter, look for the answers to these questions

• What is elasticity? What kinds of issues can elasticity help us understand?

• What is the price elasticity of demand? How is it related to the demand curve? How is it related to revenue & expenditure?

• What is the price elasticity of supply? How is it related to the supply curve?

• What are the income and cross-price elasticitiesof demand?

© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.


2

You design websites for local businesses. You charge $2,000 per website, and currently sell 12 websites per month.

Your costs are rising (including the opportunity cost of your time), so you consider raising the price to $2,500.

The law of demand says that you won’t sell as many websites if you raise your price. How many fewer websites? How much will your revenue fall, or might it increase?




A scenario

2© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

3

Elasticity� Basic idea:

Elasticity measures how much one variable responds to changes in another variable. � One type of elasticity measures how much

demand for your websites will fall if you raise your price.

� Definition: Elasticity is a numerical measure of the responsiveness of Qd or Qs to one of its determinants.


4

Price Elasticity of Demand

� Price elasticity of demand measures how much Qd responds to a change in P.

Price elasticity of demand =

Percentage change in Qd

Percentage change in P

� Loosely speaking, it measures the price-sensitivity of buyers’ demand.


5


Price elasticity of demand equals

P

Q

D

Q2

P2

P1

Q1

P rises by 10%

Q falls by 15%

15%10%

= 1.5




Example:


1



N. Gregory Mankiw


Seventh Edition

CHAPTER

ͷ

Wojciech�Ge

rson

�(183

1Ͳ19

01)









2







A scenario


3






4








5



P

Q

D

Q2

P2

P1

Q1

P rises by 10%

Q falls by 15%

15%10%

= 1.5




Example:

1



N. Gregory Mankiw


Seventh Edition

CHAPTER

ͷ

Wojciech�Ge

rson

�(183

1Ͳ19

01)









2







A scenario


3






4








5



P

Q

D

Q2

P2

P1

Q1

P rises by 10%

Q falls by 15%

15%10%

= 1.5




Example:


¨  Elasticity is unit free: Allows comparison of price sensitivity across markets. ¤  Car market and T-shirt market ¤  Xiamen market and China market


Formally,

Price elasticity of demand ✏d,p = �dQ/QdP/P =

��dQ/QdP/P

��

⇡��(Q2�Q1)/ 1

2 (Q1+Q2)

(P2�P1)/ 12 (P1+P2)

��

d (Total Revenue)

dP=

d (QP )

dP=

dQ

dPP +Q

Therefore,

d (Total Revenue)

dP> 0 , dQ

dP

P

Q> �1 , ✏d,p < 1

d (Total Revenue)

dP< 0 , dQ

dP

P

Q< �1 , ✏d,p > 1

✏ > 1 Elastic

✏ < 1 Inelastic

✏ = 1 Unit Elastic

✏ = 0 Perfectly inelastic

✏ ! 1 Perfectly elastic

1

Elasticity

Prof Jonathan Wolff ( Department of Economics University of Notre Dame)Principles of Micro Economics September 10th, 2012 9 / 44

Elasticity

Prof Jonathan Wolff ( Department of Economics University of Notre Dame)Principles of Micro Economics September 10th, 2012 10 / 44


¨  The price elasticity of demand is closely related to the slope of the demand curve.

¨  Rule of thumb: ¤  The flatter the curve, the bigger the elasticity. ¤  The steeper the curve, the smaller the elasticity.

4


18

The Determinants of Price Elasticity: A Summary

The price elasticity of demand depends on:� the extent to which close substitutes are

available

� whether the good is a necessity or a luxury

� how broadly or narrowly the good is defined

� the time horizon—elasticity is higher in the long run than the short run

The price elasticity of demand depends on:� the extent to which close substitutes are

available

� whether the good is a necessity or a luxury

� how broadly or narrowly the good is defined

� the time horizon—elasticity is higher in the long run than the short run


19

The Variety of Demand Curves

� The price elasticity of demand is closely related to the slope of the demand curve.

� Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity.

� Five different classifications of D curves.


20

Q1

P1

D

“Perfectly inelastic demand” (one extreme case)

P

Q

P2

P falls by 10%

Q changes by 0%

0%

10%= 0Price elasticity

of demand =% change in Q% change in P

=

Consumers’ price sensitivity:

D curve:

Elasticity:

vertical

none

0


21

D

“Inelastic demand”

P

QQ1

P1

Q2

P2

Q rises less than 10%

< 10%

10%< 1Price elasticity


=

P falls by 10%


D curve:

Elasticity:

relatively steep

relatively low

< 1


22

D

“Unit elastic demand”

P

QQ1

P1

Q2

P2

Q rises by 10%

10%

10%= 1Price elasticity


=

P falls by 10%


Elasticity:

intermediate

1

D curve:intermediate slope


23

D

“Elastic demand”

P

QQ1

P1

Q2

P2

Q rises more than 10%

> 10%

10%> 1Price elasticity


=

P falls by 10%


D curve:

Elasticity:

relatively flat

relatively high

> 1

5


24

D

“Perfectly elastic demand” (the other extreme)

P

Q

P1

Q1P changes

by 0%

Q changes by any %

any %0%

= infinity

Q2

P2 =Consumers’ price sensitivity:

D curve:

Elasticity:infinity

horizontal

extreme


% change in Q% change in P

=


25

A few elasticities from the real world

Eggs 0.1Healthcare 0.2Rice 0.5Housing 0.7Beef 1.6Restaurant meals 2.3Mountain Dew 4.4


Selected Price Elasticity (from Wiki)� Rice[48]

� -0.47 (Austria)� -0.80 (Bangladesh)� -0.80 (China)� -0.25 (Japan)� -0.55 (US)

� Eggs � -0.1 (US:

Household only),[54]

� -0.35 (Canada),[55]

� -0.55 (South Africa)[56]

� Livestock � -0.5 to -0.6 (Broiler

Chickens)[44]


Selected Price Elasticity (from Wiki)� Soft drinks � -0.8 to -1.0

(general)[51]

� -3.8 (Coca-Cola)[52]

� -4.4 (Mountain Dew)[52]

� Alcoholic beverages (US)[42]

� -0.3 or -0.7 to -0.9 as of 1972 (Beer)� -1.0 (Wine)� -1.5 (Spirits)

� Cigarettes (US)[41]

� -0.3 to -0.6 (General)� -0.6 to -0.7 (Youth)


Selected Price Elasticity (from Wiki)� Transport � -0.20 (Bus travel

US)[46]

� -2.80 (Ford compact automobile)[50]

� Airline travel (US)[43]

� -0.3 (First Class)� -0.9 (Discount)� -1.5 (for Pleasure

Travelers)

� Car fuel[45]

� -0.25 (Short run)� -0.64 (Long run)


Selected Price Elasticity (from Wiki)� Medicine (US) � -0.31 (Medical

insurance)[46]

� -.03 to -.06 (Pediatric Visits) [47]

� Oil (World) � -0.4

� Cinema visits (US) � -0.87 (General)[46]

� Live Performing Arts (Theater, etc.) � -0.4 to -0.9 [49]

� Steel � -0.2 to -0.3[53]

Price elasticity of demand Price elasticity of demand (✏) =

��dQ/QdP/P

��

⇡��(Q2�Q1)/ 1

2 (Q1+Q2)

(P2�P1)/ 12 (P1+P2)

��

✏ > 1 Elastic

✏ < 1 Inelastic




1


¨  When two demand curves cross ¤  P/Q is the same for both

curves ¤  (1/slope) is smaller for the

steeper curve ¨  At the common point

demand is less price elastic for the steeper curve

4-18

Price Elasticity and Slope• When two demand curves cross

• P / Q is same for both curves• (1 / slope) is

smaller for the steeper curve

– At the common point demand is less price elastic for the steeper curve

D1

D2

12

4 6 12

6

4

Quantity

Pric

e

Less ElasticMore Elastic

Price Elasticity along a Linear Demand Curve

¨  At the midpoint, demand is unit elastic

¨  At high P and low Q, demand is elastic

¨  At low P and high Q, P/Q is small

4-20

Price Elasticity Pattern• Price elasticity changes systematically as price goes

down• At high P and low Q, P / Q is large

• Demand is elastic• At the midpoint,

demand is unit elastic• At low P and high Q,

P / Q is small• Demand is

inelastic

Pric

e

b/2

a/2

a

b

1!H

1�H

1 H

Quantity

What determines Price Elasticity?

Availability of Close Substitutes

¨  McDonalds Cheeseburgers vs. Hubble Telescopes

¨  Price elasticity is higher when there exist close substitutes

Necessities vs Luxuries

¨  “Insulin" vs. “Caribbean Cruise" ¨  Necessities are more price inelastic ¨  Luxuries are more price elastic

Definition of the market

¨  “Macbook Air" vs. “Laptop Computers” ¨  Price elasticity is higher for narrowly defined

goods than more broadly defined ones

Time horizon

¨  “Gasoline in the Short Run" vs “Gasoline in the Long Run"

¨  Price elasticity is higher in the long run than in the short run.

Price Elasticity and Total Revenue

¨  Total Revenue/Expenditure = P x Q ¨  If you raise your price from $2,000 to $2,500,

would your revenue rise or fall? ¨  A price increase has two effects on revenue:

¤  Higher P means more revenue on each unit ¤  But you sell fewer units (lower Q), due to law of

demand ¨  Which of these two effects is bigger?

It depends on the price elasticity of demand.

How Total Revenue is affected by a change in price

Price elasticity of demand ✏d,p = �dQ/QdP/P =

��dQ/QdP/P

��

⇡��(Q2�Q1)/ 1

2 (Q1+Q2)

(P2�P1)/ 12 (P1+P2)

��

d (Total Revenue)

dP=

d (QP )

dP=

dQ

dPP +Q

Therefore,

d (Total Revenue)

dP> 0 , dQ

dP

P

Q> �1 , ✏d,p < 1

d (Total Revenue)

dP< 0 , dQ

dP

P

Q< �1 , ✏d,p > 1

✏ > 1 Elastic

✏ < 1 Inelastic




1

How Total Revenue is affected by a change in price

4-26

Elasticity, Price Change, and Expenditure


¨  Movie ticket price increases from $2 to $4 ¤  A and B are both below the midpoint of the curve ¤  Inelastic portion of the demand curve

¨  Total revenue increases when price increases

4-23

Price Elasticity and Total Expenditure

• Movie ticket price increases from $2 to $4– A and B are both below the midpoint of the curve

• Inelastic portion of the demand curve– Total revenue increases when price increases

Quantity (00s of tickets/day)

D

A

Expenditure = $1,000/day

12

Pric

e ($

/tick

et)

5 6

2

Quantity (00s of tickets/day)4

D

B


12

Pric

e ($

/tick

et)

6

4


¨  Movie ticket price increases from $8 to $10 ¤  Prices are both above the midpoint of the curve ¤  Elastic portion of the demand curve

¨  Total revenue decreases when price increases

4-24

Price Elasticity and Total Expenditure

• Movie ticket price increases from $8 to $10– Prices are both above the midpoint of the curve

• Elastic portion of the demand curve– Total revenue decreases

D


12


Pric

e ($

/tick

et)

2 6

8Y

Z

D


12


Pric

e ($

/tick

et)

1 6

10

Total Revenue along a Linear Demand Curve

4-25

The Effect of a Price Change on Total Expenditure

Price $12 $10 $8 $6 $4 $2 $0

Quantity 0 1,000 2,000 3,000 4,000 5,000 6,000Expenditure $0 $1,000 $1,600 $1,800 $1,600 $1,000 $0

1,800

Price ($/ticket)

Tota

l exp

endi

ture

($/d

ay)

2 6 10

1,600

1,000

12


Pric

e ($

/tick

et)

1 3 4 5 6

10

8

6

4

2

2

4-25

The Effect of a Price Change on Total Expenditure

Price $12 $10 $8 $6 $4 $2 $0

Quantity 0 1,000 2,000 3,000 4,000 5,000 6,000Expenditure $0 $1,000 $1,600 $1,800 $1,600 $1,000 $0

1,800

Price ($/ticket)

Tota

l exp

endi

ture

($/d

ay)

2 6 10

1,600

1,000

12


Pric

e ($

/tick

et)

1 3 4 5 6

10

8

6

4

2

2

Estimating Elasticities

¨  When estimating demand elasticity, need to hold fixed other determinants of demand isolate impact of change in price.

In Between Cases

(1) When eD < 1 we say Demand is Inelastic

Total Spending = P*Q increases as P increases.

(2) When eD > 1 we say

Demand is Elastic

Total Spending = P*Q decreases as P increases.

(3) When eD = 1 we say Demand is Unit Elastic

Let’s try to calculate eD in an example.

Gasoline Market in the US June 2007 and June 2008

Time Period

Per Capita Daily Consumption of Motor Gasoline

Average Price Per Gallon in Dollars

June 2007 1.32 3.05 June 2008 1.26 4.07 ǻ –.06 1.02 Average of Both Years

1.29 3.56

%ǻ

–.05 .28


¨  εd,p of US gas demand? ¨  Elastic or inelastic? ¨  As prices go up, total spending should increase or

decrease? ¨  Is this short-run elasticity or long-run elasticity?


¨  Is the price change due to supply shift or demand shift or both? ¨  To estimate price elasticity of demand, you want the demand

curve stay constant while the supply curve shifts ¨  Consumer tastes

¨  Tastes for driving higher in summer than winter. ¨  So comparing June to June

¨  Number of buyers ¨  Population grows about 1% a year

¨  Not significant. Also comparing per capita ¨  Income

¨  Income in June 2007 and June 2008 about the same (financial crisis led to income decrease after summer 2008)

¨  Prices of substitutes and complements ¨  Didn’t change much over the one year period

¨  Expectations?

Estimating long-run Elasticities

¨  One way to estimate long-run elasticity is to compare cases where prices have been different a long time.

¨  “Fuel Consumption in Europe and the U.S.” ¤  Europe has long taxed gasoline. ¤  If taxes on gasoline are high for a long time, like in

Europe, consumers will shift to fuel-efficient cars. People will move closer to where they work, etc. All these adjustments take time.

Country Average Price

$US per Gallon

Consumption Per Capita Gallons Per

Day United States 2.80 1.29

Selected Countries in Europe Norway 7.00* .30 United Kingdom 6.90 .28 Germany 6.88 .25 France 6.37 .15 Spain 5.13 .15 Italy 6.50 .21

Some Other Countries Japan 4.49 .33 Mexico 2.45 .29 China 2.29 .04

Country

Per Capita GDP

($1,000)

United States 45.5

Selected Countries in Europe Norway 51.9United Kingdom 35.7 Germany 34.3 France 32.7Spain 31.6Italy 30.4

Some Other Countries Japan 33.6Mexico 14.0China 5.3

Country Average Price

$US per Gallon

Consumption Per Capita Gallons Per

Day United States 2.80 1.29

Selected Countries in Europe Norway 7.00* .30 United Kingdom 6.90 .28 Germany 6.88 .25 France 6.37 .15 Spain 5.13 .15 Italy 6.50 .21

Some Other Countries Japan 4.49 .33 Mexico 2.45 .29 China 2.29 .04

Country

Per Capita GDP

($1,000)

United States 45.5

Selected Countries in Europe Norway 51.9United Kingdom 35.7 Germany 34.3 France 32.7Spain 31.6Italy 30.4

Some Other Countries Japan 33.6Mexico 14.0China 5.3

Table 3: Price and Per Capita Quantity

Consumed of Gasoline

The United States and Norway in 2007

Time

Period

Per Capita

Daily

Consumption

of Motor

Gasoline

Average

Price Per

Gallon in

Dollars

United

States

1.29 2.80

Norway .30 7.00

ǻ -.99 4.20

Average of

Both

Years

.80 4.90

%ǻ -1.24 .86

So: Elasticity(long run) =

%ǻQ/%ǻP = 1.24/.86= 1.44

Is this valid?

1) Is Supply Curve is shifting

between these two countries?

2) Is Demand Curve staying fixed?

A) Income

Estimating long-run Elasticities

¨  Is the supply curve shifting between the two countries?

¨  Is demand curve staying fixed? ¤  Income ¤  Price of substitutes/complements

n Can be a big problem. Public transit is much better in Norway than in the U.S. So there are really two main differences: (1) gas prices are higher and (2) public transit options are better. Both contribute to the lower consumption of gas in Norway

¤  Other factors n Population density impacts gasoline demand n Any other factors that make the demand curve in Norway

and the U.S. different


¨  The price of a pair of running shoes rises from $100 to $150, while the quantity demanded falls from 1200 to 900 ¤  Assumptions needed to calculate price elasticity of

demand ¤  Calculate the price elasticity of demand ¤  Is demand elastic, unit elastic, or inelastic ¤  Calculate total revenue before and after the price

increase ¤  By how much would the quantity demanded change if

price rises another 5%? (and what further assumptions are needed to answer this question)

Price Elasticity of Supply

8


42


� Price elasticity of supply measures how much Qs responds to a change in P.

Price elasticity of supply =

Percentage change in Qs


� Loosely speaking, it measures sellers’ price-sensitivity.

� Again, use the midpoint method to compute the percentage changes.


43

Q2


Price elasticity of supply equals

P

Q

S

P2

Q1

P1

P rises by 8%

Q rises by 16%

16%8%

= 2.0




Example:


44

The Variety of Supply Curves

� The slope of the supply curve is closely related to price elasticity of supply.


� Five different classifications

� Perfectly inelastic (ex: land), inelastic (ex: housing), unit elastic, elastic (ex: tutoring),perfectly elastic (ex: dumping inventory)


45

The Determinants of Supply Elasticity� The more easily sellers can change the quantity

they produce, the greater the price elasticity of supply. � Example: Supply of beachfront property is

harder to vary and thus less elastic than supply of new cars.

� For many goods, price elasticity of supply is greater in the long run than in the short run, because firms can build new factories, or new firms may be able to enter the market.

A C T I V E L E A R N I N G ͵Elasticity and changes in equilibrium� The supply of beachfront property is inelastic.

The supply of new cars is elastic.

� Suppose population growth causes demand for both goods to double (at each price, Qd doubles).

� For which product will P change the most?

� For which product will Q change the most?


A C T I V E L E A R N I N G ͵Answers


Beachfront property (inelastic supply):

P

Q

D1S

Q1

P1 A

When supply is inelastic, an increase in demand has a bigger impact on price than on quantity.

D2

B

Q2

P2

Perfectly Inelastic Supply - Elasticity equals 0

Quantity

Price

4

$5

Supply

100 2. ...leaves the quantity supplied unchanged.

1. An increase in price...

Perfectly Inelastic Supply

¨  Example: land on Manhattan/HK island/Xiamen ¤  Supply is completely fixed

¨  Any one-of-a-kind item has perfectly inelastic supply ¤  Work of art (Mona Lisa)

Inelastic Supply - Elasticity is less than 1

Quantity

Price

4

$5 1. A 22% increase in price...

110 100

Supply

2. ...leads to a 10% increase in quantity.

Unit Elastic Supply - Elasticity equals 1

Quantity

Price

4


125 100

Supply


Elastic Supply - Elasticity is greater than 1

Quantity

Price

4


200 100

Supply


Perfectly Elastic Supply - Elasticity equals infinity

Quantity

Price

Supply $4

1. At any price above $4, quantity supplied is infinite.

2. At exactly $4, producers will supply any quantity.

3. At a price below $4, quantity supplied is zero.


¨  If the supply curve is linear and has a zero intercept, then εs,p =1

¨  If the supply curve is linear and has a positive intercept, then εs,p >1 and Q é è εs,p =1 ê


¨  In general, elasticity of can vary over the supply curve.

¨  Consider an industry in which firms have factories with a limited capacity for production.

¨  For low levels of quantity supplied, firms can use idle capacity to respond to changes in the price

¨  As the quantity supplied rises, firms begin to reach capacity.

¨  Once capacity is fully used, increasing production further requires the construction of new plants. To induce firms to incur this extra expense, the price must rise substantially

Determinants of Supply Elasticity

¨  The more easily sellers can change the quantity they produce, the greater the price elasticity of supply ¤  Example: Supply of beach front property is harder

to vary and thus less elastic than supply of new cars ¨  For many goods, price elasticity of supply is

greater in the long run than in the short run ¤  Firms can build factories ¤  new firms may enter the market

Supply Elasticity and Equilibrium Change

¨  The supply of beachfront property is inelastic. The supply of new cars is elastic.

¨  Suppose population growth causes demand for both goods to double

¨  For which product will P change the most? ¨  For which product will Q change the most?


8


42


� Price elasticity of supply measures how much Qs responds to a change in P.




� Loosely speaking, it measures sellers’ price-sensitivity.

� Again, use the midpoint method to compute the percentage changes.


43

Q2


Price elasticity of supply equals

P

Q

S

P2

Q1

P1

P rises by 8%

Q rises by 16%

16%8%

= 2.0




Example:


44

The Variety of Supply Curves

� The slope of the supply curve is closely related to price elasticity of supply.


� Five different classifications

� Perfectly inelastic (ex: land), inelastic (ex: housing), unit elastic, elastic (ex: tutoring),perfectly elastic (ex: dumping inventory)


45

The Determinants of Supply Elasticity� The more easily sellers can change the quantity

they produce, the greater the price elasticity of supply. � Example: Supply of beachfront property is

harder to vary and thus less elastic than supply of new cars.

� For many goods, price elasticity of supply is greater in the long run than in the short run, because firms can build new factories, or new firms may be able to enter the market.

A C T I V E L E A R N I N G ͵Elasticity and changes in equilibrium� The supply of beachfront property is inelastic.

The supply of new cars is elastic.

� Suppose population growth causes demand for both goods to double (at each price, Qd doubles).

� For which product will P change the most?

� For which product will Q change the most?




Beachfront property (inelastic supply):

P

Q

D1S

Q1

P1 A

When supply is inelastic, an increase in demand has a bigger impact on price than on quantity.

D2

B

Q2

P2


9



New cars(elastic supply):

P

Q

D1

S

Q1

P1A

When supply is elastic, an increase in demand has a bigger impact on quantity than on price.

D2

Q2

P2B


49

S

How the Price Elasticity of Supply Can Vary

P

Q

Supply often becomes less elastic as Q rises, due to capacity limits.

Supply often becomes less elastic as Q rises, due to capacity limits.

$15

525

12

500

$3100

4

200

elasticity > 1

elasticity < 1


50

Other Elasticities� Income elasticity of demand: measures the

response of Qd to a change in consumer income

Income elasticity of demand =

Percent change in Qd

Percent change in income

� Recall from Chapter 4: An increase in income causes an increase in demand for a normal good.

� Hence, for normal goods, income elasticity > 0.

� For inferior goods, income elasticity < 0.


51

Other Elasticities� Cross-price elasticity of demand:

measures the response of demand for one good to changes in the price of another good

Cross-price elast. of demand =

% change in Qd for good 1

% change in price of good 2

� For substitutes, cross-price elasticity > 0 (e.g., an increase in price of beef causes an increase in demand for chicken)

� For complements, cross-price elasticity < 0 (e.g., an increase in price of computers causes decrease in demand for software)


52

Cross-Price Elasticities in the News“As Gas Costs Soar, Buyers Flock to Small Cars”

-New York Times, 5/2/2008

“Gas Prices Drive Students to Online Courses”-Chronicle of Higher Education, 7/8/2008

“Gas prices knock bicycle sales, repairs into higher gear” -Associated Press, 5/11/2008

“Camel demand soars in India” (as a substitute for “gas-guzzling tractors”)

-Financial Times, 5/2/2008

“High gas prices drive farmer to switch to mules”-Associated Press, 5/21/2008

Summary

• Elasticity measures the responsiveness of Qd or Qs to one of its determinants.

• Price elasticity of demand equals percentage change in Qd divided by percentage change in P. When it’s less than one, demand is “inelastic.” When greater than one, demand is “elastic.”

• When demand is inelastic, total revenue rises when price rises. When demand is elastic, total revenue falls when price rises.


Other Elasticities

¨  Income Elasticity of Demand

Price elasticity of demand ✏d,p= �dQ/QdP/P =

��dQ/QdP/P

��

⇡��(Q2�Q1)/ 1

2 (Q1+Q2)

(P2�P1)/ 12 (P1+P2)

��

d (Total Revenue)

dP=

d (QP )

dP=

dQ

dPP +Q

Therefore,

d (Total Revenue)

dP> 0 , dQ

dP

P

Q> �1 , ✏d,p < 1

d (Total Revenue)

dP< 0 , dQ

dP

P

Q< �1 , ✏d,p > 1

✏ > 1 Elastic

✏ < 1 Inelastic




✏d,i =

Percentage change in quantity demanded

Percentage change in income

=dQ/Q

dI/I

1

Income Elasticity of Demand

¨  Normal goods ¤  εd,i >0

¨  Inferior goods ¤  εd,i <0

Other Elasticities

¨  Cross-price Elasticity of Demand

Price elasticity of demand ✏

d,p

= �dQ/Q

dP/P

=��dQ/Q

dP/P

��

⇡��(Q2�Q1)/ 1

2 (Q1+Q2)

(P2�P1)/ 12 (P1+P2)

��

d (Total Revenue)

dP

=d (QP )

dP

=dQ

dP

P +Q

Therefore,

d (Total Revenue)

dP

> 0 , dQ

dP

P

Q

> �1 , ✏

d,p

< 1

d (Total Revenue)

dP

< 0 , dQ

dP

P

Q

< �1 , ✏

d,p

> 1

✏ > 1 Elastic

✏ < 1 Inelastic




✏

d,i

=

Percentage change in quantity demanded

Percentage change in income

=dQ/Q

dI/I

✏

d,xy

=

Percentage change in quantity demanded of good x

Percentage change in the price of good y

=dQ

x

/Qx

dP

y

/Py

1

Cross-price Elasticity of Demand

¨  Substitutes ¤  εd,xy >0

¨  Complements ¤  εd,xy <0


¨  Suppose the quantity demanded for good X decreased 25% while the price of good Y increased by 50%

¨  What is the cross-price elasticity of demand for X and Y? Are X and Y substitutes or complements? ¤  What assumptions do we need to answer these

questions?


¨  “As Gas Costs Soar, Buyers Flock to Small Cars” – NYTimes, 5/2/2008

¨  “High Cost of Driving Ignites Online Classes Boom” – Chronicle of Higher Education, 7/11/2008

¨  “Gas prices knock bicycle sales, repairs into higher gear” – Associated Press, 5/11/2008

¨  “Camel demand soars in India” (as oil price soars) – Financial Times, 5/2/2008

Can Good News for Farming Be Bad News for Farmers? ¨  Scientific discovery of new wheat hybrid that can raise

yield per acre by 20% ¨  Q é , P ê ¨  Change in total revenue depends on price elasticity of

demand ¤  Demand for wheat is usually inelastic ¤  P ê -> total revenue ê (inelastic demand)

¨  If the new hybrid hurts farmers, why would they adopt it? ¤  In competitive markets, each farmer is a price taker: it’s

better for each to sell more given market price ¤  When all farmers do this, the supply of wheat increases, the

price falls, and farmers are worse off.

Yacht Tax

¨  Proposal: luxury tax on yachts over $100,000 will yield $31 million in U.S. tax revenue

¨  Price elasticity of demand is high ¨  Outcome

¤  Tax took effect in Jan 1990 ¤  Actual tax revenue $16.6 million ¤  People bought yachts outside US to avoid tax

n  7,600 jobs in US boating industry lost

¨  Tax repealed after 2 years

The War on Drugs

¨  One adverse effect of drug use is that drug addicts often turn to robbery and other violent crimes to obtain the money needed to support their habit.

¨  One measure to stop drug-related violence: drug interdiction. i.e. stop the entry and supply of drugs

¨  What happens to drug use? ¨  What happens to the total revenue of drug sellers?

¤  Is demand for drugs elastic or inelastic? ¤  Short-run vs Long-run

The War on Drugs

The War on Drugs

¨  In the short run, increase in total revenue means ¤  Drug sellers have more incentive to engage in illicit drug

trade, leading to more powerful drug cartels and organized crime in drug-producing countries

¤  Drug addicts have to spend more for drugs, which may lead to increase in drug-related crime in drug-consuming countries

¨  In the long run, this may encourage people to break their habit and discourage the number of new users.

elasticity and its application - principles of...

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