Elasticity and its Application

Seventh Edition Elasticity Principles of Wojciech Gerson (1831-1901) Macroeconomics N. Gregory Mankiw CHAPTER 5 Elasticity and its Application ...
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Seventh Edition

Elasticity

Principles of

Wojciech Gerson (1831-1901)

Macroeconomics N. Gregory Mankiw

CHAPTER

5

Elasticity and its Application

 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.

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In this chapter, look for the answers to these questions

Price Elasticity of Demand Price elasticity of demand

• What is elasticity? What kinds of issues can

Percentage change in Qd =

Percentage change in P

elasticity help us understand?  Price elasticity of demand measures how much Qd responds to a change in P.

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

 Loosely speaking, it measures the pricesensitivity of buyers’ demand.

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

• What are the income and cross-price elasticities of 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.

A scenario…

Price Elasticity of Demand

You design websites for local businesses. You charge $200 per website, and currently sell 12 websites per month.

Price elasticity of demand

Percentage change in Qd =

Percentage change in P P

Example:

Your costs are rising (including the opportunity cost of your time), so you consider raising the price to $250.

Price elasticity of demand equals

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? © 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.

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15% = 1.5 10% 2

P rises P2 by 10% P1 D

Q2

Q1

Q

Q falls by 15%

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5

1

Calculating Percentage Changes

Price Elasticity of Demand Price elasticity of demand

Percentage change in =

 So, we instead use the midpoint method:

Qd

end value – start value x 100% midpoint

Percentage change in P

Along a D curve, P and Q move in opposite directions, which would make price elasticity negative.

P

 The midpoint is the number halfway between the start and end values, the average of those values.

P2 P1 D

We will drop the minus sign and report all price elasticities as positive numbers.

Q2

Q1

Q

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6

Calculating Percentage Changes

$250

B

D 8

12

 The price elasticity of demand equals

($250–$200)/$200 = 25%

40/22.2 = 1.8 7

P

A

if P = $135, Qd = 8600

From B to A, P falls 20%, Q rises 50%, Q elasticity = 50/20 = 2.50

D 8

12

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1

Use the following information to calculate the price elasticity of demand for hotel rooms:

From A to B, P rises 25%, Q falls 33%, elasticity = 33/25 = 1.33

B

10

Calculate an elasticity

Problem: The standard method gives different answers depending on where you start.

Demand for your websites

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ACTIVE LEARNING

Calculating Percentage Changes

$200

 The % change in Q equals

Q

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$250

$250 – $200 x 100% = 22.2% $225 12 – 8 x 100% = 40.0% 10

Going from A to B, the % change in P equals

A

$200

 Using the midpoint method, the % change in P equals

end value – start value x 100% start value

P

9

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Calculating Percentage Changes

Standard method of computing the percentage (%) change:

Demand for your websites

 It doesn’t matter which value you use as the start and which as the end—you get the same answer either way!

©stefanolunardi/Shutterstock.com

if P = $165, Qd = 7400

8

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2

ACTIVE LEARNING

1

EXAMPLE 2

“Blue Jeans” vs. “Clothing”

Applying the principles

 The prices of both goods rise by 20%. For which good does Qd drop the most? Why?  For a narrowly defined good such as blue jeans, there are many substitutes (khakis, shorts, Speedos).

Use midpoint method to calculate % change in Qd (8600 – 7400)/8000 = 15% % change in P

 There are fewer substitutes available for broadly defined goods. (Are there any substitutes for clothing?)

($165 – $135)/$150 = 20% The price elasticity of demand equals

 Lesson: Price elasticity is higher for narrowly defined goods than for broadly defined ones.

15% = 0.75 20% © 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.

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EXAMPLE 3

What determines price elasticity?

Insulin vs. Caribbean Cruises

To learn the determinants of price elasticity, we look at a series of examples. Each compares two common goods.

 The prices of both of these goods rise by 20%. For which good does Qd drop the most? Why?  To millions of diabetics, insulin is a necessity. A rise in its price would cause little or no decrease in demand.

In each example:  Suppose the prices of both goods rise by 20%.  The good for which Qd falls the most (in percent) has the highest price elasticity of demand. Which good is it? Why?  What lesson does the example teach us about the determinants of the price elasticity of 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.

13

 A cruise is a luxury. If the price rises, some people will forego it.

 Lesson: Price elasticity is higher for luxuries than for necessities.

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EXAMPLE 1

EXAMPLE 4

Breakfast Cereal vs. Sunscreen

Gasoline in the Short Run vs. Gasoline in the Long Run

 The prices of both of these goods rise by 20%. For which good does Qd drop the most? Why?

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 The price of gasoline rises 20%. Does Qd drop more in the short run or the long run? Why?

 Breakfast cereal has close substitutes (e.g., pancakes, Eggo waffles, leftover pizza), so buyers can easily switch if the price rises.

 There’s not much people can do in the short run, other than ride the bus or carpool.

 Sunscreen has no close substitutes, so a price increase would not affect demand very much.

 In the long run, people can buy smaller cars or live closer to work.  Lesson: Price elasticity is higher in the long run than the short run.

 Lesson: Price elasticity is higher when close substitutes are available. © 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.

15

14

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17

3

“Inelastic demand”

The Determinants of Price Elasticity: A Summary

< 10% % change in Q Price elasticity 1 = = of demand 10% % change in P

=0

P1

Consumers’ price sensitivity: none

D P falls by 10%

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Elasticity: 1

10%

P2

% change in Q Price elasticity = = of demand % change in P

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

0%

P1

“Unit elastic demand”

The Variety of Demand Curves

% change in Q Price elasticity = = of demand % change in P

P

Q

Q changes by 0% 20

Elasticity: >1

P2 P falls by 10%

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D

Q1

Q2

Q

Q rises more than 10% 23

4

“Perfectly elastic demand” (the other extreme)

Price Elasticity and Total Revenue

any % % change in Q Price elasticity = infinity = = of demand 0% % change in P P

D curve: horizontal

Revenue = P x Q D

P2 = P1

Consumers’ price sensitivity: extreme

P changes by 0%

Elasticity: infinity

Q1

Q2

Q

24

0.1

Healthcare

0.2

Rice

0.5

Housing

0.7

Beef

1.6

Restaurant meals

2.3

Mountain Dew

4.4

Price elasticity = of demand

20

200% = 5.0 40% E =

40% E = = 0.2 200%

10 $0

67% = 1.0 67%

0

20

40

60

% change in Q > % change in P  The fall in revenue from lower Q is greater than the increase in revenue from higher P, so revenue falls. 25

28

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Price Elasticity and Total Revenue Elastic demand (elasticity = 1.8)

The slope of a linear demand curve is constant, but its elasticity is not.

If P = $200, Q = 12 and revenue = $2400. If P = $250, Q = 8 and revenue = $2000.

P

$250

increased Demand for revenue due your websiteslost to higher P revenue due to lower Q

$200

When D is elastic, a price increase causes revenue to fall.

Q

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Percentage change in P

 If demand is elastic, then price elast. of demand > 1

Elasticity of a Linear Demand Curve

E =

Percentage change in Q

Revenue = P x Q

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P

27

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Price Elasticity and Total Revenue

A few elasticities from the real world Eggs

 A price increase has two effects on revenue:  Higher P means more revenue on each unit you sell.  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.

Q changes by any %

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$30

 Continuing our scenario, if you raise your price from $200 to $250, would your revenue rise or fall?

26

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D

8

12

Q

29

5

ACTIVE LEARNING

Price Elasticity and Total Revenue Price elasticity = of demand

1

Answers

Percentage change in Q

A. Pharmacies raise the price of insulin by 10%.

Percentage change in P

Does total expenditure on insulin rise or fall? Revenue = P x Q

 If demand is inelastic, then price elast. of demand < 1 % change in Q < % change in P

Expenditure = P x Q Since demand is inelastic, Q will fall less than 10%, so expenditure rises.

 The fall in revenue from lower Q is smaller than the increase in revenue from higher P, so revenue rises.  In our example, suppose that Q only falls to 10 (instead of 8) when you raise your price to $250. 30

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ACTIVE LEARNING

Price Elasticity and Total Revenue Now, demand is inelastic: elasticity = 0.82

If P = $200, Q = 12 and revenue = $2400. If P = $250, Q = 10 and revenue = $2500.

P

$250

B. As a result of a fare war, the price of a luxury

cruise falls 20%. Does luxury cruise companies’ total revenue rise or fall? Revenue = P x Q

$200 D

10 12

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ACTIVE LEARNING

2

Answers

increased Demand for revenue due your websites lost to higher P revenue due to lower Q

When D is inelastic, a price increase causes revenue to rise.

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2

Elasticity and expenditure/revenue A. Pharmacies raise the price of insulin by 10%.

Does total expenditure on insulin rise or fall? B. As a result of a fare war, the price of a luxury

cruise falls 20%. Does luxury cruise companies’ total revenue rise or fall?

Q

The fall in P reduces revenue, but Q increases, which increases revenue. Which effect is bigger? Since demand is elastic, Q will increase more than 20%, so revenue rises.

31

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Does Drug Interdiction Increase or Decrease Drug-Related Crime? APPLICATION:

 One side effect of illegal drug use is crime: Users often turn to crime to finance their habit.  We examine two policies designed to reduce illegal drug use and see what effects they have on drug-related crime.  For simplicity, we assume the total dollar value of drug-related crime equals total expenditure on drugs.  Demand for illegal drugs is inelastic, due to addiction issues.

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Policy 1: Interdiction

Price Elasticity of Supply

new value of drugrelated crime S2 D1

Interdiction Price of reduces Drugs the supply of drugs. P2 Since demand for drugs is inelastic, P1 P rises proportionally more than Q falls.

Price elasticity of supply

S1

initial value of drugrelated crime Q2 Q1

Quantity of Drugs 36

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Policy 2: Education Price of Drugs

D2

S initial value of drugrelated crime

P1 P2

Q2 Q1

37

Q

Q2

Q rises by 16% 39

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 Rule of thumb: The flatter the curve, the bigger the elasticity. The steeper the curve, the smaller the elasticity.  Five different classifications…

40

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“Perfectly inelastic” (one extreme) 0%

% change in Q Price elasticity = = of supply % change in P

Percentage change in Qs Percentage change in P

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

P

S curve: vertical

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

Elasticity: 0 38

10%

=0

S

P2

Sellers’ price sensitivity: none

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

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Q1

16% = 2.0 8%

Quantity of Drugs

Price Elasticity of Supply =

Price elasticity of supply equals

S

P rises P2 by 8% P1

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

D1

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Price elasticity of supply

P

The Variety of Supply Curves

new value of drugrelated crime

P and Q fall. Result: A decrease in total spending on drugs, and in drug-related crime.

Percentage change in P

Example:

Result: an increase in total spending on drugs, and in drug-related crime

Education reduces the demand for drugs.

Percentage change in Qs =

P1 P rises by 10%

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Q1

Q

Q changes by 0% 41

7

“Inelastic”

“Perfectly elastic” (the other extreme)

< 10% % change in Q Price elasticity 10% % change in Q Price elasticity >1 = = of supply 10% % change in P

Elasticity: >1

P changes by 0%

The Determinants of Supply Elasticity

% change in Q Price elasticity = = of supply % change in P

Elasticity: =1

Elasticity: infinity

S

P2 = P1

Sellers’ price sensitivity: extreme

P1 P rises by 10%

P

S curve: horizontal

S

Sellers’ price sensitivity: relatively low Elasticity: 0.

A

 For inferior goods, income elasticity < 0. Q

Q1 Q2 © 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.

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3

ACTIVE LEARNING

Other Elasticities

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

 Cross-price elasticity of demand: measures the response of demand for one good to changes in the price of another good

New cars (elastic supply): P

% change in Qd for good 1 Cross-price elast. = of demand % change in price of good 2

D1 D2

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

S

B

P2 P1

A

Q1

Q2

Q

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S

12

elasticity >1

100 200

“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

Q

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

500 525

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Cross-Price Elasticities in the News

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

4 $3

52

“As Gas Costs Soar, Buyers Flock to Small Cars” -New York Times, 5/2/2008

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

elasticity