Chapter 4 Elasticity Fall 20131 8

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1

Chapter 4: Elasticity


2

Learning Objectives

1. Define price elasticity of demand Explain its determinants

2. Calculate price elasticity of demand3. Understand how changes in price affect

total revenue Relate to price elasticity of demand

4. Define cross-price elasticity and income elasticity

5. Define price elasticity of supply Explain what determines this elasticity

6. Calculate price elasticity of supply


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Drug Enforcement and Local Theft

Hypothesis Drug users steal to buy drugs Increasing drug enforcement will decrease theft

Analysis Increased enforcement reduces supply of drugs

Price of drugs increases Quantity demanded decreases

Is this policy successful in decreasing the prevalence of theft?


4

Drug Enforcement and Local Theft

Theft goes down ONLY IF total expenditures on drugs decreases

Meaning the amount of crime that drug users commit depends not on the quantity of drugs they consume but rather on their total expenditures

• How responsive is quantity demanded to price?

Total expenditures on drugs increased rather than decreased!

Expect more crime


5

Elasticity

It is a measure of responsiveness of one variable to a change in an another variable Slope measures a form of

responsiveness But if a different unit is used then the

value of the slope is different which biases the magnitude of the response

Elasticity corrects for this issue Unit choice does not change the value

of elasticity


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Price Elasticity of Demand

Price elasticity of demand Percentage change in quantity

demanded from a 1% change in price Measure of responsiveness of quantity

demanded to change in priceExample:

Price of beef decreases 1% Quantity of beef demanded

increases 2% Price elasticity of demand is – 2

P

Q


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Calculate Price Elasticity of Demand

Symbol for elasticity is ε Lower case Greek letter epsilon

For small percentage changes in price

ε = Percentage change in quantity demanded

Percentage change in price

Price elasticity of demand is always negative Ignore the sign Focus on the value


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Elastic Demand

If price elasticity is greater than 1, demand is elastic Percentage change in quantity demanded is

greater than percentage change in price Quantity demanded is responsive to price

3


Inelastic

Unit elastic

Elastic

210


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Inelastic Demand

If price elasticity is less than 1, demand is inelastic Percentage change in quantity demanded is less

than percentage change in price Quantity demanded is not very responsive to price

3


Inelastic

Unit elastic

Elastic

210


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Unit Elastic Demand

If price elasticity is 1, demand is unit elastic Price and quantity demanded change by

the same percentage

3


Inelastic

Unit elastic

Elastic

210


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Example: Demand for Pizza

Old New % ChangePrice $1.00 $0.97 3%

Quantity 400 404 1%



ε = 1%

3%= 0.33 Demand is inelastic


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Determinants of Price Elasticity of Demand

•More options, more elastic•Salt•Morton's salt (brand)

Substitution Options

•Larger share, more elastic•New car•Salt

Budget Share

•Longer time to adjust, more elastic•Air conditioner•Gasoline

Time


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Examples of Elasticities

Green peas 2.80Restaurant

meals 1.63Shoes 0.70Coffee 0.25

Automobiles 1.35Foreign air

travel 0.77

Movies 0.87Theater, opera 0.18


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Price Elasticity Notation

ΔQ is the change in quantity ΔQ / Q is percentage change in

quantityΔP is change in price

ΔP / P is percentage change in price



ε = ΔQ / Q

ΔP / P


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Price Elasticity: Graphical View

ε = ΔQ / Q

ΔP / P

ε = ΔQ

Q

P

ΔPx

ε = P

Q

ΔQ

ΔPx

ε = PQ

1slope

x

P – Δ P

Pric

e

P

D

A

Q Q + Δ Q

Δ Q

Δ P

Quantity


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Price Elasticity: Graphical View

At point AP = 28Q = 3Slope = 20 / 5 = 4

ε = PQ

1slope

x

ε = 28

3

1

4x = 2.33

8

Pric

e

28

D

A

3 8

Δ Q

Δ P

Quantity


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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 elastic for the steeper curve

D1

D2

12

4 6 12

6

4

Quantity

Pric

e

Less ElasticMore Elastic


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Price Elasticity on a Straight-Line Demand Curve

Price elasticity is different at each point

Slope is the same for the demand curve

P/Q decreases as price goes down and quantity goes up

ε = PQ

1slope

x


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Price Elasticity Pattern

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

Demand is elasticAt the midpoint,

demand is unit elasticAt low P and high Q,

P / Q is small Demand is

inelastic

Pric

e

b/2

a/2

a

b

1

1

1

Quantity

Price elasticity changes systematically as price goes down


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Two Special Cases

Perfectly Elastic Demand Infinite price elasticity of

demand

Perfectly Inelastic Demand

Zero price elasticity of demand

Price

Quantity

D

Price

Quantity

D


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The Midpoint Formula for Elasticity of Demand

Elasticity is different at each point on the demand curve

Compare 2 points Answer depends on which

point is the starting point Start at A and elasticity is 2 Start at B and elasticity is 1

A more stable solution is needed

Use the midpoint formula

P

Q

ΔP Δ Q

43

4 6

AB


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The Midpoint Formula for Elasticity of Demand

Midpoint formula Use average quantity in the numerator Use average price in the denominator

Elasticity using midpoint formula is 1.40

ΔQ / [(QA + QB)/2]Δ P / [(PA + PB)/2]ε =

Δ Q / (QA + QB)Δ P / (PA + PB)ε =

P

Q

ΔP Δ Q

43

4 6

AB


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Elasticity and Total Expenditure

When price increases, expenditures can increase, decrease or remain the same The change in expenditures depends on elasticity

Terminology: total expenditures = total revenue Calculated as P x Q

Graphing idea: total expenditures is the area of a rectangle with height P and width Q Example: P = 2 and

Q = 4

Price

Quantity

D2

4

Expenditures = 8


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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


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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 when price increases

D


12


Pric

e ($

/tick

et)

2 6

8Y

Z

D


12


Pric

e ($

/tick

et)

1 6

10


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Price Changes and Total Expenditure Changes

Price $12 $10 $8 $6 $4 $2 $0Quantity 0 1,000 2,000 3,000 4,000 5,000 6,000Expenditure $0 $10,0

00$16,0

00$18,0

00$16,0

00$10,0

00 $0

18,000

Price ($/ticket)

Tota

l exp

endi

ture

($/d

ay)

2 6 10

16,000

10,000

12


Pric

e ($

/tick

et)

1 3 4 5 6

10

8

6

4

2

2


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Elasticity, Price Change, and Expenditures


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Cross-Price Elasticity of Demand

Substitutes and complements affect demand

Cross-price elasticity of demand Percentage change in quantity demanded

of good A from a 1 percent change in the price of good B

Sign of cross-price elasticity shows relationship between the goods: Focus on sign and value

Complements have negative cross-price elasticity

Substitutes have positive cross-price elasticity


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Income Elasticity of Demand

Income elasticity of demand Percentage change in quantity

demanded from a 1 percent change in income

Income elasticity of demand can be positive or negative Focus on sign and value

Normal goods have a positive income elasticity

Inferior goods have a negative income elasticity


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Price Elasticity of Supply

Price elasticity of supply Percentage change in quantity

supplied from a 1 percent change in price

Always positive Focus on intercept

Price elasticity of supply = ΔQ / Q

ΔP / P

Price elasticity of supply = PQ

1slope

x


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If supply curve has a positive intercept Price elasticity of supply

decreases as Q increases

Graph shows Slope = 2 At A, P = 8 and Q = 2

• Price elasticity of supply = (8 / 2) (1 / 2) = 2.00

At B, P = 10 and Q = 3• Price elasticity of

supply = (10 / 3) (1 / 2) = 1.67

2

8A

3

10 B

Quantity

Pric

e

4

S


32


If supply curve has a zero intercept Price elasticity of supply

is 1.00 Graph shows

Slope = 1 / 3 At A, P = 4 and Q = 12

• Price elasticity of supply = (4 / 12) (3) = 1.00

At B, P = 5 and Q = 15• Price elasticity of

supply = (5 / 15) (3) = 1.00

15

5B

ΔP

Δ Q

S

12

4 A

Quantity

Pric

e


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Perfectly Inelastic Supply

Zero price elasticity of supply No response to

change in price

Example: Land in Cairo Supply is

completely fixed Any one-of-a-kind

item has perfectly inelastic supply Work of art (Mona

Lisa) Hope Diamond

Price

Quantity

S


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Perfectly Elastic Supply

Infinite price elasticity of supply Sell all you can at a

fixed price

Inputs purchased at a constant price No volume discounts

Constant proportions of production

Lemonade example Cost of production is

14¢ at all levels of Q Marginal cost

P = 14¢

Price

Quantity

S


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Determinants of Price Elasticity of Supply

•Uses adaptable inputs, more elastic

Input Flexibility

•Resources move where needed, more elastic

Mobility of Inputs

•Alternative inputs easy to find, more elastic

Produce Substitute Inputs

•Long run, more elasticTime


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Supply Bottleneck: Unique Inputs

Over time, most producers develop alternative production methods and a variety of input choices The more flexible the production

process is, the more elastic supply isWhen production relies on a single

input, supply is highly inelastic No alternatives to singular talent

Sports stars building a winning team Actors and musicians

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Chapter 4 Elasticity Fall 20131 8