price elasticity of demand overheads. how much would your roommate pay to watch a live fight? how...

Price Elasticity of Demand

Overheads

How much would your roommate payto watch a live fight?

How does Showtime decide howmuch to charge for a live fight?

What about Hank and Son’s Concrete?

How much should they charge per square foot?

Can ISU raise parking revenue by raising parking fees?

Or will the increase in price drive demanddown so far that revenue falls?

All of these pricing issues revolve around the issue of how responsive the quantity demanded is to price.

Elasticity is a measure of how responsiveone variable is to changes in another variable?

The Law of Demand

The law of demand states that whenthe price of a good rises,and everything else remains the same, the quantity of the good demanded will fall.

The real issue is how far it will fall.

Q D h(P, ZD)

The demand function is given by

QD = quantity demanded

P = price of the good

ZD = other factors that affect demand

The inverse demand function is given by

P h 1(Q D , ZD)

P g(Q D , ZD )

To obtain the inverse demand function wejust solve the demand function for Pas a function of Q

Examples

QD = 20 - 2P

2P + QD = 20

2P = 20 - QD

P = 10 - 1/2 QD

Slope = - 1/2

Examples

QD = 60 - 3P

3P + QD = 60

3P = 60 - QD

P = 20 - 1/3 QD

Slope = - 1/3

The slope of a demand curve is given by thechange in Q divided by the change in P

One measure of responsiveness is slope

Q D h(P, ZD)

slope ΔQ D

ΔP

For demand

The slope of an inverse demand curve is given bythe change in P divided by the change in Q

P g(Q D, ZD)

slope ΔP

ΔQ D

For inverse demand

QD = 60 - 3P

Examples

Slope = - 1/3

Slope = - 3

P = 20 - 1/3 QD

QD = 20 - 2P

Examples

Slope = - 1/2

Slope = - 2

P = 10 - 1/2 QD

We can also find slope from tabular data

Q P0 102 94 86 78 610 5

Q P

slope ΔQ D

ΔP 2

1 2

Q P0 101 9.52 93 8.54 85 7.56 77 6.58 69 5.510 511 4.512 413 3.514 315 2.516 217 1.518 119 0.520 0

Demand for Handballs

Q P0 101 9.52 93 8.54 85 7.56 77 6.58 69 5.510 511 4.512 413 3.514 315 2.516 217 1.518 119 0.520 0


0

1

2

3

4

5

6

7

8

9

10

11

0 2 4 6 8 10 12 14 16 18 20 22

Quantity

Pri

ce

P

Q P0 101 9.52 93 8.54 85 7.56 77 6.58 69 5.510 511 4.512 413 3.514 315 2.516 217 1.518 119 0.520 0


0

1

2

3

4

5

6

7

8

9

10

11

0 2 4 6 8 10 12 14 16 18 20 22

Quantity

Pri

ce

Q P

Q = 2 - 4 = -2Q = 2 - 4 = -2

P = 9 - 8 = 1P = 9 - 8 = 1

slope ΔP

ΔQ D 1

2

Problems with slope as a measure of responsiveness

Slope depends on the units of measurement

The same slope can be associated withThe same slope can be associated withvery different percentage changesvery different percentage changes

Examples

QD = 200 - 2P

2P + QD = 200

2P = 200 - QD

P = 100 - 1/2 QD

slope ΔP

ΔQ D 1

2

Q P0 1001 99.52 993 98.54 985 97.56 977 96.58 969 95.510 9511 94.512 9413 93.514 93

Consider data on racquets

Let P change from 95 to 96

P = 96 - 95 = 1

Q = 8 - 10 = -2

Q P

A $1.00 price change when P = $95.00 is tiny

Graphically for racquetsDemand for Racquets

88

90

92

94

96

98

100

102

0 2 4 6 8 10 12 14 16 18

Quantity

Pri

ce

Large % change in Q

Small % change in P

Slope = - 1/2

Graphically for hand balls

Large % change in Q Large % change in P

Slope = - 1/2


0

1

2

3

4

5

6

7

8

9

10

11

0 2 4 6 8 10 12 14 16 18 20 22

Quantity

Pri

ceP

P = 7 - 6 = 1

Q = 6 - 8 = -2

So slope is not such a good measureof responsiveness

Instead of slope we use percentage changes

The ratio of the percentage change in one variableto the percentage change in another variableis called elasticityelasticity

εD %ΔQ D

%ΔP

ΔQ D

Q D

ΔPP

The Own Price Elasticity of DemandOwn Price Elasticity of Demandis given by

There are a number of ways to computepercentage changes

InitialInitial point method for computing

The Own Price Elasticity of DemandOwn Price Elasticity of Demand

εD %ΔQ D

%ΔP

ΔQ D

Q D

ΔPP

Price Elasticity of Demand (Initial Point Method) P Q

6 85.5 95 104.5 114 12

εD

(8 10)8

(6 5)6

(8 10)8

6(6 5)

QP

28

61

128

1.5

FinalFinal point method for computing


Price Elasticity of Demand (Final Point Method) P Q

6 85.5 95 104.5 114 12

εD

(8 10)10

(6 5)5

(8 10)10

5(6 5)

QP

210

51

1010

1.0

εD %ΔQ D

%ΔP

ΔQ D

Q D

ΔPP

The answer is very differentThe answer is very differentdepending on the choice of the depending on the choice of the base pointbase point

So we usually useSo we usually use

The midpointThe midpoint method for computing


ΔQ D Q1 Q0 or Q0 Q1

Elasticity of Demand Using the Mid-Point

εD %ΔQ D

%ΔP

ΔQ D

Q D

ΔPP

Q D 12

(Q1 Q0)

For QD we use the midpoint of the Q’s

Similarly for pricesSimilarly for prices

ΔP P1 P0 or P0 P1

P 12

(P1 P0)

For P we use the midpoint of the P’s

ε

(Q1 Q0 )

12

(Q1 Q0)

(P1 P0 )

12

(P1 P0)

(Q1 Q0 )

(Q1 Q0)

(P1 P0)

(P1 P0)

εD %ΔQ D

%ΔP

ΔQ D

Q D

ΔPP

Price Elasticity of Demand (Mid-Point Method) Q P

8 69 5.510 511 4.512 4

(Q1 Q0)

(P1 P0)

(P1 P0)

(Q1 Q0)

(Q1 Q0)

(Q1 Q0)

(P1 P0)

(P1 P0)

εD %ΔQ D

%ΔP

ΔQ D

Q D

ΔPP

(8 10)(6 5)

(6 5)(8 10)

( 2)(1)

(11)(18)

2218

119

Classification of the elasticity of demand

Inelastic demand

When the numerical value of the elasticity of demand is between 0 and -1.0, we say that demand is inelasticinelastic.

%ΔQ D

%ΔP< 1

%ΔQ D < %ΔP


Elastic demand

When the numerical value of the elasticity of demand

is less than -1.0, we say that demand is elasticelastic.

%ΔQ D

%ΔP> 1

%ΔQ D > %ΔP


Unitary elastic demand

When the numerical value of the elasticity of demand is equal to -1.0, we say that demand is unitary elasticunitary elastic.

%ΔQ D

%ΔP 1

%ΔQ D %ΔP


Perfectly elastic - D = -

Perfectly inelastic - D = 0

horizontalhorizontal

verticalvertical

Elasticity of demand with linear demand

Consider a linear inverse demand function

P A BQ D

P 12 0.5Q D

The slope is (-B) for all values of P and Q

For example,

The slope is -0.5 = - 1/2

P Q12 011.5 111 210.5 310 49.5 59 68.5 78 87.5 97 106.5 116 125.5 135 144.5 154 163.5 173 18

Demand for Diskettes

0123456789

10111213

0 2 4 6 8 10 12 14 16 18 20 22

Quantity

Pri

ce

ΔQ D

ΔP 2.0

P Q

P Q

ΔQΔP

(P1 P0)

(Q1 Q0)

εD %ΔQ D

%ΔP

ΔQ D

Q D

ΔPP

(8 10)(8 7)

(8 7)(8 10)

( 2)(1)

(15)(18)

3018

53

The slope is constant but the elasticity of demand will vary

P Q12 011.5 111 210.5 310 49.5 59 68.5 78 87.5 97 106.5 116 125.5 135 144.5 154 163.5 173 18

P Q

εD %ΔQ D

%ΔP

ΔQ D

Q D

ΔPP

(14 16)(5 4)

(5 4)(14 16)

( 2)(1)

(9)(30)

1830

35


P Q12 011.5 111 210.5 310 49.5 59 68.5 78 87.5 97 106.5 116 125.5 135 144.5 154 163.5 173 18

P Q

ΔQΔP

(P1 P0)

(Q1 Q0)


A linear demand curve becomes more inelasticas we lower price and increase quantity

εD %ΔQ D

%ΔP ΔQ

ΔP

(P1 P0)

(Q1 Q0)

P smaller

Q larger

The elasticity gets closer to zero

Q P Elasticity Expenditure0 12 02 11 -23.0000 224 10 -7.0000 406 9 -3.8000 548 8 -2.4286 6410 7 -1.6667 7012 6 -1.1818 7214 5 -0.8462 7016 4 -0.6000 6418 3 -0.4118 5420 2 -0.2632 4022 1 -0.1429 2224 0 -0.0435 0


NoteNoteWe do not say that demand is We do not say that demand is elasticelasticor or inelasticinelastic ….. …..

We say that demand is elastic or We say that demand is elastic or inelastic inelastic at a given pointat a given point

εD %ΔQ D

%ΔP

ΔQ D

Q D

ΔPP

ΔQΔP

(P1 P0)

(Q1 Q0)

ExampleExample

Constant with linear demandConstant with linear demand

The Own Price Elasticity of DemandOwn Price Elasticity of Demandand Total Expenditure on an ItemTotal Expenditure on an Item

How do changes in an items price affectHow do changes in an items price affectexpenditure on the item?expenditure on the item?

If I lower the price of a product, will the increasedIf I lower the price of a product, will the increasedsales make up for the lower price per unit?sales make up for the lower price per unit?

Expenditure for the consumerExpenditure for the consumeris equal to revenue for the firmis equal to revenue for the firm

Revenue = R = price x quantity = PQRevenue = R = price x quantity = PQ

Expenditure = E = price x quantity = PQExpenditure = E = price x quantity = PQ

P = change in price

Modeling changes in price and quantity

Q = change in quantity

The Law of Demand says that

as P increases Q will decrease

P P Q Q

P = initial price

P = change in price

So

P + P = final price

Q = initial quantity

Q = change in quantity

Q + Q = final quantity

Initial Revenue = PQ

So

P + P = final price

= P Q + P Q + P Q + P Q

Q + Q = final quantity

Final Revenue = (P + P) (Q + Q)

Now find the change in revenue

R = final revenue - initial revenue

= P Q + P Q + P Q + P Q - P Q

= P Q + P Q + P Q

%R = R / R = R / P Q

ΔRPQ

ΔP Q P ΔQ ΔP ΔQPQ

ΔRPQ

ΔP QPQ

P ΔQPQ

ΔP ΔQPQ

We can rewrite this expression as follows

%ΔR ΔPP

ΔQQ

ΔP ΔQPQ

%ΔR %ΔP %ΔQ

Classification of the elasticity of demandInelastic demand

%ΔQ D

%ΔP< 1 %ΔQ D < %ΔP

%ΔR %ΔP %ΔQ

% Q and % P are of opposite sign so%R has the same sign as %P

+ -

Classification of the elasticity of demandInelastic demand

%ΔQ D

%ΔP< 1 %ΔQ D < %ΔP

%ΔR %ΔP %ΔQ

% Q and % P are of opposite sign so%R has the same sign as %P

- +

Lower price lower revenue

Higher price higher revenue

Classification of the elasticity of demandElastic demand

%ΔQ D

%ΔP> 1 %ΔQ D > %ΔP

%ΔR %ΔP %ΔQ

% Q and % P are of opposite sign so%R has the opposite sign as %P

Higher price lower revenue

Lower price higher revenue

+ -

Classification of the elasticity of demandUnitary elastic demand

%ΔQ D

%ΔP 1 %ΔQ D %ΔP

%ΔR %ΔP %ΔQ

% Q and % P are of opposite sign so theireffects will cancel out and %R = 0.

+ -

Q P Elasticity Revenue0 12 02 11 -23.0000 224 10 -7.0000 406 9 -3.8000 548 8 -2.4286 6410 7 -1.6667 7012 6 -1.1818 7214 5 -0.8462 7016 4 -0.6000 6418 3 -0.4118 5420 2 -0.2632 4022 1 -0.1429 2224 0 -0.0435 0

Tabular data Elastic

Revenue risesInelastic

Revenue falls

Price falls

Price falls

0 12 0 2 11 -23.0000 22 4 10 -7.0000 40 6 9 -3.8000 54 8 8 -2.4286 6410 7 -1.6667 7012 6 -1.1818 7214 5 -0.8462 7016 4 -0.6000 6418 3 -0.4118 5420 2 -0.2632 4022 1 -0.1429 2224 0 -0.0435 0

Graphical analysisQ P Elasticity RevenueDemand for Diskettes

0123456789

10111213

0 2 4 6 8 10 12 14 16 18 20 22

Quantity

Pri

ce

Demand

A

B

CC

P0, Q0

P1, Q1

Lose B, gain A, revenue rises

0 12 0 2 11 -23.0000 22 4 10 -7.0000 40 6 9 -3.8000 54 8 8 -2.4286 6410 7 -1.6667 7012 6 -1.1818 7214 5 -0.8462 7016 4 -0.6000 6418 3 -0.4118 5420 2 -0.2632 4022 1 -0.1429 2224 0 -0.0435 0

Graphical analysisQ P Elasticity RevenueDemand for Diskettes

0123456789

10111213

0 2 4 6 8 10 12 14 16 18 20 22

Quantity

Pri

ce

Demand

P1, Q1

Lose A, gain B, revenue falls

P0, Q0

AAB

Factors affecting the elasticity of demand

Availability of substitutes

Importance of item in the buyer’s budget

Availability of substitutes

The easier it is to substitute for a good,

the more elastic the demand

With many substitutes, individuals willmove away from a good whose price increases

Examples of goods with “easy “substitution

Gasoline at different stores

Soft drinks

Detergent

Airline tickets

Local telephone service

Narrow definition of product

The more narrowly we define an item,

the more elastic the demand

With a narrow definition, there will lots ofsubstitutes

Examples of narrowly defined goods

Lemon-lime drinks

Corn at a specific farmer’s market

Vanilla ice cream

Food

Transportation

“Necessities” tend to have inelastic demand

Necessities tend to have few substitutes

Examples of necessities

Salt

Insulin

Food

Trips to Hawaii

Sailboats

Demand is more elastic in the long-run

There is more time to adjust in the long run

Examples of short and long run elasticity

Postal rates

Gasoline

Sweeteners

Factors affecting the elasticity of demand

Importance of item in the buyer’s budget

The more of their total budget consumersspend on an item,

the more elastic the demand for the good

The elasticity is larger because the item hasThe elasticity is larger because the item hasa large budget impacta large budget impact

“Big ticket” items and elasticity

Housing

Big summer vacations

Table salt

College tuition

The End

price elasticity of demand overheads. how much would your roommate pay to watch a live fight? how...

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