elasticity of demand

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• Learn the meaning of the elasticity of demand.

• Examine what determines the elasticity of demand.

• Learn the meaning of the elasticity of supply.

• Examine what determines the elasticity of supply.

In this lecture you will…In this lecture you will…

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– Elasticities are tools you can use to quantify the impact of changes in prices, income, and advertising on sales and revenues.

– is a measure of how much buyers and sellers respond to changes in market conditions

THE ELASTICITY OF DEMANDTHE ELASTICITY OF DEMAND

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Elasticity – the concept

• The responsiveness of one variable to changes in another

• When price rises, what happens to demand?

• Demand falls• BUT!• How much does demand fall?

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Elasticity – the concept

• If price rises by 10% - what happens to demand?

• We know demand will fall• By more than 10%?• By less than 10%?• Elasticity measures the extent to which

demand will change

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Elasticity

• 4 basic types used:• Price elasticity of demand• Income elasticity of demand• Cross elasticity • Price elasticity of supply

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• Price elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good.

• Price elasticity of demand is the percentage change in quantity demanded given a percent change in the price.

Price Elasticity of DemandPrice Elasticity of Demand

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• Availability of Close Substitutes• Necessities versus Luxuries• Definition of the Market• Time Horizon

The Price Elasticity of Demand and Its The Price Elasticity of Demand and Its DeterminantsDeterminants

A price elasticity of -6.25 means that for each one percent change in

price the quantity demanded will change by 6.25 percent

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• Demand tends to be more elastic:– the larger the number of close substitutes.– if the good is a luxury.– the more narrowly defined the market.– The longer the time period.

The Price Elasticity of Demand and Its The Price Elasticity of Demand and Its DeterminantsDeterminants

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• The price elasticity of demand is computed as the percentage change in the quantity demanded divided by the percentage change in price.

Computing the Price Elasticity of Computing the Price Elasticity of DemandDemand

Price elasticity of demand= Percentage change in quantity demandedPercentage change in price

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• Inelastic Demand– Quantity demanded does not respond

strongly to price changes.– Price elasticity of demand is less than one.

• Elastic Demand– Quantity demanded responds strongly to

changes in price.– Price elasticity of demand is greater than

one.

A Variety of Demand CurvesA Variety of Demand Curves

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• Perfectly Inelastic– Quantity demanded does not respond to

price changes.• Perfectly Elastic

– Quantity demanded changes infinitely with any change in price.

• Unit Elastic– Quantity demanded changes by the same

percentage as the price.

A Variety of Demand CurvesA Variety of Demand Curves

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How Elastic Is Elastic?

Demand is elastic if the price elasticity of demand is greater than 1, inelastic if the price elasticity of demand is less than 1, and unit-elastic if the price elasticity of demand is exactly 1.

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E = 0

0 Quantity

Price Demand

100

1. An increase in price…

$4.00

$5.00

2. …leaves the quantity demanded unchanged.

Figure 5-1 a): Perfectly Inelastic Figure 5-1 a): Perfectly Inelastic DemandDemand

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E < 1

0 Quantity

Price

100

1. A 22% increase in price…

$5.00

2. … Leads to a 11% decrease in quantity demanded.

Demand

$4.00

90

Figure 5-1 b): Inelastic DemandFigure 5-1 b): Inelastic Demand

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E = 1

0 Quantity

Price

100


$5.00


Demand

$4.00

80

Figure 5-1 c): Unit Elastic DemandFigure 5-1 c): Unit Elastic Demand

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E > 1

0 Quantity

Price

100


$5.00


Demand

$4.00

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Figure 5-1 d): Elastic DemandFigure 5-1 d): Elastic Demand

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E =

0Quantity

Price

2. At exactly $4, consumers will buy any quantity.

$4.00 Demand

1. At any price above $4, quantity demanded is zero.

3. At any price below $4, quantity demanded is infinite.

Figure 5-1 e): Perfectly Elastic DemandFigure 5-1 e): Perfectly Elastic Demand

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Example

Point Formula for Price Elasticity of Demand or Measurement of elasticity at apoint on the demand

curve

• The exact formula for calculating an elasticity at the point A on the demand curve.

• Note: we’ll take absolute value

atAPX

XPelasticity

D

A

A

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Example: Elasticity Calculation at “A”

• Slope = (40-32)/(10-14)=-2

• 1/slope = -1/2• P/X = 36/12 = 3 at

point A• P/X x 1/slope

= -1.5• Elasticity of

demand = -1.5 • Absolute value of

the elasticity = 1.5

Linear Demand Curve

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35

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40

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10 11 12 13 14

Quantity

Pric

e A

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Exercise -- Linear Demand• Compute the elasticity

at the point indicated in red on the table (X=18,P=24).

• Slope = -2• 1/Slope = -1/2• P/X = 24/18 = 4/3• Elasticity = -2/3

Quantity Price10 4011 3812 3613 3414 3215 3016 2817 2618 2419 2220 20

21

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Price

Quantity2 4 6 8 10 120

6

5

4

3

2

1

7

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Elasticity is larger than 1.

Elasticity is smaller than 1.

Figure 5-5: A Linear Demand CurveFigure 5-5: A Linear Demand Curve

Elasticities and Linear Demand

• The elasticity varies along a linear demand (or supply) curve. This is illustrated in the linear demand curve table above.

• Note: Usually we would report last column as absolute value

Linear Demand

Quantity Price Slope 1/SlopeExact

Elasticity10 4011 38 -2 -0.5 -1.727312 36 -2 -0.5 -1.500013 34 -2 -0.5 -1.307714 32 -2 -0.5 -1.142915 30 -2 -0.5 -1.000016 28 -2 -0.5 -0.875017 26 -2 -0.5 -0.764718 24 -2 -0.5 -0.666719 22 -2 -0.5 -0.578920 20

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• Because the price elasticity of demand measures how much quantity demanded responds to the price, it is closely related to the slope of the demand curve.

Slope of the Demand Curve P is the

change in price. (P<0)

Price

Quantity

Demand

X X + X

X

P

P+ PP

X is the change in quantity.

• slope = P/ X

XP

slope

• 1/slope = X/ P

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Slope Compared to Elasticity• The slope measures the rate of change of

one variable (P, say) in terms of another (X, say).

• The elasticity measures the percentage change of one variable (X, say) in terms of another (P, say).

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Arc Formula for Elasticity - General

• Although the exact formula for calculating an elasticity is useful for theory, in practice economists usually calculate an approximation called the arc elasticity.

• You are really approximating the elasticity between two points.

• Need two points to perform the calculation.

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Arc Formula for Own Price Elasticity of Demand

• Get two points of the demand curve: Points A and B.

• Consider PA and XA and PB and XB from the demand relationship.

• Note: we’ll take absolute value

PavgPPXavgXXelasticity BA

BA

/)(/)(

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Using the Midpoint Method to Calculate Elasticities

The midpoint method is a technique for calculating the percent change. In this approach, we calculate changes in a variable compared with the average, or midpoint, of the starting and final values.

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• The midpoint formula is preferable when calculating the price elasticity of demand because it gives the same answer regardless of the direction of the change.

• point Method: A Better Way to Calculate Percentage Changes and Elasticities

The Midpoint Method: A Better Way to The Midpoint Method: A Better Way to Calculate Percentage Changes and Calculate Percentage Changes and

ElasticitiesElasticities

(Q2 - Q1) / [(Q2 + Q1) / 2]

(P2 - P1) / [(P2 + P1) / 2]Price elasticity of demand =

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Using the Midpoint Method to Calculate Elasticities

100 x of value Average

in Change in change %X

XX

2/)

2/)

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12

21

12

( -

( -

demand of elasticity Price

PPPPQQQQ

Average value of X =Starting value of X + final value of X

2

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• From Point A to Point B: Price rise = 50% and Quantity fall = 33% • From Point B to Point A: Price fall = 33% and Quantity rise = 50%

(80 - 120) / [(80 + 120)/ 2]

(6 - 4) / [(6 + 4)/ 2]Price elasticity of demand =

• Point A: Price = $4 Quantity = 120

• Point B: Price = $6 Quantity = 80

= 1Mid point method

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Estimating ElasticitiesTABLE 5-1Some Estimated PriceElasticities of Demand

GoodPrice elasticity

of demandInelastic demand

Eggs 0.1Beef 0.4Stationery 0.5Gasoline 0.5

Elastic demandHousing 1.2Restaurant meals 2.3Airline travel 2.4Foreign travel 4.1

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Elasticity and Total Revenue

The total revenue is the total value of sales of a good or service. It is equal to the price multiplied by the quantity sold.

(5-6) soldquantity Price revenue Total

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• Total revenue is the amount paid by buyers and received by sellers of a good.

• Computed as the price of the good times the quantity sold.

TR = P x Q

Total Revenue and the Price Elasticity Total Revenue and the Price Elasticity of Demandof Demand

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When price elasticity of demand is equal to unity, the total expenditure remains the same with the fall or rise in price.

When price elasticity of demand is greater than one, the total expenditure will increase with the fall in price and will decrease with the rise in price.

When price elasticity of demand is lesser than one, the total expenditure will decrease with the fall in price and will increase with the rise in price.

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Table 5-1. Elasticity and Total Revenue Table 5-1. Elasticity and Total Revenue along a Linear Demand Curvealong a Linear Demand Curve

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• Income elasticity of demand measures how much the quantity demanded of a good responds to a change in consumers’ income.

• It is computed as the percentage change in the quantity demanded divided by the percentage change in income.

Other Demand ElasticitiesOther Demand Elasticities

In co m e e la stic ity o f dem an d =

P ercen tag e ch an ge in q u an tity d em an d ed

P ercen tag e ch an ge in in co m e

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• Types of Goods– Normal Goods– Inferior Goods

• Higher income raises the quantity demanded for normal goods but lowers the quantity demanded for inferior goods.


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• Goods consumers regard as necessities tend to be income inelastic– Examples include food, fuel, clothing, utilities,

and medical services.• Goods consumers regard as luxuries tend to

be income elastic.– Examples include sports cars, furs, and

expensive foods.


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• Cross-Price elasticity of demand measures how much the quantity demanded of a good responds to a change in the price of another good.

• It is computed as the percentage change in the quantity demanded divided by the percentage change in the price of the second good.


co elasticity of demand =

Percentage change in quantity demandedPercentage change

in the price of good 2.

Cross

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Cross elasticity of substitutes is positive and large. The higher the coefficient, the better substitutes the goods are

If coefficient of elasticity is more than one, then goods are close substitutes, if less than one-----poor substitutes and if infinite than perfect substitutes.

For complementary goods the cross elasticity of demand is negative.

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• Price elasticity of supply is a measure of how much the quantity supplied of a good responds to a change in the price of that good.

• Price elasticity of supply is the percentage change in quantity supplied given a percent change in the price.

PRICE ELASTICITY OF PRICE ELASTICITY OF SUPPLYSUPPLY

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• Ability of sellers to change the amount of the good they produce.– Beach-front land is inelastic.– Books, cars, or manufactured goods are elastic.

• Time period. – Supply is more elastic in the long run.

The Price Elasticity of Supply and Its The Price Elasticity of Supply and Its DeterminantsDeterminants

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• The price elasticity of supply is computed as the percentage change in the quantity supplied divided by the percentage change in price.

Computing the Price Elasticity of Computing the Price Elasticity of SupplySupply

P rice e las tic ity o f sup p ly =

P ercen tag e ch an g e in qu an tity sup p lied

P ercen tag e chang e in p rice

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• … using the midpoint method, we calculate the percent change in the price as (2.10 - 1.90) / 2.00 x 100 = 10%

• Similarly, we calculate the percent change in the quantity supplied as (11 000 - 9000) / 10 000 x 100 = 20%

20%Price elasticity of supply =

• Suppose an increase in the price of milk from $1.90 to $2.10 a litre raises the amount that dairy farmers produce from 9000 to 11 000 L per month…

= 2.0

Computing the Price Elasticity of Computing the Price Elasticity of SupplySupply

10%

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E = 0

0 Quantity

Price Supply

1. An increase in price…

$5.00

2. …leaves the quantity supplied unchanged.

100

$4.00

Figure 5-6 a): Perfectly Inelastic SupplyFigure 5-6 a): Perfectly Inelastic Supply

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E < 0

0 Quantity

PriceSupply

100


$5.00

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

$4.00

110

Figure 5-6 b): Inelastic SupplyFigure 5-6 b): Inelastic Supply

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E = 1

0 Quantity

Price

Supply

100


$5.00


$4.00

125

Figure 5-6 c): Unit Elastic SupplyFigure 5-6 c): Unit Elastic Supply

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E > 1

0 Quantity

Price

Supply

100


$5.00


$4.00

200

Figure 5-6 d): Elastic SupplyFigure 5-6 d): Elastic Supply

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E =

0Quantity

Price

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

$4.00 Supply

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

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

Figure 5-6 e): Perfectly Elastic SupplyFigure 5-6 e): Perfectly Elastic Supply

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0Quantity

Price

$3

100

$4

200

$12

500

$15

525

Elasticity is greater than 1

Elasticity is less than 1

Figure 5-7: Figure 5-7: How the price elasticity of How the price elasticity of supply can varysupply can vary

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• Good news bad news for farmers• OPEC• Drugs and crime

THREE APPLICATIONS OF THREE APPLICATIONS OF SUPPLY, DEMAND, AND SUPPLY, DEMAND, AND

ELASTICITYELASTICITY

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Increase in Supply

Demand

S1

$3

Quantity of Wheat

Price of Wheat

S2

2. … leads to a fall in price…

3. …and a proportionately smaller increase in quantity sold. As a result revenue falls from $300 to $220.

1. When demand is inelastic, an increase in supply…

110100

$2

Figure 5-8: Figure 5-8: An Increase in Supply in the An Increase in Supply in the Market for WheatMarket for Wheat

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Demand

S1

Quantity of Oil

Price of Oil

S2

1. In the short run, when supply and demand are inelastic, a shift in supply…

2. … leads to a large increase in price…

P1

P2

Demand

S1

Quantity of Oil

S2

1. In the long run, when supply and demand are elastic, a shift in supply…

2. … leads to a small increase in price…

P1

P2

Price of Oil

(a) Oil Market in the Short Run (b) Oil Market in the Long Run

Figure 5-9: Figure 5-9: A Reduction in Supply in A Reduction in Supply in the World Market for Oilthe World Market for Oil

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Demand

S1

Quantity of Drugs

Price of Drugs

S2

1. Drug interdiction reduces the supply of drugs…

2. … which raises the price…

P1

P2

D1

Supply

1. Drug education reduces the demand for drugs…

2. … which reduces the price…

(a) Drug Interdiction (b) Drug Education

Q1Q2

3. … and reduces the quantity sold.

Q2

3. … and reduces the quantity sold.

Quantity of Drugs

Price of Drugs

D2

P1

Q1

P2

Figure 5-10: Figure 5-10: Policies to Reduce the of Policies to Reduce the of Illegal DrugsIllegal Drugs

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• Price elasticity of demand measures how much the quantity demanded responds to changes in the price.

• Price elasticity of demand is calculated as the percentage change in quantity demanded divided by the percentage change in price.

• If a demand curve is elastic, total revenue falls when the price rises.

• If it is inelastic, total revenue rises as the price rises.

SummarySummary

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• The income elasticity of demand measures how much the quantity demanded responds to changes in consumers’ income.

• The cross-price elasticity of demand measures how much the quantity demanded of one good responds to the price of another good.

• The price elasticity of supply measures how much the quantity supplied responds to changes in the price.

SummarySummary

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• In most markets, supply is more elastic in the long run than in the short run.

• The price elasticity of supply is calculated as the percentage change in quantity supplied divided by the percentage change in price.

• The tools of supply and demand can be applied in many different types of markets.

SummarySummary

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The EndThe End

elasticity of demand

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