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Stephen ChiuUniversity of Hong Kong

Elasticity

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Example 4.1

The Western tunnel, which has low travel, is now charging $50 per car. Should it reduce the toll to $40, say? Two factors for consideration.1. Its travel will increase. 2. But the toll per car is lower.

The net impact on its revenue depends on the responsiveness of quantity demanded to the price reduction.

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Price Elasticity of Demand

The Price Elasticity of Demand is a measure of the responsiveness of the quantity demanded of a good to a change in the price of that good.

Formally, it is the percentage change in the quantity demanded that results from a 1 percent change in its price.

Percentage change in quantity demanded

Percentage change in price

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Elasticity

Generally, price elasticity is a measure of the responsiveness of the quantity demanded of a good to a change in the price of that good

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Example 4.2

The price of pork falls by 2% and the quantity demanded increases by 6%Then the price elasticity of demand for pork is

Percentage change in quantity demanded

Percentage change in price

6%2%

= 3

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Example 4.3.

If a 1 percent rise in the price of shelter caused a 2 percent reduction in the quantity of shelter demanded, the price elasticity of demand for shelter would be

2%1%

= 2

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Price Elasticity of Demand Measuring Price Elasticity of Demand

Observations Price elasticity of demand is always negative (i.e.,

an inverse relationship between price and quantity). For convenience we often drop the negative sign.

(For other types of elasticity, the sign is crucial and cannot be dropped.)

Percentage change in quantity demandedPercentage change in price

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Price Elasticity of Demand

Price in Change PercentageDemandedQuantity in Change Percentage

0

Price elasticityof demand

Elastic

Unit elastic

inelastic

1 2 3

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Example 4.4. What is the elasticity of demand for sushi?

Originally Price = $10/piece Quantity demanded = 400 pieces/day

New Price = $9.7/piece Quantity demanded = 404 pieces/day, then

Inelastic!

(404 - 400)/400(9.7 - 10)/10

= 1%3%

=1

3

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Example 4.5. What is the elasticity of Hong Kong Disney passes?

Originally Price = $1600Quantity demanded = 10,000 passes/year

New Price = $1520Quantity demanded = 12,000 passes/year, then

Elastic!

(12000 - 10000)/10000(1520 - 1600)/1600

= 20%5%

= 4

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Determinants of Price Elasticity of Demand

1. Availability of substitutes - Elasticity increases with availability of substitutes.

2. Proportion of income used to buy the good - the higher the fraction of income spent on a good, the higher is elasticity.

3. Temporary versus permanent change in price - if the price change is temporary people react more to it. Suppose there is a one-day sale….

4. Short run versus long run - elasticity increases over time. If there is a sudden price increase, individuals will take some time to find other substitutes and make suitable changes. So quantity will not respond as much in the short run.

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Example 4.6.Price Elasticity Estimates for Selected Products

Good or service Price elasticityGreen peas 2.80Restaurant meals 1.63Automobiles 1.35Electricity 1.20Beer 1.19Movies 0.87Air travel (foreign) 0.77Shoes 0.70Coffee 0.25Theater, opera 0.18

Why is the price elasticity of demand more than 14 times larger for green peas than for theater and opera performances?

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A Graphical Interpretationof Price Elasticity

For small changes in price

)/)(/( elasticity Price QPΔPΔQPΔPQΔQ

Where Q is the original quantity and P is the original price.

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A Graphical Interpretationof Price Elasticity

For small changes in price PΔPQΔQ elasticity Price

Quantity

Pric

e

P

D

A

Q

P - P

Q + Q

Q

P

slopeQP A 1 at elasticity icePr

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Example 4.7. Calculating Price Elasticity of Demand

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Quantity

Pric

e

1

D

A

2 3 4 5

16

12

8

4

4520

intercept horizontalintercept vertical

slope

32

128

41

38

A

Question:What is the price elasticityof demand when P = $8?

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Example 4.8. Price Elasticity and the Steepness of the Demand Curve

D1

D2

12

4 6 12

6

4

Quantity

Pric

e

What is the price elasticity of Demand for D1 & D2 when P = $4?

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612

144

1

D

212

61

44

2

D

ObservationIf two demand curves have a point in common, the steeper curve must be less elastic with respect to price at that point.

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Example 4.9. Price Elasticity Regions along a Straight-Line Demand Curve

12

D

4 6 10 12

6

4

1

When P = $1

Quantity

Pric

e

51

1261

101

D

212

61

44

D

When P = $4

ObservationPrice elasticity varies at every point along a straight-line demand curve

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Price Elasticity Regions along a Straight-Line Demand Curve

Quantity

Pric

e

b/2

a/2

a

b

1

1

1

ObservationPrice elasticity varies at every point along a straight-line demand curve

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Perfectly Elastic Demand Curve

Quantity

Pric

e

) y (elasticit demandelastic

Perfectly

If the price increases a little, the quantity demanded will drop to zero. If the price drops a little, the quantity demanded will increase a lot.

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Perfectly Inelastic Demand Curve

Quantity

Pric

e

)0 y (elasticit demandinelasticPerfectly

The quantity demanded is not responsive to any change in price.

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Elasticity and Total Expenditure

Total Expenditure = P x QMarket demand measures the quantity (Q) at

each price (P) Total Expenditure = Total Revenue

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Example 4.10. The Demand Curve for Movie Tickets

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Quantity (100s of tickets/day)

Pric

e ($

/tick

et)

1 3 4 5 6

10

8

6

4

2

0 2

Total expenditure ($/day)

12Price ($/ticket)

010 10008 16006 18004 16002 10000 0

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Total Expenditure as a Function of Price

1,800

Price ($/ticket)

Tota

l exp

endi

ture

($/d

ay)

2 6 8 10 12

1,600

1,000

0 4

12

Quantity (100s of tickets/day)

Pric

e ($

/tick

et)

1 3 4 5 6

10

8

6

4

2

0 2

Total revenue is at a maximum at the midpoint on a straight-line demand curve.

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Example 4.11.

What happens to total expenditure on shelter when the price is reduced from $12/sq yd to $10/sq yd?

0

161412108642

Price ($/sq yd)

(sq yds/wk) 4 6 8 10 12

Reduction in expenditure from sale at a lower price

Increase in expenditure from additional sales

F

E

G

14 16Quantity

When price goes down, total expenditure will rise [fall] if the gain from sale of additional units is larger [smaller] than the loss from the sale of existing units at the lower price.

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Example 4.12. Elasticity and Total Expenditure

Should a rock band raise or lower its price to increase total revenue? Assume P=$20, Q=5,000, and =3.

Total revenue = $20 x 5,000 = $100,000/week

If P is increased 10%, Q will decrease 30% Total revenue = $22 x 3,500 = $77,000/week

If P is lowered 10%, Q will increase 30% Total revenue = $18 x 6,500 = $177,000/week

Note: Cost does not change with Q. Maximizing total revenue is the same as maximizing total profit.

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Elasticity and Total Expenditure

If demand is... A price increase will... A price reduction will...

elastic

inelastic

reduce totalexpenditure

increase totalexpenditure

increase totalexpenditure

reduce totalexpenditure

P Q P Qx = P Q P Qx =

P PQx =QP Q PQx =

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A demand curve with constant elasticity

Q

P

Unitary elastic: PxQ=k

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Example 4.13.

A director of a big bus company said, "For each 1 percent fare hike, we lose 0.2 percent of our riders." We can conclude that:

a. a fare increase will increase total revenue.b. demand for bus service will go up as fares increase.c. demand is price elastic.d. a 10 percent fare hike will produce a 20 percent reduction

in riders.e. the price elasticity is 5. We are told that when P/P = 1%, Q/Q = 0.2%. Elasticity = (Q/Q)/(P/P) = 0.2. (inelastic)So answer a is correct. A fare increase will increase total

revenue.

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Cross-Price Elasticity of Demand

The percentage by which quantity demanded of the first good changes in response to a 1 percent change in the price of the second goodSubstitute Goods

When the cross-price elasticity of demand is positive

Complement GoodsWhen the cross-price elasticity of demand is

NegativeNow keeping the sign is important!

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Income Elasticity of Demand

The percentage by which quantity demanded changes in response to a 1 percent change in incomeNormal Goods

Income elasticity is positive

Inferior GoodsIncome elasticity is

negative

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The Price Elasticity of Supply

Price Elasticity of SupplyThe percentage change in the quantity

supplied that occurs in response to a 1 percent change in price

PPQQ supply of elasticity Price

slope1

QP supply of elasticity Price

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Example 4.14. A Supply Curve for Which Price Elasticity Declines as Quantity Rises

2

8A

22128 A

3

10 B

3521310 B

Quantity

Pric

e

0

4

S

8

2

Observations:1. Elasticity >02. Elasticity >1 for linear supply

curve that has a positive Y-intercept.

3. Elasticity decreases as quantity increases.

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Example 4.15. A Supply Curve for Which Price Elasticity is unity

S

15

5B

P

Q

12

4A

Quantity

Pric

e

0

The price elasticity of supply will always equal 1 at any point along a straight-line supply curve that passes through the origin.

1515155 B

14/1212/4 A

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A Perfectly Inelastic Supply Curve

Quantity of land in Central

(1,000s of acres)

Pric

e ($

/acr

e)

0

S

Elasticity = 0 at everypoint along a verticalsupply curve

What is the price elasticity of supply of land within Central?

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A Perfectly Elastic Supply Curve

Quantity of lemonade

(cups/day)

Pric

e (c

ents

/cup

)

0

14 S

If MC is constant, then theprice elasticity of supply at every pointalong a horizontal supply curve is infinite

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Determinants of Supply Elasticity

1. Flexibility of inputs2. Mobility of inputs3. Ability to produce substitute inputs4. Time

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End