Ka-fu Wong University of Hong Kong

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Ka-fu WongUniversity of Hong Kong

Elasticity

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Example 4.1

Will the China’s trade balance (export – import) deteriorate if RMB appreciates (say, from 1USD=8.1RMB to 1USD=7.8RMB)?

1. China’s imports become less expensive. Quantity demanded for import may increase.

2. China’s Exports become more expensive. Quantity demanded for export may decrease.

The impact of RMB appreciation on the trade balance depends on the responsiveness of import demand and export demand to the appreciation.

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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, 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 will always be negative

(i.e., an inverse relationship between price and quantity).

For convenience sometimes we drop the negative sign.

Percentage change in quantity demanded

Percentage change in price

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Price Elasticity of Demand

0

Price elasticityof demand

Elastic

Unit elastic

inelastic

-1-2-3

Price in Change Percentage

DemandedQuantity in Change Percentage

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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%=

-13

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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 - the higher the number of substitutes, the more responsive people are to price changes. 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 - the response of quantity demanded that day will be much greater than the response to quantity when prices are expected to decrease permanently.

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 much in the short run.

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Example 4.6.Price Elasticity Estimates for Selected Products

Good or service Price elasticity

Green peas -2.80

Restaurant meals -1.63

Automobiles -1.35

Electricity -1.20

Beer -1.19

Movies -0.87

Air travel (foreign) -0.77

Shoes -0.70

Coffee -0.25

Theater, 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 QPΔPΔQPΔP

QΔQ

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 PΔP

QΔQ elasticity Price

Quantity

Pri

ce

P

D

A

Q

P - P

Q + Q

Q

P

slopeQ

P A

1 at elasticity icePr

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Example 4.7. Calculating Price Elasticity of Demand

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Quantity

Pri

ce

1

D

A

2 3 4 5

16

12

8

4

45

20

intercept horizontal

intercept vertical

slope

3

2

12

8

4

1

3

8

xA

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

Pri

ce

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

2

1

612

1

4

41

D

2

1261

4

42

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

Pri

ce

5

1

1261

10

1

D

2

1261

4

4

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

Pri

ce

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

Pri

ce

)- y (elasticit demand

elastic

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

Pri

ce

)0 y (elasticit demand

inelasticPerfectly

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)

Pri

ce (

$/ti

cket

)

1 3 4 5 6

10

8

6

4

2

0 2

Total expenditure ($/day)

12

Price ($/ticket)

010 10008 16006 18004 16002 1000

0 0

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Total Expenditure as a Function of Price

1,800

Price ($/ticket)

To

tal

ex

pe

nd

itu

re (

$/d

ay

)

2 6 8 10 12

1,600

1,000

0 4

12

Quantity (100s of tickets/day)

Pri

ce

($

/tic

ke

t)

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

negative

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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

PP

QQ supply of elasticity Price

slope

1

Q

P 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

10B

3

521310 B

Quantity

Pri

ce

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

Pri

ce

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 challenge

Construct an example of supply curve so that price elasticity increases as quantity rises.

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A Perfectly Inelastic Supply Curve

Quantity of land in Central

(1,000s of acres)

Pri

ce (

$/ac

re)

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)

Pri

ce (

cen

ts/c

up

)

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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Example 4:16. Why are gasoline prices so much more volatile than car prices?

Differences in marketsDemand for gasoline is more inelasticGasoline market has larger and more frequent

supply shifts

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Greater Volatility in Gasoline Prices than in Car Prices

Quantity(millions of gallons/day)

Pri

ce (

$/g

allo

n)

0 6

1.69

S’

D

1.02

7.2

S

Gasoline

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Greater Volatility in Gasoline Prices than in Car Prices

Pri

ce (

$1,0

00s/

car)

D

17

S’

11Quantity

(1,000s of cars/day)Cars

16.4

12

S

Cars

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Example 4.17. Earnings of YAO Ming

Why does YAO Ming earn an annual basketball salary of some US$4.5 million?

YAO Ming is a unique and essential inputs, an example of ultimate supply bottleneck.

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Other examples of unique and essential inputs

Dr. Joseph YAM?

Mr Mirko Saccani?“The fee was agreed to be $120 million for eight years' of unlimited [Latini]dance lessons and competitions, and Mr Saccani would be her dancing partner and instructor by such agreements.” (SCMP 2006-06-14, CITY3)

Who was she, the plaintiff?Mimi Monica Wong, head of HSBC's private banking in Asia.

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Example 4.18. So why are the fares so different?

If you start in Kansas City and you fly to Honolulu round-trip, the fare is a lot lower than if you start the same trip in Honolulu and fly to Kansas City round-trip. Passengers travel on same planes, consuming the same fuel, the same in-flight amenities, and so on. So why are the fares so different?

By Karen Hittle, a student of Robert Frank.

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Example 4.18. So why are the fares so different?

If you are starting in Kansas City and going to Honolulu, you are probably going on vacation. You could go lots of different places. You could go to Florida, to Barbados, to Cancun. Because vacationers have many destinations to choose from, airlines must compete fiercely for their business. Given economies of scale inherent in larger aircraft, carriers have a strong incentive to fill additional seats by targeting lower prices to the people who are more sensitive to price – vacationers.

But if you are starting in Honolulu on a trip to Kansas City, you are probably not a vacationer. More likely, you either have business or family reasons for traveling. So you are probably not shopping for a destination if you are going to Kansas City.

That is why the fares are so different.

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Example 4.19.

Other things being equal, the increase in rents that occur after rent control are abolished is smaller when

A. the own price elasticity of demand for rental homes is price inelastic.

B. the own price elasticity of demand for rental homes is price elastic.

C. the own price elasticity of demand for rental homes has unitary price elasticity.

D. rented homes and owned homes are substitutes. E. rented homes and owned homes are complements.

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Example 4.19.

Rent control is a form of PRICE CEILING. Price Ceiling is set at a price LOWER than the market equilibrium

price. Excess demand (i.e., shortage) results.

P

Q

D S

Pe

Price Ceiling

Trading Loci

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Example 4.19.

And when the Price Ceiling is lifted, the market equilibrium quantity and price should be restored eventually.

Price (rent) should increase.

P

Q

D S

Price Ceiling

Because supply is upward sloping,↑P → ↑ TR

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P

Q

D S

Pe

Price Ceiling

Relative inelastic

Relative elastic

Hence, the increase in rents that occur AFTER abolishing rent control is smaller when(B) The own price elasticity of demand is elastic.

Example 4.19.

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End