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### Chapter 4Elasticity

Elasticity

Example 4.1

- Will the China’s trade balance (export – import) deteriorate if RMB appreciates (say, from 1USD=8.1RMB to 1USD=7.8RMB)?
- China’s imports become less expensive. Quantity demanded for import may increase.
- 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.

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.

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

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

6%

-3

=

-2%

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%

-2

=

1%

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.

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

-1

(404 - 400)/400

1%

=

=

(9.7 - 10)/10

-3%

3

Inelastic!

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

- Originally
- Price = $1600
- Quantity demanded = 10,000 passes/year
- New
- Price = $1520
- Quantity demanded = 12,000 passes/year, then

(12000 - 10000)/10000

20%

=

=

-4

(1520 - 1600)/1600

-5%

Elastic!

Determinants of Price Elasticity of Demand

- Availability of substitutes - the higher the number of substitutes, the more responsive people are to price changes. Elasticity increases with availability of substitutes.
- Proportion of income used to buy the good - the higher the fraction of income spent on a good, the higher is elasticity.
- 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.
- 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.

Example 4.6.Price ElasticityEstimates 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?

A Graphical Interpretationof Price Elasticity

- For small changes in price

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

P

P

P - P

Q

D

Q

Q + Q

A Graphical Interpretationof Price Elasticity- For small changes in price

Price

Quantity

A

Example 4.7.Calculating Price Elasticity of Demand20

16

12

Price

8

Question:

What is the price elasticity

of demand when P = $8?

4

1

2

3

4

5

Quantity

D1

6

4

D2

4

6

12

Example 4.8.Price Elasticity and the Steepness of the Demand CurveWhat is the price elasticity ofDemand for D1 & D2 when P = $4?

Observation

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

Price

Quantity

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

When P = $4

When P = $1

12

6

Price

Observation

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

4

D

1

4

6

10

12

Quantity

a/2

b/2

b

Price Elasticity Regions along a Straight-Line Demand CurveObservation

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

Price

Quantity

Quantity

Perfectly Elastic Demand CurveIf 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.

Quantity

Perfectly Inelastic Demand CurveThe quantity demanded is not responsive to any change in price.

Elasticity and Total Expenditure

- Total Expenditure = P x Q
- Market demand measures the quantity (Q) at each price (P)
- Total Expenditure = Total Revenue

10

8

6

Price ($/ticket)

4

2

0

1

2

3

4

5

6

Quantity (100s of tickets/day)

Example 4.10. The Demand Curve for Movie TicketsPrice ($/ticket)

Total expenditure ($/day)

12

0

10

1000

8

1600

6

1800

4

1600

2

1000

0

0

10

1,800

1,600

8

6

Price ($/ticket)

1,000

Total expenditure ($/day)

4

2

0

2

4

6

8

10

12

0

1

2

3

4

5

6

Price ($/ticket)

Quantity (100s of tickets/day)

Total Expenditure as a Function of PriceTotal revenue is at a maximum at themidpoint on a straight-line demand curve.

Example 4.11.

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

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.

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 e=-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.

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 DP/P = 1%, DQ/Q = -0.2%.
- Elasticity = (DQ/Q)/(DP/P) = -0.2. (inelastic)

So answer a is correct. A fare increase will increase total revenue.

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 good
- Substitute Goods
- When the cross-price elasticity of demand is
- positive
- Complement Goods
- When the cross-price elasticity of demand is
- negative

Income Elasticity of Demand

- The percentage by which quantity demanded changes in response to a 1 percent change in income
- Normal Goods
- Income elasticity is
- positive
- Inferior Goods
- Income elasticity is
- negative

The Price Elasticity of Supply

- Price Elasticity of Supply
- The percentage change in the quantity supplied that occurs in response to a 1 percent change in price

A

8

4

2

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

10

8

- Observations:
- Elasticity >0
- Elasticity >1 for linear supply curve that has a positive Y-intercept.
- Elasticity decreases as quantity increases.

Price

0

2

3

Quantity

B

5

A

4

P

Q

Price

0

12

15

Quantity

Example 4.15. A Supply Curve for Which Price Elasticity is unityThe price elasticity of supply will always equal 1 at any point along a straight-line supply curve that passes through the origin.

A challenge

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

Elasticity = 0 at every

point along a vertical

supply curve

A Perfectly Inelastic Supply CurveWhat is the price elasticity of supply of land within Central?

Price ($/acre)

0

Quantity of land in Central

(1,000s of acres)

price elasticity of supply at every point

along a horizontal supply curve is infinite

S

A Perfectly Elastic Supply CurvePrice (cents/cup)

14

0

Quantity of lemonade

(cups/day)

Determinants of Supply Elasticity

- Flexibility of inputs
- Mobility of inputs
- Ability to produce substitute inputs
- Time

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

- Differences in markets
- Demand for gasoline is more inelastic
- Gasoline market has larger and more frequent supply shifts

S

1.69

1.02

D

7.2

6

Greater Volatility in Gasoline Prices than in Car PricesGasoline

Price ($/gallon)

0

Quantity

(millions of gallons/day)

S

17

16.4

D

11

12

Greater Volatility in Gasoline Prices than in Car PricesCars

Price ($1,000s/car)

Quantity

(1,000s of cars/day)

Cars

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.

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.

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.

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.

Example 4.19.

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

- the own price elasticity of demand for rental homes is price inelastic.
- the own price elasticity of demand for rental homes is price elastic.
- the own price elasticity of demand for rental homes has unitary price elasticity.
- rented homes and owned homes are substitutes.
- rented homes and owned homes are complements.

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

D

S

Trading Loci

Pe

Price Ceiling

Q

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

D

S

Because supply is upward sloping,

↑P → ↑ TR

Price Ceiling

Q

Example 4.19.

Relative inelastic

P

D

S

Pe

Price Ceiling

Relative elastic

Q

Hence, the increase in rents that occur AFTER abolishing rent control is smaller when

(B) The own price elasticity of demand is elastic.

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