Elasticity

HOW MUCH MORE OR LESS?DOES IT MATTER?

THE LAW OF DEMAND SAYS...

Consumers will buy more when prices go down and less when prices go up

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ElasticityElasticity shows how sensitive quantity is

to a change in price.

1. Elasticity of DemandElasticity of Demand- • Measurement of consumers

responsiveness to a change in price.• What will happen if price increase? How

much will it effect Quantity Demanded

Who cares?• Used by firms to help determine prices

and sales• Used by the government to decide how to

tax

Inelastic Demand

Inelastic Demand

•If price increases, quantity demanded will fall a little•If price decreases, quantity demanded increases a little.

In other words, people will continue to buy it.

20%

5%

INelastic = Quantity is INsensitive to a change in price.

Examples:•Gasoline•Milk•Diapers

A INELASTIC demand curve is steep! (looks like an “I”)

•Chewing Gum•Medical Care•Toilet paper

Inelastic Demand

20%

5%

General Characteristics of INelastic Goods:

•Few Substitutes•Necessities•Small portion of income•Required now, rather than later •Elasticity coefficient less than 1

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Extreme CasePRICE ELASTICITY OF DEMAND

Perfectly Inelastic DemandD1

Ed = 0

P

Q

When a price change results in no change whatsoever in the quantity demanded, that good is said to be perfectly inelastic. An example: A diabetics need for insulin.

Elastic Demand

Elastic Demand

•If price increases, quantity demanded will fall a lot•If price decreases, quantity demanded increases a lot.

In other words, the amount people buy is sensitive to price.

Elastic = Quantity is sensitive to a change in price.

An ELASTIC demand curve is flat!Examples:•Soda•Boats•Beef

•Real Estate•Pizza•Gold

Elastic DemandGeneral Characteristics of

Elastic Goods:• Many Substitutes• Luxuries• Large portion of income• Plenty of time to decide• Elasticity coefficient greater than 1

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Perfectly Elastic DemandP

Ed = D2

Q0

PRICE ELASTICITY OF DEMAND

Extreme CaseWhen a small price change causes buyers to increase or decrease their purchases drastically the good is said to be perfectly elastic. Foreign currency exchange. Example: If one firm increased the price of dollars, above market equilibrium – no one would buy from that firm. They would buy from cheaper alternatives.

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PRICE ELASTICITY OF DEMAND

Refinement – The Midpoint Formula

Ed =

Change inquantity

Sum ofQuantities/2

Change inprice

Sum ofprices/2

Elastic or Inelastic?Beef-

Gasoline- Real Estate-

Medical Care- Electricity-

Gold-

Elastic- 1.27INelastic - .20Elastic- 1.60INelastic - .31INelastic - .13Elastic - 2.6

What about the demand for insulin for

diabetics?

Perfectly INELASTIC(Coefficient = 0)

What if % change in quantity demanded equals

% change in price?

Unit Elastic (Coefficient =1)45 Degrees

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PRICE ELASTICITY & TOTAL REVENUE

Price Elasticity is...

Inelastic from 0 to 1Typical of necessities one must have

Elastic from 1 to Typical of luxuries one wants

Elastic from 1 to

Unit elastic when exactly = 1Price change does not reduce total revenue

Total Revenue TestUses elasticity to show how changes in price will

affect total revenue (TR). (TR = Price x Quantity)

Elastic Demand- • Price increase causes TR to decrease• Price decrease causes TR to increase

Inelastic Demand- • Price increase causes TR to increase• Price decrease causes TR to decrease

Unit Elastic-• Price changes and TR remains unchanged

Ex: If demand for milk is INelastic, what will happen to expenditures on milk if price increases?

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PRICE ELASTICITY & TOTAL REVENUE

When prices are low, TR So is total revenue

Quantity Demanded

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PRICE ELASTICITY & TOTAL REVENUE

Total revenue riseswith price to a

point...TR

Quantity DemandedQ

P

D

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PRICE ELASTICITY & TOTAL REVENUE

Total revenue riseswith price to a

point...

then declines

P

D

Q Quantity Demanded

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then declinesTotal revenue riseswith price to a

point...

Quantity DemandedQ

D

P

PRICE ELASTICITY & TOTAL REVENUE

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PRICE ELASTICITY & TOTAL REVENUE

Total revenue rises

with price to a point...

then declines

Quantity Demanded

P

D

Q

TR

Total Revenue Test

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PRICE ELASTICITY & TOTAL REVENUE

Quantity Demanded

P

D

Q

TR

Total revenue riseswith price to a

point...

InelasticDemand Inelastic

Demand

then declines

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PRICE ELASTICITY & TOTAL REVENUE

Quantity Demanded

P

D

Q

TR

Total revenue riseswith price to a

point...then declines

ElasticDemand

InelasticDemand

ElasticDemand

InelasticDemand

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PRICE ELASTICITY & TOTAL REVENUE

Quantity Demanded

P

D

Q

TRTotal revenue rises

with price to a point...

then declines

ElasticDemand

InelasticDemand

InelasticDemand

ElasticDemand

UnitElastic

Is the range between A and B, elastic, inelastic, or unit elastic?

A

B

10 x 100 =$1000 Total Revenue

5 x 225 =$1125 Total Revenue

Price decreased and TR increased, so…

Demand is ELASTIC

125%

50%

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Elastic, Inelastic, or Unit Elastic?

D

D

S

T

U

Quantity Demanded

(d)

U' 0 7 14

10

20

$30 Pri

ce

Elasticity Practice

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30

.

Producer surplus is the area above the supply curve and below the

horizontal line indicating the price the producers receive. It represents the

difference between the minimum price that producers are willing to accept

and the price they actually receive summed over all units sold. Prior to the

imposition of the tax, the price the producers receive is the market price of

$5. As a result, producer surplus is equal to:

($5-$2)*90*1/2 = 135

a) Calculate the producer surplus

before the tax.

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(i) Calculate the amount of tax revenue.

Tax revenue is equal to the per unit tax amount ($2) multiplied by the

number of units sold under the tax (60 calculators). So the tax

revenue is equal to $120.

(b) Now assume a per-unit tax of

$2 is imposed whose impact is

shown in the graph above.

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(b) Now assume a per-unit tax

of $2 is imposed whose

impact is shown in the

graph above.

(ii) What is the after-tax price that the sellers now keep?

The price that consumers will pay after the imposition of the tax is $6.

Net of the $2 tax, producers will receive $4 per unit sold.

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(b) Now assume a per-unit tax of

$2 is imposed whose impact is

shown in the graph above.

(iii) Calculate the producer surplus after the tax.

As before, producer surplus is the area above the supply curve and

below the horizontal line indicating the price the producers receive.

Following the imposition of the tax, however, the price producers

receive is $4 and the number of units sold is 60. As a result, producer

surplus is equal to:

($4-$2)*60*1/2 = 60

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(c) Is the demand price elastic, inelastic, or unit

elastic between the prices of $5 and $6?

Explain.

An increase in price from $5 to $6 represents

a percentage change of

($6-$5)/$5.50 = 18.18181%

The resulting change in quantity demanded is

a reduction from 90 units to 60 units,

representing a percentage change of

(60-90)/75 = -40%

The demand elasticity over this range is then calculated as the ratio

of the % change in quantity over the % change in price, or

-40%/18.18181% = -2.2

Since the absolute value of elasticity is greater than 1, demand is

considered elastic.

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In the absence of externalities, the tax will lead to allocative inefficiency.

Prior to the tax, the sum of consumer and producer surplus was 270.

Following the tax, the sum of consumer and producer surplus is 120, plus

government revenues of 120, for a total surplus of 240. So the tax results in

a reduction of total surplus of 30. As a result, the outcome is no longer

allocatively efficient.

(d) Assuming no externalities,

how does the tax affect

allocative efficiency? Explain.

2. Price Elasticity of SupplyElasticity of Supply- • Elasticity of supply shows how sensitive producers

are to a change in price.

Elasticity of supply is based on time limitations.Producers need time to produce more.

INelastic = Insensitive to a change in price (Steep curve)• Most goods have INelastic supply in the short-run Elastic = Sensitive to a change in price (Flat curve)• Most goods have elastic supply in the long-runPerfectly Inelastic = Q doesn’t change (Vertical line)• Set quantity supplied

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The formula is for Price Elasticity of Supply

Es =

Change inquantity

Sum ofQuantities/2

Change inprice

Sum ofprices/2

3. Cross-Price Elasticity of Demand• Cross-Price elasticity shows how sensitive a product

is to a change in price of another good • It shows if two goods are substitutes or complements

% change in price of product “A”% change in quantity demanded of product “B”

• If coefficient is negative (shows inverse relationship) then the goods are complements

• If coefficient is positive (shows direct relationship) then the goods are substitutes

P increases 20% Q decreases 15%

Exy =

• Income elasticity shows how sensitive a product is to a change in INCOME

• It shows if goods are normal or inferior

% change in income% change in quantity demanded

• If coefficient is negative (shows inverse relationship) then the good is inferior• If coefficient is positive (shows direct relationship) then the good is normal

Ex: If income falls 10% and quantity falls 20%…

Income increases 20%, and quantity decreases 15% then the good is a…

4. Income-Elasticity of Demand

INFERIOR GOOD

Ei =

1996 Micro FRQ #2

The Toledo arena holds a maximum of 40,000 people. Each year the circus performs in front of a sold out crowd. (a) Analyze the effect on each of the following of the addition of a fantastic new death-defying trapeze act that increases the demand for tickets.

(i)The price of tickets(ii)The quantity of tickets sold

(b) The city of Toledo institutes an effective price ceiling on tickets. Explain where the price ceiling would be set. Explain the impact of the ceiling on each of the following.

(i) The quantity of tickets demanded(ii) The quantity of tickets supplied

(c) Will everyone who attends the circus pay the ceiling price set by the city of Toledo. Why or why not? 40