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Elasticity

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Elasticity

THE LAW OF DEMAND SAYS...

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

HOW MUCH MORE OR LESS?

DOES IT MATTER?

Elasticity shows how sensitive quantity is to a change in price.

Elasticity 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 = Quantity is INsensitive to a change in price.

- 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%

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

Examples:

- Gasoline
- Milk
- Diapers

- Chewing Gum
- Medical Care
- Toilet paper

General Characteristics of INelastic Goods:

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

20%

5%

PRICE ELASTICITY OF DEMAND

Extreme Case

Perfectly Inelastic Demand

D1

P

Ed = 0

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 = Quantity is sensitive to a change in price.

- 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.

An ELASTIC demand curve is flat!

Examples:

- Soda
- Boats
- Beef

- Real Estate
- Pizza
- Gold

General Characteristics of Elastic Goods:

- Many Substitutes
- Luxuries
- Large portion of income
- Plenty of time to decide
- Elasticity coefficient greater than 1

PRICE ELASTICITY OF DEMAND

Extreme Case

When 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.

Perfectly Elastic Demand

P

D2

Ed =

Q

0

Change in

quantity

Change in

price

Ed

=

Sum of

Quantities/2

Sum of

prices/2

PRICE ELASTICITY OF DEMAND

Refinement –

The Midpoint Formula

What about the demand for insulin for diabetics?

Beef-

Gasoline-

Real Estate-

Medical Care-

Electricity-

Gold-

Elastic- 1.27

INelastic - .20

Elastic- 1.60

INelastic - .31

INelastic - .13

Elastic - 2.6

What if % change in quantity demanded equals % change in price?

Perfectly INELASTIC

(Coefficient = 0)

Unit Elastic (Coefficient =1)

45 Degrees

Elastic from 1 to

PRICE ELASTICITY & TOTAL REVENUE

Price Elasticity is...

Inelastic from 0 to 1

Typical of necessities one must have

Elastic from 1 to

Typical of luxuries one wants

Unit elastic when exactly = 1

Price change does not reduce total revenue

Uses 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?

PRICE ELASTICITY & TOTAL REVENUE

When prices are low,

TR

So is total revenue

Quantity Demanded

PRICE ELASTICITY & TOTAL REVENUE

Total revenue rises

with price to a

point...

TR

P

D

Q

Quantity Demanded

PRICE ELASTICITY & TOTAL REVENUE

Total revenue rises

with price to a

point...

then declines

P

D

Q

Quantity Demanded

PRICE ELASTICITY & TOTAL REVENUE

Total revenue rises

with price to a

point...

then declines

P

D

Q

Quantity Demanded

PRICE ELASTICITY & TOTAL REVENUE

Total Revenue Test

Total revenue rises

with price to a

point...

then declines

P

TR

D

Quantity Demanded

Q

PRICE ELASTICITY & TOTAL REVENUE

Total revenue rises

with price to a

point...

then declines

P

TR

Inelastic

Demand

D

Inelastic

Demand

Q

Quantity Demanded

PRICE ELASTICITY & TOTAL REVENUE

Total revenue rises

with price to a

point...

then declines

P

TR

Elastic

Demand

Inelastic

Demand

D

Elastic

Demand

Inelastic

Demand

Q

Quantity Demanded

PRICE ELASTICITY & TOTAL REVENUE

Total revenue rises

with price to a

point...

then declines

P

TR

Unit

Elastic

Elastic

Demand

D

Inelastic

Demand

Elastic

Demand

Inelastic

Demand

Q

Quantity Demanded

10 x 100 =$1000 Total Revenue

5 x 225 =$1125 Total Revenue

A

Price decreased and TR increased, so…

Demand is ELASTIC

50%

B

125%

D

S

T

U

D

Elastic, Inelastic, or Unit Elastic?

Price

$30

20

10

0

7

14

U'

Quantity Demanded

(d)

Elasticity Practice

28

29

a) Calculate the producer surplus before the tax.

.

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

(b) Now assume a per-unit tax of $2 is imposed whose impact is shown in the graph above.

(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.

(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.

(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

(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.

(d) Assuming no externalities, how does the tax affect allocative efficiency? Explain.

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.

Elasticity of Supply-

- Elasticity of supply shows how sensitiveproducers 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-run
Perfectly Inelastic = Q doesn’t change (Vertical line)

- Set quantity supplied

Change in

quantity

Change in

price

Es

=

Sum of

Quantities/2

Sum of

prices/2

The formula is for Price Elasticity of Supply

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 quantity demanded of product “B”

Exy =

% change in price of product “A”

P increases 20%

Q decreases 15%

- If coefficient is negative (shows inverse relationship) then the goods are complements
- If coefficient is positive (shows direct relationship) then the goods are substitutes

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

It shows if goods are normal or inferior

% change in quantity demanded

Ei =

% change in income

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

INFERIOR GOOD

- 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%…

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