Elasticity ProblemsElasticity Problems

P

QDD

%

%

ECO 284 - Microeconomics - Dr. D. Foster

Income

QDY

%

%

Z

XDZX P

Q

%

%

Elasticity Problems

1. If the price of butter goes up 50% and the quantity demanded falls by 10%, what is the price elasticity of demand? Is this elastic or inelastic?

Why?

P

QDD

%

%

εD = 10%/50% = .20

This is inelastic (< 1.0) … It is likely to be a small portion of our budgets.

Elasticity Problems

2. If the price of the Rolling Stones’ CD, Semi-Serious, is reduced from $20 to $18, and the quantity demanded (say, on a per month basis) rises by 10%, what is the price elasticity of demand? Is this elastic or inelastic? Why?

P

QDD

%

%

εD = 10%/[$2/$20] = 10%/10% = 1.0

This is “unit elastic” (= 1.0) … It doesn’t easily fit into any categories insofar as elastic vs. inelastic goes.

Elasticity Problems

3. If the price of gas goes up by 30% and the quantity demanded falls from 1,000,000 gallons/day to 900,000 gallons/day, what is the price elasticity of demand? Is this elastic or inelastic? Why?

P

QDD

%

%

εD = [100,000/1,000,000]/30% = 10%/30% = .33

This is inelastic (< 1.0) … It is likely to be considered a necessity.

Elasticity Problems

3. (con’t) If the price, then, falls back by 30%, would you predict the response by consumers will be elastic or inelastic? Why?

P

QDD

%

%

It would still be inelastic…Consumers will buy more when the price falls. (that is just the law of demand at work)But, they will not buy a lot more.

Elasticity Problems

4. A popular pair of Nike shoes, the Paris Hilton Liteweights, is reduced in price from $80 to $40, while the quantity demanded rises from 10,000 pairs/week to 20,000 pairs/week. What is the price elasticity of demand? Is this elastic or inelastic? Why?

P

QDD

%

%

εD = [10,000/10,000]/[$40/$80] = 100%/50% = 2.0

This is elastic (> 1.0) … It is likely that there are many substitutes available.

Elasticity Problems

5. What do execs at Pepsi expect TR to do when they have a sale on their soft drink? Why?

P

QDD

%

%

Expect revenues to rise!!!Demand is elastic . . . lots of substitutes.

A price of $15will max. revenue.

6. You manage a concert hall that seats 500. Consider the following demand information. What do you charge?

At a price of: Amount sold is:

$10 500

$15 400

$20 200

ElasticityTax Problem

For the accompanying For the accompanying graph, assume that graph, assume that equilibrium starts at equilibrium starts at point A. Consider the point A. Consider the effects of a tax, which effects of a tax, which will decrease the supply, will decrease the supply, for two alternative for two alternative demand curves, Ddemand curves, DA A and and

DDBB..

S’

S

A

price

DA

DBquantity

$1.40

$1.10

$1.00

$.90

$.60

10080500

a. A $.50 per unit tax is placed on this good – does S’ show the new supply curve?

Yes, supply “decreases” and shifts up by $.50 (see q=80).

DA - From $100 to $55; total revenue fell by $45.DB - From $100 to $112; total revenue rose by $12.

S’

S

A

price

DA

DBquantity

$1.40

$1.10

$1.00

$.90

$.60

10080500

b. What is the change in total revenue along DA and DB?

$100

$55

$112

For the accompanying For the accompanying graph, assume that graph, assume that equilibrium starts at equilibrium starts at point A. Consider the point A. Consider the effects of a tax, which effects of a tax, which will decrease the supply, will decrease the supply, for two alternative for two alternative demand curves, Ddemand curves, DA A and and

DDBB..

ElasticityTax Problem

DA is elastic (P - TR) while DB is inelastic (P - TR).

S’

S

A

price

DA

DBquantity

$1.40

$1.10

$1.00

$.90

$.60

10080500

c. What does this tell you about the price elasticity

for each demand curve?

For the accompanying For the accompanying graph, assume that graph, assume that equilibrium starts at equilibrium starts at point A. Consider the point A. Consider the effects of a tax, which effects of a tax, which will decrease the supply, will decrease the supply, for two alternative for two alternative demand curves, Ddemand curves, DA A and and

DDBB..

ElasticityTax Problem

S’

S

A

price

DA

DBquantity

$1.40

$1.10

$1.00

$.90

$.60

10080500

As an additional exercise, we can calculate the price elasticity for each demand curve:

D for DA is (50/100)/(.1/1) = 50%/10% = 5.0

D for DB is (20/100)/(.4/1) = 20%/40% = 0.5

For the accompanying For the accompanying graph, assume that graph, assume that equilibrium starts at equilibrium starts at point A. Consider the point A. Consider the effects of a tax, which effects of a tax, which will decrease the supply, will decrease the supply, for two alternative for two alternative demand curves, Ddemand curves, DA A and and

DDBB..

ElasticityTax Problem

S’

S

A

price

DA

DBquantity

$1.40

$1.10

$1.00

$.90

$.60

10080500

d. What will be the tax revenue collected in each case? DA - Tax revenue = ($.50)*50 units = $25.DB - Tax revenue = ($.50)*80 units = $40.

$25

$40

For the accompanying For the accompanying graph, assume that graph, assume that equilibrium starts at equilibrium starts at point A. Consider the point A. Consider the effects of a tax, which effects of a tax, which will decrease the supply, will decrease the supply, for two alternative for two alternative demand curves, Ddemand curves, DA A and and

DDBB..

ElasticityTax Problem

Elasticity ProblemsElasticity Problems

P

QDD

%

%

ECO 284 - Microeconomics - Dr. D. Foster

Income

QDY

%

%

Z

XDZX P

Q

%

%