Transcript Elasticity Problems

Elasticity Problems
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ECO 284 - Microeconomics - Dr. D. Foster
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Elasticity Problems
A. What do execs at Pepsi expect TR to do when they
have a sale on their soft drink? Why?
Expect revenues to rise!!!
Demand is elastic . . . lots of substitutes.
B. You manage a concert hall that seats 500. Consider
the following demand information. What do you charge?
A price of $15
will max. revenue.
At a price of:
Amount sold is:
$10
500
$15
400
$20
200
Elasticity Problems
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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?
εD = 10%/50% = .20
This is inelastic (< 1.0) …
It is likely to be a small portion of our budgets.
Elasticity Problems
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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?
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.
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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?
εD = [100,000/1,000,000]/30% =
10%/30%
This is inelastic (< 1.0) …
It is likely to be considered a necessity.
= .33
Elasticity Problems
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3. (con’t) If the price, then, falls back by 30%, would
you predict the response by consumers will be elastic
or inelastic? Why?
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
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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?
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
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5. DishTV has lowered its subscription TV prices by
10% and its subscription base rose by 15%.
(a) What is the price elasticity of demand for DishTV?
Is this elastic or inelastic? Why?
εD = 15%/10% = 1.5
It is elastic – substitutes?
(b) If DirecTV sees its subscription base fall by 8%, what is the
cross price elasticity of demand for DirecTV? For DishTV?
εXZ = -8%/+10% = -.8
It is a substitute & inelastic. Can’t tell!
(c) If incomes rise by 3% and subscription base for DishTV rises by 9%,
what is the income elasticity of demand for DishTV?
εy = 9%/3% = 3.0
It is a normal good and income elastic.
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Elasticity Problems
6. Consider the demand
curve. As it is a straight
line, there is an elastic
portion, an inelastic
portion and point of
unitary elasticity. Identify
where, along this demand,
the total revenue would
be maximized. [Total
revenue equals price
times quantity.]
P
Q
Increase TR by P along
elastic portion and P along
inelastic portion.
Elasticity
Tax Problem
S’
price
S
7/8. For the accompanying
graph, assume that
equilibrium starts at point A.
Consider the effects of a
tax, which will decrease the
supply, for two alternative
demand curves, DA and DB.
$1.40
$1.10
A
$1.00
$.90
DA
$.60
DB
quantity
0
50
80
100
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).
Elasticity
Tax Problem
S’
price
S
For the accompanying
graph, assume that
equilibrium starts at point A.
Consider the effects of a
tax, which will decrease the
supply, for two alternative
demand curves, DA and DB.
$1.40
$1.10
A
$1.00
$112
$55$100
$.90
$.60
DA
DB
quantity
0
50
80
100
b. What is the change in total revenue along DA and DB?
DA - From $100 to $55; total revenue fell by $45.
DB - From $100 to $112; total revenue rose by $12.
Elasticity
Tax Problem
S’
price
S
For the accompanying
graph, assume that
equilibrium starts at point A.
Consider the effects of a
tax, which will decrease the
supply, for two alternative
demand curves, DA and DB.
$1.40
$1.10
A
$1.00
$.90
DA
$.60
DB
quantity
0
50
80
100
c. What does this tell you about the price elasticity for
each demand curve?
DA is elastic (P - TR) while DB is inelastic (P - TR).
Elasticity
Tax Problem
S’
price
S
For the accompanying
graph, assume that
equilibrium starts at point A.
Consider the effects of a
tax, which will decrease the
supply, for two alternative
demand curves, DA and DB.
$1.40
$1.10
A
$1.00
$.90
DA
$.60
DB
quantity
0
50
80
100
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
Elasticity
Tax Problem
S’
price
S
For the accompanying
graph, assume that
equilibrium starts at point A.
Consider the effects of a
tax, which will decrease the
supply, for two alternative
demand curves, DA and DB.
$1.40
$1.10
A
$40
$25
$1.00
$.90
DA
$.60
DB
quantity
0
50
80
100
d. What will be the tax revenue collected in each case?
DA - Tax revenue = ($.50)*50 units = $25.
DB - Tax revenue = ($.50)*80 units = $40.
Elasticity
Tax Problem
S’
price
S
For the accompanying
graph, assume that
equilibrium starts at point A.
Consider the effects of a
tax, which will decrease the
supply, for two alternative
demand curves, DA and DB.
$1.40
$1.10
A
$1.00
$.90
DA
$.60
DB
quantity
0
50
80
100
e. Shade in the lost consumer & producer surplus.
Elasticity Problems
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%Income
ECO 284 - Microeconomics - Dr. D. Foster