Download ECON 1001 AB Introduction to Economics I Dr. Ka

Chapter 7
Efficiency and Exchange
Odd-numbered Qs. And Q.10
Problem #1, Chapter 7 (1)
• Suppose the weekly demand and supply curves for used DVDs
in Lincoln, Nebraska, are as shown in the diagram. Calculate
– The weekly consumer surplus
– The weekly producer surplus
– The maximum weekly amount that producers and consumers in
Lincoln would be willing to pay to be able to buy and sell used DVDs in
any given week
Problem #1, Chapter 7 (2)
S
Price ($/DVD)
12
10.50
7.5
6
D
0
2
6
18
Quantity (DVDs/week)
48
Solution to Problem #1 (1)
• The weekly consumer surplus
– Recall consumer surplus refers to the difference between consumer’s
reservation price and the actual market price
– Graphically, it is the area under the demand curve but above the
actual market price
– In this problem, the equilibrium is achieved at a a price where Q(D) =
Q(S)
• The equilibrium price is $10.50 per DVD
– At an equilibrium price of $10.50 the corresponding
equilibrium quantity is 6 units of DVD per week
Solution to Problem #1 (2)
• The weekly consumer surplus
– (1/2) (Highest consumer’s reservation price – actual market price) *
actual market quantity
– (1/2) ($12 - $10.50) * 6 = $4.5
• The weekly producer surplus
– Recall producer surplus refers to the difference between producer’s
reservation price and the actual market price
– Graphically, it is the area above the supply curve but under the actual
market price
Solution to Problem #1 (3)
• The weekly producer surplus
– (1/2) (Actual market price – lowest producer’s reservation price) *
actual market quantity
– (1/2) ($10.50 - $6) * 6 = $13.5
• The maximum weekly amount that producers and consumers
in Lincoln would be willing to pay in a week
– In other words, it refers to the total gains from trading in used DVDsthe total economic surplus
– Total economic surplus = consumer surplus + producer surplus
– Total economic surplus = $4.5 + $13.5 = $18 per week
Problem #3, Chapter 7 (1)
• The Kubak crystal caves are renowned for their stalactites and
stalagmites. The warden of the caves offers a tour each
afternoon at 2pm sharp. The cave can be shown to only four
people per day without disturbing their fragile ecology.
Occasionally, however, more than four people want to see the
caves on the same day. The following table lists the people
who wanted to see the caves on September 24, 2003,
together with their respective times of arrival and reservation
prices for taking that day.
Problem #3, Chapter 7 (2)
Arrival Time
Reservation Price ($)
Herman
1:48
20
Jon
1:50
14
Kate
1:53
30
Jack
1:56
15
Penny
1:57
40
Fran
1:59
12
Faith
2:00
17
Solution to Problem #3 (1)
• A) If the tour is “free” and the warden operates it on a firstcome, first served basis, what will the total consumer surplus
be for the four people who get to go on the tour on that day?
• Note that the capacity is only 4 people per day
• If it serves on a first-come, first served basis, only Herman, Jon,
Kate and Jack are able to see the caves
• Since the tour is free, assume both the production cost and
actual market price are zero
• The consumer surplus is thus exactly to consumer’s
reservation price
Solution to Problem #3 (2)
• The total consumer surplus
– Sum of visitors’ reservation prices
– = $20 + $14 + $30 + $15 = $79 per day
• B) Suppose the warden solicits volunteers to postpone their
tour by offering increasing amounts of cash compensation
until four people still wish to see the caves that day. If he
gives each volunteer the same compensation payment, how
much money will he have to offer to generate the required
number of volunteers? What is the total economic surplus
under this policy?
Solution to Problem #3 (3)
• Recall reservation price refers to the maximum price that a
consumer is willing to pay for a good or service
• It reflects how much does a consumer value on that good or
service
• Based on the reservation prices, an offer of $15 compensation
will attract Jon, Jack and Fran to postpone their visit to the
caves
• After the proposal of this offer, Herman, Kate, Penny and Faith
are able to visit the caves without having to watch out their
arrival time
Solution to Problem #3 (4)
• As a result, the total economic surplus:
– = $20 + $30 + $40 +17 = $107 per day
• However, all the four visitors have to pay a total of $45 ($15*3)
cash compensation
• On the whole, the total of $45 cash compensation is not
actually cost, as the compensation represents the gains of the
non-visitors (Jon, Jack and Faith)
• The cash compensation is simply a TRANSFER from the visitors
to non-visitors; it neither increases or decreases the total
economic surplus
• Hence, the new total economic surplus is $107 per day
Solution to Problem #3 (5)
• C) Why is the compensation policy more efficient than the
first-come, first served policy?
• It is more efficient as the compensation policy generates a
higher total economic surplus ($107 per day) rather than just
$79 per day under the first-come, first served policy
• It creates a market trading the rights on the visit to the caves.
Non-visitors’ reservation prices are compensated by the
visitors
• Visitors pay an opportunity cost of $15 to ensure the visit to
the cave, and thus only those who value the visit more than
$15 will actually accept the deal
Solution to Problem #3 (6)
• D) Describe a way of financing the warden’s compensation
payments that will make everyone, including the warden,
either better off or no worse off than under the first-come,
first-served approach
• Auction
• Suppose the warden auctions off the admission rights
• Starting zero, the auction price steadily goes up by $1
increment until only 4 people are willing to visit the caves
• It will stop when the auction price reaches $16
• Faith, Penny, Herman and Kate will be the four visitors
• As a result, the warden will collect $64 from the auction
Solution to Problem #3 (7)
• The warden will give a refund to Herman and Kate, who would
have gotten to go for free under the first-come, first-served
policy- they will be just as well off as before
• The warden will then give $16 to Jack which is $1 more than
enough to compensate him for not visiting
• The warden will also give $15 to Jon, which is again $1 more
than enough to compensate him for not visiting
• Thus, both Jon and Jack gain $1 from the auction
• Faith is $1 better off than before ($17 reservation -$16
auction fee); Penny is $24 better off ($40 reservation - $16
auction fee) All others are same as well off as before
Problem #5, Chapter 7
• Is a company’s producer surplus the same as its profit? (Hint:
A company’s total cost is equal to the sum of all marginal costs
incurred in producing its output, plus any fixed costs.)
Solution to Problem #5 (1)
• Producer surplus refers to the total difference between the
actual market price and the producer’s reservation price
• Producer’s reservation price refers to the lowest price that he
or she is willing to produce
• A perfectly competitive firm charges a price =MC
• As a result, producer’s reservation price = marginal cost
• In other words, producer surplus is the difference between the
total revenue and the sum of all marginal costs incurred
Solution to Problem #5 (2)
• Total profit = Total revenue – total cost
• Total revenue = Price * Quantity
• Total cost = given in the hint – sum of all the marginal costs
plus fixed costs
• Since producer surplus does not cover any of fixed costs, it is
thus not equal to profit
Problem #7, Chapter 7
• The municipal water works of Cortland draws water from two
sources: an underground spring and a nearby lake. Water from
the spring costs 2 cents per 100 gallons to deliver, and the spring
has a capacity of 1 million gallons per day. Water from the lake
costs 4 cents per 100 gallons to deliver and is available in
unlimited quantities. The demand for water in the summer
months in Cortland is P= 20 - 0.001Q, where P is the price of
water in cents per 100 gallons and Q is the quantity demanded
in hundreds of gallons per day. The demand curve for water in
the winter months is P= 10 – 0.001Q. If the water works wants
to encourage efficient water use, how much should it charge for
water in the summer months? In the winter months?
Demand for summer months
20
Ds
Price per 100 gallons
Price per 100 gallons
Solution to Problem #7 (1)
Demand for winter months
10
Dw
Qw
Qs
20,000
hundreds
of gallons
10,000
hundreds
of gallons
Solution to Problem #7 (2)
• The cost of water from underground spring is cheaper than
that from lake
• Therefore, the municipal water works should always to try
satisfy the demand by water from underground spring
– The application of Low-hanging Fruits Principle
• The relatively small demand for water in winter months can
be served by underground spring alone
• Therefore, the price should be equal to the (marginal) cost of
water from underground spring, which is 2 cents per 100
gallons in the winter months
Solution to Problem #7 (3)
• The relative large demand for water in summer months must
be satisfied by extracting water from lake which has a larger
supply than underground spring
• Again, the price should be equal to the (marginal) cost of
water from lake, which is 4 cents per 100 gallons in the winter
months
Problem #9, Chapter 7
• The government of Islandia, a small island nation, imports
heating oil at a price of $2 per gallon and makes it available to
citizens at a price of $1 per gallon. If Islandians’ demand curve
for heating oil is given by P = 6-Q, where P is the price per
gallon in dollars and Q is the quantity in millions of gallons per
year, how much economic surplus is lost as a result of the
government’s policy?
Solution to Problem #9 (1)
P ($/gal)
6
2
1
Q (millions of gal/yr)
4
5
6
Solution to Problem #9 (2)
• At a per gallon price of $1, Islandians consume 5 million
gallons of oil per year
• However, this level of consumption is attributed to the price
control set of the government
• The true per unit cost is actually $2 per gallon
• If the government charges where P= MC, Islandians will only
demand for 4 million gallons of oil per year
• Therefore, if Islandians consume 5 gallons of oil per year at
the controlled price of $1, there will be an economic loss that
is equal to the difference between the total cost of oil and
Islandians’ reservation prices for oil
Solution to Problem #9 (3)
P ($/gal)
6
Loss in total economic
surplus
2
1
Q (millions of gal/yr)
4

5
6
That is (1/2) ($2 - $1) * (5 – 4) = $0.5 million gallon per year
Problem #10, Chapter 7
Refer to problem 9. Suppose each of the 1million Islandian
households has the same demand curve for heating oil.
P ($/gal)
6
Loss in total economic
surplus
2
1
Q (millions of gal/yr)
4
5
Solution to Problem #10 (1)
a) What is the household demand curve?
The household demand curve with be the same as in problem 9,
instead, the only differences is the scaling.
P ($/gal)
6
Loss in total economic
surplus
2
1
Q (gal/yr)
4
5
Solution to Problem #10 (2)
b) How much consumer surplus would each household lose if it had to
pay $2 per gallon instead of $1 per gallon for heating oil, assuming
there were no other changes in the household budget?
A
P ($/gal)
6
2
1
B
C
E
D
Q (gal/yr)
4
5
Solution to Problem #10 (3)
With the subsidy, $1 per gallon, household’s consumer surplus:
(Area of ADE) ($6/gal - $1/gal)(5gal/yr) (1/2) = $12.5/yr
Without subsidy, $2 per gallon, household’s consumer surplus:
(Area of ABC) ($6/gal - $2/gal)(4gal/yr) (1/2) = $8/yr
The lost in Total Consumer surplus = $12.5/yr - $8/yr
= $4.5/yr
That is the area of BCED.
Solution to Problem #10 (4)
c) With the money saved by not subsidizing oil, by how much could
the Islandian government afford to cut each family’s annual taxes?
Government’s oil subsidy to each household is ($1/gal)(5gal/yr) =
$5/yr.
If government imposes oil subsidy to subsidized the poor, the
government needs to collect a higher tax from the taxpayers.
Now, if the government not subsidizing oil, then the taxpayers,
who were need to pay the higher tax, pay a lower tax than before,
$5/yr less.
Therefore, the government could cut each household’s taxes by
$5/yr by not subsidizing oil.
Solution to Problem #10 (5)
d)
If the government abandoned its oil subsidy and implemented the tax cut,
by how much would each family be better off?
Implement the tax cut, household saves $5/yr on tax.
Household’s net gain would be $5/yr - $4.5/yr it loses in consumer surplus
from its heating oil purchases, $0.5/yr.
Solution to Problem #10 (6)
e) How does the resulting gain for 1 million families compare with
your calculation of the lost surplus in problem 9?
The aggregate net gain from tax cut and removal of subsidy is
$500,000/yr.
Total Economic surplus lost resulting from oil subsidy is
$500,000/yr.
The gain from tax cut and removal of oil subsidy is the same as the
loss in Economic Surplus.
Therefore, it is better for the government not to use the oil subsidy
to help the poor. Instead, government should find a more efficient
solution.
Extra Question #1, Chapter 7
• Tax is always a distortion to a perfectly competitive market; it
always works to decrease the total economic surplus
• True or False, and provide an explanation
Solution to Extra #1 (1)
• Graphically, equilibrium is achieved at the intersection of
demand curve and supply curve
• In general, total economic surplus is maximized at equilibrium
P
S
CS
P*
PS
D
0
Q
Q*
Solution to Extra #1 (2)
• However, there are exceptions!
– The demand curve does not fully capture the complete benefit
(willingness to pay)
– The supply curve does not fully capture the complete production cost
• Thus, if there is positive or negative externality, the total
economic surplus at equilibrium may be either overestimated
or underestimated
Solution to Extra #1 (3)
• Example
• The supply curve of a manufacturing firm is often
underrepresented the true production cost
• The supply curve often fails to take account of pollution cost
which is then fully bared by society
• In other words, there is unaccounted negative externality in
the market
Solution to Extra #1 (4)
S with negative externality
P
P*’
S
CS’
Economic loss
P* PS’
D
0
Q
Q*’ Q*
Solution to Extra #1 (5)
• Any solution to correct the estimation of supply curve that
renders a true production cost or a true willingness to
produce?
• Imposition of tax may shed some light to elimination of
negative externality
• If a per unit tax that is exactly equal to the per unit negative
externality arising from the production is imposed, the
introduction of pollution tax can help eliminate the economic
loss
Solution to Extra #1 (6)
S with a per unit tax
P
P*’
S
CS’
Economic loss eliminated
P* PS’
D
0
Q
Q*’ Q*