Chapter 7 Problem 2 - the School of Economics and Finance

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Chapter 7
Efficiency and Exchange
Even-numbered Qs.
• Efficient (or Pareto efficient):
“A situation is efficient if no change is possible that will help
some people without harming others.” – Efficient (or Pareto
efficient)”
- any change to make any person better off is impossible
without making someone else worse off.
• Is market equilibrium an efficient situation?
• Yes, the market equilibrium price leads to the largest possible
surplus for both sellers and buyers.
• The market equilibrium price is the only price at which sellers
and buyers cannot design a surplus-enhancing transaction.
• Market equilibrium is said to be efficient:
- If market is at disequilibrium, a transaction that will make at
least some people better off without harming others can
always be found. All mutually beneficial transactions have
taken place.
-i.e. if the market price is below the equilibrium price – Excess demand.
-A transaction can always take place to obtain more economic surplus and
none of the buyers or sellers is harmed by this transaction, i.e. increase the
price such that the market is back to the equilibrium price and quantity
level.
• Market equilibrium is said to be efficient:
- If demand curves capture all relevant benefits and supply
curves capture all relevant costs.
Tax and Deadweight loss
• Regardless the government imposes the tax on the
sellers or the buyers, the tax burden and deadweight
will be the same.
• The tax burden and deadweight loss depends on the
relative elasticity of supply and demand curve
•Tax on producers can be viewed as a "cost
of doing business" for the producers
P
S+T
•The supply curve shifts to the left, S+T
S
T
P1
•After tax is imposed, the new equilibrium is
at P1 , Q1
•The new market equilibrium price is higher ,
P1, and the buyers are paying a higher price
to purchase this good
PE
P2
D
Q1
QE
Q
•However, the producers are not receiving
this higher price,P1. Part of this higher price
goes to government as the tax and
producers are receiving a lower price, P2
•Government tax revenue is the rectangle
area between P1 and P2
•So, who is really paying the tax? Buyers? Or producers?
•Generally, both buyers and producers share the tax burden
• Buyers pay P1 , Producers receive P2.
•Therefore, part of the tax is paid by buyers. Buyer’s tax burden is
•Part of the tax is paid by producers. Producer’s tax burden is
Who bears the tax?
• The tax burden is not always equally share between buyers
and producers. It depends on the relative elasticity of supply
and demand.
• The more elastic demand is, the more of the tax falls on
producers. (This also applies if government imposes tax on
buyers)
S +T
P
S
consumers
P’
PE
E
D
P”
Q’
QE
Q
producers
Who bears the tax?
• The tax burden is not always equally share between buyers
and producers. It depends on the relative elasticity of supply
and demand.
• The more elastic supply is, the more of the tax falls on
consumers. (This also applies if government imposes tax on
buyers)
S+T
P
S
P’
PE
P’’
Consumers
E
Producers
D
Q’ QE
Q
Deadweight loss
• DWL is the reduction in the sum of consumer surplus and
producer surplus results from the adoption of a policy.
• The size of deadweight loss depends on the reduction in the
quantity sold
• The reduction in the quantity sold will depend upon the
elasticity of demand and supply
– The more elastic demand or supply is, the larger the decrease in
quantity, the larger the deadweight loss will be
– The more inelastic demand or supply is, the smaller the decrease in
quantity, the smaller the deadweight loss will be and could be zero if
perfectly inelastic (no change in the quantity sold and consumed)
How much deadweight loss?
•If Demand is price elastic, buyers are relatively sensitive to
the price change
-A small change in price leads to a large change in quantity
-Tax imposition, either on buyers or producers, will increase the
equilibrium price; thus, it leads to a relatively large decrease in
quantity
-The larger the change in quantity, the larger is the deadweight loss
P
S’
P
S’
S
S
P’
P’
PE
T
E
T
D
P’’
PE
P’’
E
D
Q’
QE
Q
Q’ QE
Q
How much deadweight loss?
•If Supply is price inelastic, sellers are relatively insensitive to
the price change
-A small change in price leads to a small change in quantity
-Tax imposition, either on buyers or producers, will increase the
equilibrium price; thus, it leads to a relatively small decrease in
quantity
-The smaller the change in quantity, the smaller is the deadweight
lossP
S’
P
S
S’
T
P’
PE
P’’
S
E
T
P’
PE
E
P’’
D
D
Q’ QE
Q
Q’ QE
Q
How much deadweight loss?
• If Demand or Supply curve is perfectly elastic or inelastic, only one party will
bear all the tax burden.
Perfectly Elastic Demand:
Perfectly Elastic Supply
Producers bear all tax burden
Consumers bear all tax burden
S”
P
P
S
P’
T
PE = P’’
PE = P’
E
Tax
T
S’
Tax
E
S
D
P’’
D
Q’
QE
Q
Q’
QE
Q
How much deadweight loss?
Perfectly Inelastic Demand:
Perfectly inelastic Supply
Consumers bear all tax burden
DWL equals to zero
Producers bear all tax burden
DWL equals to zero
S”
P
D
S
P
S
P’
T
Tax
PE = P’
E
PE = P’’
T
P’’
E
Tax
D
Q’ =QE
Q
Q’ = QE
Q
Additional Question #1
The concept of efficiency is illustrated by which of
the following statements?
A)
B)
C)
D)
E)
The production of the good generates very little pollution.
At equilibrium, all mutually beneficial transactions have
taken place.
The production of the good generates very few by-products.
The consumption of the good produces very little waste.
At disequilibrium, no mutually beneficial transactions have
occurred.
Ans: B
• In economics, efficiency denotes a state at which all potential
gains from exchange have been captured.
• Recall that the definition of Pareto Optimality is “a state at
which one cannot be made better off without making others
worse off”.
• Any pollution or by-products related to exchange or
production are taken into account. There can be little, or
much pollution, as long as efficiency is attained.
• E.g. Hong Kong vs Africa
HK is a place with terrible pollution, while Africa still has clean
air. Is the situation regarded as ‘inefficient/ disequilibrium/ not
optimal’ in Economics?
• Should we ‘balance/ equalize’ the pollution level between Africa
and HK? The ans is ‘NO’ obviously, WHY?
• We chose to sacrifice the clean air in HK in exchange for the
amazing economic development. Thus, econ surplus would
definitely drops if we ‘move’ some of our industries to Africa.
• Therefore, B is the correct answer.
Additional Question #2
Compared to the first-come-first-served allocation scheme
airlines used in the past, the voluntary compensation
scheme now in place
A)
B)
C)
D)
E)
Discriminates against the poor.
Improves efficiency for only the wealthy.
Tricks the poor into unnecessarily delaying their travel.
Improves efficiency for all travellers.
Encourages passengers to show up early.
Ans: D
• Airlines usually have their flights overbooked.
• That means, airlines accept more reservations than the actual
no. of seats on each flight.
• When a flight is overbooked, at the time of check-in, the
airline company has to find some ways to settle who will
board the plane, and who will not.
• In the past, it is done according to the ‘first-come-first served’
principle.
• The ones arriving at the check-in counter early can get the
boarding pass. (some can even be upgraded!)
• The few that are relatively late will get an apology from the
airline, and will be arranged onto another flight, which usually
results in a delay.
• Some time ago, airline companies ditched the ‘first-comefirst-served’ scheme, and took up the ‘voluntary
compensation scheme’.
• Airlines realise that among the passengers, some value
punctuality of arrival more than others.
• Those who can postpone their plans are likely to be willing to
accept some compensation from the airline for not taking the
planned flight.
• People would be willing to delay their plans as long as the
compensation is enough to cover the costs (e.g. time cost)
• Whether a passenger is poor or wealthy is not the direct
reason to evaluate his costs of delays.
• It is his own valuation of time cost that counts.
• Therefore, by offering a voluntary compensation when a flight
is overbooked, those who have a lower reservation price for
punctuality are willing to be delayed.
(who are they? People with low time cost)
• Those who values punctuality most can arrive at the
destination on time. They are people with high time cost. E.g.
Bill Gates
• This improves efficiency for all travellers (D).
• FCFS scheme is designed to help the poor and to improve the
economic surplus.
• However, this scheme does not generate the highest possible
economic surplus.
• i.e. The following is the arrival time for passengers and the most
they are willing to pay to fly now. Since the flight is overbooked, only
2 passengers can get onto the flight.
A
1:00pm
$5
B
1:05pm
$4
C
1:30pm
$10
D
2:00pm
$20
• Under FCFS, Consumer A and B will be served, Total consumer
surplus is $9.
• Under Cash compensation, if the Airline offers at least $1 more to
those consumers with the lowest reservation price, i.e. $6, consumer
A and B will volunteer to wait for another flight.
• Now, the Airline is only serving those consumers with the highest
reservation price, consumer C and D. Total consumer surplus is
$30.
• It is more efficient under the cash compensation scheme, as
the compensation policy generates a higher total economic
surplus ($30) rather than just $9 under the first-come, first
served policy
• Consumer A and B are now $1 and $2 better off.
• Consumer C and D are now able to get onto the flight.
• Therefore, under Cash compensation scheme, everyone is
better off.
Additional Question #3
Demand for cigarettes is price inelastic for adults,
but price elastic for teenagers. Therefore, a tax on
cigarettes will
A)
B)
C)
D)
E)
Not raise very much tax revenue.
Not generate deadweight loss.
Generate more tax revenue from adults and have a greater
effect on the number of cigarettes smoked by teenagers.
Have a greater effect on the number of cigarettes smoked
by adults than by teenagers.
Generate more tax revenue from teenagers than from
adults.
Ans: C
• We can almost immediately eliminate options A and
B.
• A: not raise very much tax revenue. How much is
‘much’?
• B: a tax always generates some deadweight loss
unless the demand/supply curve is perfectly
inelastic/elastic.
• Therefore, options A and B are not the answers.
• Option D is also very obviously wrong.
• Adults’ demand is price inelastic; teenagers’ demand is price
elastic.
• That means adults are less sensitive to price changes than
teenagers.
• Therefore, a tax should have greater effect on no. of cigarettes
smoked by teenagers, not adults.
• Option C is the answer.
• A tax imposed on a good whose demand is price inelastic
results in a higher tax revenue than in the case where demand
is price elastic.
• When demand is price elastic, a small increase in price will
lead to a huge drop in quantity demanded. Therefore, tax
revenue from the teenagers’ market would be smaller.
P
DAdults
Tax revenue
from Adults
Tax revenue
from Teenagers
S’
S
DTeenagers
Q
Additional Question #4
Suppose that instead of taxing the producers, a tax of an
equal dollar amount per unit is imposed on consumers in
the market shown. Relative to the tax on producers,
A)
B)
C)
D)
E)
The tax on consumers would generate more deadweight
loss.
The burden of the tax on consumers would be more equally
shared between consumers and producers.
Consumers would bear a greater share of the tax burden.
The effect on deadweight loss and tax burdens would be
the same.
The price paid by consumers would increase by more.
Ans: D
• When a per-unit tax is
imposed, supply curve shifts
leftwards,
• If the same tax is imposed
on consumers, consumer
demand curve shifts down
by the same ‘vertical
distance’
• Thus, new equilibrium price
and quantity will be the
same under the 2 types of
tax.
Price
9
Supply plus tax
8
Supply
7
6
5
4
3
2
1
D em and
• Hence, D.
0
10 20
30
40
50
60
70
U nits per day
Additional Question #5
A tax on Commodity A will generate ? deadweight loss
relative to an equivalent tax on Commodity B.
A)
B)
C)
D)
E)
More
Less
Equal
Zero
An in determinate amount of
Ans: B
Commodity B
Commodity A
PB
PA
DA
SA’
SB’
SA
SB
DB
QA
Tax
QB
• Deadweight loss is the result of distortion from Pareto
efficient allocation because of anything but price (e.g. tax).
• The larger the distortion, the higher the deadweight loss.
• Therefore, we need to identify, when a tax is imposed,
distortion from which market would be higher.
• DB is more price elastic than DA.
• That means consumers of Commodity B is more sensitive to
price changes than consumers of Commodity A.
• When %↑PA = %↑PB, %↓QdB > %↓QdA. (Larger drop in Qd
for B)
• In other words, the distortion caused by a tax would be
smaller in Market A than in Market B.
• Hence, the answer is B.
Chapter 7 Problem 2
2) Refer to problem 1. Suppose a coalition of students from Lincoln
High School succeeds in persuading the local government to impose
a price ceiling of $7.50 on used DVDs, on the grounds that local
suppliers are taking advantage of teenagers by charging exorbitant
prices.
a) Calculate the weekly shortage that result from this policy.
S
Price ($/DVD)
12
10.5
7.5
6
D
2
6
18
48
Quantity (DVDs/week)
a) Calculate the weekly shortage of used DVDs that will result from this
policy.
With price ceiling of $7.50, the quantity supplied from sellers is 2 DVDs
per week.
By using vertical interpretation, with quantity of 2 DVDs per week,
buyers are willing to pay a higher price for an additional DVDs.
The quantity demanded at the current price of $7.50 is 18 DVDs per
week.
Thus, the price ceiling leads to an Excess Demand of 16 DVDs per
week (18 DVDs/wk – 2 DVDs/wk). Buyers cannot buy as much as
they are willing to at the current price of $7.50.
Therefore, the weekly shortage of used DVDs result from the price
ceiling policy is 16 DVDs per week.
b) Calculate the total economic surplus lost every week as a result of the price
ceiling.
2 methods to find the lost in economic surplus.
Price ($/DVD)
Price ($/DVD)
S
S
12
12
x
x
10.5
10.5
7.5
7.5
6
6
D
2
6
18
Quantity (DVDs/week)
48
D
2 6
18
Quantity (DVDs/week)
48
Method 1:
With price ceiling of $7.50, sellers will sell only 2 DVDs/wk. Therefore, total economic
surplus will be reduced by the shaded area.
S
Price ($/DVD)
12
x
Weekly economic surplus lost
is the area of the shaded
triangle.
Economic
surplus
lost
10.5
7.5
6
D
2 6
18
48
Quantity (DVDs/week)
To find the area of the shaded triangle, we need to calculate the value of X in the graph.
First, derive the Demand Curve:
Demand Curve: P = 12 – 0.25Q
At Q = 2, P = 12 – 0.25(2)
P = 11.5
Weekly economic surplus lost is,
(11.5 – 7.5)(6-2) (1/2) = $8/wk
Method 2:
With price ceiling of $7.50, sellers will sell only 2 DVDs/wk.
Price ($/DVD)
S
12
11.5
10.5
Without Price ceiling, sellers sell 6 DVDs at P = $10.5 .
Consumer surplus: $4.5/wk
Producer surplus: $13.5/wk
Total Economic Surplus = $18/wk
7.5
6
D
2 6
18
48
With Price ceiling of $7.5, only 2 DVDs/wk will
be sold.
Consumer surplus:
(12-11.5)(2) (1/2) + (11.5-7.5)(2) = $8.5/WK
Producer surplus:
(7.5-6)(2) (1/2) = $1.5/wk
Total Economic Surplus = $10/wk
Quantity (DVDs/week)
Therefore, total economic surplus lost as a result of price ceiling is,
$18/wk - $10/wk = $8/wk
Chapter 7 Problem 4
4) Suppose the weekly demand for a certain good, in thousands of
units, is given by the equation P = 8 – Q, and the weekly supply of
the good is given by the equation P = 2 + Q, where P is the price in
dollars.
Price ($/unit)
8
P=2+Q
P*
2
P=8-Q
Q*
Quantity (1000s/wk)
8
a) Calculate the total weekly economic surplus generated at the market
equilibrium.
Price ($/unit)
8
P=2+Q
P*
2
P=8-Q
Q*
8
Quantity (1000s/wk)
Find the equilibrium price, P*, and quantity, Q*:
At equilibrium, Supply = Demand
2+Q=8–Q
Q* = 3
P* = 5
Equilibrium Price, P*, is $5/unit.
Equilibrium Quantity, Q*, is 3,000 units/wk.
P=2+Q
Price ($/unit)
8
C.S
5
P. S
2
P=8-Q
3
8
Quantity (1000s/wk)
Consumer surplus: ($8 - $5)(3/wk) (1/2) = $4.5/wk ($4,500/wk)
Producer surplus: ($5 - $2) (3/wk) (1/2) = $4.5/wk ($4,500/wk)
Therefore, total economic surplus is $9,000/wk.
b) Suppose a pre-unit tax of $2, to be collected from sellers, is
imposed in this market. Calculate the direct loss in economic
surplus experienced by participants in this market as a result of the
tax.
The tax of $2 is equivalent to the increase of $2 in the cost of
production to sellers.
Supply curve shift to left from $2 to $4.
S’ P = 4 + Q
Price ($/unit)
8
Tax
S P=2+Q
P**
5
4
2
P=8-Q
Q** 3
Quantity (1000s/wk)
8
Initially, the equilibrium price, P*, is $5; equilibrium quantity, Q*, is
3,000units/wk.
After the tax of $2, the equilibrium price increases and equilibrium
quantity decreases. The Total Economic Surplus will be decreased.
New supply curve after the tax is now: P = 4 + Q
At equilibrium, SC = DC
4+Q=8–Q
Q** = 2
P** = 6
The new equilibrium price, P** = $6/unit
The new equilibrium quantity, Q** = 2,000 units/wk
With the tax, buyers now pay $6/unit; pay $1/unit more than before.
CS = (8-6)(2) (1/2) = $2,000/wk
Net of the $2 tax, sellers now receive $4/unit; receive $1 less than before.
PS = (4-2)(2) (1/2) = $2,000/wk
Suppose the tax revenue simply evaporates after collection, the tax revenue is not
going to offset other taxes. Both sellers and buyers together are now getting less
Total Economic Surplus than without tax.
S’ P = 4 + Q
Total Economic Surplus =
$4,000/wk.
Initially, Total Economic
Surplus is = $9,000/wk
Therefore, the direct loss in
Total Economic Surplus is
$9,000/wk - $4,000/wk =
$5,000/wk.
Price ($/unit)
8
6
Tax
P=2+Q
CS
5
4
PS
2
P=8-Q
2 3
8
c) How much government revenue will this tax generate each week?
If the revenue is used to offset other taxes paid by participants in
this market, what will be their net reduction in total economic
surplus?
A pre-unit tax of $2 will generate a tax revenue of $4,000/wk ($2
x 2,000/wk).
If this tax revenue is used to offset other tax paid by participants in
the market, then the participants can reduce other tax by the same
tax amount.
Counting the revenue from the tax as part of total economic surplus,
the new total economic surplus is thus:
CS + PS + Tax
$2,000/wk + $2,000/wk + $4,000/wk
= $8,000/wk
Or $1,000/wk less than without the tax
That is, the Deadweight Loss – the reduction in total economic
surplus that results from the adoption of policy, e.x., tax.
Area of the Deadweight loss = ($6/unit - $4/unit)(3/wk – 2/wk) (1/2)
= $1/wk, or $1,000/wk.
S’ P = 4 + Q
Price ($/unit)
8
Tax
P=2+Q
Deadweight loss
6
5
4
2
P=8-Q
2
3
Quantity (1000s/wk)
8
Chapter 7 Problem 6
6) In Charlotte, North Carolina, citizens can get their electric power
from two sources: a hydroelectric generator and a coal-fired steam
generator. The hydroelectric generator can supply up to 100 units
of power per day at a constant marginal cost of 1 cent per unit.
The steam generator can supply any additional power that is
needed at a constant marginal cost of 10 cents per unit. When
electricity costs 10 cents per unit, residents of Charlotte demand
200 units per day.
a) Draw the marginal cost curve of electric power production in
Charlotte.
a) Draw the marginal cost curve of electric power production in
Charlotte.
Steam
Price (cents/unit)
10
Marginal cost of power
Hydroelectric
1
100
Units of power per day
b) How much should the city charge for electric power? Explain.
Should it charge the same price for a family whose power comes
from the hydroelectric generator as it does for a family whose
power comes from the steam generator?
Government’s goal is to maximized the total economic surplus.
Total economic surplus is maximized when market price equals to
the MC.
According to low-hanging-fruit principle, the government should first use
the cheapest source, e.g., hydroelectric generator. Only when the quantity
demanded exceeds the units that hydroelectric generator could provided,
the city will turn to the next least expensive source, e.g., steam generator.
Total demand for electricity is 200 units per day.
It is 100 units per day more than it could be supplied by
hydroelectric generator.
Therefore, Steam generator was needed to supply the extra 100
units per day.
All marginal contributions to supply after 100 units per day must
come from steam generator, and the marginal cost of steam
generator is 10 cents per unit.
Therefore, the city should charge 10 cents per unit for electric
power since that is the marginal cost when residents use at least
100 units per day.
The government should charge the same price, 10 cents per unit, to
all users, even those who are receiving their power from the less
expensive supplier, the hydroelectric facility.
If those hydroelectric users were to cut their 100 units of
consumption, they would free up 100 units of hydroelectric capacity.
The cut back of their electricity consumptions will enable the city to
divert that 100 units of power per day to some other households
that are currently getting its electricity from steam generator for
which the cost of production is high, 10 cents per unit.
By diverting the 100 units of power, it will decrease the consumption
of steam generator by 100 units of power. The cost of saving from
steam generator is exactly equal to 10 cents per day, the marginal
cost of electricity.
That is, Resources are used efficiently.
If government charges the hydroelectric generator consumers at
price less than 10 cents per unit, say, 1 cents per unit, they will
expand their usage until the MB equals exactly the MC. They will
“over use” the city’s electricity.
Resources are used inefficiently.
That unit of electricity could have been used to serve the consumers
who are currently using the steam generator, 10 cents per unit.
Thus, it leads to a loss in economic surplus of 9 cents per unit if set
price at 1 cent per unit.
Chapter 7 Problem 8
8) Phil’s demand curve for visits to the Gannett walk-in medical clinic is
given by P = 48 – 8Q, where P is the price per visit in dollars and Q
is the number of visits per semester. The marginal cost of providing
medical services at Gannett is $24 per visit. Phil has a choice
between two health policies, A and B. Both policies cover all the
costs of any serious illness from which Phil might suffer. Policy A
also covers the cost of visits to the walk-in clinic, whereas policy B
does not. Thus, if Phil chooses policy B, he must pay $24 per visit
to the walk-in clinic.
Phil’s Demand Curve
P ($/visit)
48
P = 48 – 8Q
24
Q (visits/semester)
a) If the premiums the insurance company charges for policies A and B
must cover their respective costs, by how much will the two premiums
differ, and what will be the difference in Phil’s total expenditure for
medical care under the two policies?
Policy A covers the cost of visits; Policy B does not.
Therefore, the premiums will be differ by the numbers of visiting the clinic.
P ($/visit)
48
P = 48 – 8Q
•At P=$24/visit, Phil will demand 3
visits/semester.
•At P=$0/visit, Phil will demand 6
visits/semester.
Phil will make 3 more
visits/semester to the clinic at
P=$0/visit (policy A).
24
3
6
Q (visits/semester)
• Phil will make 3 more visits/semester to the clinic at P=$0/visit
(policy A).
• Phil’s total expenditure on medical care (insurance premiums
plus payments for office visits) will thus differ by the cost of
those three extra visits, namely $72/semester.
• Since policy A covers the cost of visit, it has to reimburse the
cost of 6 visits. The premium under policy A will be
(6visit/semester)($24/visit) = $144/semester, greater than
policy B’s.
b)
•
•
•
•
•
Which policy will Phil choose?
MB>MC
Policy A and B differ by the 3 extra visits.
Under Policy A:
His extra expense to the 3 extra visits is 3($24/visit), $72/semester.
His value to the 3 extra visits is the area of ABC (consumer surplus at
P=0), $36/semester.
Since that is less than his extra expense under policy A, he will choose
policy B.
P ($/visit)
48
P = 48 – 8Q
A
24
B
3
C
6
Q (visits/semester)
c) What is the most Phil would be willing to pay for the right to continue
buying that policy?
•
Consumer surplus, difference between a buyer’s reservation price and the
price actually paid.
•
•
Policy B, he visits up to 3 visits/semester and needs to pay the $24/visit.
His reservation price up to 3 visits/semester is $48/visit. The cost of visit is
$24/visit.
Therefore, the most that Phil would be willing to pay for the right to continue
buying policy B is $36/semester.
•
P ($/visit)
48
P = 48 – 8Q
24
3
6
Q (visits/semester)
End of Chapter 7

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