chapter 7 efficiency and exchange even-numbered qs
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Chapter 7Efficiency 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.
• 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 and Deadweight loss
P
PE
QE Q
D
S
•Tax on producers can be viewed as a "cost of doing business" for the producers
•The supply curve shifts to the left, S+T
•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
•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
S+T
P1
Q1
T
•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
P2
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)
P
Q
S
QE
EPE
D
S +T
P’
P”
consumers
producers
Q’
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)P
QD
S
QE
EPE
S + T
P’’
P’
Q’
Consumers
Producers
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?
P
Q
D
S
QE
EPE
T
P’
P’’
Q’
P
QD
S
QE
EPET
P’
P’’
Q’
•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
S’S’
How much deadweight loss?
P
Q
S
QE
EPET
P’
P’’
Q’
P
Q
S
QE
EPET
P’
P’’
Q’
D D
S’
S’
•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 loss
How much deadweight loss?
P
Q
S
QE
EPE = P’
P’’
Q’
D
Perfectly Elastic Demand:Producers bear all tax burden
S”
T
Perfectly Elastic SupplyConsumers bear all tax burden
P
Q
S
QE
EPE = P’’
TP’
Q’
D
S’
• If Demand or Supply curve is perfectly elastic or inelastic, only one party will bear all the tax burden.
Tax
Tax
How much deadweight loss?
P
Q
S
Q’ = QE
EPE = P’
TP’’
D
Perfectly inelastic SupplyProducers bear all tax burdenDWL equals to zero
Perfectly Inelastic Demand:Consumers bear all tax burdenDWL equals to zero
P
Q
S
QE
EPE = P’’
T
Q’ =
DS”
P’
Tax
Tax
The concept of efficiency is illustrated by which of the following statements?
A) The production of the good generates very little pollution.B) At equilibrium, all mutually beneficial transactions have
taken place.C) The production of the good generates very few by-
products.D) The consumption of the good produces very little waste.E) At disequilibrium, no mutually beneficial transactions have
occurred.
Additional Question #1
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 AfricaHK 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.
Compared to the first-come-first-served allocation scheme airlines used in the past, the voluntary compensation scheme now in place
A) Discriminates against the poor.B) Improves efficiency for only the wealthy.C) Tricks the poor into unnecessarily delaying their travel.D) Improves efficiency for all travellers.E) Encourages passengers to show up early.
Additional Question #2
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-come-first-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.
• 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.
A 1:00pm $5
B 1:05pm $4
C 1:30pm $10
D 2:00pm $20
• 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.
Demand for cigarettes is price inelastic for adults, but price elastic for teenagers. Therefore, a tax on cigarettes will
A) Not raise very much tax revenue.B) Not generate deadweight loss.C) Generate more tax revenue from adults and have a greater
effect on the number of cigarettes smoked by teenagers.D) Have a greater effect on the number of cigarettes smoked
by adults than by teenagers.E) Generate more tax revenue from teenagers than from
adults.
Additional Question #3
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
Q
DAdults
DTeenagers
S
S’
Tax revenue from Adults
Tax revenue from Teenagers
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) The tax on consumers would generate more deadweight loss.
B) The burden of the tax on consumers would be more equally shared between consumers and producers.
C) Consumers would bear a greater share of the tax burden.D) The effect on deadweight loss and tax burdens would be
the same.E) The price paid by consumers would increase by more.
Additional Question #4
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.
• Hence, D.
P rice 9 S u pp ly p lu s tax 8 7 S u pp ly 6 5 4 3 2 1 D em an d
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 U n its per day
A tax on Commodity A will generate ? deadweight loss relative to an equivalent tax on Commodity B.
A) MoreB) LessC) EqualD) ZeroE) An in determinate amount of
Additional Question #5
Ans: B
Commodity A Commodity B
PA
QA
PB
QB
SA SB
DA
DB
Tax
SA’ SB’
• 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 22) 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.
12
10.5
6 18 48
7.5
2
6
Quantity (DVDs/week)
Pri
ce (
$/D
VD
)
S
D
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 $7.50.
Therefore, the weekly shortage of used DVDs result from the price ceiling policy is 16 DVDs per week.
b) Calculate the total economic surplus lost every week as a result of the price ceiling.2 methods to find the lost in economic surplus.
12
10.5
18 48
7.5
2 6
6
Quantity (DVDs/week)
Price ($/DVD)S
D
12
10.5
18 48
7.5
2 6
6
Quantity (DVDs/week)
Price ($/DVD)
x
S
D
x
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.
12
10.5
18 48
7.5
2 6
6
Quantity (DVDs/week)
Pri
ce (
$/D
VD
)
S
D
Weekly economic surplus lost is the area of the shaded triangle.
x
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 – 0.25QAt Q = 2, P = 12 – 0.25(2)
P = 11.5Weekly economic surplus lost is,(11.5 – 7.5)(6-2) (1/2) = $8/wk
Economic surplus
lost
Method 2: With price ceiling of $7.50, sellers will sell only 2 DVDs/wk.
12
10.5
18 48
7.5
2 6
6
Quantity (DVDs/week)
Price ($/DVD)S
D
Without Price ceiling, sellers sell 6 DVDs at P = $10.5 . Consumer surplus: $4.5/wkProducer surplus: $13.5/wkTotal Economic Surplus = $18/wk
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/WKProducer surplus: (7.5-6)(2) (1/2) = $1.5/wkTotal Economic Surplus = $10/wk
11.5
Therefore, total economic surplus lost as a result of price ceiling is,$18/wk - $10/wk = $8/wk
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.
Chapter 7 Problem 4
P = 2 + Q
P = 8 - Q
Pri
ce (
$/u
nit
)
Quantity (1000s/wk)
8
2
P*
Q* 8
a) Calculate the total weekly economic surplus generated at the market equilibrium.
P = 2 + Q
P = 8 - Q
Pri
ce (
$/u
nit
)
Quantity (1000s/wk)
8
2
P*
Q* 8
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
P = 8 - Q
Pri
ce (
$/u
nit
)
Quantity (1000s/wk)
8
2
5
3 8
C.S
P. S
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 = 2 + Q
P = 8 - Q
Pri
ce (
$/u
nit
)
Quantity (1000s/wk)
8
2
5
3 8
S’ P = 4 + Q
4
Tax
P**
Q**
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 + QAt equilibrium, SC = DC4 + Q = 8 – Q
Q** = 2P** = 6
The new equilibrium price, P** = $6/unitThe new equilibrium quantity, Q** = 2,000 units/wk
P = 2 + Q
P = 8 - Q
Pri
ce (
$/u
nit
)8
2
5
3 8
S’ P = 4 + Q
4
Tax
6
2
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.
CS
PS
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.
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
P = 2 + Q
P = 8 - Q
Pri
ce (
$/u
nit
)
Quantity (1000s/wk)
8
2
5
8
S’ P = 4 + Q
4
Tax
6
2 3
Deadweight loss
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.
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.
Chapter 7 Problem 6
a) Draw the marginal cost curve of electric power production in Charlotte.
Pric
e (c
ents
/uni
t)
Units of power per day
10
100
1
Hydroelectric
Steam
Marginal cost of power
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.
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 $24 per visit to the walk-in clinic.
Chapter 7 Problem 8
P ($/visit)
48
Q (visits/semester)
24
P = 48 – 8Q
Phil’s Demand Curve
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
Q (visits/semester)
24
P = 48 – 8Q
•At P=$24/visit, Phil will demand 3 visits/semester.•At P=$0/visit, Phil will demand 6 visits/semester.
3 6
Phil will make 3 more visits/semester to the clinic at P=$0/visit (policy A).
• 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.
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
Q (visits/semester)
24
63
P = 48 – 8Q
A
CB
b) Which policy will Phil choose?
P ($/visit)
48
Q (visits/semester)
24
63
• 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 = 48 – 8Q
c) What is the most Phil would be willing to pay for the right to continue buying that policy?
End of Chapter 7