Download Evans School of Public Affairs, Mark Long PBAF 516

Evans School of Public Affairs, Mark Long
PBAF 516: Microeconomic Policy Analysis
Problem Set 6 -- Answers
Market Failures – Noncompetitive Markets, Public Goods, Externalities, Asymetric Information
1. Suppose there are two firms in an industry. Discuss why the prisoner’s dilemma is likely to be faced
by these oligopolists when they decide on the prices to set. Discuss why it is in the interest of society
to prevent the two firms from colluding and setting one price for their good.
If the two oligopolists set prices together, they could effectively work like a monopolist (they would
face one demand curve and would choose to produce at Qm, where MR = MC). They would both
charge a high price and produce a quantity of output that below the socially optimal amount Q*
(where P=MC). However, if they are playing this game for one time period, it is in both firms’
interests to cheat by lowering their price below the agreed upon price. As such, (high P, high P) is
not a Nash equilibrium. However, (low P, low P) is a Nash equilibrium – so long as my rival is
charging a low price, it is in my interest to charge a low price. If I charge a high price, I will get no
customers.
In a repeated game, the oligopolists may be able to maintain (high P, high P) by the threat of
retaliation – that is, if you lower your price, I will do so as well and we’ll both be punished for a
period of time – thus, I can make it worthwhile for my competitor to maintain a high price. Since this
form of collusion would keep output below the social optimum, it is in society’s interest to ban
collusion.
2. For each of the public programs below, list what market failures might be (or are) used as partial
rationale for having the program:
The rationales are debatable for a) and f)
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
Automobile safety belt requirements – externalities?
Regulations on automobile pollution – externalities
Ballistic missile defense shield – public good
Unemployment compensation – eliminates adverse selection
Medicare (medical care for the aged) – eliminates adverse selection
Medicaid (medical care for the indigent) – eliminates adverse selection?
Federally insured mortgages – might help to reduce informational problems
Law requiring appliances to disclose energy usage – provides information (public good)
National Weather Service – provides information (public good)
Imposing marketing constraints on Microsoft – controls a monopoly
Operating the Hubble space telescope – provides information (public good)
3. A firm has proposed to build an ugly factory right on the banks of a beautiful river in town. The town
has 10,000 citizens who all value the view of the river at $100 each. The factory will provide
$900,000 of profit for the firm. The city is trying to decide whether a zoning law should be passed to
outlaw the construction of the factory.
a. Assume that there are no transaction costs. If the city rules that the firm has a right to construct
the factory, will it choose to construct it? Fully explain your answer.
This is an example of a situation where the Coase theorem can be used. The people of the town
will choose to pay the firm not to build the factory since their combined value of the river exceeds
Evans School of Public Affairs, Mark Long
PBAF 516: Microeconomic Policy Analysis
the value of the factory to the firm. The total payout will be something between $900,000 and
$1,000,000.
b. How will your answer to part (a) change if the city rules that the firm does not have the right to
build the factory? Explain.
The firm will not build the factory since it cannot offer enough money to sway the public’s
decision.
c. Explain how the introduction of transaction costs could affect the answers to parts (a) and (b).
If the transaction costs were sufficiently high, the total cost of the payout and the transaction
itself may exceed the benefit to the town. They may not find it beneficial to try and dissuade the
firm from building the factory in part (a). There will be no change to the answer to part (b).
d. What are examples of transaction costs that may be relevant for this situation?
The fact that the benefit of the view is spread over so many people may make it prohibitively
costly for individuals to get together and make the necessary bargaining agreement to keep the
firm from building the factory.
4. Suppose there are two groups in a community. They have different demands for public television.
Their demand curves are the following:
Group 1: P = $150-Q
Group 2: P = $250-Q
Q is the number of hours of public television programming.
a. Explain why broadcast television is a public good (ignoring cable television).
Television is a public good, because once it is broadcasted, it can be viewed by anyone without
limiting another's consumption (i.e. non-rival) and anyone with an antenna can view it (i.e. nonexcludable).
b. On one graph, plot both groups' demand curves.
Evans School of Public Affairs, Mark Long
PBAF 516: Microeconomic Policy Analysis
$
400
SMB
250
200
150
S
Market D
50 100 150 250
Q
c. If the price is $200, how much is the total demanded?
50 hours by group 1.
d. If the price is $100, how much is the total demanded?
150 hours by group 1 and 50 hours by group 2.
e. Sketch the market demand curve on your graph. (See Dark Solid Line Above)
f. Suppose that public television can be produced at a constant marginal cost of $200 per hour. Plot
the market supply curve on your graph. (See S Line Above)
g. How much would be produced by the private market? What is the social value of this
production? Does social marginal cost equal social marginal benefit?
The private market would only produce 50 hours (paid for by group 1). The marginal benefit at
50 hours is $200 for Group 1 and $ 100 for Group 2 (who free-rides). The social marginal
benefit is the sum of these, $300. SMB > SMC, which means the market underprovides the public
good.
h. On the same graph or a new one, plot the total social marginal benefit curve. (See Dark Dashed
Line Above).
i. What is the efficient number of hours of public television?
SMB = (150-Q) + (250-Q) = 400 – 2Q
SMC = 200
SMB = SMC
400 – 2Q = 200
200 = 2Q
100 = Q
Evans School of Public Affairs, Mark Long
PBAF 516: Microeconomic Policy Analysis
5. Suppose that demand and supply for barrels of oil is given by the following equations:
Demand:
Supply:
a)
P = 120 – (2/3)Q
P = 30 + (1/3)Q
Compute the equilibrium price and quantity.
120 – (2/3)Q = 30 + (1/3)Q
90 – (2/3)Q = (1/3)Q
90 = Q
P = 120 – (2/3)90
P = 60
b) Suppose that there exists a $30 negative externality per barrel of oil. The government, however,
over-estimates this externality and places a $45 per barrel tax on consumers of the oil. Compute the
change in social surplus as a result of the subsidy. Is society better off after the tax is imposed?
Compute the consumer and producer shares of the tax. Explain why one group pays a larger share of
the tax burden.
P
Supply with
Tax
SMC = PMC +
Externality
120
S = PMC
New
DWL
Original
DWL
75
60
30
SMB
Qtax=45 Q*=60
Qe = 90
180
SS = CS + PS + Positive Externalities – Negative Externalities + Tax Revenues – Government
Expenditure
Under the original market equilibrium:
CS = ½ (120-60) (90) = 2700
PS = ½ (60-30) (90) = 1350
Neg. Ext. = 90*30 = 2700
SS = 2700 + 1350 + 0 – 2700 + 0 – 0 = 1350
Q
Evans School of Public Affairs, Mark Long
PBAF 516: Microeconomic Policy Analysis
Next, calculate the equilibrium with the tax. It is a bit easier to do this adding the tax to the supply
curve (although you would get the same results subtracting the tax from the demand curve).
New supply curve = PMC + tax
Demand:
Supply:
P = 120 – (2/3)Q
P = 30 + (1/3)Q + 45 = 75 + (1/3)Q
120 – (2/3)Q = 75 + (1/3)Q
45 – (2/3)Q = (1/3)Q
45 = Qtax
Pconsumer = 120 – (2/3)45
Pconsumer = 90
Psupplier = Pconsumer - Tax
Psupplier = 90 – 45 = 45
Under the market equilibrium with the tax imposed:
CS = ½ (120-90) (45) = 675
PS = ½ (45-30) (45) = 337.5
Neg. Ext. = 45*30 = 1350
Tax Rev. = 45*45 = 2025
SS = 675+ 337.5 + 0 – 1350 + 2025 – 0 = 1687.5
Social surplus has increased by $337.50 – thus, society is better off after the tax is imposed
(however, we could even be better off if the tax were reduced to $30).
****
An alternate way to solve for the change in social surplus is by calculating the change in DWL:
First compute the socially efficient quantity Q*. Q* is where SMC = SMB.
SMC
= PMC
+ Negative Externality
= 30 + (1/3)Q + 30
= 60 + (1/3)Q
SMC
60 + (1/3)Q
Q* = 60
= SMB
= 120 – (2/3)Q
Now, compute the deadweight loss of the original equilibrium.
At Qe = 90, SMB = 60 and SMC = 90
DWL = ½ (Qe – Q*) (SMC at Qe – SMB at Qe)
DWL = ½ (90 – 60) (90 – 60)
DWL = 450
Evans School of Public Affairs, Mark Long
PBAF 516: Microeconomic Policy Analysis
Now, compute the deadweight loss of the tax equilibrium.
At Qtax = 45, SMB = 90 and SMC = 75
DWL = ½ (Q* – Qtax) (SMB at Qtax – SMC at Qtax)
DWL = ½ (60 – 45) (90 – 75)
DWL = 112.5
The change in DWL = 112.5 – 450 = – 337.5. This result tells us that SS increased by $337.50.
****
The price to the consumer rises from $60 to $90 per barrel. The price to the suppliers falls from $60
to $45 dollars per barrel. Thus, consumers bear $30 of the tax, and suppliers bear the remaining
$15 of the tax per barrel. Consumers pay a higher share of the tax burden because demand for oil is
more inelastic than supply.
Browning and Zupan Problems:
15.4
A lump-sum tax would have no effect on a monopolist’s output and price decision (assuming that
the tax did not cause the monopolists profits to fall to a negative amount), but would come out of
the firm’s profit. This is because the lump-sum tax does not affect the monopolist’s MC curve.
15.12
a)
b)
c)
d)
e)
A: Medium, B: Low. This yields a total value of $130.
No. Given A chooses Medium, B will want to alter its output to medium or high.
A does not have a dominant strategy. For B, High is a dominant strategy as B’s payoffs
are highest when playing High regardless of A’s strategy.
The only Nash equilibrium is (High, High). There is no incentive for either firm to switch
away from that choice once there. It does not maximize the total value from the oil field
since the total value is only $80. The total value of the field is maximized when A chooses
Medium and B chooses Low, for a total value of $130.
Yes. A is willing to pay B up to $65 if B were to produce Low -- if B produces Low, A will
produce Medium (which raises A's profit from $60 at the Nash Equilibrium to $125).
Moving from the Nash Equilibrium (High, High) to (Medium, Low) lowers B's profits by
$15 (from $20 to $5) – thus, B needs a payment of at least $15 to be enticed to agree to
this combination of strategies. A mutually beneficial exchange could occur with A paying
B between $15 and $65 for B to produce Low.
Given the Nash Equilibrium payout of $20, B would be willing to sell the
company if they received more than $20. If A owned the company, they would get $130,
rather than their current $60. Thus, A is willing to pay B up to $70 for the company. The
feasible transaction would have A pay B between $20 and $70 for the company.