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The Economics of Regulation:
Answers to Problems
Eric Rasmusen
April 27, 2013
http://rasmusen.org/g406/reg-rasmusen.htm, erasmuse@Indiana.edu
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Problems
(Answers at http://rasmusen.org/g406/999-answers.pdf )
Chapter 1: Markets
1. Why are well-defined property rights useful for surplus maximization?
Include at least two reasons in your answer.
Answer. Property rights encourage people to create goods because
they retain the benefit of their effort. They also discourage the unproductive rentseeking of people who compete to take goods by stealth or
force and the unproductive defensive efforts to counter such people.
2. If demand is given by Q = 12 − P and supply is given by Q = P , what
is the equilibrium quantity?
Answer. Then 12 − P = P , so P = 6, so Q = 6 also.
3. Suppose demand for widgets is given by Q = 24 − P , and supply is
given by Q = 3(P − 4) if the price exceeds 4 and Q = 0 otherwise.
(a) Draw the curves and calculate the equilibrium price and quantity
(not necessarily to scale, but showing the shapes and labelling the
values where the curves cross the axes).
Answer. The equilibrium is found from 24-P = 3(P-4), so24 −
P = 3P − 12, so36 = 4P and P = 9. Then Q=15. The supply
curve cuts the axis at (Q=0, P=4) and the demand curve at (Q=0,
P=24) and (Q=24, P=0).
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(b) If the government forbids sale of widgets at a price of less than 12,
what is the change in producer surplus? Give a numerical answer.
Answer. If P=12, sales are from the demand curve, at Q =
24 − P = 12. The original producer surplus is area A+B+C. This
has height (9-4) and width 15, so its area is .5(5)(15) = 37.5.
The new producer surplus is area A+B+D. If Q=12, the price on
the supply curve is found from 12= 3(P-4), so 12=3P-12 and P=8.
Thus, area A = .5(8-4)(12) = 24 and areas B+D= (12-8)(12) =
48 and the total producer surplus is 24+48=72. That means the
increase is 72-37.5 = 34.5.
4. Show on a supply-and-demand diagram the deadweight loss if the federal
government required the price of health insurance to drop at least 10%
below the current market price.
Answer. This is a price ceiling, quantity traded will drop, resulting in
the deadweight loss of L shown in the diagram.
5. Suppose the monopoly in the diagram below chose a price of 25.
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(a) What would be the deadweight loss from allocative inefficiency?
Answer. The deadweight loss is .5(25-10)(30-15) = .5(15)(15)= 112.5.
(b) What would be the consumer surplus if the price were 10?
Answer. The consumer surplus at a price of 10 would be .5(40-10)(300) = 450.
6. Suppose a city imposes a price floor on hamburgers sold at restaurants.
(a) On a diagram show the resulting loss of total social surplus if rationing is efficient.
Answer. The loss in surplus will be Z+X after the price rises from P0
to P1. Producer surplus will rise to V+Y. The lowest-cost firms will
produce— those with costs between C0 and C1.
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(b) Explain how the loss of total surplus would change if rationing were
inefficient.
Answer. The loss would increase. Some of the firms with costs between C0 and C1 would not be able to find buyers, and instead some of
those firms with costs between C1 and P0 will produce. Those high-cost
firms won’t earn as high a surplus, so total surplus will fall.
7. This question is left blank.
8. A regulation adds $1,000 and $500 to the incomes of Smith and Jones,
but subtracts $300 and $600 from the incomes of Lee and Brown. According to surplus maximization, the result is
(a) A definite improvement.
(b) A definite worsening.
(c) Neither an improvement nor a worsening.
(d) Both an improvement and a worsening.
9. If we assume efficient rationing instead of inefficient rationing, how do
surplus under a minimum wage change?
(a) Employer surplus rises and worker surplus falls.
(b) Employer and worker surplus fall.
(c) Employer and worker surplus rise.
(d) Employer surplus falls and worker surplus rises.
(e) None of the above.
10. Let supply be Q = 12+P and demand be P = 32−Q. The equilibrium
price is
(a) Less than 1
(b) 1.1-3.
(c) 3.1-8.
(d) 8.1-12.
(e)More than 12
Chapter 2: Market Failure
1. Why does the equilibrium output in a market with a negative externality
not maximize total surplus?
Answer. If there is a negative externality, then the social marginal
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cost is greater than the private marginal cost. The sellers will look
only at the private marginal cost, and in equilibrium that equals the
marginal benefit to consumers. If output were reduced, total surplus
would rise because the social marginal cost at the competitive output
is greater than the marginal benefit to consumers.
2. What is the difference between a value curve and a demand curve?
Answer. The value curve’s height measures the actual benefit the consumer receives from buying a unit of a product— the amount he would
pay if he were perfectly-informed— while the demand curve shows how
much he is willing to pay in his current state of information.
3. In a neighborhood of homes with small children, Smith builds a concrete
swimming pool in his backyard. Explain why this could simultaneously
create both positive and negative externalities.
Answer. There will be excess demand, and if rationing is inefficient
then some of the consumers who cannot find a willing provider of a
transplant will value the transplant more highly than some of the consumers who do succeed in finding a provider.
4. If unregulated, paper manufacturing creates water pollution. Suppose
that if paper sales are Q then the cost of the water pollution to people
downstream is 3Q, and that supply and demand take their conventional
moderately price-elastic shapes.
(a) Draw a diagram to show the levels of paper sales under laissez faire
equilibrium and under optimal regulation.
Answer. The cost of the water pollution to people downstream is 3 per
unit of paper sold; if amount Q is sold, the cost is 3Q. Thus, the social
cost is always 3 higher than the supply curve, as shown in the diagram
above. The supply and demand curves take their typical shapes, neither
being perfectly elastic (flat). The initial output is where the supply and
demand curves cross, Q(no reg.). The optimal regulation would reduce
sales to Q(reg.), where the marginal social cost crosses the demand
curve.
(b) Show how much total surplus increases going from laissez faire to
optimal regulation, and how the total cost of water pollution changes.
Answer. Total surplus increases by area C going from laissez faire to
optimal regulation, because the units between Q(reg) and Q(no reg.)
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have a social cost in excess of the their social benefit, the height of the
demand curve. The pollution cost to third parties is the area between
the social cost curve and the supply curve. That is area A+B+C under
laissez faire, since output is Q(no reg.), and it falls to area A under
regulation.
5. Explain how a regulation that ends up reducing sales of a product could
increase total surplus. Assume that the good has no externalities.
Answer. Suppose the good has lower quality than consumers believe.
For convenience, suppose it has zero value. It still is costly to produce,
so the marginal benefit is less than the marginal cost and a reduction
in sales will increase surplus.
6. If killing cockroaches has positive externalities, the market failure is
that
(a) Cockroaches will be eliminated too soon.
(b) Too few cockroaches will be killed.
(c) City regulation will be imposed on restaurants so they are forced
to kill more cockroaches than is efficient.
(d) People will not know that they should kill cockroaches.
(e) None of the above.
7. Using a diagram, show the deadweight loss if consumers systematically
underestimate the value of a product, valuing it at 80% of its true worth
to them. Explain in words why that area is lost surplus.
Answer. The value curve always gives a value 80% of the demand
curve height. In ignorance of this, consumers buy too little. The shaded
area is lost surplus because it represents the excess of the true benefit
to consumers of consuming more over the cost to producers. I gave
credit for either flat or upward-sloping supply curves.
[The diagram is not in the answer file yet.]
Note that even at the lower quantity, the consumer surplus is measured
using the value curve, not the demand curve. The consumers decide
how much to buy using their estimated demand curve, but their actual
satisfaction is given by the value curve.
Chapter 3: Government Failure
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1. Read the Huffington Post’s “Chicago Food Trucks: City Council Overwhelmingly Approves Mayor’s Ordinance,” http://www.huffingtonpost.com/
2012/07/25/chicago-food-trucks-alder 0 n 1701249.html.
(a) What effect would banning food trucks have on the supply and demand curves for fast food?
Answer. It would shift back the supply curve, but leave the demand
curve unaffected. (Even better: it might shift in the demand curve too,
since there would be less selection for consumers.) Or, you might have
talked about the market for brick-and-mortar-restaurant food. In that
market, the demand curve would shift out.
(b) Why might we expect government failure in the regulation of food
trucks?
Answer. Restaurant owners will be more politically aware than food
truck owners. Consumers will be rationally ignorant, not paying very
much attention to regulation. Thus, the political forces will be weighted
toward regulation to help restaurant owners even if that hurts consumers more.
It was not a correct answer to say “because the regulation will reduce
surplus”. That is the definition of government failure. The question
here is why government failure would occur: why the government would
impose regulations that do not maximize surplus.
(c) Think of some form of market failure that restaurants could use as
an excuse to justify the banning of food trucks.
Answer. Think of some form of market failure that restaurants could
use as an excuse to justify the banning of food trucks. Answer. If the
safety of the food from trucks cannot be monitored well enough by the
city health department, that could be a reason to ban them. Or, if
they create congestion in the streets.
The fact that food truck competition drives down restaurant profits is
NOT market failure. That is how the free market works to maximize
surplus. Any profits lost by the restaurants are gained by the food
trucks or by consumers. This is a very important point.
2. The function of the Office of Management and the Budget in making
pollution regulations is
(a) Nothing.
(b) It writes the first draft.
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(c) It reviews the drafts written by the Environmental Protection Agency.
(d) It makes public comment on every regulation so as to give the
President’s view.
3. Government failure in making a regulation is most likely when
(a) Its costs are short-run and its benefits are long-run.
(b) Its costs and benefits are both short-run.
(c) Its costs and benefits are both long-run.
(d) Its costs and benefits are both extremely clear.
4. Explain how the ideas of the tyranny of the majority and rational ignorance are alike and unlike each other.
Answer. The idea of the tyranny of the majority is that the majority
of voters in a democracy can impose their will on the minority. The
idea of rational ignorance is that voters will not become informed about
their vote unless they think it is worth the cost to become informed,
and so will often remain ignorant. Both of these things lead to government failure, but in different ways. The problem with the tyranny of
the majority is that a policy will pass a vote even if it hurts the minority
more than it helps the majority. The problem with rational ignorance
is that even the majority might vote the wrong way, or not vote at all, if
the voters do not bother to become informed. The problem of rational
ignorance will often lead to something like “tyranny of the minority”,
because the minority will often have more concentrated interests and
thus more incentive to become informed than the majority.
5. When the federal government makes a regulation,
(a) It announces and starts enforcing the regulation, but it allows comment.
(b) It announces and start enforcing the regulation, but does not allow
comment for 60 days.
(c) It announces the regulation and starts enforcing it, but only the
OMB may comment.
(d) It announces a regulation but does not start enforcing it
till after a public comment period.
(e) None of the above.
6. The incentives of the agency setting electrical standards for wiring in
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new houses will lead it to
(a) Overly strict requirements.
(b) Overly lax requirements.
(c) Overly rapid changes in requirements.
(d) Impose higher requirements on the party not in office.
(e) Impose lower requirements on foreign firms.
7. Every regulation must be reviewed by the
(a) SEC.
(b) OMB.
(c) CEA.
(d) Dept. of Justice.
(e) White House.
8. The government’s Center for Disease Control’s incentives are likely to
lead it to
(a) Say that the risk of swine flu is less than it really is.
(b) Say that the risk of swine flu is greater than it really is.
(c) Ignore swine flu.
(d) Blame swine flu on the Democratic Party.
(e) Blame swine flu on the poor handwashing habits of the average
American.
Chapter 4: Time, Life, and Taxes
1. The average rate of inflation from 1926 to 2011 was closest to which
number?
(a) 2%.
(b) 3%.
(c) 5%.
(d) 7%.
(e) 10%.
2. Let the supply curve be P = Q and the demand curve be P = 24 − 2Q.
(a) If a tax of 3 per unit is imposed on buyers, what is the change in
the equilibrium price and quantity, producer and consumer surplus and
revenue?
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Answer. First, figure out what happens if there is no tax. Equating
supply and demand, P s = Qs so
Qs = 24 − 2Qd ,
so Q=8. In that case, using either demand or supply, P=8 too.
The producer surplus is .5(8-0)(8)=32 and the consumer surplus is .5
(24-8)(8) = 64. Total surplus is 96.
Next, figure out what happens if a tax of 3 is imposed on buyers. The
demand curve will shift in, towards zero– with the tax, they’re less
eager to buy. A good way to think about it is to ask at what price
they’ll demand exactly Q=0. Before, that was at P=24. Now, they
have to pay the tax of 3, so even if the price is 3 lower, at P=21,
they’ll demand zero. Thus, it must be that the new demand equation
is P d + 3 = 24 − 2Qd , so P d = 21 − 2Qd , so if Q=0, P=21.
Equate supply and demand using the new demand curve, so
Qs = 21 − 2Qd
and Q=7. That means P=7 too, since P s = Qs . As a result, PS =
.5(7)(7) = 24.5, and CS = .5(21-7)7 = 49. Tax revenue is the tax of
3 per unit times the output of 7, so it equals 21. Adding those three
things up yields 94.5 in total surplus. That’s down by 1.5 from the
pre-tax surplus, so the deadweight loss is 1.5.
(b) If a tax of 3 per unit is imposed on sellers instead, what is the
result?
Answer. Now let’s put the tax on the seller. The supply curve will
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shift, because sellers are less eager to sell. Before, if the price rose above
0, there’d be positive supply. Now, since they have to pay the tax of
3, quantity supplied would be zero at that price. The price has to rise
to 3 before quantity supplied becomes positive. So now, P s − 3 = Qs ,
so P s = Qs + 3 and if P=3, Q=0.
Equate supply and demand using the new demand curve so
Qs + 3 = 24 − 2Qd
and Q=7. Using the supply curve, P = 7 + 3 = 10.
Producer surplus is .5(10-3)(7) = 24.5. Consumer surplus is .5 (2410)(7) = 49. Government revenue is (3)(7)=21. So everything is the
same as with the tax being on buyers, including total surplus of 94.5
and deadweight loss of 1.5.
3. The after-inflation return on Treasury bills from 1926 to 2011 was closest to which number?
(a) 0%.
(b) 1%.
(c) 2%.
(d) 3%.
4. Market demand is Q=12-P and market supply is Q=2P. To cover the
costs of pollution cleanup, a tax of $1/unit is imposed, to be paid by
the sellers out of their sales revenue. How much will the prices firms
charge rise or fall?
Answer. In the pretax equilibrium, 12-P=2P, so P=4. After the tax is
imposed, the sellers receive only P-1 per unit sold, not P, so the supply
curve changes to Q= 2(P-1). Equating this to the demand curve, 12P=2(P-1) so 12-P = 2P-2, 14 = 3P, P = 4 2/3. The price has risen by
2/3.
5. The federal government chooses a discount rate for government bridge
projects that
(a) Equals the government’s cost of capital.
(b) Is lower than the government’s cost of capital.
(c) Is close to the private sector’s aftertax return on investment.
(d) Is close to the private sector’s pretax return on investment.
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6. If the total wages for crabfishing over 10 years are $3,000 higher than
wages in fishing jobs that have 1 in 1,000 fewer deaths over that time
period, the value of a statistical life for crab fishermen is
(a) Less than $5 million.
(b) Between $5 million and $8 million.
(c) Between $8 million and $20 million.
(d) More than $20 million.
7. How does the forensic approach to the value of life differ from the valueof-a-statistical-life approach?
Answer. Under the forensic approach, the analyst estimates the present
value of future earnings of the person. Under the statistical life approach he sees how much the person is willing to spend to avoid small
risks and uses the probability of those small risks to scale up to the
value of a life.
8. Suppose jam is initially untaxed, but then the Indiana General Assembly imposes a special sales tax of 3% on it, paid by the consumer at the
cash register.
(a) Show on a diagram how this affects the equilibrium price, and show
the triangle loss in social surplus.
Answer. The price falls from P0 to P1 . Total surplus falls by the
amount of the triangle A + B because of the smaller output. I have
drawn the new curve slanting because this is a percentage tax, so
strictly speaking it ought to swivel the demand curve— but I did not
expect you to include that detail.
(b) Next the General Assembly adds a 3% value-added tax on jam, paid
by the seller, while retaining the 3% tax on consumers. Show on a
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diagram what further effect this has on the equilibrium price and the
triangle loss.
Answer. The price will rise compared to with just the tax on buyers’
to P2. We can’t say how much— it could even rise above the original
price before any taxes were imposed. That depends on the shapes of
the supply and demand curves. It will definitely reduce output further,
though, and the triangle loss will increase by amounts C+D+E+F. You
can use the original supply and demand curve to find the lost surplus,
because they reflect the social benefit and the social cost of sales.
Chapter 5: Monopoly
1. The demand curve facing a firm is Q = 340 − 0.5P . You do not know
its marginal cost. It is currently charging P = 200. What advice can
you give the firm?
(a) It should raise its price.
(b) It should reduce its price.
(c) It should keep its price the same.
(d) Without knowing the marginal cost, it is unclear whether the firm
is pricing correctly or not.
2. The demand curve for widgets is Q=24-P. Marginal cost is constant at
4 and the fixed cost is 1. One firm has a monopoly.
(a) What price will the firm choose?
Answer. The demand curve can be rewritten as P = 24 − Q.P rof it =
P Q−4Q−1 = (24−Q)Q−4Q−1 = 24Q−Q2 −4Q−1. The derivative
of profit with respect to Q is 24 - 2Q -4. Setting that equal to zero,
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we get 20-2Q=0 so Q=10. From the demand curve, the price is then
P=24-Q = 14. Show your work for problems like this, so if you make
a mistake I can give you partial credit.
(b) Suppose the firm is taxed 2 per unit. How much would this raise or
lower social surplus?
Answer. The effect of a tax is similar to an increase in marginal cost.
Now the firm’s profit is P Q − 4Q − 2Q − 1 = (24 − Q)Q − 6Q − 1 =
24Q − Q2 − 6Q − 1. The derivative of profit with respect to Q is 24 2Q -6. Setting that equal to zero, we get 18-2Q=0 so Q=9. From the
demand curve, the price is then P=24-Q = 15.
Social surplus will fall, because the gains from trade on the units from
Q=9 to Q=10 are lost. The size of the loss is A+B in the diagram
below, which is .5(10−9)(15−14)+(14−4)(10−9) = .5(1)(1)+(10)(1) =
10.5. Note that area C wasn’t part of social surplus even before the
tax, because it is the original monopoly triangle loss.
3. Let the demand function be Q= 120-2P and the marginal cost function
be MC=20. Suppose there are two firms active in the market.
(a) Using the Cournot model, what will be the reaction function of Firm
1?
Answer. Note that P = 60-Q/2. Firm 1’s profit function is
P rof it = P Q1 −T C1 = [60−(Q1+Q2)/2)]Q1−20Q1 = 60Q1−
The first order condition is
60 − Q1 − Q2/2 − 20 = 0.
Q21
−Q2·Q1 /2−20Q1.
2
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Solving for Q1, we get Q1=40-Q2/2, which is the reaction function.
(b) What will be the equilibrium price?
Answer. Since the two firms are symmetric, so we can guess that
Q1=Q2. In that case, using the reaction function, Q1=40-Q1/2, so 1.5
Q1=40 and Q1 = 80/3. Then, P = 60 - (80/3+80/3)/2 = 60- 80/3 =
180/3-80/3 = 100/3 or 33.3333.
Beware of solving for the monopoly price instead of the duopoly price.
4. The demand curve facing a firm is P= 6 - 2/Q and its marginal cost
is MC=2Q.
(a) What is the monopoly output?
Answer. Marginal revenue is found from the demand curve, P= 6 Q/2. It is MR= P = 6-Q, sloping down twice as fast so it hits the
Q-axis half as far down as the demand curve does. Or,
M R = (dP/dQ)Q + P = (−.5)Q + (6 − Q/2) = 6 − Q.
Then MC=MR yields 2Q= 6-Q, so Q=2.
Or, you could find the Q that maximizes total profit. If the marginal
cost is 2Q, then the total cost is Q2. Having realized that, and ignoring
any possible fixed cost, profit is
P Q − T C = (6 − 2/Q)Q − Q2.
Differentiating with respect to Q and setting the derivative equal to
zero yields
6 − Q − 2Q = 0
so Q=2.
(b) At the monopoly output, would an increase of 1% in the price cause
revenue to rise, or to decline?
Answer. Revenue would decline. The decline in sales would be more
than 1%, because demand is always elastic at the monopoly price. A
firm with marginal cost of zero will maximize revenue, and so will
choose a price where the elasticity is -1, so any firm with positive cost
will choose a price that makes demand elastic. If revenue would rise
from a decline in quantity and an increase in price, the firm would have
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raised the price already, because that would both increase revenue and
reduce costs (because Q would fall).
You can see this from the Lerner Condition too, because it says that
at the monopoly price and output,
(P − M C)/P = −1/(elasticity)
Since P − M C < P , it must be that the elasticity is between −1 and
−inf inity, so it is elastic.
Or, you could see that (5 − 4)/5 = −1/5, so the elasticity is −5.
You could also compute out the actual elasticity, though I didn’t expect
that much detail. The elasticity is (dQ/dP) (P/Q). Rewriting demand
by solving the demand equation for Q we get Q = 12 − 2P . Thus,
dQ/dP = −2. If Q =2, then P=5, so the elasticity is (−2)(5/2) = −5,
very elastic.
5. How is the Prisoner’s Dilemma similar to the problem faced by duopolists?
Answer. In a Prisoner’s Dilemma, the dominant strategy is to Confess, yet (Confess, Confess) has the worst payoffs for both players.
Duopolists have a dominant strategy to choose high output and low
price, but that yields the worst profits for both of them.
6. The market demand curve is Q = 38 − P . There are two firms. One
firm has MC=1 and the other MC= 6. If they choose outputs simultaneously (the Cournot model), what outputs will they choose?
Answer. We can rewrite the demand curve as P = 38 − (Q1 + Q2 ).
Firm 1’s profit function is then P Q1 − 1 ∗ Q1 or
[38 − (Q1 + Q2 )]Q1 − Q1
Maximizing with respect to Q1 yields the first-order condition
38 − 2Q1 − Q2 − 1 = 0
which can be rearranged to give the reaction function
Q1 = 18.5 − Q2 /2.
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Firm 2’s profit function is P Q2 − 6 ∗ Q2 or
[38 − (Q1 + Q2 )]Q2 − 6Q2
Maximizing with respect to Q1 yields the first-order condition
38 − Q1 − 2Q2 − 6 = 0
which can be rearranged to give the reaction function
Q2 = 16 − Q1 /2.
Substituting this last expression into Firm 1’s reaction function yields
Q1 = 18.5 − [16 − Q1 /2]/2
which solves to Q1 = 18.5 − 8 + Q1 /4 so Q1 (3/4) = 10.5 and Q1 = 14.
Then, Q2 = 16 − 14/2 = 9.
7. The company Apex has a total cost of T C = 2 + 4A and the company
Brydox has a total cost of T C = B, where A and B are their outputs.
The market demand facing both firms is Q = 36−P , where Q = A+B.
(a) Find an equation for Apex’s reaction curve.
Answer. Apex’s profit function is
P rof it(Apex) = P A−T Ca = (36−A−B)A−2−4A = 36A−A2 −BA−2−4A = 32A−A2 −
Differentiating yields
dP rof it/dA = 32 − 2A − B = 0,
so 32-B = 2A and A= 16-B/2, which is the reaction function.
(b) Find Apex’s equilibrium output.
Answer. Brydox’s profit function is
P rof it(Brydox) = P B−T Cb = (36−A−B)B−B = 36B−B 2 −BA−B = 35B−B 2 −BA
Differentiating yields
dP rof it/dB = 35 − 2B − A = 0,
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so 35-A = 2B and B= 17.5-A/2, which is the reaction function.
Solving this with A’s reaction curve yields: A = 16 = B/2 = 16 −
(17.5 − A/2)/2 = 16 − 8.75 + A/4, so (3/4)A = 7.25 and A = 9.67.
(c) Show what a reaction curve diagram would look like for two firms
when one of them has MC=3 and the other one has MC=10.
Answer. We do not have the demand curves, so we cannot draw this
exactly, but the information provided does tell us something about the
reaction curves. Let firm 1 have MC=10 and firm 2 have MC=3. Then
the monopoly quantities are different for the two firms: Qm1 < Qm2,
as shown in the figure. The shutdown price will also be higher for firm
1, so its reaction curve will hit the axis at a smaller amount of output
by its rival. These two things mean that the intersection of the two
reaction curves will be at a higher output for the lower-cost firm, firm
2.
8. Let the demand curve be Q = 23 − P if P ≤ 23 and 0 otherwise.
(a) If there is one firm, with a marginal cost of 1 for outputs less than
8 and 3 for outputs greater than 8, and a fixed cost of 2, what will be
its output and price?
Answer. Suppose output is less than 8, so MC=1. Revenue is P Q =
(23 − Q)Q = 23Q − Q2 , so, taking the derivative with respect to Q,
marginal revenue is M R = 23 − 2Q. If we try to set this equal to
MC=1, we would get 1 = 23 − 2Q and Q = 11, but that output is
too high for the MC=1 to be valid. Trying MC=3, if MC=MR then
3 = 23 − 2Q and Q=10. In that case, P = 13.
Note that the fixed cost is irrelevant to the price.
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(b) If there are two firms with marginal costs of 1 each and fixed costs
of 2 each, what will be the output of each firm according to the Cournot
model? What will happen to output if the fixed costs increase to 3 for
each firm?
Answer. Firm 1’s profit function is π1 = P Q1 − T C1 = (23 − Q1 −
Q2 )Q1 − 1Q1 − 2) = 23Q1 − Q21 − Q2 Q1 − Q1 − 2 = 22Q1 − Q21 − Q2 Q1 -2.
Setting the derivative equal to zero, we get 22 − 2Q1 − Q2 = 0, so
Q1 = 11 − Q2 /2.
Since the firms are symmetric, Q1 = Q2 . Therefore, Q1 = 11 − Q1 /2,
so (1.5)Q1 = 11 and Q1 = 22/3, or 7.33...
An increase in the fixed cost will have no effect.
Chapter 6: Monopolizing
1. In Europe, antitrust law is enforced by
(a) The Council of Ministers.
(b) The European Parliament.
(c) The European Trade Commission.
(d) The Competition Commission.
2. If an industry has firms with market shares of .21, .19, .03, .25, .02,
.10, and .20, and the firms with shares of .10 and .20 merge, which of
the following numbers is closest to the increase in the Herfindahl Index?
(a) 200.
(b) 300.
(c) 400.
(d) 500.
3. How could a merger both reduce competition and increase total surplus?
Answer. If it reduced costs enough, that would outbalance the increased
price and reduced quantity (or the price might even fall).
4. Suppose that in the benzene market the market shares of the three top
sellers are 20%, 30%, and 40% and the 10 remaining firms each have
market shares of 1%.
Answer. (a) What is the Herfindahl Index for this industry?
Answer. 20*20+30*30+40*40 + 10*1*1 = 400+900+1600+10 = 2910.
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(b) Would the Justice Department and FTC be likely to allow merger
of the 10 small firms?
Answer. Merger of the 10 firms would change their contribution to
the Herfindahl from 10 to 1*10*10 = 100, an increase of just 90. The
Guidelines say that mergers that raise concentration by less than 100
are almost always permissible.
5. Read “How Driving Prices Lower Can Violate Antitrust Statutes ’Monopsony’ Suits Mount As Companies Are Accused of Squeezing Suppliers,”
http://fmpc.uconn.edu/research/milk/WSJ012704.pdf .
(a) Why did the anti-trust authorities make the sale of grain silos a
condition for allowing Cargill to merge with Continental Grain?
Answer.In locations where the merged companies would have the only
two silos for storing bought grain, the sale meant competition would
be preserved because some third company would now own one of the
silos.
(b) Would it violate the anti-trust laws for International Paper to take
advantage of its market power to bid low for timber? Explain.
Answer.No. The anti-trust laws do not forbid a company from bidding
low, so long as it does not try to arrange with other companies to bid
low. Note that the mergers which previously occurred might have been
illegal monopolizing, but not the firms low prices.
(c) What exactly is International Paper accused of doing?
Answer.In the article, what International Paper is charged with is
organizing a cartel of timber-buying companies so that they would bid
low for timber from growers. This would be illegal regardless of whether
IP had any market power. If International Paper went directly to the
growers and offered low prices, or offered low prices to the timber buying
companies, that would be legal.
6. A merger is illegal if
(a) The companies are in banking.
(b) One company is about to fail.
(c) The companies are in the same market.
(d) The companies are conglomerates.
(e) It would tend to monopolize the market.
7. If an industry has 4 firms with market shares of 10% each and one big
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firm captures the rest of the market then the Herfindahl Index is closest
to which number?
(a) 40.
(b) 1,600.
(c) 400.
(d) 16,000.
(e) 4,000.
8. An industry has eight firms with market shares of 10%,and 1 firm with
20%.
(a) What is the Herfindahl Index?
Answer. 8 · 102 + 202 = 1, 200.
(b) If three of the smaller firms merge, by how much does the Herfindahl
Index increase? What if four merge?
Answer. If three merge, before they contributed 3 ∗ 102 = 300. Now,
they contribute 302 = 900. Thus, the increase is 600.
If four merge, before they contributed 4 ∗ 102 = 400. Now, they contribute 402 = 1600. Thus, the increase is 1200.
9. Even before the Sherman Act, cartels had what problem? (a) Price
discrimination.
(b) Free riding.
(c) Rational ignorance.
(d) Predatory pricing.
(e) Exclusive dealing.
10. Two companies who propose to merge admit that prices might be higher
after the merger, but say that production costs would be much lower.
(a) Is it possible that the merger would reduce prices? Explain.
Answer. The merger could reduce prices if the cost savings were great
enough. In a competitive market, price =MC, but if that MC is lower
in the monopolized market, the price at the quantity where MC=MR
might be even lower. For example, if the competitive MC were high
enough so that the quantity demanded were zero, a fall in MC through
merger could lead the merged firm to reduce the price to where sales
were positive.
(b) Show, using a diagram, a scenario under which the merger could
raise total surplus even if the price rose.
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Answer. The diagram here is taken from Chapter 6. If the two firms
merge and marginal cost falls from C0 to C1, but the price rises from
P0 to P1, producers gain X+V-Z, while consumers lose W+Y. Then
net gain is X-Y-Z, which can be positive, as in the diagram: the cost
savings exceeds the increase in the triangle loss from monopoly underproduction.
Chapter 7: Natural Monopoly
1. In rate-of-return regulation, an electric utility is guaranteed:
(a) A certain rate of return.
(b) A minimum rate of return.
(c) A maximum rate of return.
(d) A fixed sales level.
(e)A fixed price level.
2. An electric utility has a marginal cost of 20 for both residential and
business customers. Business customers have more elastic demand.
The utility could charge 28 to all customers and it would break even,
earning enough to cover its fixed cost of 100, though a monopoly would
charge even more. Assume that at P=28, the quantity demanded by
business customers is the same as for residential customers. Explain
why the utility should use Ramsey pricing and charge more to residential
customers if its goal is to maximize total surplus while not making a
loss.
Answer.If the utility charges more than 28 to residential customers, it
can charge less to business customers, but it must keep its total profit
from falling below zero.
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We are told that business customers have more elastic demand. As
a result, if we lower the price to them by 1% and raise it by 1% to
residential customers, the gain in sales X to businesses will be greater
than the loss Y to residences (it might be a gain of X= 2% from business
sales and a loss of Y=.5% from residential sales, for example). Thus,
the utility’s revenue will actually rise.
The triangle loss from the business market will fall by .5(1%)(28)X.
The triangle loss from the residential market will rise by .5(1%)(28)Y.
The combination of triangle losses from both markets will fall, since X
is bigger than Y. Thus, the utility can actually make more profit by
charging more to residences and less to businesses while also reducing
total triangle losses.
3. Suppose a company has a fixed cost of 10 and a marginal cost that is
constant at 3. The demand curve is P = 24 − Q. Explain why this is
a natural monopoly. Contrast regulation that sets the price at marginal
cost with regulation that sets it at average cost. How do the outputs
and surpluses differ? (You don’t have to calculate the exact value of
the price, but do give a formula for it.)
Answer. This is a natural monopoly because the average cost curve
is downward sloping, so whatever firm is biggest has the lowest average cost and can underprice its competitors. If all firms priced at
marginal cost, they’d all price under average cost, which couldn’t be
an equilibrium, and in fact it would be inefficient to have production
by more than one firm since that would raise production costs for the
same output.
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A regulator could set P=MC so P=3, but then the firm would have
profits of -10 from its fixed cost and would exit the industry. Thus,
marginal-cost pricing requires a subsidy of 10. Output would be such
that 3 = 24 − Q, so Q=21.
A regulator could instead set P=AC. We need to compute average
cost to find the value. Total cost is TC=10+3Q, so average cost is
AC=10/Q +3. If the price equals average cost, then from the demand
curve, 24-Q=10/Q +3. We can rewrite that as 21Q − Q2 = 10. That
yields a price above marginal cost, so there will be a deadweight loss,
with area equal to half of the increase in price from P=AC to P=MC
times the reduction in quantity.
You wouldn’t have to compute Output is Q = 20.5, roughly, so P = 3.5
and AC = 10/20.5 +3 which is also about 3.5 (and would be exactly
if we used Q=20.5125, the exact solution). The deadweight loss would
be about .5 (3.5-3)(21-20.5) = .125.
4. Why do the forces of competition not achieve surplus maximization in
an industry that is a natural monopoly?
Answer.
A natural monopoly has a downward sloping average cost curve. Thus,
if the price equals a firms marginal cost, it is less than average cost and
the firm cannot survive. This means that firms undercutting each others prices cannot achieve an equilibrium with P=MC. It is not enough
to say that a monopoly has lower surplus— you need to explain why
the forces of competition permit the monopoly to persist.
5. A state park is selling firewood at $10/bundle and juice at $2/bottle.
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Firewood costs the park $7/bundle and juice costs $1/bottle. The elasticities of demand for firewood and juice are 1.2 and 0.4. In what
direction could the park change prices to increase profit while leaving
consumer surplus unchanged?
Answer. Ramsey pricing says that -Elasticity*(P-MC)/P should be
the same for each good. Right now that expression is equal to 1.2(107)/10=.36 for wood and 0.4(2-1)/2=.2 for juice. The price of wood
should be lowered and the price of juice should be increased so the two
values come closer to each other. A common mistake was to look just
at the elasticities, but (P-MC)/P matters too. Also, the aim is not to
get -Elasticity*(P-MC)/P=1, as it would be in a monopoly— it is just
to get that expression equal for wood and for juice.
Chapter 8: Information
1. The supply of cheap beer is perfectly elastic at a price of 8. Demand is
given by P = 12-Q/2. The beer is worth 2 less than consumers believe,
however, because it causes liver disease.
(a) What is the free market equilibrium price?
Answer. The price is initially such that 8 = 12-Q/2 so Q/2 = 4 and
Q=8 and P = 8. Or, simply note that if supply is perfectly elastic at
8 then 8 has to be the market price.
(b) The government is trying to decide between two policies (i) Teach
consumers about liver disease, or (ii) Impose a tax of 2 per unit of sales
on the producers. What will be sales under each policy?
Answer. Informed of the true value, the demand curve changes to P
= 10 Q/2, so 8 = 10-Q/2, Q/2=2, and Q=4. Under the tax, the price
rises to 10 but the demand curve stays the same as before, so 10= 12
Q/2. This solves to Q=4, the same outcome.
2. Suppose we buy 10% of our widgets from Apex and 90% from Brydox.
Apex’s widgets fail with probability .5 and Brydox’s with probability
.1. A widget has just failed. What is the probability it is from Brydox?
(a) 0 to 5%.
(b) 5.1-10%.
(c) 10.1-13%.
(d)13.1-20%.
(e) Over 20%.
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3. 13% of the people interviewed for a banking position have enough talent
for the job, but the interviewer isn’t sure which ones. 10% of talented
people and 4% of untalented people can answer his Tough Question. He
interviews Smith and Smith answers the Tough Question correctly. Is
the probability that Smith is talented over 50% or under it? (You do
not have to do computations or get computations right to get credit, but
you must provide either a verbal or a mathematical explanation.)
Answer. The number would be under 50%. Imagine a talent pool of
1000 people. 130 would be talented, and 13 of them could answer the
question. 870 would be untalented, and around 30 of them (34.8, to
be exact) could answer it. Thus, the proportion of talented to total
answerers would be 13/(13+34.8), which is is less than .5. This is an
example of Bayesian reasoning.
4. Discuss the advantages and disadvantages of three different government
policies for dealing with the dangers of muscle-building drugs.
Answer. Here are three policies:
1. Ban the drugs. This will stop the danger, but will also prevent people
from using it who are aware of the dangers but want the benefits.
2. Require each drug to be sold with a warning label about its dangers.
This will inform users, but will require some cost for the labels and the
warnings may not be understood or even read by many users, especially
if they just obtain pills from coaches or friends.
3. Require each drug to be sold only if the buyer signs off on a special
paper saying he is aware of the dangers. This will also inform users,
and will make it more likely that they read the warnings. It will greatly
increase the cost, tho, if this paperwork has to be filed away as proof
it was done.
5. For reputation to work, it must be that:
(a) Costs must be sufficiently high.
(b) The price must equal marginal cost.
(c) The price must be below marginal cost.
(d) The price is above marginal cost.
(e) None of the above.
Chapter 9: Labor
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1. After the state of Indiana mandates that every employer provides free
daycare for its employees, will wages rise, fall, or stay the same?
Answer. Wages would fall. If they did not, then employers would
demand a lower quantity of labor than before the mandate, and workers
would supply a higher quantity, which would create excess supply and
downward pressure on wages as employers found they could reduce
wages and still attract as many workers. This is true whether the
regulation is efficient or inefficient.
2. In Smallville, 50 workers will work for as little as $10/hour and 200
workers will work for as little as $20/hour. The number of jobs employers will offer is L where L = 100-2W.
(a) What is the equilibrium price and quantity of labor? Show this using
a diagram.
Answer. At a wage of 20, L= 100-2W =60 units of labor will be hired.
Supply equals demand there, so it is an equilibrium.
(b) What is the workers’ surplus in equilibrium?
Answer. The first 50 workers are being paid 20 and they would have
worked for 10, so their surplus is 500. The last 10 workers are earning
zero surplus.
(c) If a minimum wage of $30/hour is imposed, what is the workers’
surplus?
Answer. Employment falls to L = 100-2W = 40. Those 40 workers
have a surplus of 40*20=800.
3. Italy requires employers to provide severance of about one year’s salary
for an employee who has worked for that employer for 13 years. What
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is the effect of this requirement on the annual salary, employment, and
worker surplus in the long run? Explain using a graph.
Answer. The salary definitely falls, whether the severance pay is an
efficient benefit or an inefficient one, because both the labor supply and
labor demand curves shift down, by y and x in the diagram below. The
effect on employment and surplus depends on whether severance pay
is efficient. We can deduce that it is not, because otherwise employers
would be providing it already. (Remember to always first ask: “Is
there market failure?”)As a result, labor demand will fall more than
labor supply and the equilibrium salary will fall more than the benefit
of severance pay to a worker. Being worse off from employment than
before, fewer workers will offer to work; employment will fall from L0 to
L1. With salary plus benefit value and employment both down, worker
surplus falls too.
GRAPH NOT INCLUDED HERE
4. Right-to-work states have: (a) Looser child-labor laws.
(b) Higher minimum wages.
(c) Mandated health insurance.
(d) Stronger unions.
(e) Weaker unions.
5. Suppose some employers currently are not providing daycare to their
employees’ children. Show the effect of mandated employer-provided
daycare on employment and wages.
Answer. If the fringe benefit is efficient, reducing wages more than
it increased costs, employers are already providing it. Hence, we can
assume that for firms presently providing it, daycare is efficient and
for those who are not, it is inefficient. The only effect of a mandate is
to impose it on those who are not providing it currently, so the effect
would be purely inefficient.
Wages would fall whether it was efficient or not. We can conclude from
the inefficiency of the mandate that employment will fall too, as in the
diagram below.
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Chapter 10: Banking
1. Suppose that 80% of banks are solvent, of which only 20% have invested in mortgage-backed securities. Of the insolvent banks, 60% have
invested in those securities. If a government bank examiner finds that a
particular bank has invested in those securities, what is the probability
that it is insolvent?
Answer. The total percentage of banks that have invested in those
securities is .8(.2) + .2(.6) = .16+.12 = .28. The percentage that are
insolvent and have invested in them is .12. Thus, the probability an
investing bank is insolvent is .12/.28= 3/7.
2. Why does the government want banks to have a high capital ratio?
Answer. The government wants a high capitalization ratio for banks
because it provides them with deposit insurance, emergency Fed loans,
and bailouts, so if the bank is leveraged it is the government that bears
much of the risk. Also, the government would want systemic risk to
fall even if it didn’t intervene in crises. The answer is not just that a
high capitalization ratio reduces the risk of bankruptcy (though that
received partial credit) because the same is true of all other companies
too, but the government is not concerned with the capitalization of
Microsoft, Kroger, etc.
3. An entrepreneur has an idea that will yield 20% if it works and 2% if it
fails,both having equal probability, for any size of investment. He can
borrow at 5% and starts with 20 million in assets. His expected profit
will be highest if he borrows:
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(a) Nothing.
(b) .1-2 million dollars.
(c) 2.1-4 million dollars.
(d)4.1-17 million dollars.
(e) 17.1-19 million dollars.
4. Cutting a mortgage-backed security into tranches: (a) Always reduces
total risk.
(b) Always increases total risk.
(c) Sometimes creates a new, less risky asset.
(d) Sometimes reduces total risk.
5. The loss in surplus from someone being evicted for not paying his mortgage equals: (a) The market value of the house.
(b) His value for the house.
(c) The lost use of the house till someone new moves in.
(d) The remaining amount of his mortgage.
Chapter 11: Externalities
1. (a) Why does Levitt say in “The SuperFreakonomics Global-Warming
Fact Quiz,” http://www.freakonomics.com/2009/10/23/the-superfreakonomics-global-warming-fact-quiz/
that we should use climate engineering instead of a carbon tax?
Answer. He has two reasons. (1) A carbon tax will reduce emissions,
but that will only delay warming, not stop it. Warming will continue for
many years, and eventually reach the same high temperatures it would
without the carbon tax. (2) Reducing emissions is very expensive—
over a trillion dollars per year— whereas geoengineering is extremely
cheap by comparison. Thus, if the goal is to maximize net benefit or
reduce net cost, geoengineering is superior.
(b) Levitt omits a major reason why global engineering is a more practical solution than carbon taxes. What is that? Discuss.
Answer. He omits the difficulty of implementation because of the international free rider problem. Carbon taxes must be imposed worldwide, or some countries will keep on increasing their emissions. In fact,
the non-taxing countries will increase emissions all the faster, because
their industries will be advantaged and will export carbon-heavy goods
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to the high-tax countries. The non-taxing countries will see no need to
tax if other countries are doing the taxing, and no country can benefit
by unilaterally imposing a carbon tax. In addition, some countries will
prefer global warming to a carbon tax even if a carbon tax could be
imposed worldwide—India and Russia, for example. Geoengineering,
on the other hand, can be done unilaterally, and it is cheap enough
that one medium-sized country could find it profitable to do it even if
it had to bear the entire cost itself.
He also omits the advantage that geoengineering can be tried on a
smaller scale, and later, so that if warming turns out not to be such a
problem, large costs have not been incurred.
(c) Would a higher discount rate make Levitt’s solution for global warming more attractive or less attractive relative to cap-and-trade? Discuss.
Answer. With a high discount rate, geoengineering is more attractive
because its cost could be delayed till many years from now, whereas to
significantly delay global warming a cap-and-trade policy would have
to start in the next fifty years. On the other hand, if discount rates are
very low, cap-and-trade has the problem that without exorbitant cost
it doesn’t seem to be a permanent solution, and if the discount rate
is low, the costs of warming further out than 100 years would matter
more than with a high discount rate.
2. Suppose the supply curve is P s = 2Qs , the demand curve is P d =
48 − 3Qd , and each transaction creates an externality with marginal
cost X = Q. What is the optimal pollution tax?
Answer.
What we need to do here is figure out the social marginal benefit and
marginal cost curves and find at what quantity they intersect. Then
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we need to set the pollution tax equal to the marginal cost of the
externality at that quantity.
The social marginal benefit curve is the same as the demand curve here.
The social marginal cost curve adds up the private marginal cost— the
height of the supply curve— and the externality. Thus, we add 2Q and
Q and get M Csocial = 3Q. Equating that to social marginal benefit
yields
3Q = 48 − 3Q,
so Q=8. At Q=8, the externality marginal cost is also 8, so that should
be the amount of the tax. The equilibrium price will be 16, from the
demand curve, so buyers will buy 8 units.
3. Smith has noisy parties at his house, which bothers neighbor Jones. If
the assumptions of the Coase Theorem are met, then the assignment
of who gets to control the noise:
(a) Results in less noise.
(b) Does not affect the amount of noise.
(c) Increases the amount of noise.
(d) Helps Smith and not Jones.
(e) Helps Jones and not Smith.
4. Suppose the supply curve is P s = 2Qs , the demand curve is P d =
48 − 3Qd , and each transaction creates an externality with marginal
cost X = Q. What is the optimal pollution tax?
Answer. What we need to do here is figure out the social marginal
benefit and marginal cost curves and find at what quantity they intersect. Then we need to set the pollution tax equal to the marginal cost
of the externality at that quantity.
The social marginal benefit curve is the same as the demand curve here.
The social marginal cost curve adds up the private marginal cost— the
height of the supply curve— and the externality. Thus, we add 2Q and
Q and get M Csocial = 3Q. Equating that to social marginal benefit
yields
3Q = 48 − 3Q,
so Q=8. At Q=8, the externality marginal cost is also 8, so that should
be the amount of the tax. The equilibrium price will be 16, from the
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demand curve, so buyers will buy 8 units.
5. If the marginal cost of tires is increasing, and the marginal cost of the
air pollution externality from making tires is falling, then the optimal
pollution tax:
(a) Will equal the private marginal cost of tires.
(b) Will equal the marginal benefit from tires.
(c) Will equal the externality cost at an output of zero tires.
(d) Will equal the marginal externality cost before the tax is imposed.
(e) Will equal the marginal externality cost once the tax is
imposed.
Chapter 12: Conservation
1. Two brothers own a ranch. They are both hunting for caribou. Show
using a game matrix the problem that will result unless they talk with
each other about their hunting.
Answer. We can use the game matrix in Table 12.1 of the book. Let
the brothers be called Row and Column. If they each hunt a lot of
caribou, they will deplete the stock and both be unhappy. They will
do that, following individual interest, unless they can get together and
make a binding agreement to both only hunt a little. This might be a
legal agreement, or might be some kind of credible promise, enforced
by their ethical or religious beliefs or by shame at lying.
2. Why is there a better case for the government regulation of fishing than
for the government regulation of copper mining?
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Answer. Overfishing is a common-pool resource problem. If there
is no regulation, a prisoner’s dilemma exists in which each fisherman
will catch too many fish now, ruining future fishing. They would all
be better off if there were limits on the annual catch for each person.
Copper mining has no such problem. Each person can mine the copper
on his own land, and the only effect on others is to slightly reduce the
price of copper, which is a pecuniary externality, not a real externality.
3. Chateau LaTour is one of only five “premier grand cru” red Bordeaux
wines. In 2013 a bottle of the 2004 vintage cost $664 (http://www.
wine-searcher.com/find/ch+latour/2004). It will be at its optimal age to
drink around 2020. What can you predict about the price of this wine?
Will it ever all be used up?
Answer. We can predict that the price of the wine will rise over time
until 2020. It will rise at the discount rate for assets of moderate uncertainty, because if it was always at the 2020 price, nobody would want
to buy it before 2020, and if it jumped suddenly from 2019 to 2020,
everybody would want to buy it in 2019 to make the easy capital gain.
4. Read the article, “U.S. Gas Exports Clear Hurdle: Study Citing Benefits Could Hasten Approvals From Obama Administration,” http://online.
wsj.com/article/SB10001424127887324001104578161461770971222.html.
(a) Would allowing companies to export natural gas from the United
States really “slightly cut into the real wage of U.S. workers” or lead to
a “massive wealth transfer from working Americans”? Would it really
help total surplus in the U.S.? Credit will be given only for explanations,
not the yes/no answers.
Answer. Allowing natural gas exports would slightly cut into the
wage of US workers, because it would increase the price of natural gas
by increasing demand for US natural gas. It would not be a massive
wealth transfer. It would increase total surplus in the US because US
owners of natural gas fields would benefit more than US consumers of
natural gas would lose.
(b) Are environmental groups correct that allowing exports of natural
gas would raise U.S. production?
Answer. Yes. By increasing the demand for U.S. natural gas, it would
increase the price and the equilibrium quantity.
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(c) Which market failure justifies requiring export permits for natural
gas?
(i) Poor information.
(ii) Running out of nonrenewable resources.
(iii) Market power.
(iv) There is no market failure.
5. The single biggest cost of recycling paper is:
(a) Transportation by the city truck to the recycling center.
(b) The energy used at the paper mill.
(c) The labor used at the paper mill.
(d) The labor cost of the household doing the recycling.
(e) The labor cost to the city of collecting recylables.