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Test Questions for end of chapter.
I’ll arrange these by chapter. Then I’ll puthte question at the end of the chapter, and the answers at the end of
the book. For now, I’ll put the first 4 chapters answers at the end.
CHAPTER 1 MARKETS
1. Why are well-defined property rights useful for surplus maximization? Include at least two reasons in your 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. 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) (2 points) 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).
(b) (2 points) 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.
(a) The equilibrium is found from 24-P = 3(P-4), so 24-P=
3P-12, so 36=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).
Price
24
(b) 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.
Supply
12
D
9
8
B
C
A
Demand
4
12
15
24
Quantity
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.
1. 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.
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4. Suppose the monopoly in the diagram below chose a price of 25.
(a) (2 points)What would be the deadweight loss from allocative inefficiency?
(b) (2 points) What would be the consumer surplus if the price were 10?
Price
40
(a) The deadweight loss is .5(25-10)(30-15) = .5(15)(15)= 112.5.
(b) The consumer surplus at a price of 10 would be .5(40-10)(30-0) =
450.
Demand
25
Marginal Cost
10
10
15
30
40
Quantity
5. Suppose a city imposes a price floor on hamburgers sold at
restaurants.
(a) (2 points) On a diagram show the resulting loss of total
social surplus if rationing is efficient.
(b) (2 points) Explain how the loss of total surplus would change if rationing were inefficient.
(a)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.
(b)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.
1. Show on a supply-and-demand diagram how much orange
growers would pay to set a price floor higher than the free-market price of oranges.
Answer. They would pay V+Y- (Y+X)= V-X. A common mistake was to ignore the lost surplus area X.
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3. 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.
23. 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.
{\bf (e) None of the above
7. 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.
9. Let supply be Q=12+P and demand be P= 32-Q. The equilibrium price is
(a) Less than1
(b) 1.1-3.
(c)3.1-8.
{\bf (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 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?
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.
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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.
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 priceelastic shapes. \\
(a) Draw a diagram to show the levels of paper sales under laissez faire equilibrium and under optimal regulation. \\
(b) Show how much total surplus increases going from laissez faire to optimal regulation, and how the total cost of
water pollution changes.
.
Social Cost
Price
C
A
B
Supply
Demand
Q(reg)
Q(no reg.)
Quantity
(a) 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) Total surplus increases by area C going from laissez faire to optimal regulation, because the units between Q(reg) and Q(no reg.) 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.
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.\\
{\bf (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.
\noindent
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
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surplus.
% \includegraphics[width=6in]{test05.jpg}\\
\noindent
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. \\
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. \\
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CHAPTER 3: GOVERNMENT FAILURE
1. Read the Huffington Post’s “Chicago Food Trucks: City Council Overwhelmingly Approves
Mayor's Ordinance,” \url{http://www.huffingtonpost.com/2012/07/25/chicago-food-trucksalder_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. 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. \\
{\bf (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\\
{\bf (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.
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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.\\
{\bf (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 new houses will lead it to \\
{\bf (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.\\
{\bf (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.\\
{\bf (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.
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1. The average rate of inflation from 1926 to 2011 was closest to which number?\\
(a) 2\%.\\
{\bf (b) 3\%}.\\
(c) 5\%.\\
(d) 7\%.\\
(e) 10\%.
\noindent
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? \\
(b) If a tax of 3 per unit is imposed on sellers instead, what is the result?
\includegraphics[height=2in]{review1.jpg}
(a) First, figure out what happens if there is no tax. Equating supply and demand, $P^s=Q^s$ so
$$
Q^s= 24-2Q^d,
$$
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 $P^d+3 = 24-2Q^d$, so $P^d = 21 - 2Q^d$, so if Q=0, P=21.
Equate supply and demand using the new demand curve, so
$$
Q^s= 21-2Q^d
$$
and Q=7. That means P=7 too, since $P^s=Q^s$. 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) Now let's put the tax on the seller. The supply curve will 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, $P^s-3 = Q^s$, so $P^s= Q^s+3$ and if P=3, Q=0.
Equate supply and demand using the new demand curve so
$$
Q^s+3 = 24-2Q^d
$$
and Q=7. Using the supply curve, $P=7+3=10$.
Producer surplus is .5(10-3)(7) = 24.5. Consumer surplus is .5 (24-10)(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.\\
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{\bf (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,
12-P=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. \\
{\bf (d) Is close to the private sector’s pretax return on investment. }\\
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\\
{\bf (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 value-of-a-statistical-life approach?
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.
(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 diagram what further effect this has on the equilibrium price and the triangle loss.
(a) 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.
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P
Supply
A
P0
B
P1
Demand
Demand minus tax
Q
(b) 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.
Supply plus tax
P
Supply
C
P0
P2
P1
A
D
E B
F
Demand
Demand minus tax
Q
CHAPTER 5: ANTITRUST I
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. \\
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(a) What price will the firm choose?\\
(b) Suppose the firm is taxed 2 per unit. How much would this raise or lower social surplus?
Answer.
(a) The demand curve can be rewritten as P = 24-Q. Profit = PQ4Q -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,
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) The effect of a tax is similar to an increase in marginal cost.
Now the firm’s profit is PQ- 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
Profit = PQ1 – TC1 = [60-(Q1+Q2)/2)] Q1 – 20 Q1 = 60 Q1- Q12/2 –Q2Q1/2 – 20Q1.
The first order condition is
60-Q1-Q2/2 -20 =0.
Solving for Q1, we get Q1=40-Q2/2, which is the reaction function.
(b) What will be the equilibrium price in the previous question?
Answer. Since the two firms are symmetric, so we can guess that Q 1=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 = 6080/3 = 180/3-80/3 = 100/3 or 33.3333.
Some people solved 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?
(b)At the monopoly output, would an increase of 1\% in the price cause revenue to rise, or to decline?
(a) 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, you
MR = (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 Q 2.. Having realized that,
and ignoring any possible fixed cost, profit is
PQ-TC = (6-2/Q)Q - Q2.
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Differentiating with respect to Q and setting the derivative equal to zero yields
6 – Q – 2Q =0
so Q=2.
(b) 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 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- MC)/P = -1/(elasticity)
Since P-MC<P, it must be that the elasticity is between -1 and – infinity, 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.
Any one of those ways to answer the question would have received full credit. Realizing that elasticity mattered scored partial credit.
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.
\noindent
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?
We can rewrite the demand curve as $P= 38 - (Q_1+Q_2)$. Firm 1's profit function is then $PQ_1-1*Q_1$ or
$$
[38 - (Q_1+Q_2)]Q_1-Q_1
$$
Maximizing with respect to $Q_1$ yields the first-order condition
$$
38 - 2Q_1 - Q_2-1 =0
$$
which can be rearranged to give the reaction function
$$
Q_1 = 18.5- Q_2/2.
$$
Firm 2's profit function is $PQ_2-6*Q_2$ or
$$
[38 - (Q_1+Q_2)]Q_2-6Q_2
$$
Maximizing with respect to $Q_1$ yields the first-order condition
$$
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38 - Q_1 - 2Q_2-6 =0
$$
which can be rearranged to give the reaction function
$$
Q_2 = 16- Q_1/2.
$$
Substituting this last expression into Firm 1's reaction function yields
$$
Q_1 = 18.5- [16- Q_1/2]/2
$$
which solves to $Q_1=18.5-8+Q_1/4$ so $Q_1 (3/4) = 10.5$ and $Q_1=14$. Then, $Q_2= 16-14/2 = 9$.
7. The company Apex has a total cost of TC = 2+ 4A and the company Brydox has a total cost of
TC= 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.
Apex’s profit function is
Profit(Apex) = P A – TC_a = (36-A-B)A – 2 – 4A = 36A- A^2 – BA – 2 – 4A = 32A – A^2 –BA-2
Differentiating yields
dProfit/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.
Brydox’s profit function is
Profit(Brydox) = P B – TC_b = (36-A-B)B – B = 36B- B^2 – BA – B = 35B – B^2 –BA
Differentiating yields
dProfit/dB = 35-2B –A =0,
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.
(b) 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.
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.
\noindent
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8.
Let the demand curve be $Q=23-P$ if $P \leq 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?
{\it Suppose output is less than 8, so MC=1. Revenue is $PQ = (23-Q)Q = 23Q - Q^2$,
so, taking the derivative with respect to Q, marginal revenue is $MR=23-2Q$. 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.} \\
(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?
{\it
Firm 1's profit function is $\pi_1= PQ_1 - TC_1 = (23-Q_1-Q_2)Q_1 - 1Q_1 - 2)
= 23Q_1 -Q_1^2 - Q_2Q_1 - Q_1 -2 = 22Q_1-Q_1^2 - Q_2Q_1$-2. Setting the
derivative equal to zero, we get $22-2Q_1 -Q_2=0$, so
$Q_1= 11 -Q_2/2. $
Since the firms are symmetric, $Q_1=Q_2$. Therefore, $Q_1= 11-Q_1/2$, so
$(1.5)Q_1 = 11$ and $Q_1 = 22/3$, or 7.33...
An increase in the fixed cost will have no effect.}
CHAPTER 6:
1. In Europe, antitrust law is enforced by \\
(a) The Council of Ministers.\\
(b) The European Parliament.\\
(c) The European Trade Commission.\\
{\bf (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.\\
{\bf (c) 400.}\\
(d) 500.
15
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\%. \\
(a) What is the Herfindahl Index for this industry? \\
(b) Would the Justice Department and FTC be likely to allow merger of the 10 small firms?
Answer.
(a) 20*20+30*30+40*40 + 10*1*1 = 400+900+1600+10 = 2910.
(b) Yes. 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,’’ \url{ http://fmpc.uconn.edu/research/milk/WSJ012704.pdf}. 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 firm’s 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 timberbuying 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\\
{\bf (e) It would tend to monopolize the market.} \\
7. If an industry has 4 firms with market shares of 10\% each and one big firm captures the rest of the market
then the Herfindahl Index is closest to which number? \\
(a) 40.\\
(b) 1,600.\\
(c) 400\\
16
(d) 16,000\\
{\bf (e) 4,000. }
\noindent
8. (a) An industry has eight firms with market shares of 10\%,and 1 firm with 20\%.
What is the Herfindahl Index? \\
{\it The Index is $8*10^2 + 1*20^2 = 800+400=1200. $}
(b) If three of the smaller firms merge, by how much does the Herfindahl Index
increase? What if four merge?
{\it If three merge, before they contributed $3*10^2= 300$. Now, they contribute
$30^2=900$. Thus, the increase is 600.
If four merge, before they contributed $4*10^2= 400$. Now, they contribute
$40^2=1600$. Thus, the increase is 1200.} \\
9. Even before the Sherman Act, cartels had what problem?
(a) Price discrimination.\\
{\bf (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. \\
(b) Show, using a diagram, a scenario under which the merger could raise total surplus
even if the price rose.
Answer. (a) 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) The diagram to the left 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.
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CHAPTER 7: NATURAL MONOPOLY
CHAPTER 7 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
firm’s marginal cost, it is less than average cost and the firm cannot survive. This means that firms
undercutting each other’s 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.
chpater 7 7. A state park is selling firewood at $10/bundle and juice at $2/bottle. 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(10-7)/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.
\noindent
2. 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.)
\includegraphics[height=2in]{review2.jpg}
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.
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
$21Q - Q^2 = 10.$ 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.
\bigskip
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\noindent
3. 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.
\includegraphics[height=2in]{review3.jpg}
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.
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.
\bigskip
CHAPTER 11
\noindent
5. Suppose the supply curve is $P^s = 2Q^s$, the demand curve is $P^d=48 - 3Q_d$, and each transaction
creates an externality with marginal cost $X= Q$. What is the optimal pollution tax?
\includegraphics[height=2in]{review4.jpg}
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 $MC_{social} = 3Q$. 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.
\documentclass[12pt,epsf]{article}
Quiz 3 G406 Fall 2012--Answers
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This is a closed-book test. There are 14 points in total. Please answer every question. You
may use the back of the page if you need extra space on which to write. The test is 1/2 hour in
length.
1. (2 points) What is deposit insurance?
Deposit insurance is an arrangement in which the government (or a private insurer) agrees to repay depositors if the
bank becomes insolvent. It is not a good answer to say that deposit insurance is insurance on deposits. Also, the
question asked what deposit insurance is, not who provides it or why it is useful. I didn’t take off points for adding
answers to those questions too, but I did if you didn’t get round to saying what deposit insurance is.
2. (2 points) 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?
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.
3. (2 points) Why does the government want banks to have a high capitalization ratio?
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.
4. (4 points) The supply of cheap beer is perfectly elastic at a price of 8. Demand is given by P = 12Q/2. The beer is worth 2 less than consumers believe, however, because it causes liver disease.
(a) What is the free market equilibrium 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?
(a) 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) 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.
5. (4 points) 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 is the effect of this requirement on the annual salary, employment, and worker surplus in the
long run? Explain using a graph.
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.
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