1. The market for economic textbooks can be described by the following demand curve:
Q = 400 – 10P
a. If each firm's marginal cost is 5, calculate the market output and price under
perfect competition.
In perfect competition, P = MR, so profit maximization occurs where MC = P
 the inverse demand is given by: 10P = 400 – Q  P  40  1 Q
10
1
Q  5  MC , and then solving for Q:
Setting P = MC: P  40 
10
P  40  5  1 Q  35  1 Q so Q = 350.
10
10
In perfect competition P = MC, so P = 5 (could also substitute Q = 350 into the inverse
demand curve P  40  350  5 ).
10
b. Assume that a single firm can monopolize the market. Calculate market output
and price for the monopoly.
Monopolist profit maximize where MC = MR. Now we need to find MR.
Total revenues are price (inverse demand) times quantity,
R(q) = P*Q  (40  1 Q)Q  40Q  1 Q 2
10
10
dR(q)
Marginal revenue is
 40  1 Q
5
dq
dR(q)
Setting this equal to MC:
 40  1 Q  5  MC and then solving for Q:
5
dq
40  5  1 Q  so Q = 175.
5
Price is found by substituting the profit maximizing quantity into the inverse demand
curve: P  40  175  40  17.5  22.50 , so P = $22.50
10
c. Calculate the loss of efficiency resulting from the monopolization.
DWL = ½ b*h = ½ (350-175)(22.5-5)=1531.25
2. Consider an industry that has eight firms with the following market share percentages: 30, 20, 12,
10, 10, 8, 7, and 3. Calculate the CR4 and the HHI.
CR4 = 72
HHI  30 2  20 2  12 2  10 2  10 2  8 2  7 2  3 2  1,766
3. Now consider an industry that has eight firms with the following market share percentages: 20,
20, 16, 16, 9, 8, 6, and 5. Calculate the CR4 and the HHI.
CR4=20+20+16+16=72
HHI  20 2  20 2  16 2  16 2  9 2  8 2  6 2  5 2  1,518
4. Which industry is more concentrated? Explain. Which has more market power? Explain.
The one in number 2 is more concentrated because it has a higher HHI even though CR4 is the
same. We can’t determine market power because we don’t know price elasticity of demand.
5. True or False: Third Degree Price discrimination always increases economic efficiency, relative
to what would be achieved by a single, uniform monopoly price. Explain.
False. If the aggregate quantity does not increase, then third degree price discrimination lowers
welfare.
6. Suppose that Coca-Cola uses a new type of vending machine that charges a price according to the
temperature outside. On “hot” days demand is Q  300  2 P . On “cool” days the demand is
Q  200  2 P . The marginal cost is always 20 cents.
a. What price should the machine charge on “hot” days? What about on “cool” days?
1
QC  200  2 PC  PC  100  QC  MRC  100  QC
2
Now, equate marginal revenue for a cold day with marginal cost.
100  QC  20  QC  80  PC  100 
1
(80)  60
2
1
QH  300  2PH  PH  150  Q H  MRH  150  QH
2
Now, equate marginal revenue for a hot day with marginal cost.
1
150  QH  20  QH  130  PH  150  (130)  85
2
Coca-Cola will charge 60 cents on a cold day and 85 cents on a hot day.
b. Suppose ½ the days are “hot” and the other ½ are “cool”. If Coca-Cola uses a single
price, what price should it set?
If half of the days are hot and other half are cold, then the expected aggregate demand faced by the
Coca-Cola is
QA 
1
1
(300  2 P )  ( 200  2 P )  250  2 P
2
2
Hence, the expected marginal revenue is
MRA  125  QA
Now, equate expected marginal revenue with marginal cost.
125  QA  20  QA  105  PA  72.5
c. What happens to profits with price discrimination? Efficiency?
1
[(85  20)(130)  (60  20)(80)]  5825
2
Profits without price discrimination = (72.5  20)(105)  5512.5
Profits with price discrimination =
Hence, profit is higher with discrimination.
Efficiency is the same (since QC  80 and QH  130 but these occur ½ the time aggregate quantity
is 105 with or without price discrimination.
7. Suppose that a monopoly “church fair” produces “amusement rides” and faces the situation
depicted in the diagram below for each of its customers.
a) If the firm can charge only one price for its amusement rides, what price will maximize the firm's
profits? $0.60______ What are the firm’s profits? $1.6________ What is the consumer surplus?
$0.80___________
b) Now suppose the firm can perfectly price discriminate (1st degree), how many amusement rides
should the firm sell? _8_____ What are the firm’s profits? $3.2_______ How much should it
charge for each amusement ride? $varies based on D $0.9. $0.8,…_____________
c) How could the firm achieve the same profits as in part b) by using a "two-part pricing"? What is
the deadweight loss? Set entry fee equal to $3.2 and charge $0.20 per ride. No deadweight
loss (at Qefficient)