Problem Set 1
56 pts total. 6 pts extra credit.
1. (12 pts) A monopolist faces a market demand curve given by:
Q = 240 − P
and a cost function of
C (Q) = 10 + 40Q + Q2
(a) (4 pts) Find the proﬁt maximizing quantity and price. Calculate the monopoly’s
proﬁts and consumer surplus.
(b) (5 pts) What price and output level would have been produced by this industry
under perfect competition (P = M C )? Calculate consumer surplus and ﬁrm
proﬁts at the competitive output level. Calculate the deadweight loss due to
(c) (2 pts) Suppose the government wanted use a per-unit subsidy of $S to incentivize
the monopolist at the competitive output level. What is the value of $S and how
much would the total subsidy cost?
(d) (1 pt) Would you recommend for or against using the subsidy as an incentive to
produce at the competitive level?
2. (8 pts – 2 each) Label the following practices as ﬁrst, second or third degree price
discrimination (or not price discrimination)
(a) An airline charges fees for customers who check in bags
(b) A fast food restaurant lets you double the size of your drink for only 20 cents
(c) A college charges lower tuition to an economically disadvantaged student
(d) A grocery store mails out coupon ﬂiers
3. (14 pts) Oceanic Airlines is the sole provider of ﬂights to and from Dharma Island.
They face two types of customers: business travelers and leisure travelers. The demand
by business travelers is:
QB = 100 − PB
and the demand by leisure travelers is:
QL = 400 − 4PL
The cost function is:
C (Q) =
Q + 10Q + 50
(a) (5 pts) Suppose that Oceanic cannot distinguish between the two types of travelers. Calculate the proﬁt maximizing price and quantity. Calculate proﬁt and the
consumer surplus for each type of traveler.
(b) (2 pts) Oceanic wants to distinguish between business and leisure travelers by
charging more for customers who show up at the airport wearing a suit and
carrying a laptop bag or briefcase. What might go wrong with this plan? Propose
an alternative strategy for Oceanic to distinguish between business and leisure
(c) (7 pts) Suppose now that Oceanic can distinguish between the two types of travelers and that they can prevent resale of tickets. Calculate the proﬁt maximizing
prices and quantities for each type of traveler. Calculate proﬁt and consumer
surplus for each type of traveler.
4. (12 pts) You provide homework solving services to your two “friends”, Alice and Bob.
Their demand for homework solutions are:
PA = 100 − 2QA
PB = 100 − QB
You have a constant marginal cost of providing solutions equal to 10 per solution
(a) (2 pts) Show that at any price level, the consumer surplus that Alice receives is
less than the consumer surplus that Bob receives.
(b) (5 pts) Find the Oi Tariﬀ. Calculate your proﬁts and consumer surplus for Alice
(c) (5 pts) Find the optimal tariﬀ. Calculate your proﬁts and consumer surplus for
Alice and Bob.
5. (10 pts) Two ﬁshermen share a pond. Each ﬁsherman can choose to ﬁsh heavily (H),
moderately (M), or sparingly (S). Each ﬁsherman’s choice will have an eﬀect on the
number of ﬁsh the other ﬁsherman can catch, according to the following payouts. The
ﬁrst number represents the payout of ﬁsherman A, the second number represents the
payout to ﬁsherman B.
S (5,5) (4,11) (1,14)
Fisherman A M (9,4) (8,10) (2,13)
H (10,2) (7,9) (1,10)
(a) (2 pts) What combination of ﬁshing patterns maximizes the total number of ﬁsh
(b) (2 pts) Does A or B have any dominant or dominated strategies? Which ones?
(c) (2 pts) What is the Nash equilibrium outcome if both players move simultaneously?
(d) (2 pts) Would the outcome change if we let either A or B choose ﬁrst?
(e) (2 pts) You have the power to impose a tax on heavy ﬁshing. What is the smallest
level of tax (as measured in units of ﬁsh) that you should impose on heavy ﬁshing
in order to make the answer from (a) a Nash equilibrium?
6. (Extra Credit – 6 pts) There are two types of consumers, 1 and 2, with demands:
P1 (Q) = a − b1 Q
P2 (Q) = a − b2 Q
The monopolist has a marginal cost function given by
M C (Q)
(a) (2 pts) Show that if there is no price discrimination, then the proﬁt-maximizing
price and quantity, (P ∗ , Q∗ ), satisfy:
M C (Q∗ ) = a − 2
b1 + b2
a + M C (Q∗ )
(b) (4 pts) Under third degree price discrimination, let (P1 , Q1 ) and (P2 , Q2 ) be the
proﬁt maximizing prices and quantities for consumers 1 and 2, respectively. Show
Q1 + Q2 = Q∗
a + M C (Q∗ )
P1 = P2 =
That is, under this particular kind of demand system, a monopolist that can
practice third-degree price discrimination will not beneﬁt from doing so. It will
choose prices that are the same for both customers and equal to the price level
under no price discrimination.
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