Econ 101
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
monopoly.
(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

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(b) A fast food restaurant lets you double the size of your drink for only 20 cents
more
(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) =

12
Q + 10Q + 50
10

(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
travelers.
(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
and
PB = 100 − QB
2

You have a constant marginal cost of providing solutions equal to 10 per solution
provided.
(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
and Bob.
(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.
Fisherman B
S
M
H
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
caught?
(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
and
P2 (Q) = a − b2 Q
3

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
and
P∗ =

b1 b2
Q∗
b1 + b2

a + M C (Q∗ )
2

(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
that:
Q1 + Q2 = Q∗
and that:

a + M C (Q∗ )
P1 = P2 =
2
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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