Economics 476 Problem Set 7
1. Strategic Commitment and Entry Dete
ence. An Incumbent monopolist (INC) is threat-
ened by an Entrant (E). If the Entrant actually enters, the Incumbent can either Accom-
modate entry (A) or Fight (F) by starting a price war. Additionally, prior to entry the
Incumbent can make itself Aggressive by paying a sunk cost K. Otherwise, it is Passive
Pass. The entrant knows whether the Incumbent has played Agg or Pass. Here is the game
in extensive form, including payoffs (πE, πI) . NOTE that the Entrant’s payoff is first!
INC
INC INC
EE
(0,πM −K) (0,πM)
Agg Pass
In Out In Out
F A F A
(πw, πw) (πd,πd −K) (πw, πw) (πd, πd)
a. Suppose πM = 100, πd = 30, and πw = −10. What is the equili
ium if K = 0? Find a
value of K that such that the Incumbent will deter Entry by playing Aggressive.
. For unknown values of πM , πd, and πw, solve the game using backward induction. What
2 conditions must be satisfied for entry dete
ence to work?
c. Find the range of all values of K that such that the Incumbent will play Agg and dete
entry.
2. (Limit Quantities) Suppose a market has inverse demand P = 100 − Q. An incumbent
monopolist, Firm 1, moves first, choosing its output q1. The incumbent has cost function
c(q1) = 40q1. A potential entrant, Firm 2, decides whether to enter or not. Its total cost is
100 + 40q2, where 100 is sunk cost paid upon entry.
a. Suppose entrant observes the incumbent producing output q1, then decides whether to
enter or not. Find the entrant’s optimal output (assuming it enters) as a function of q1.
. Solve for the limit output q1 that is just large enough to deter entry.
3. (Limit Pricing). Suppose an Entrant with marginal cost c = 20 is considering entering a
market to challenge an Incumbent monopolist. The monopolist is either a High Cost firm
(MC = 40) or a Low Cost firm (MC = 10). Market demand is Q = 100 − P. A High
cost monopolist would set Pm = 70 and produce Qm = 30. A Low cost firm monopolist
would set Pm = 55 and Qm = 45. The Incumbent’s profits as a function of marginal cost are
π(c) =
(
100−c
2
)2
in period 1 and also in period 2 if no entry occurs. In period 2, the Entrant
observes the Incumbent’s period 1 price and chooses to Enter or not. If it Enters, the two
firms compete as Bertrand price competitors, choosing prices simultaneously.
a. Suppose the Entrant must pay a sunk cost K = 200 if it enters. Suppose the Entrant can
observe the type (cost function) of the Incumbent before entry. Find the Entrant’s profit
(including K) if it enters against a High cost firm and against a Low cost firm. Could a High
cost Incumbent deter entry by setting Pm = 55 in period 1?
. Suppose instead that the Entrant cannot observe the Incumbent’s type. Assume also that
the Incumbent cannot reveal its type in any way that is believable by the Entrant. All the
Entrant knows is that the probability that the firm is Low cost is ρ. If the Incumbent is a
High cost firm, find a condition (which will depend on ρ) under which it might Limit price
y setting its price P1 = 55 in period 1 to mimic a low cost firm.
4. Predatory Pricing. A certain would-be monopolist firm produces with cost function
C(q1) = XXXXXXXXXX5q
2
1. Inverse demand is P = 200 − Q, where Q is the total output of all
sellers. Suppose that the other firm in the market has cost function C(q2) = 100 + 110q2.
Suppose Firm 1 sets P = 74 and produces enough output to support that price. Is this
predatory pricing under the Areeda-Turner rule (P < AV C)? Recall that AV C = TV C/q
and that TV C is total cost excluding any fixed costs.