EC620 Assignment 3 Due: Monday, December 13, in class Fall 2021 Instructions: Assignments must be written using a word processor (i.e. hand-written assignments will not be accepted) and submitted in...

EC620 Assignment 3
Due: Monday, December 13, in class Fall 2021
Instructions: Assignments must be written using a word processor (i.e. hand-written
assignments will not be accepted) and submitted in class as a hard copy. Students can
complete assignments individually or in a group of 2 or 3 students.
Question 1 : Limit Pricing and Asymmetric Information (40 marks)

A market consists of an incumbent and an entrant who face constant marginal cost and
an inverted demand given by P = 24 − Q. The entrant’s costs are common knowledge and
are equal to marginal cost of cH = 12 and a fixed entry cost F = 10. The incumbent’s
marginal costs are not known by the entrant and are either cH = 12 or cL = 6. Prior to
observing the incumbent’s period 1 output the entrant believes that there is a 60%
probability that the incumbent is low cost. The firms play a two stage game. In the first
stage the incumbent is a monopolist and chooses output which is observed by the
entrant. In the second stage the entrant (i) forms beliefs about the incumbent’s costs
ased on the incumbent’s period 1 output and (ii) decides on whether or not to enter.
The entrant enters if they believe their expected profits to be positive. If entry occurs
firms engage in Cournot competition. In deciding on period 1 output the incumbent
maximizes the discounted sum of period 1 and period 2 profits where ρ = 0.9 is the
discount factor assigned to period 2 profits. For each of the proposed strategies given
elow determine if

(i) the low cost incumbent’s period 1 output (??
1(??)) is a best response to the
entrant’s entry strategy
(ii) the high cost incumbent’s period 1 output (??
1(??)) is a best response to the
entrant’ entry strategy
(iii) the entrant’s beliefs are consistent with the incumbents’’ period 1 output
choices and the entrant’s entry choice is rational given their beliefs.

a) (10 marks). Case 1
 High cost incumbent period 1 output : ??
1(??) = 6
 Low cost incumbent period 1 output : ??
1(??) = 9
 Entrant beliefs and entry strategy
 If ??
1 ≥ 7 entrant believes incumbent is low cost and stays out
 if ??
1 < 7 entrant believes incumbent is high cost and enters.
) (10 marks). Case 2
 High cost incumbent period 1 output : ??
1(??) = 6
 Low cost incumbent period 1 output : ??
1(??) = 11
 Entrant beliefs and entry strategy
 If ??
1 ≥ 10 entrant believes incumbent is low cost and stays out
 if ??
1 < 10 entrant believes incumbent is high cost and enters.
Fall 2021
EC620 Assignment 3 Page | 2

c) (10 marks). Case 3
 High cost incumbent period 1 output : ??
1(??) = 6
 Low cost incumbent period 1 output : ??
1(??) = 11
 Entrant beliefs and entry strategy
 If ??
1 ≥ 11 entrant believes incumbent is low cost and stays out
 if ??
1 < 11 entrant believes incumbent is high cost and enters.
d) (10 marks). Case 4
 High cost incumbent period 1 output : ??
1(??) = 10
 Low cost incumbent period 1 output : ??
1(??) = 10
 Entrant beliefs and entry strategy
 If ??
1 ≥ 10 entrant believes incumbent is low cost with 60% probability
and stays out
 if ??
1 < 10 entrant believes incumbent is high cost and enters.
Question 2: Mergers in Differentiated Cournot (20 marks)
Pre-merger market structure n > 2 single-product firms
Competition Differentiated Cournot
Demand pi = a – qi – dQ-
Single product Cost ??
? = ??? + ?
Multi-product Cost ??
? = ?(??1 + ??2) + 2? − ?
a) (5 marks). Solve for the pre-merger equili
ium outputs and profits per firm.
) (10 marks). Solve for the post-merger equili
ium outputs and profits per firm for a
merger between 2 single product firms.
c) (5 marks). Now let a = 130, c = 10, n = 5, d = ½. For what values of x is merger
profitable? Does a profitable merger raise welfare?
Question 3 Horizontal Mergers in Successive oligopoly. (20 marks)
Consider a successive oligopoly model consisting of N vertically integrated firms, n non-
integrated dealers and m non-integrated manufacturers. The marginal cost of the
integrated firm and non-integrated manufacturer is equal to c. The marginal cost of the
non-integrated dealer equals the wholesale price (w) charged by the non-integrated
manufacturers. Retail demand is given by P = a – Q.
a) (10 marks). Solve for the equili
ium output and profits of each firm, the retail price
(P) and the wholesale price (w).
) (10 marks). Let the pre-merger market structure be N = N*, n = n* and m = m*.
Determine for what combinations of N*, n* and m* the mergers below are profitable.
Does the market structure of the stage that is not experiencing a merger determine
whether or not the merger is profitable?
i) A horizontal dealer merger of the two non-integrated dealers
ii) A horizontal manufacturer merger of the two non-integrated manufacturers
Fall 2021
EC620 Assignment 3 Page | 3

Question 4: Stackelberg Follower Mergers with Increasing Marginal Cost (20 marks)
Pre-merger market structure 1 leader
Followers: ns = n > 2 single-plant, nm = 0 multi-plant
Competition Stackelberg
Demand P = a – Q
Single plant follower Cost ??
? = ??? + ???
2
Multi-plant follower Cost ??
? = ?(??1 + ??2) + ?(??1
2 + ??2
2 )
Leader Cost ?? = ???
a) (10 marks). Solve for the following variables as functions of ns, nm and a – c
 Profits of the leader, single plant followers and multi-plant followers
 Industry output
) (5 marks). Determine for what integer values a 2-follower merger that lowers ns from n
to n – 2 and raises nm from 0 to 1 is profitable
c) (5 marks). Let a – c = 60. Pick an integer value of n > 2 that results in profitable merger.
Determine if the merger enhances welfare