# ECON 326 Suppose two ?rms facing a demand D(p) compete

ECON 326Page 1 of 2 Summer 2015Name:Industrial OrganizationPractice ProblemsBertrand Competition With Di?erent CostsSuppose two ?rms facing a demand D(p) compete by setting prices simultaneously (BertrandCompetition). Firm 1 has a constant marginal cost c1 and Firm 2 has a marginal cost c2 .Assume c1 < c2 , i.e., Firm 1 is more e cient.(a) Show that (unlike the case with identical costs) p1 = c1 and p2 = c2 is not a Nash-Bertrandequilibrium.(b) Is there any equilibrium in pure strategies?. If yes, ?nd it. If not, explain.Cournot CompetitionSuppose there are two identical ?rms engaged in quantity competition (Cournot competition). The demand is P = 1 Q where Q = q1 + q2 . Assume that ?rmâs i total cost of2qiproduction is T C(qi ) = 2 .(a) Compute the Cournot equilibrium (i.e., quantities, price, and pro?ts).Cournot Competition And MergersSuppose there are three identical ?rms engaged in quantity competition (Cournot competition). The demand is P = 1 Q where Q = q1 + q2 + q3 . To simplify, assume that themarginal cost of production is zero.(a) Compute the Cournot equilibrium (i.e., quantities, price, and pro?ts).(b) Suppose Firm 2 and Firm 3 merge turning the market into a duopoly. Show that thepro?t of each of the two merged ?rms falls.(c) Suppose now that all the three ?rms merge. What happens to pro?ts?ECON 326Page 2 of 2Cournot Competition With Di?erent CostsSuppose there are two ?rms engaged in quantity competition (Cournot competition). Thedemand is P = 2 Q where Q = q1 + q2 . Assume c1 = 1 and c2 = 1 , i.e., Firm 2 is more24e cient.(a) Compute the Cournot equilibrium (i.e., quantities, price, and pro?ts).(b) How is the Cournot equilibrium a?ected by the cost di?erence of the ?rms.In?nitely Repeated Cournot and CollusionSuppose there are two identical ?rms engaged in quantity competition (Cournot competition). Every period each ?rm decides how much to produce, and the game is repeated forever.Demand is P = 1 Q where Q = q1 + q2 and marginal cost of production is zero. Suppose?rms use the same discount factor .(a) Compute the Cournot equilibrium (i.e., quantities, price, and pro?ts).(b) Find the monopoly equilibrium (i.e., quantity, price, and pro?t).(c) Suppose now that ?rms collude and each of them uses the following strategy:(a) In the ?rst period produces the monopoly quantity.m m(b) In subsequent periods, if the previous period equilibrium was (q1 , q2 ) then producethe monopoly quantity; otherwise produce the Cournot quantity.(d) Show that if the discount rate is large enough, collusion can be an equilibrium in thein?nitely repeated game.(e) What happens in the ?nitely repeated game?