Question

2. Consider a Cournot competition model with two firms, 1 and 2. They produce identical goods in the same market with demand function P= 100-5Q with Q=91 +92. Furthermore, their production process generates pollution to the environment, which increases their cost of production. Their cost functions are given by C1(91,92) = 109,- +5Q and C291,92) = 15922 +45Q. a (10pts) Calculate their equilibrium quantities, price, and profits for both firms. b. (5pts) Consider they collude and form a cartel. That is, they perform together as a monopoly and maximize their total profits. Calculate new equilibrium quantities, price, and profits. c. (5pts) Explain why profits change from question (a) to question (b). What are the reasons for this change? (Hint: Consider both monopolistic competition and externality)

Answer 1

a = 9:+92 p 100-50 CF 1092 +5% . Ce=1592 + 450. Pause Break (er) For firme , P= 100-sq. co - 1097 +591 for firm 2 tot - 15z + 45a. me - 309. +45 MR = MC Pecofit - Rouence - Cost Revenue - 1009, - Sq? MR = 100 109, 100 - 1092 = 3092 tus Mc = 209, +5 MR = MC 100 - 1091 = 209, +5 q2 = 1.375 Peure = 100-5 (1.376). 2 93.125 Profile for $1.575-532 Revence = 100 (1-315-5 (1-3757² = 128.04 Cost = 10(1.375)+541.373) = 25.78 30g = 95 12. = 3.17 Pence : 100 - 5(3.17) Peure = 84.15 Rouenice - 100 (3.17) - 5 (3.1772 = 266.75 Cost = 1003.17)² + 5(3.17), 2 116.34 Pecafuta 150.41 I Preoft = 128.04-25-18 102.26 802 - got on

(b) If they calleede Co=a+C2 and form a cartel ( Q = ditaz) - 8+, dalla asht&sit a as sest est dose on 2 100 - 2012 z YH 801 - 001 ) - 20 C aw - uw - 80l- Qal est sos Cost a 20.8 402 Perofit - Revence - Cost = 59.64 Reneren = 80.48

c) both firm will loss after collusion, they were better off when they are producing seprately.