I need help with Question 1.B. I completed Question 1.A, which should be correct. However, my approach to 1.B seems wrong, because the answers (quantity, price, profit values) seem incorrect compared to the values found in 1.A. Where did I go wrong with my approach to 1.B, and how would you approach 1.B?

This particular question is related to Oligopoly theory in Microeconomics. This homework is from a Master's level class (or upper division undergraduate level) in antitrust and competition, which involves concepts in microeconomics and game theory.

Thank you!

Week 5 1 Reinforcing the lecture Topic : . Price - fixing collusion - effect on competitors. F out Skim Ch 4 of Text . Economics 580 Problem Set #4 ac (due next Tuesday 12 noon) 1. Let market demand be given by Q = 200 - P. Each firm's cost function is C(qi) = 20qi, where i = 1, 2. Homogenous Product 1 case outcome (a) Using the Cournot model, find each firm's output, price and profit. special case of psze4is 1 Case outcome (b) Suppose that the duopolists collude. Find their joint profit-maximizing price, output, and profit. The firms act as a Monopolist . calc. in 1(b) " compete " 2 cases outcomes (c) Suppose now that each firm has two strategies: Cooperate or Defect. If a firm plays Cooperate, it chooses half of the collusive quantity level in (b). collusive Q-level 18 If a firm plays Defect, it chooses the noncooperative quantity level in (a). non co-op Q-level 1 (a) 4 cases outcomes Present the 2-by-2 matrix game, determine the Nash equilibrium outcome, and discuss the implications of the outcome. Alternatively , you can " optimally defect " I take as given . by optimizing to find Q. (more complex ) (d) Suppose the game in (c) is repeated infinitely many times. Each firm has will be discussed a discount factor o. Determine the critical discount factor above which in lecture. cooperation between the two firms can be sustained (i.e., playing grim trigger strategy by both firms is an equilibrium in the repeated game). 2. Explain generally (i) to what extent collusion / cooperation between the firms can be sustained, (ii) why collusion/ cooperation can create problems, and (iii) what we can do about it. Provide two real world examples of collusion /cooperation among players and discuss the above issues briefly. keep to AT/ C firm cases variations 3. (optional) Exercise 4.11 in the textbook. in problems 4. (optional) Exercise 4.12 in the textbook. 5. (optional) Exercise 4.13 in the textbook. OVan D in pro PS 4 ) [ Econ 580 ] market demand : Q = 200 - Cost function for each firm = ( ( ) zig, 1= 1, 2 ( b ) suppose the duopolists collude . Find : joint TT- max P, Q , IT . ( Q) Using cournot model , find each firm's = output ( qu) , price ( P. ) , ( TT ) profit If Firm 1 8 2 collude , they act as a monopolist . Market Demand : 0 = q , + 9 2 Q = 200 - P Demand function Market Demand : Q = 1 + 92 Q = 200 - P Inverse Demand P = 200 - @ Demand function Firm cost . C ( 9 1 ) = 209 i P = 200 - Q Demand Firm IT = T ; = P . ( ig ! ) . q - c (gi ) Firm IT : IT , = P . ( q ; ) . q ; - c (qi ) b - in : a, c ( g= ) Firm 1 IT : IT , = ( 200 - 9 , - 952) :9 - 20 0 Acting as monopolists , Firms 1 & 2 set MR = MC , 7 9 , , 82 TS = 2009 - 84 - 91 92 - 209+ If = - 87 - 9192+ 180g TR = P. Q = ( 200 - 1 ) Q = 200Q - Q2 Firm 1 IT-max . Problems : Of IT MR = OR = 200- 20 = 200 ( 8, + 82 ) 2Q FOC : 2 71 =- 29 - 92 + 180 = 0 180 - 92 - 81 MC = 209 , + 2092 = 20Q ( TC = 20Q2 ) 2 monopolist sets MR = MC - Qm Firm 2 IT : TT2 = ( 200 - 281 - 2 ) %2 - 209% z MR = MC 12 7 200%2 - 9182 - 82 - 209-2 200 - 2Q = 20Q TT 2 = - 92 - 9, 92 + 180gz 200 22Q - Q = 9.09 Firm 2 TT - max Problem : max Iz FOC 2 1 12 = - 292 - 81 + 180 = 0 180 - 81 = $2 P = 200- Q = 190.9 = P 292 2 : 9 = 180-92 180 - 180-91 . T = TR - TC 2 2 2 180 + 61 . 1 = 45+ 481 TT = ( 200 Q - Q 2 ) - 20Q 2 2 IT = ( 200 ( 9 .09 ) - (9.09 ) 2 ) - 20 ( 9.09 ) 2 8 1 = 45 + 481 48 = 45 - 8 1 = 45 7 0 Firm 1 81 7 60 Quantity IT = 82.81 . Q = 91 + %2 - 82 = 60 /Firm 2 Quantity, Q = 120 market equilibrium Quantity Co . P = 200- Q - P = 80 market Equilibrium price TTI = P . 9 , - C (8 , ) = ( 80 ) ( 60 ) - 20 ( 60 ) = 4800 - 1200 = 3600 = TT , TIz = P. $2 - C (q,) = (80 )60) - 20 (60) = 13600 = Tz Firm 1 & 2 Profits