a. They compete in quantities with each other (Cournot-Nash equilibrium).b. They collude as though they are all plants of the same single multi-plant monopoly.c. B and C act as two plants of a single multi-plant monopoly “B+C”, which competes in quantities (Cournot competition) against A. PROBLEM (3)total cost function TC(Q) = 3Q2. Calculating the market price under each of the 5 scenarios below, rank/order theConsumer Surplus in each scenario (don't calculate each CS; just rank them);In a market with demand Q = 780 - p, there are 3 identical firms, A, B and C; each with a

Market demand function : Q = 780 - p Inverse demand function : p = 780 - Q Where , Q = Q1 + Q2 + Q3 p = 780 - ( Q1 + Q2 + Q3 ) Cost function : C = 3Q2 a . ) In Cournot- Duopoly Model all the firms simultaneously optimize their outputs taking other firms output as constant . For Firm 1 : Optimal production condition : MR = MC TR = p*Q1 = (780 - ( Q1 + Q2 + Q3 ))Q1 MR = d(TR)/dQ1 = 780 - 2Q1 - Q2 - Q3 MC = d(C)/dQ1 = 6Q1 Putting values into condition : 780 - 2Q1 - Q2 - Q3 = 6Q1 8Q1 = 780 - Q2 - Q3 ---(i) (best response function of firm 1 ) Similarly , best response functions of all other firms will be symmetric as the firms face same demand and cost conditions : 8Q2 = 780 - Q1 -Q3 ---(ii) (best response function of firm 2 ) 8Q3 = 780 - Q1 - Q2 ----(iii) (best response function of firm 3 ) Now , we solve add these equations in order to get value of (Q = Q1 + Q2 + Q3 ) On adding we get , 8(Q1+ Q2 +Q3 ) = 780 - 2(Q1 + Q2 +Q3 ) 10 Q = 780 Q* = 78 We put this value into demand function : p = 780 - Q * P* = 780 - 78 P* = 702 b .) In collusion all the firms jointly maximize their profits acting as a monopolistic entity : Optimal condition for a monopoly : MR = MC TR = p*Q = ( 780 - Q )Q MR = 780 - 2Q MC = 6Q Putting in condition : 780 - 2Q = 6Q Q = 97.5 Putting in demand condition : P** = 682.5 c .) Let the Output of B+C be (Qbc ) and Output of firm A be (Q1 ) Demand function : P = 780 - (Q1 + Qbc ) For Firm 1 : Optimal production condition : MR = MC TR = p*Q1 = (780 - ( Q1 +Qbc))Q1 MR = d(TR)/dQ1 = 780 - 2Q1 - Qbc MC = d(C)/dQ1 = 6Q1 Putting in condition : 780 - 2Q1 -Qbc = 6Q1 8Q1 = 780 - Qbc (Reaction function of firm A ) For Merged Entity : Optimal production condition : MR = MC TR = p*Qbc = (780 - ( Q1 +Qbc))Qbc MR = d(TR)/dQbc = 780 - 2Qbc - Q1 MC = d(C)/dQbc = 6Qbc MR = MC 780 - 2Qbc - Q1 = 6Qbc 8Qbc = 780 - Q1 Adding 2 reaction functions we get same as in part (a) : Q* = 78 We put this value into demand function : p = 780 - Q * P* = 780 - 78 P* = 702 Consumer Surplus declines as prices increase . So , consumer surplus in part a = CS in part c < CS in part ( b)