Question

1. Suppose the two firms cannot collude and instead compete in the Cournot Model in the market described in question 1 (market demand is still Q=18-P) with the same cost (C(Q)=1/2 *Q^2).
   1. Set up firm 1’s profit maximization.
      
      
      
   2. Solve for firm 1’s best response function.
      
      
      
      
   3. Solve for firm 1’s quantity, firm 2’s quantity, the equilibrium market quantity, and price. Show your work.
      
      
   4. Is this a Nash equilibrium?
      
      
   5. Do consumers prefer the Cournot competition equilibrium over the collusion of the two firms in question 3?
      
      
   6. Do the two firms prefer Cournot competition over colluding (assuming the collusion agreement is to split joint profits equally)?

Answer 1

d) e) NOW g Yes it is a Ne Collusion MR=Mc 18-2 Q = Q. 18-30, 0" = 6, P = 18-6 =12 80 C$ = Vg (18-12) x6 = 18 In coumot CS = Vo (18-9)x9 = 8112 40.5. Thus au Cournot Eqm 80 consumens Preeffero comnot compt Ans Higher as of Joint T un Cournot N. P.Q - C(0) (9) 2 - 1/2(9)2 92/9 = 40.5 2x 6-1,6)2 72-18= 54 un collusion T cu

As higher joint profits in collusion, so two firms prefer this only