Answer Happy

Question 1 Consider two firms competing under Bertrand Price Competition and they have the following total costs of production, TC1 =1001 TC2 =1002 In other words, both firms have constant marginal costs of $10 per unit. Let the market demand be given by P = 100 - Q, where Q is the market quantity and equals Q1 + Q2. Under Cournot competition, the equilibrium is Q1 =Q2 = 30andP, =P2=40. a) Suppose the firms begin under Cournot Quantity Competition and are now competing under Bertrand Price Competition, prove that there is a profitable deviation for Firm 1 to set a price of P, = 39. What is the profit of Firm 2 after Firm 1's deviation? b) Continuing with the situation stated in a), show that there is a profitable deviation for Firm 2 to set a price of P2 =38(while FirmlisatP1 =39). c) Prove that the Bertrand equilibrium prices are P1 = P2 = 10. (Show that there is no profitable deviation for any Firm to set a different price.) d) Illustrate the two firm's best response functions on a graph under Bertrand Competition.