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7. Two firms compete in a market to sell a homogeneous product with inverse demand function P = 600 - 30. Each firm produces at a constant marginal cost of $300 and has no fixed costs. Use this information to compare the output levels and profits in settings characterized by Cournot, Stackelberg, Bertrand, and collusive behavior. PQ1/Q1 = 300 600Q1 - 3Q21 -3Q1Q2/ = 300 300- 6Q1 - 3Q2 = 300 Q1 = 1/6(600 -300 - 3Q2) Q1 = 50 - 1/2Q2 Reaction function for firm 1 Q2 = 50 - 1/2Q1 Reaction function for firm 2 Cournot Q2 = = 1/6(600 -300 - 3Q1) Q2 = 50 - 1/2Q1 Q2 = 50 - 1/2(50 - 1/2Q1) Q2 = 50 - 25 + 1/4Q1 Q1 = 100/3 = 33.33 Output Q2 = 100/3 = 33.33 Output Equilibrium market price P = 600 - 3(Q2 + Q2) 600 - 3(100/3 + 100/3) = 400 Profits for firm 1 Profits for firm 2 III = TRI - C1 112 = TR2 - C2 = PQ1 - C1 = PQ2 - C2 = 400 * 100/3 - 300 * 100/3 = 400 * 100/3 - 300 * 100/3 = 10000/3 = $3,333.33 For firm 1 = 10000/3 = $3,333.33 For firm 2Stackelberg QL = (600 - 300)/2*3 = 50 Firm 1 output is QL = 50 OF = (600 - 300)/4*3 = 25 Firm 2 output is QF = 25 P = 600 -3*75 = 375 II1 = (375-300) * 50 = 3750 Profit for firm 1 112 = 75*25 = 1875 Profit for firm 2 Bertrand Under this competition, price is equal to marginal cost and profits are zero 600 - 3Q = 300 Q = 100 Output = 100 P = Zero Collusive Behavior MR=MC 600 - 6Q = 300 300 = 6Q Q = 50 Output P = 600 - 3*50 = 450 II = (450 - 300) * 50 = 7500 Profits