1) explain the part b, why is that the profit maximising condition? 2) explain why the collusive price would be 6, 3) explain how do I know the firm is not covering fixed costs, thanks !

* Suppose that duopoly firms have a fixed cost of production equal to f100, but marginal costs are zero. Further suppose that these firms do not produce identical products. Firm 1 faces a demand curve Q1 = 12 - 2P, + P2 and Firm 2 faces a demand curve of Q2 = 12 - 2P2 + P1. a. Are the two goods substitutes or complements? b. Assuming that firms compete over prices, solve for the Bertrand equilibrium prices and quantities. ANSWER: a. Substitutes. If the price of one product increase, demand for the other increases. b. m1 = P1Q1 - 100 = 12P1 - 2P? + P1P2 - 100. Maximising profit with respect to P1 results in firm 1's best response function: P1 = 3 + = P2. Firm 2's best response function is P2 = 3 + = P1. The firm's are mutually best responding where prices are E4 and where quantity is 8. You can verify on your own that the collusive price would be E6. Note that both firms are not covering fixed costs, so they will likely exit the market in the long run