Consider an industry with two firms competing in prices and producing a homogeneous product at a constant marginal cost c = 20 and no fixed costs. The market demand is given by P(Q) = 100-2Q. 1. What are the optimal competitive prices, quantities and profits? (1 point) 2. If firms were able to collude, which price, quantity and profit would they agree on? (1 point) 3. How would firm 1 cheat on its competitor and which profit would it get? (1 point) 4. Under which conditions would the collusive agreement be an equilibrium? Explain the role of the time horizon and the type of strategies needed. (2 point) 5. Write the condition for firm 1 to find it optimal to collude and express the resulting critical discount factor delta as a function of the profits. What is the minimum delta in this context? (2 points)