(1) Suppose that two identical rms produce widgets and that they are the only firms in the market. Their costs are given by C.1 =60Q1 and C2 = GOQ2 , where Q1 is the output of Firm 1 and Q 2 is the output of Firm 2. Price is determined by the following demand curve: P=300-Q Where Q =Q1+ Q2 a. Find the CournotN ash equilibrium. Calculate the profit of each firm at this equilibrium. b. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm's profit. c. Suppose Firm 1 were the only firm in the industry. How would market output and Firm 1's profit differ from that found in part (b) above? Ii Returning to the duopoly of part (b), suppose Firm 1 abides by the agreement but Firm 2 cheats by increasing production. How many widgets will Firm 2 produce? What will be each rm's profit? (2) Two competing firms are each planning to introduce a new product. Each will decide whether to produce Product A, Product B, or Product C. They will make their choices at the same time. The resulting payoffs are shown below. Firm2 A B c | A | 10,10 | 0,10 | 10,20 Firml | B | 10,0 |20,20 | 5, 15 | c | 20,10 | 15, -5 | 30, -30 a. Are there any Nash equilibria in pure strategies? If so, what are they? b. If both firms use maxmin strategies, what outcome will result? c. If Firm 1 uses a maxmin strategy and Firm 2 knows this, what will Firm 2 do? (3) Joe and Sarah's Investment Dilemma