1. Consider a market with demand P(Q) = 72 -30. Sup- pose that firms compete by setting prices in a Bertrand duopoly. Answer the following questions (i-iii) for each situation (a-b): i) What price would each firm want to set if they were the only firm in the market? ii) Write out the reaction function for each firm (this should tell what price one firm should set for all prices that the other firm could set between 0 and DO) . iii) Determine all Bertrand equilibria. Assume the following: . firms can only set prices in full dollars. . if a firm is indifferent between more than one price, they always set the lowest of those prices. (a) MC1 = 20 and MC2 = 20. (b) MC1 = 20 and MC2 = 10. 2. Consider a market with demand P(Q) = 42-2Q in which two firms compete. Firm 1 faces TO1 (Q) =90 and firm 2 faces TC2(Q) = 4Q. Suppose that firm 1 chooses their quantity first, then firm 2 sees that quantity, and then firm 2 sets their quantity (Stackelberg duopoly). (a) Find the reaction function for firm 2. (b) What is the marginal revenue for firm 1 (given that they know that firm 2 will best respond)? (c) Find the Stackelberg equilibrium (Q1, Q3, P*). (d) Determine profits for each firm and consumer sur- plus. (e) Which firm is better off? 3. Suppose that Pepsi and Coke are competing in a horizon- tally differentiated Bertrand market and setting prices. The demand curves are as follows: Qc = 100 - 2Pc + Pp Qp = 90 - 5Pp + 4Pc Coke face marginal cost MCc = 16 and Pepsi faces marginal cost MCp = 6. (a) Write the equation for the demand for coke in terms of price Po as a function of Pp and Qc. (b) Determine the marginal revenue for Coke as a func- tion of Pp and Qc. (c) Find the equation that tells how much Coke would produce for any price Pp using the above