d) (1 point) Now suppose both firms are capacity-constrained: Firm 1 can produce at most 13 units, and Firm 2 can produce at most 41 units. If firms set different prices, consumers will first buy from the firm charging the lower price. Once that firm's supply is exhausted, consumers will buy from the firm charging the higher price until that firm's supply is exhausted. What is Firm 1's equilibrium profit? Two firms, Firm 1 and Firm 2, compete by simultaneously choosing prices. Both firms sell an identical product for which each of 100 consumers has a maximum willingness to pay of $40. Each consumer will buy at most 1 unit, and will buy it from whichever firm charges the lowest price. If both firms set the same price, they share the market equally. Costs are given by c, (q,) = 16g,. Because of government regulation, firms can only choose prices which are integer numbers, and they cannot price above $40. Answer the following: a) (0.25 point) if Firm 1 chooses p, = 37, Firm 2's best response is to set what price? 36 b) (0.25 point) If Firm 2 chooses the price determined in the previous question, Firm T's best response is to choose what price? 35 c) (1 point) If Firm 1 chooses pi = 6, Firm 2's best response is a range of prices. What is the lowest price in this range? 7 d) (1 point) Now suppose both firms are capacity-constrained: Firm 1 can produce at most 13 units, and Firm 2 can produce at most 41 units. If firms set different prices, consumers will first buy from the firm charging the lower price. Once that firm's supply is exhausted, consumers will buy from the firm charging the higher price until that firm's supply is exhausted. What is Firm 1's equilibrium profit? 312 3 . Consider the following oligopolistic market. In the first stage, Firm 1 chooses quantity ? 1q1. Firms 2 and 3 observe Firm 1's choice, and then proceed to simultaneously choose . 2q2 and . 3q3, respectively. Market demand is given by ? (? )=100-? p(Q)=100-Q, and ? =? 1+? 2+? 3Q=q1+q2+q3. Firm 1's costs are ?1(?1)=3? 1c1(q1)=3q1, firm 2's costs are ?2(? 2)=4? 2c2(q2)=4q2 and firm 3's costs are ? 3(?3)=4? 3c3(q3)=4q3. Starting from the end of the game, you can express Firm 2's best response function in terms of ? 1q1 and ?3q3, and you can similarly express Firm 3's best response function in terms of 1q1 and ? 2q2. Using these, answer the following questions. a) (0.5 point) If Firm 1 chooses . 159q1=9, what quantity will Firm 2 choose? b) (0.5 point) If Firm 1 chooses . 1=100q1=100, what quantity will Firm 2 choose? c) (1 point) In the subgame perfect Nash equilibrium of this game, firm 1 produces what quantity? d) (0.5 point) In the subgame perfect Nash equilibrium of this game, firm 2 and firm 3 each produce what quantity? Consider the following oligopolistic market. In the first stage, Firm 1 chooses quantity q1. Firms 2 and 3 observe Firm 1's choice, and then proceed to simultaneously choose ; and q), respectively. Market demand is given by p(Q) = 100 - Q, and ( = 41 + 42 + 43. Firm 1's costs are ci(91) = 31. firm 2's costs are cy(42) = 442 and firm 3's costs are Cy(9)) = 493- Starting from the end of the game, you can express Firm 2's best response function in terms of 9, and 43, and you can similarly express Firm 3's best response function in terms of q, and 92. Using these, answer the following questions. a) (0.5 point) If Firm 1 chooses 41 9, what quantity will Firm 2 choose? 29 b) (0.5 point) If Firm 1 chooses q1 = 100, what quantity will Firm 2 choose? O V c) (1 point) In the subgame perfect Nash equilibrium of this game, firm 1 produces what quantity? 49.5 d) (0.5 point) In the subgame of this game, firm 2 and firm 3 each produce what quantity? 15.5 Quiz 8 A manufacturer of flash drives has a profit function =?-10? 2n=t-10q2 where ?t is the price charged for a flash drive and . 2q2 is the cost of producing a drive whose capacity is . q gigabytes. A consumer of type e has a utility