(1) Two firms produce goods that are imperfect substitutes. If firm 1 charges price pi and firm 2 charges price p2, then their respective demands are q1 = 12 – 2p1 +p2 and 42 = 12 + P1 – 2p2. So this is like Bertrand competition, except that when p1 > P2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c= 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, pi = the optimal price for firm 1 if it is known that firm 2 charges a price P2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. BR1 (p2) is

(1) Two firms produce goods that are imperfect substitutes. If firm 1 charges price pi and firm 2 charges price p2, then their respective demands are q1 = 12 – 2p1 +p2 and 42 = 12 + P1 – 2p2. So this is like Bertrand competition, except that when p1 > P2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c= 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, pi = the optimal price for firm 1 if it is known that firm 2 charges a price P2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. BR1 (p2) is

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…
7. Jie is a firm manager deciding its sales quantity strategy. His firm is in a market with another competitor, and he is the leader in the sequential game. Collusion is impossible. The market inverse demand function is P = 16 – Q, where Q is the total quantity of q? the production. The cost functions of Jie's firm and the other firm are c(g) and c(q) = q?, respectively. So Jie should set the quantity as С. 4 A. 8 В. 6 D. 2
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Suppose the robot assistant market consists of two firms: MultiTech and MicroRobo. Each of the two firms must simultaneously choose to set either a high price or a low price for its robots. If both MultiTech and MicroRobo set a high price, their profits will be SEK 30 million each. Conversely, if they both set a low price, their profits will be only SEK 3 million. On the other hand, if one firm sets a high price while the other sets a low price, the high-priced firm will incur a loss of SEK 15 million, while the low-priced firm will gain a profit of SEK 90 million. Answer the following questions: a) Write the payoff matrix of this game. b) How many Nash equilibria are there? Identify each equilibrium, what is the dominant strategy? c) Suppose MultiTech has a well-known brand, therefore receiving profits 15% higher than MicroRobo in all strategies. Explain how this would affect the payoff matrix and the firms' strategies.
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