1. Consider the following payoff matrix in which the numbers indicate the profit in millions of dollars for a duopoly based either on a high-pric or a low-price strategy. Firm A High-price Low-price A = $650 B = $300 A = $500 High-price B = $500 Firm B A = $300 B = $650 A = $400 B = $400 Low-price (a) What will be the result when each firm chooses a high-price strategy? (b) What will be the result when Firm A chooses a low-price strategy while Firm B maintains a high-price strategy? (c) What will be the result when Firm B chooses a low-price strategy while Firm A maintains a high-price strategy? (d) What will be the result when each firm chooses a low-price strategy? (e) What two conclusions can you draw about collusion?

1. Consider the following payoff matrix in which the numbers indicate the profit in millions of dollars for a duopoly based either on a high-pric or a low-price strategy. Firm A High-price Low-price A = $650 B = $300 A = $500 High-price B = $500 Firm B A = $300 B = $650 A = $400 B = $400 Low-price (a) What will be the result when each firm chooses a high-price strategy? (b) What will be the result when Firm A chooses a low-price strategy while Firm B maintains a high-price strategy? (c) What will be the result when Firm B chooses a low-price strategy while Firm A maintains a high-price strategy? (d) What will be the result when each firm chooses a low-price strategy? (e) What two conclusions can you draw about collusion?

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter13: best-practice Tactics: Game Theory

Section: Chapter Questions

Problem 3E

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1. Perloff Chapter 14, Exercise 3.13 3.13 A duopoly faces an inverse market demand function of p = 120 - Q. Firm 1 has a constant marginal cost of 20. Firm 2's constant marginal cost is 40. Calculate the output of each firm, market output, and price in (a) a collusive equilibrium or (b) a Nash-Cournot equilibrium. (Hint: See Solved Problem 14.10.) M
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Two firms produce identical products at zero cost, and theycompete by setting prices. If each firm charges a low price,then both firms earn profits of zero. If each firm charges ahigh price, then each firm earns profits of £30. If one firmcharges a high price and the other firm charges a low price,the firm that charges the lower price earns profits of £50, andthe firm charging the higher price earns profits of zero. (a) Which oligopoly model best describes this situation?(b) Write this game in normal form.(c) Suppose the game is infinitely repeated. Can theplayers sustain the "collusive outcome" as a Nashequilibrium if the interest rate is 50 percent? Explain. Please answer the a, b and c parts.
3. Consider a duopoly with a demand curve given by P = a -bQ, where a and b are positive constants and Q is the total production by the two firms. Firms sell identical goods and have an identical constant marginal cost of production c. Fixed costs are equal to zero. We assume firms choose quantities simultaneously (Cournot competition). a. Obtain the first order condition of profit maximization for each firm. Use graphical analysis and economic intuition to explain what they represent. b. Obtain the profit maximizing quantity for each firm. Explain what they represent using game theory concepts c. Demonstrate using relevant graphical analysis and economic intuition that the results obtained in b are not a Pareto Optimum for the firms involved. d. How would the graphical analysis in part a change if Firm A had a fixed cost of production