There are two firms in a market and they compete in a Nash-Cournot manner. Firm 1 faces the demand function p1(q1,92) = - 91 - 92, and has a total cost function TC1 = (91)2. Firm 2 faces the demand function p2(91,92) = 160 - 92 - 91, and has at cost function TC2 = (92)2. Answer each of the following questions. a. Find the Nash-Cournot equilibrim output v and price v for firm 1. b. Find the Nash-Cournot equilibrim output v and price v for firm 2.
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- Consider two firms that compete according to the Cournot model. Inverse demand is P (Q) = 16 − Q. Their cost functions are C (q1) = 2q1 and C (q2) = 6q2 (a) Solve for Nash equilibrium quantities of each firm (b) Suppose firm 2 becomes more inefficient and its cost function changes to C (q2) = xq2 where x > 6. How large must x be to cause firm 2 to not want to produce anything in equilibrium?Suppose that two companies – AlphaTech and BetaLabs – are competing for market share and must simultaneously decide whether to develop a new product. Both companies are reluctant to make a decision as it is only economical for one company to develop a new product. Each company earns nothing if they decide not to develop a new product. One company can earn $50 million by developing a new product only if their competitor does not. If both companies decide to develop a new product, they each lose $10 million. Complete the payoff matrix to represent this game. Based on your solution in part (a), determine the maximin solution.Consider two beer producers, POTUS Pilsner and Supreme Court Stout. If they advertise, they can both sell more beer and increase their revenue. However, the cost of advertising more than offsets the increased revenue so that each producer ends up with a lower profit than if they do not advertise. On the other hand, if only one advertises, that producer increases its market share and also its profit. Construct a payoff matrix using the following hypothetical information: If neither producer advertises, each earns a profit of $35 million per year. If both advertise, each earns a profit of $20 million per year. If one advertises and the other does not, the producer who advertises earns a profit of $50 million and the producer who does not advertise earns a profit of $9 million. If POTUS Pilsner wants to maximize profit, will it advertise? Briefly explain. If Supreme Court Stout wants to maximize profit, will it advertise? Briefly explain. Is there a dominant strategy for each…
- Boeing and Airbus have to decide whether to invest in the development of a Super Jumbo for long distance travel; if they both develop successfully the new plane, their profits will drop by 50 millions a year; if only one develop the Super Jumbo, it will make 80 millions a year in additional profits, whereas the profits of the other firm will drop by 30 millions a year; if no firm develops the plane, nothing changes. Based on giveninformation, construct Matrix Representation of Boeing and Airbus Companies game. Using a payoff matrix to determine the equilibrium outcome Suppose there are only two firms that sell tablets: Padmania and Capturesque. The following payoff matrix shows the profit (in millions of dollars) each company will earn, depending on whether it sets a high or low price for its tablets. Capturesque Pricing High Low Padmania Pricing High 9, 9 3, 15 Low 15, 3 7, 7 For example, the lower-left cell shows that if Padmania prices low and Capturesque prices high, Padmania will earn a profit of $15 million, and Capturesque will earn a profit of $3 million. Assume this is a simultaneous game and that Padmania and Capturesque are both profit-maximizing firms. If Padmania prices high, Capturesque will make more profit if it chooses a price, and if Padmania prices low, Capturesque will make more profit if it chooses a price. If Capturesque prices high, Padmania will make more profit if it chooses a price, and if Capturesque prices low, Padmania…Consider trade relations between the United States and Mexico. Assume that the leaders of the two countries believe the payoffs to alternative trade policies are shown in the following payoff matrix: United States' Decision Low Tariffs High Tariffs Mexico's Decision Low Tariffs $28 billion, $28 billion $20 billion, $30 billion High Tariffs $30 billion, $20 billion $25 billion, $25 billion The dominant strategy for the United States is always to choose tariffs. The dominant strategy for Mexico is always to choose tariffs. True or False: The Nash equilibrium outcome for trade policy is for the United States to have low tariffs and Mexico to have high tariffs. True False In 1993, the U.S. Congress ratified the North American Free Trade Agreement, in which the United States and Mexico agreed to reduce trade barriers simultaneously. True or False: Given the trade strategy decisions in the table, the United States is better off and…
- Three firms produce identical products and compete in a market where the inverse demand function is P(q1, q2, q3) = 78 − q1− q2− q3. Each has a per-unit cost of 14 and zero fixed cost. They simultaneously choose quantities. In scenario (a), find the Nash equilibrium of this game and let A = firm 2's profit in the Nash equilibrium. In scenario (b), assume that the firms form a cartel, i.e., they act as a monopoly and split the profit evenly. If the total quantity produced by the cartel is Q, then the inverse demand is P(Q) = 78 - Q. Let B = firm 2's profit in the cartel. Calculate the value of A - B and enter your answer in the box below. Please round your answer to 3 decimal places (e.g., write 4/3 as 1.333).Consider a market dominated by two firms with identical cost functions C(q) = c*q for some constant “c”, both facing inverse demand function P(Q) = a – b*Q. Firms are in Bertrand competition by simultaneously setting prices (i.e., static, one-shot, simultaneous move game). If prices offers are equal, the two firms split the market. Suppose firms can pick only one of two prices: a high price or a low price. Construct an example with a 2 X 2 Normal Form payoff matrix using the profit functions of each firm as payoffs, and show that the low price is the Nash equilibrium. Now suppose firms can pick any price. Construct an argument to show that any pair of prices offered by the firms in which p>c is NOT a Nash equilibrium. Suppose again that firms can pick only one of two prices: high or low, but now suppose they have committed to a price-match guarantee. Construct another 2 X 2 Normal Form payoff matrix using the profit functions of each firm, and show whether high or low price (or…Two firms compete in prices in a market for a homogeneous product. In this market there are N > 0 consumers; each buys one unit if the price of the product does not exceed $10, and nothing otherwise. Consumers buy from the firm selling at a lower price. In case both firms charge the same price, assume that N/2 consumers buy from each firm. Assume zero production cost for both firms. Suppose that the firms set prices simultaneously in a game that is repeated infinitely. Let denote the time- discount parameter. Propose trigger price strategies for both firms yielding the collusive prices of ($10, $10) each period. Calculate the minimal value of that would enforce the trigger price strategies you proposed.