Construct a numerical example based on a linear demand function and two firms with identical, constant marginal costs. a) Use your model to show that, a Cournot duopolist can "do better" by producing the monopoly output, under the assumption that its competitor reacts and adjusts its output optimally. b) How does this result compare to what the Stackelberg model predicted?
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Construct a numerical example based on a linear demand function and two firms with identical, constant marginal costs.
a) Use your model to show that, a Cournot duopolist can "do better" by producing the
b) How does this result compare to what the Stackelberg model predicted?
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- Cournot duopolists face a market demand curve given by P = 60 – 1/2Q, where Q is total market demand in units. Each firm can produce output at a constant marginal cost of $15/unit. a) What is the equilibrium price and quantity produced by each firm? b) What if the firm's engaged in Bertrand competition? c) What if one of the firms chose its quantity before its competitor? What is the name for this sort of competition? d) Which of the three forms of competition gives the greatest social surplus?Could you answer #2 please? Thanks! 1. Reproduce the numerical example from the chapter on Monopolistic Competition in the book by Krugman & Obstfeld. If you do not have the book, here is the relevant information (the model and the equations are the same as those in the slides). Consider two countries, Home and Foreign, with the following market sizes: SH = 900,000 and SF = 1,600,000. The demand function for industry i is represented by Q = S[( 1 / n − 1 / 30,000) ∙ (Pi − P)] While the total cost function is represented by TC = 750,000,000 + 5,000 ∙ Q (a) Compute the long-run equilibrium price and the long-run number of varieties in Home and in Foreign under AUTARKY. (b) Compute the long-run equilibrium price and the long-run number of varieties in the integrated market when there is FREE TRADE. (c) Compare (a) and (b) and show that both countries are better off. 2. Now suppose that the two countries that we considered in the numerical example of the previous exercise were to…Reproduce the numerical example from the chapter on Monopolistic Competition in the book by Krugman & Obstfeld. If you do not have the book, here is the relevant information (the model and the equations are the same as those in the slides). Consider two countries, Home and Foreign, with the following market sizes: SH = 900,000 and SF = 1,600,000. The demand function for industry i is represented by Q = S[( 1 / n − 1 / 30,000) ∙ (Pi − P)] While the total cost function is represented by TC = 750,000,000 + 5,000 ∙ Q (a) Compute the long-run equilibrium price and the long-run number of varieties in Home and in Foreign under AUTARKY. (b) Compute the long-run equilibrium price and the long-run number of varieties in the integrated market when there is FREE TRADE. (c) Compare (a) and (b) and show that both countries are better off. Now suppose that the two countries that we considered in the numerical example of the previous exercise were to integrate their automobile market with a…
- Consider two price-setting oligopolies supplying consumers in a certain region of a country. Firm 1 employs many of the people living there and the local government subsidizes its operations. In all other respects, the firms are identical-they have the same constant marginal cost, MC = 4, and produce the same good. The demand function for Firm 1 is q1 = 600 - 50p1 - 20p2 and for Firm 2 is q2 = 600 - 50p2 - 20p1, where p1 is Firm 1's price and p2 is Firm 2's price. a. What are the Nash-Bertrand equilibrium prices and quantities without the subsidy? b. What are they if Firm 1 receives a per-unit subsidy of S = 1? Compare the two equilibria.Market demand for widgets is p = 160 - 2Q. Whether there is just one firm selling widgets or many firms selling widgets, the marginal cost and average cost is 100.Assume there are two firms selling widgets acting as Stackelberg duopolists, with Firm 1 moving first and Firm 2 following. Further assume that Firm 1's marginal profit function at its maximum is Mπ(q1) = 75 - q1, where q1 is the amount of widgets sold by Firm 1. What is the quantity sold for each firm?Options are:Firm 1 sells 0 Firms 2 sells 80Firm 1 sells 25 firm 2 sells 64.5Firm 1 sells 15, Firm 2 sells 30Firm 1 sells 7.5 Firm 2 sells 15From question 12 (Stackelberg duopolists), what is the price of widgets?Options are:1501158565The demand function in a duopoly market is P(Q) = 300-0.3Q, where P is the price and Q is the total quantity demanded. Both companies have the same constant marginal cost, What is the deadweight loss if both companies maximize their profits and they are not allowed to cooperate? (MR is not MC since its not monopoly)
- Two firms are engaged in Cournot (simultaneous quantity) competition. Market-level inverse demand is given by P = 160 − 4Q Firm 1 has constant marginal costs of MC1 = 8, while Firm 2 has constant marginal costs of MC2 = 24. 1) Does there exist a low enough positive marginal cost for firm 1 such that firm 1 acts like a monopoly in this market, if so what is the MC if not why?Consider any market that has a demand curve given by: Qd = 240 - 2P. Where Qd is the total quantity demanded in the market, given in millions of units and P is the market price, calculated in monetary units. Imagine that there are 2 Cournot oligopolists operating in this market with Cmg = CVme = 15 and fixed monthly costs equal to 1,400. About this market, ask yourself: a) What is the reaction curve of oligopolists? b) What will be the production of each of the companies? c) What is the selling price practiced by oligopolists? d) What is the profit of each of the oligopolists? e) Imagine that one of the companies managed to implement a process innovation capable of halving its Cmg and CVme, so that they would go from 15 to 7.5. This investment implies an additional monthly expense of $1,800. Discuss the statement: "If this situation occurs, the innovative company will not implement variable cost reduction, as the quantity supplied in the market will increase very little; prices will…Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function: P=200-QA - QB where QA and QB are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are TCA = 1,500 + 55QA + Q₁² Assume that the firms form a cartel to act as a monopolist and maximize total industry profits (sum of Firm A and Firm B profits). In such a case, Company A will produce units and sell at Similarly, Company B will produce At the optimum output levels, Company A earns total profits of $ total industry profits are $ At the optimum output levels, the marginal cost of Company A is $ Cournot Equilibrium Company A Company B Total Industry Selling price The following table shows the long-run equilibrium if the firms act independently, as in the Cournot model (i.e., each firm assumes that the other firm's output will not change). Total industry output Price Output…
- Imagine any market divided by 2 Cournot oligopolists who have identical costs Marginal cost = Average cost = 200. About this market, ask yourself: a) If the demand curve for this market is given by Q = 1250 - 2.5P, where Q is the total quantity demanded in the market and P is the selling price, both given in units, what is the reaction curve of the oligopolists? b) What will be the quantity produced and the selling price of the oligopolists? c) A strategist considers that a good marketing campaign would be able to expand the Demand of this market to Q = 1,500 - 2.5P and that in this way, oligopolists could produce the same amount and make significantly greater profits. Such a campaign would generate a reduction in profits in the order of 70,000. Is it worth making this investment in marketing?Suppose Clomper's is a monopolist that manufactures and sells Stompers, an extremely trendy shoe brand with no close substitutes. The following graph shows the market demand and marginal revenue (MR) curves Clomper's faces, as well as its marginal cost (MC), which is constant at $30 per pair of Stompers. For simplicity, assume that fixed costs are equal to zero; this, combined with the fact that Clomper's marginal cost is constant, means that its marginal cost curve is also equal to the average total cost (ATC) curve. First, suppose that Clomper's cannot price discriminate. That is, it must charge each consumer the same price for Stompers regardless of the consumer's willingness and ability to pay. On the following graph, use the black point (plus symbol) to indicate the profit-maximizing price and quantity. Next, use the purple points (diamond symbol) to shade the profit, the green points (triangle symbol) to shade the consumer surplus, and the black points (plus symbol) to shade the…Consider an industry composed of only two firms, each producing an identical product. The two firms have identical constant marginal costs of production, zero fixed costs, and behave as leader-follower (Stackelberg duopolists). Which of the following conditions will hold in equilibrium? a) at least one firm makes zero profit no b) both firms make decisions at the same time yes c) the firm that moves first will make lower profit than the other firm yes d) one of the firms chooses its price first no no e) the combined profit of Stackelberg duopolists is higher than that of Bertrand duopolists yes f) the equilibrium price is greater than the equilibrium price under perfect competition but less than the equilibrium price in a Cournot model of duopoly > >