The inverse market demand for a certain good is: -2/ P = 100- where Q is the industry output. There are two symmetric firms producing the good, each with the following cost function: TC; = 10g, where q, is the output of the ith firm (i=1,2). (a) Suppose that the firms are competing in quantities. If someone produces more than their share of the cartel output, the other firm punishes them by re- verting to the Cournot output. What is the critical value of the discount factor 8? (b) Now assume that the detection lag (the time required to discover and re-

The inverse market demand for a certain good is: -2/ P = 100- where Q is the industry output. There are two symmetric firms producing the good, each with the following cost function: TC; = 10g, where q, is the output of the ith firm (i=1,2). (a) Suppose that the firms are competing in quantities. If someone produces more than their share of the cartel output, the other firm punishes them by re- verting to the Cournot output. What is the critical value of the discount factor 8? (b) Now assume that the detection lag (the time required to discover and re-

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

Chapter12: Price And Output Determination: Oligopoly

Section: Chapter Questions

Problem 2E

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There are two firms in the blastopheme industry. The demand curve for blastophemes is given by p=2100-3q. Each firm has one manufacturing plant and each firm i has a cost function C(qi)=qi2 , where qi is the output of firm i. The two firms from a cartel and arrange to split total industry profits equally. Under this cartel arrangement, what will they do if they want to maximize joint profits?.
Suppose the market demand for a product is Q(P) = 120 – P. There are no fixed costs of operating in this industry, but there are variable costs VC(Q) = 20Q. (b) Suppose there are two firms A and B in this industry, with identical costs functions (as above), who are thinking of colluding to maintain the monopoly quantity. What profits would they be able to make if they would split the monopoly quantity equally, i.e. QA = QB = QM/2? (d) Is the cartel as described in (b) sustainable if the firms interact only once? Justify and then interpret your answer. PLEASE ONLY ANSWER D SINCE I ALREADY UNDERTAND B
Cournot model: linear demand; identical firms. Q(P)=D-P TC(C)=cQ, where D>c a) Suppose that there are 2 firms. They can either choose to produce the Cournot quantity, or choose to produce one half of the monopoly quantity. Write down the 2X2 “payoff matrix” for this game. b) If D= 6 and c = 2, suppose that the game is repeated infinitely often with a discount factor of beta. For what values of beta will it be possible to sustain collusion? c) Now consider the same game with 3 firms. Compute the profits in the static Cournot- Nash equilibrium, and the profits when the 3 firms each produce one third of the monopoly quantity. For what values of beta will it be possible to sustain collusion in this case?
Consider an industry with two firms, each having marginal costs and total costs equal to zero. The industry demand is P = 100 − Q where Q = Q1 + Q2 is total output. 4. If the firms interact only once, is there a profitable deviation (cheating) from cartel for any firm? Find the profit of the firms in case of cheating. If a firm deviates from cartel (cheats) it will play its profit maximizing quantity, which is the quantity on its best response function. Now, use the best response function of firm 1 to find firm 1's cheating quantity, when firm 2 follows the rules of the cartel. Use the demand curve to find the new price level and then calculate profits. 5. Design a 2x2 normal form payoff matrix with strategies cartel and cheat. Complete the payoffs using the profits you calculated in the previous parts. Firm 2 Cartel Cheat Firm 1 Cartel Cheat 6. Now, assume that players interact twice. Hence the game is a twice repeated game. Is it possible to have (cartel,cartel) as an outcome?…
Cournot’s Model of Duopoly) Joe and Rebecca are small-town ready-mix concrete duopolists. The market demand function is Qd=5500-25P, where P is the price of a cubic metre of concrete and Qd is the number of cubic metres demanded every year. The marginal cost is $40 per cubic metre. Competition in this market is described by the Cournot model. (a)Given Rebecca’s output is 2000, what is Joe’s residual demand function? What is Joe's output so he maximizes his profit? (b)If Rebecca’s output is qR, what is Joe’s best response function? (c)If Joe’s output is qj, what is Rebecca’s best response function? (d)Plot both Joe and Rebecca’s best response functions on one graph, where the the horizontal axis represents Rebecca’s output qR and the vertical axis represents Joe's output qR. (e)What is the meaning of the interception of the two best response functions?
Gamma and Zeta are the only two widget manufacturers in the world. Each firm has a cost function given by: C(q) = 10+20q + q^2, where q is number of widgets produced. The market demand for widgets is represented by the inverse demand equation: P = 200 - 2Q where Q = q1 + q2 is total output. Suppose that each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists). a) What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm? Equilibrium quantity for each firm__ price__ profit__ b) It occurs to the managers of Gamma and Zeta that they could do a lot better by colluding. If the two firms were to collude in a symmetric equilibrium, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case? Equilibrium quantity for each firm__ price__ profit__ c) What minimum discount factor is required…
Two dairy farmers produce milk for a local town with local milk demand given by Q=100-1/3P(P denotes price measured in Rands, Q denotes the quantity measured in liters). Both farmers have the same cost function given by TC=150+2q(wheredenotes output).(a) Determine the reaction function of each farmer. (b) Find the Cournot-Nash equilibrium. (c) Calculate profits for each farmer (d) Suppose that both farmers decide to form a cartel, determine profitsfor each farmer under the cartel (e) What output should farmer 1 produce if he/she expects their rival to produce 20 units? (f) Calculate the profits if farmer 2 decides to break the cartel agreement (g) Does joining a cartel offer any benefits to both farmers? Justify your answer (h) What if farmer 1 is a leader and farmer 2 a follower, determine the price, quantity and profits made by these two farmers. Please solve d, e,f,g and h
Two dairy farmers produce milk for a local town with local milk demand given by Q=100-1/3P(P denotes price measured in Rands, Q denotes the quantity measured in liters). Both farmers have the same cost function given by TC=150+2q(wheredenotes output).(a) Determine the reaction function of each farmer. (b) Find the Cournot-Nash equilibrium. (c) Calculate profits for each farmer (d) Suppose that both farmers decide to form a cartel, determine profitsfor each farmer under the cartel (e) What output should farmer 1 produce if he/she expects their rival to produce 20 units? (f) Calculate the profits if farmer 2 decides to break the cartel agreement (g) Does joining a cartel offer any benefits to both farmers? Justify your answer (h) What if farmer 1 is a leader and farmer 2 a follower, determine the price, quantity and profits made by these two farmers. Please answer g and h
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 QAQA and QBQB 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+Qa2 TCb=1,200+20Qb+2Qb2 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 units and sell at $ . At the optimum output levels, Company A earns total profits of $ and the marginal cost of Company B earns total profits of $ . Therefore, the total industry profits are $ . At the optimum output levels, the marginal cost of Company A is $ and the marginal…
Producers in three countries have formed a cartel to sell a highly-priced product. Suppose the world demand for the product is consistent with the equation: P=80-0.005QT NB: QT is the total cartel sales. The producers have managed to maximise profit at a price of R70 per unit. Suppose the members have the following total cost functions; Member 1: TC=7382 + 10Q + 0.05Q2 Member 2: TC= 9374 + 20Q + 0.02Q2 Member 3: TC=7432 + 30Q + 0.03Q2 : Derive: a) Marginal revenue b) Output of member 1,2 and 3 c) Total cartel output.
In the Nash equilibrium of a Cournot game with two firms who have identical marginal costs, each firm chooses to produce half of the quantity that would be produced by a monopolist, given the same aggregate demand and marginal cost.(a) True. (b) False.
An oligopoly firm faces a kinked demand curve with the two segments given by: P = 230 – 0.5Q and P = 280 – 1.5Q. The firm currently has a constant marginal cost, MC of $150. State the assumptions of the kinked demand model in terms of price-matching and elasticity.