4.8 In the Cournot oligopoly of Section 4.2.1, suppose that J = 2. Let each duopolist have constant average and marginal costs, as before, but suppose that 0 < c' < c². Show that firm 1 will have greater profits and produce a greater share of market output than firm 2 in the Nash equilibrium.
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- Try the analysis with an n-firm Cournot oligopoly in which one firm innovates to reduce cost from c to c/2. For this problem, assume n = 2, and use the demand and cost numbers used in the lecture. That is, let inverse market demand be given by P = 100 - Q, and let marginal cost be constant at 50 per unit before the innovation, and 25 per unit after the innovation. (a) Compute what the duopolist stands to gain from innovating. How does it compare to the perfectly competitive firm and to the monopolist? (b) What can you conclude about the relationship between concentration and innovationConsider two Cournot oligopolists, firm 1 and firm 2, in a homogenous product market. The market demand is P = 100 – 3Q and each firm has a constant marginal cost MC=10. The Cournot equilibrium quantity for each firm is: a. 7.5 b. 10 c. 5 d.15Instructions: Answer to the best of your ability. Show all of your work, the details, on this excel tab. Suppose two firms compete as Cournot Oligopolists. The profit functions of these two firms are π_1=(150-q_1-q_2 ) q_1-20q_1 π_2=(150-q_1-q_2 ) q_2-22q_2 Which generate the following best response functions. q_1=(150-20)/2-1/2 q_2 q_2=(150-20)/2-1/2 q_1 a. Plot these reaction functions in a graph with q1 on the horizontal axis and q2 on the vertical axis. b. Derive, I want to see your work, the Nash equilibrium outcome of this game. c. How does the Nash equilibrium change if the demand curve shifts out, a bigger intercept on the demand equation.
- Consider a market with a duopolist structure. Each firm has similar marginal costs. Based on this information, we can conclude that: ProfitsDeceit > ProfitsCollusion > ProfitsDuopoly > ProfitsTrust in collusion ProfitsDeceit > ProfitsDuopoly > ProfitsCollusion > ProfitsTrust in collusion ProfitsDeceit > ProfitsTrust in collusion > ProfitsDuopoly > ProfitsCollusion ProfitsCollusion > ProfitsDuopoly > ProfitsDeceit > ProfitsTrust in collusionq18 Consider a Cournot duopoly with the following inverse demand function: P = 600 − 6Q1 − 6Q2 . The firms' marginal costs are identical and are given by MCi(Qi) = 3Qi. Based on this information, firm 1 and 2's marginal revenue functions are a. MR1(Q1,Q2) = 600 − 12Q1 − 6Q2 and MR2(Q1,Q2) = 600 − 6Q1 − 12Q2. b. MR1(Q1,Q2) = 600 − 6Q1 − 12Q2 and MR2(Q1,Q2) = 600 − 12Q1 − 6Q2. c. MR1(Q1,Q2) = 600 − 12Q1 − 12Q2 and MR2(Q1,Q2) = 600 − 12Q1 − 12Q2 d. MR1(Q1,Q2) = 300 − 12Q1 and MR2(Q1,Q2) = 300 − 12Q2.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.
- On a diagram whose axes are the quantities produced by two identical Cournot oligopolists and compare them with a perfect price-fixing agreement that splits the monopoly profits between them. Then in the same diagram show the Stackelberg equilibrium output with one firm a leader and the other a follower. Compare it with the previous two situations.The figure below shows the market conditions facing two firms, Brooks, Inc., and Spring, Inc., in the domestic market for large utility pumps. Each firm has constant long-run costs, so that MC0 = AC0. As competitors in a duopoly, there are a number of models to determine output and prices. Assume that the Bertrand duopoly model applies, so that they both set price equal to their marginal cost. Initial output in this market will be 16,000 per year (this is split between the two firms), at a price of $300. (a) At the initial equilibrium, what is total surplus (consumer surplus plus producer surplus)? Suppose that Brooks, Inc. and Spring, Inc. form a joint venture, River Company, whose utility pumps replace the output sold by the parent companies in the domestic market. Assuming that River Company operates as a monopolist and that its costs equal MC0 = AC0, what is: (b) The price? (c) The output? (d) Total profit? (e) The resulting deadweight loss from River Company operating as a…The figure below shows the market conditions facing two firms, Brooks, Inc., and Spring, Inc., in the domestic market for large utility pumps. Each firm has constant long-run costs, so that MC0 = AC0. As competitors in a duopoly, there are a number of models to determine output and prices. Assume that the Bertrand duopoly model applies, so that they both set price equal to their marginal cost. Initial output in this market will be 16,000 per year (this is split between the two firms), at a price of $300. Suppose that Brooks, Inc. and Spring, Inc. form a joint venture, River Company, whose utility pumps replace the output sold by the parent companies in the domestic market. Assuming that River Company operates as a monopolist and that its costs equal MC0 = AC0, what is: (b) The price?
- The figure below shows the market conditions facing two firms, Brooks, Inc., and Spring, Inc., in the domestic market for large utility pumps. Each firm has constant long-run costs, so that MC0 = AC0. As competitors in a duopoly, there are a number of models to determine output and prices. Assume that the Bertrand duopoly model applies, so that they both set price equal to their marginal cost. Initial output in this market will be 16,000 per year (this is split between the two firms), at a price of $300. Suppose that Brooks, Inc. and Spring, Inc. form a joint venture, River Company, whose utility pumps replace the output sold by the parent companies in the domestic market. Assuming that River Company operates as a monopolist and that its costs equal MC0 = AC0, what is: (e) The resulting deadweight loss from River Company operating as a monopoly?The figure below shows the market conditions facing two firms, Brooks, Inc., and Spring, Inc., in the domestic market for large utility pumps. Each firm has constant long-run costs, so that MC0 = AC0. As competitors in a duopoly, there are a number of models to determine output and prices. Assume that the Bertrand duopoly model applies, so that they both set price equal to their marginal cost. Initial output in this market will be 16,000 per year (this is split between the two firms), at a price of $300. Suppose that Brooks, Inc. and Spring, Inc. form a joint venture, River Company, whose utility pumps replace the output sold by the parent companies in the domestic market. Assuming that River Company operates as a monopolist and that its costs equal MC0 = AC0, what is: (c) The output? (d) Total profit?Consider a COURNOT duopoly. Market demand is P(Q)=18-2Q, and each firm faces a marginal cost of $5 per unit. How much does each firm's producer surplus increase if firms can collude with each other? Assume the firms evenly split the producer surplus that comes from colluding.
