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5. Consider a version of the Cournot duopoly game, where firms 1 and 2 simul taneously...
5. Consider a version of the Cournot duopoly game, which will be thoroughly analyzed in Chapter...
5. Consider a version of the Cournot duopoly game, which will be thoroughly analyzed in Chapter 10. Two firms (1 and 2) compete in a homogeneous goods market, where the firms produce exactly the same good. The firms simultaneously and independently select quantities to produce. The quantity selected by firm i is denoted q, and must be greater than or equal to zero, for i - 1,2. The market price is given by p-2 - q1 -q2. For simplicity, as...
Consider the Cournot duopoly model in which two firms, 1 and 2, simul- taneously choose the...
Consider the Cournot duopoly model in which two firms, 1 and 2, simul- taneously choose the quantities they supply, q1 and q2. The price each will face is determined by the market demand function (q1, q2) = a − b(q1 + q2). Each firm has a probability μ of having a marginal unit cost of cL, and a probability 1 − μ of having a marginal unit cost of cH, cH > cL. These probabilities are common knowledge, but the...
1. Consider the following asymmetric version of the Cournot duopoly model. Two firms compete by simultaneously...
1. Consider the following asymmetric version of the Cournot duopoly model. Two firms compete by simultaneously choosing the quantities (q, and q2) they produce. Their products are homogeneous, and market demand is given by p- 260-2Q, where Q-q +q2. Firm 1 has a cost advantage; Firm 1 produces at zero cost, while Firm 2 produces at a constant average cost of 40. (The difference in costs is what makes this an asymmetric game.) a. Derive both firms' profit functions, as...
7. Consider an asymmetric Cournot duopoly game, where the two firms have different costs of production....
7. Consider an asymmetric Cournot duopoly game, where the two firms have different costs of production. Firm 1 selects quantity qı at a pro- duction cost of 291. Firm 2 selects quantity 92 and pays the produc- tion cost 492. The market price is given by p = 12 – 91 - 92. Thus, the payoff functions are u(91,92) = (12 – 91 - 92.91 – 291 and uz(9192) = (12 – 91 - 92)92 – 492. Calculate the firms'...
Problem 1 Consider the following Cournot's duopoly, where two identical firms compete by setting quantities. Suppose...
Problem 1 Consider the following Cournot's duopoly, where two identical firms compete by setting quantities. Suppose the Market demand is P = 80 - 2Q and firm's cost function is TC = 20qi, where i = 1,2 (a) Determine each firm's equilibrium quantity, profit and the market equilibrium price. Explain (b) Suppose firms decide to form a cartel. In the static (one-period) case, will they be able to sustain the cartel? Explain using the appropriate pay-off matrix (c) How will...
1. (25 points) Consider two firms, 1 and 2, producing an identical good simul taneously. This...
1. (25 points) Consider two firms, 1 and 2, producing an identical good simul taneously. This good has market demand given by the demand function y (12 p)/3, where p is price, and y yi y2 is market quantity. yi represents the amount produced by firm i. Suppose production cost is 2yi1 for each firms (a) Solve algebraically for these firms' reaction functions, expressing each firm's optimal output level given the level of its competitor's out- put.(5 pts) (b) Graph...
Problem 2. Gibbons 1.5 Consider the following two finite versions of the Cournot duopoly model. First,...
Problem 2. Gibbons 1.5 Consider the following two finite versions of the Cournot duopoly model. First, suppose each firm must choose either half the monopoly quantity, 4m/2 = (a - c)/4, or the Cournot equilibrium quantity, 4c = (a - c)/3. No other quantities are feasible. Show that this two-action game is equivalent to the Prisoner's Dilemma: each firm has a strictly dominated strategy, and both are worse off in equilibrium than they would be if they cooperated. Second, suppose...
2. (Cournot Model) Consider a Cournot duopoly. The market demand is p=160 - q2. Firm 1's...
2. (Cournot Model) Consider a Cournot duopoly. The market demand is p=160 - q2. Firm 1's marginal cost is 10, and firm 2's marginal cost is also 10. There are no fixed costs. A. Derive each firm's best response function B. What is the Nash equilibrium of this model? Find the equilibrium market price. C. Find the equilibrium profit for each firm D. Find the equilibrium consumer surplus in this market. 3. (Bertrand Model) Consider a Bertrand duopoly. The market...
Question 5 Demand in a market dominated by two firms (a Cournot duopoly) is determined according...
Question 5 Demand in a market dominated by two firms (a Cournot duopoly) is determined according to: P = 200 – 2(Q1 + Q2), where P is the market price, Q1 is the quantity demanded by Firm 1, and Q2 is the quantity demanded by Firm 2. The marginal cost and average cost for each firm is constant; AC=MC = $60. The cournot-duopoly equilibrium profit for each firm is _____. Hint: Write your answer to two decimal places. QUESTION 6...
1. Consider the coupon game. But suppose that instead of decisions being made simultaneously, they are made sequentially, with Firm 1 choosing first, and its choice observed by Firm 2 before Firm 2 ma...
1. Consider the coupon game. But suppose that instead of
decisions being made simultaneously, they are made sequentially,
with Firm 1 choosing first, and its choice observed by Firm 2
before Firm 2 makes its choice.
a. Draw a game tree representing this game.
b. Use backward induction to find the solution. (Remember that
your solution should include both firms’ strategies, and that Firm
2’s strategy should be complete!)
2. Two duopolists produce a homogeneous product, and each has a...
5. Consider a version of the Cournot duopoly game, which will be thoroughly analyzed in Chapter 10. Two firms (1 and 2) compete in a homogeneous goods market, where the firms produce exactly the same good. The firms simultaneously and independently select quantities to produce. The quantity selected by firm i is denoted q, and must be greater than or equal to zero, for i - 1,2. The market price is given by p-2 - q1 -q2. For simplicity, as...
1. Consider the following asymmetric version of the Cournot duopoly model. Two firms compete by simultaneously choosing the quantities (q, and q2) they produce. Their products are homogeneous, and market demand is given by p- 260-2Q, where Q-q +q2. Firm 1 has a cost advantage; Firm 1 produces at zero cost, while Firm 2 produces at a constant average cost of 40. (The difference in costs is what makes this an asymmetric game.) a. Derive both firms' profit functions, as...
7. Consider an asymmetric Cournot duopoly game, where the two firms have different costs of production. Firm 1 selects quantity qı at a pro- duction cost of 291. Firm 2 selects quantity 92 and pays the produc- tion cost 492. The market price is given by p = 12 – 91 - 92. Thus, the payoff functions are u(91,92) = (12 – 91 - 92.91 – 291 and uz(9192) = (12 – 91 - 92)92 – 492. Calculate the firms'...
Problem 1 Consider the following Cournot's duopoly, where two identical firms compete by setting quantities. Suppose the Market demand is P = 80 - 2Q and firm's cost function is TC = 20qi, where i = 1,2 (a) Determine each firm's equilibrium quantity, profit and the market equilibrium price. Explain (b) Suppose firms decide to form a cartel. In the static (one-period) case, will they be able to sustain the cartel? Explain using the appropriate pay-off matrix (c) How will...
1. (25 points) Consider two firms, 1 and 2, producing an identical good simul taneously. This good has market demand given by the demand function y (12 p)/3, where p is price, and y yi y2 is market quantity. yi represents the amount produced by firm i. Suppose production cost is 2yi1 for each firms (a) Solve algebraically for these firms' reaction functions, expressing each firm's optimal output level given the level of its competitor's out- put.(5 pts) (b) Graph...
Problem 2. Gibbons 1.5 Consider the following two finite versions of the Cournot duopoly model. First, suppose each firm must choose either half the monopoly quantity, 4m/2 = (a - c)/4, or the Cournot equilibrium quantity, 4c = (a - c)/3. No other quantities are feasible. Show that this two-action game is equivalent to the Prisoner's Dilemma: each firm has a strictly dominated strategy, and both are worse off in equilibrium than they would be if they cooperated. Second, suppose...
2. (Cournot Model) Consider a Cournot duopoly. The market demand is p=160 - q2. Firm 1's marginal cost is 10, and firm 2's marginal cost is also 10. There are no fixed costs. A. Derive each firm's best response function B. What is the Nash equilibrium of this model? Find the equilibrium market price. C. Find the equilibrium profit for each firm D. Find the equilibrium consumer surplus in this market. 3. (Bertrand Model) Consider a Bertrand duopoly. The market...
1. Consider the coupon game. But suppose that instead of
decisions being made simultaneously, they are made sequentially,
with Firm 1 choosing first, and its choice observed by Firm 2
before Firm 2 makes its choice.
a. Draw a game tree representing this game.
b. Use backward induction to find the solution. (Remember that
your solution should include both firms’ strategies, and that Firm
2’s strategy should be complete!)
2. Two duopolists produce a homogeneous product, and each has a...
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