Consider a duopoly Cournot game, where Firm 1 and Firm 2 have the same marginal cost...
Consider a duopoly Cournot game, where Firm 1 and Firm 2 have the same marginal cost of production c = 3. The total quantity produced by the firms is Q. The demand function is p(Q) = 84 − Q.
a.) Write down Firm 1’s profit function.
b.) * Calculate Firm 1’s best-response function.
c.) * Find the pure-strategy Cournot-Nash equilibrium of this game.
d.) * Show that the firms make strictly positive profit in equilibrium.
e.) Explain intuitively why the firms are able to make strictly positive profit in equilibrium
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Consider a duopoly Cournot game, where Firm 1 and Firm 2 have
the same marginal cost...
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...
6. Entry Deterrence 2: Consider the Cournot duopoly game with demand p= 100 - (qı+q2) and...
6. Entry Deterrence 2: Consider the Cournot duopoly game with demand p= 100 - (qı+q2) and variable costs c;(q;) = 0 for i € {1, 2}. The twist is that there is now a fixed cost of production k > 0 that is the same for both firms. Assume first that both firms choose their quantities simultaneously. Model this as a normal-form game. b. Write down the firm's best-response function for k = 1000 and solve for a pure-strategy Nash...
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...
Cournot: Consider a Cournot duopoly in which firms A and B simultaneously choose quantity. Both firms...
Cournot: Consider a Cournot duopoly in which firms A and B simultaneously choose quantity. Both firms have constant marginal cost of $20 and zero fixed cost. Market demand is given by: P = 140 − qA − qB. (a) Derive the best-response functions for each firm and plot them on the same graph. (b) Calculate the profits of each firm in the Nash Equilibrium outcome.
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'...
Consider a cournot model of a duopoly market where Firm X and Firm Y operate. Each...
Consider a cournot model of a duopoly market where Firm X and Firm Y operate. Each firm has marginal cost equal to $20, and the market demand is Q = 100 - (1/2) P. There are no fixed costs. a) Show the best-response function of each firm. b) Calculate the profit-maximizing output level for each firm. c) What is the equilibrium price? d) Calculate the profit for each firm.
Problem three Two firms in a homogencous-product duopoly market (firm 1 and firm 2) have the following cost and demand functions: TC 4 TC24q2 and Q-40-P: Q-+2 a Derive the reaction function/best-resp...
Problem three Two firms in a homogencous-product duopoly market (firm 1 and firm 2) have the following cost and demand functions: TC 4 TC24q2 and Q-40-P: Q-+2 a Derive the reaction function/best-response function for each firm. b) Assume that the firms play a simultaneous move game. Characterize the Nash Equilibrium. cSuppose the two firms play game is a sequential game with the following timing of events: 1. Firm 1 chooses output 2. Firm 2 observes firm 1's output and then...
In Cournot duopoly , the inverse demand function is P=150-Q Firm 1 and Firm costs are...
In Cournot duopoly , the inverse demand function is P=150-Q Firm 1 and Firm costs are C1=1000+12q1 and C2=2000+6q2 What is the profit maximization , best reaction function to find Nash equilibrium Price
(16 points) Cournot Duopoly. Market demand is p(Q) = 50 – 4Q, where Q = 4+...
(16 points) Cournot Duopoly. Market demand is p(Q) = 50 – 4Q, where Q = 4+ 42. Firm 1's cost function is C (91) = 0, and firm 2 has a cost function C2(92) = 1092- The two firms engage in Cournot competition; they simultaneously choose a quantity and the price adjusts so that the market clears. (a) Formally write firm 1's profit maximization problem (b) Find firm l's best response function. (c) Take as given that firm 2's best...
Consider a Bertrand duopoly in a market where demand is given by Q firm has constant marginal cost equal to 20 100 - P. Each (a) If the two firms formed a cartel, what would they do? How much profit...
Consider a Bertrand duopoly in a market where demand is given by Q firm has constant marginal cost equal to 20 100 - P. Each (a) If the two firms formed a cartel, what would they do? How much profit would eaclh firm make? (6 marks) (b) Explain why the outcome in part (a) is not a Nash Equilibrium. Find the set of Nash Equilibria and explain why it/they constitute Nash equilibria. (6 marks) (c) Now suppose that instead of...
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...
6. Entry Deterrence 2: Consider the Cournot duopoly game with demand p= 100 - (qı+q2) and variable costs c;(q;) = 0 for i € {1, 2}. The twist is that there is now a fixed cost of production k > 0 that is the same for both firms. Assume first that both firms choose their quantities simultaneously. Model this as a normal-form game. b. Write down the firm's best-response function for k = 1000 and solve for a pure-strategy Nash...
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...
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 three Two firms in a homogencous-product duopoly market (firm 1 and firm 2) have the following cost and demand functions: TC 4 TC24q2 and Q-40-P: Q-+2 a Derive the reaction function/best-response function for each firm. b) Assume that the firms play a simultaneous move game. Characterize the Nash Equilibrium. cSuppose the two firms play game is a sequential game with the following timing of events: 1. Firm 1 chooses output 2. Firm 2 observes firm 1's output and then...
(16 points) Cournot Duopoly. Market demand is p(Q) = 50 – 4Q, where Q = 4+ 42. Firm 1's cost function is C (91) = 0, and firm 2 has a cost function C2(92) = 1092- The two firms engage in Cournot competition; they simultaneously choose a quantity and the price adjusts so that the market clears. (a) Formally write firm 1's profit maximization problem (b) Find firm l's best response function. (c) Take as given that firm 2's best...
Consider a Bertrand duopoly in a market where demand is given by Q firm has constant marginal cost equal to 20 100 - P. Each (a) If the two firms formed a cartel, what would they do? How much profit would eaclh firm make? (6 marks) (b) Explain why the outcome in part (a) is not a Nash Equilibrium. Find the set of Nash Equilibria and explain why it/they constitute Nash equilibria. (6 marks) (c) Now suppose that instead of...
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