2) Consider the Stackelberg Model of Duopoly in the class slides. Assume that Firm 1 and...
2) Consider the Stackelberg Model of Duopoly in the class slides. Assume that Firm 1 and Firm 2 have different marginal costs of productions—that is, Firm 1’s marginal cost of production is c1 and Firm 2’s is c2. Under this assumption, answer the following questions.
i) Let Firm 1 choose its quantity first. Find Firm 2’s reaction function and the backwards-induction outcome of the game. Also, find the profit of each firm at the backwards-induction outcome.
ii) Let Firm 2 choose its quantity first. Find Firm 1’s reaction function and the backwards-induction outcome of the game. Also, find the profit of each firm at the backwards-induction outcome.
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2) Consider the Stackelberg Model of Duopoly in the class
slides. Assume that Firm 1 and...
In the Stackelberg model we saw in class there were two firms 1 and 2. Suppose...
In the Stackelberg model we saw in class there were two firms 1 and 2. Suppose that the market demand is p(Q) = 60−Q, where as in class Q is the aggregate quantity. The const function for firm 1 is c1(q1) = 10q1 and the cost function for firm 2 is c2(q2) = q2. Firm 1 is the leader and Firm 2 is the follower. (a) Solve for the follow’s reaction function, and the leader’s maximization problem. (b) Describe the...
Two firms are participating in a Stackelberg duopoly. The demand function in the market is given...
Two firms are participating in a Stackelberg duopoly. The demand function in the market is given by Q = 2000 − 2P. Firm 1’s total cost is given by C1(q1) = (q1) 2 and Firm 2’s total cost is given by C2(q2) = 100q2. Firm 1 is the leader and Firm 2 is the follower. (1) Write down the inverse demand function and the maximization problem for Firm 1 given that Firm 2 is expected to produce R2(q1). (2) Compute...
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...
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
2. (15 pts) Consider a Stackelberg duopoly game of quantity competition in U.S. cigarettes between Philip...
2. (15 pts) Consider a Stackelberg duopoly game of quantity competition in U.S. cigarettes between Philip Morris (PM, biggest brand is Marlboro) and RJ Reynolds (RJR, biggest brand is Camel). Philip Morris is the leader, and Reynolds is the follower. (We will obviously ignore state-minimum pricing and taxes for this question.) Market demand is described by the inverse demand function P 12 0.005Q. Each firm has a constant unit cost of production equal to 2. Prices are in S/pack, and...
Cournot vs. Stackelberg Oligopoly Suppose the inverse demand function and the cost functions for two duopolists...
Cournot vs. Stackelberg Oligopoly Suppose the inverse demand function and the cost functions for two duopolists are given by: P = 100 – (Q1 + Q2) C1(Q1) = 2Q1 C2(Q2) = 2Q2 a. Cournot: Assume two Cournot duopolists. i. What is firm 1’s Quantity and Profit? R1 = (100-Q1-Q2) * Q1 R1 = 100Q1 - Q12 - Q2Q1 MR1 = 100 - 2Q1 - Q2 C1(Q1) = 2Q1 MC1 = 2 MR1 = MC1 ii. What is firm 2’s Quantity...
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...
4. A Consider Cournot model of oligopoly where each firm simultaneously makes a quantity decision. Let...
4. A Consider Cournot model of oligopoly where each firm simultaneously makes a quantity decision. Let yi and y2 denote the quantities 1 and 2, respectively. Let P(Y) = 100-Y be the market-clearing price when the aggregate quantity on the market is Y y1 +y2. Assume that the cost function of firm 1 and firm 2 are as follows. C1(n)-60y1 and C2(2) 60y2. (a) Write down the profit function of firm 1 and firm 2. (of a homogeneous product) produced...
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...
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.
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...
2. (15 pts) Consider a Stackelberg duopoly game of quantity competition in U.S. cigarettes between Philip Morris (PM, biggest brand is Marlboro) and RJ Reynolds (RJR, biggest brand is Camel). Philip Morris is the leader, and Reynolds is the follower. (We will obviously ignore state-minimum pricing and taxes for this question.) Market demand is described by the inverse demand function P 12 0.005Q. Each firm has a constant unit cost of production equal to 2. Prices are in S/pack, 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...
4. A Consider Cournot model of oligopoly where each firm simultaneously makes a quantity decision. Let yi and y2 denote the quantities 1 and 2, respectively. Let P(Y) = 100-Y be the market-clearing price when the aggregate quantity on the market is Y y1 +y2. Assume that the cost function of firm 1 and firm 2 are as follows. C1(n)-60y1 and C2(2) 60y2. (a) Write down the profit function of firm 1 and firm 2. (of a homogeneous product) produced...
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...
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