Homework Answers
To find the Best Response Function of the firms we need to solve their respective profit maximization problem.
And to find the Nash Equilibrium , we need to simultaneously solve the two Best Response Functions.
Because of asymmetricity, the
two firns produce different quantities in Equilibrium. Marginal
Cost of firm 1 is lesser than Marginal Cost of Firm 2 , therefore
the firm 1 will produce more .
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7. Consider an asymmetric Cournot duopoly game, where the two firms have different costs of production....
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...
Exercise 5: Two firms compete in a centralized market by choosing quantity produced (91,92) simultaneously. Aggregate p...
Exercise 5: Two firms compete in a centralized market by choosing quantity produced (91,92) simultaneously. Aggregate production determines price, according to the following inverse demand function: p = [85 - 2 (91 +92)]. Firm l's total costs of production) are TC = 541. Firm 2's total costs are TC2 = 1592 a. Graph the combination of quantities (91,92) that yield the following profits: 11 (91.42) = T12 (91,92) = 450 ; 11 (41,42) = 500 ; 200; 12 (91,92) =...
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.
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...
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, where firms 1 and 2 simul taneously and independently select quantities to produce in a market. 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 - 100 - 2q Suppose that each firm produces at a cost of 20 per unit. Further, assume that each firm's payoff is defined as its profit....
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...
Q4. Suppose a duopoly is characterized by the following profits: if the two firms collude and...
Q4. Suppose a duopoly is characterized by the following profits: if the two firms collude and charge the joint profit-maximizing price, they each earn a profit equal to 1500 in each period; if the two firms charge the Cournot–Nash price, they each earn a profit equal to 1200 in each period; and if one firm defects while the other charges the joint profit-maximizing price, the firm that defects earns 3000 and the other earns 0. [20 marks] a) [3 marks]...
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 game with 2 firms. Inverse demand function is given by P = 20...
Consider a Cournot game with 2 firms. Inverse demand function is given by P = 20 - (91 +92). The firm has MC=AC=5. Firms choose qi e 0,00) a) Find the Nash equilibrium (9:47). Calculate profits in equilibrium. b) Now suppose that a firm also has to pay a fixed cost of 20 if it produces some output. Write down the cost function of the firm. c) Find the Nash equilibrium (91:97) fixed costs are 20. Calculate equilibrium profits. How...
Consider a Cournot game with 2 firms. Inverse demand function is given by P= 20 –...
Consider a Cournot game with 2 firms. Inverse demand function is given by P= 20 – (91 +92). The firm has MC=AC=5. Firms choose qi € (0,0) a) Find the Nash equilibrium (9*.*). Calculate profits in equilibrium. b) Now suppose that a firm also has to pay a fixed cost of 20 if it produces some output. Write down the cost function of the firm. c) Find the Nash equilibrium (9.97) fixed costs are 20. Calculate equilibrium profits. How does...
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...
Exercise 5: Two firms compete in a centralized market by choosing quantity produced (91,92) simultaneously. Aggregate production determines price, according to the following inverse demand function: p = [85 - 2 (91 +92)]. Firm l's total costs of production) are TC = 541. Firm 2's total costs are TC2 = 1592 a. Graph the combination of quantities (91,92) that yield the following profits: 11 (91.42) = T12 (91,92) = 450 ; 11 (41,42) = 500 ; 200; 12 (91,92) =...
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...
5. Consider a version of the Cournot duopoly game, where firms 1 and 2 simul taneously and independently select quantities to produce in a market. 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 - 100 - 2q Suppose that each firm produces at a cost of 20 per unit. Further, assume that each firm's payoff is defined as its profit....
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...
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 game with 2 firms. Inverse demand function is given by P = 20 - (91 +92). The firm has MC=AC=5. Firms choose qi e 0,00) a) Find the Nash equilibrium (9:47). Calculate profits in equilibrium. b) Now suppose that a firm also has to pay a fixed cost of 20 if it produces some output. Write down the cost function of the firm. c) Find the Nash equilibrium (91:97) fixed costs are 20. Calculate equilibrium profits. How...
Consider a Cournot game with 2 firms. Inverse demand function is given by P= 20 – (91 +92). The firm has MC=AC=5. Firms choose qi € (0,0) a) Find the Nash equilibrium (9*.*). Calculate profits in equilibrium. b) Now suppose that a firm also has to pay a fixed cost of 20 if it produces some output. Write down the cost function of the firm. c) Find the Nash equilibrium (9.97) fixed costs are 20. Calculate equilibrium profits. How does...
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