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5. (i) Consider a Cournot quantity setting game of simultaneous moves. Solve for the rationalizable strategies...
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) =...
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...
Two profit-maximizing firms compete in a market. Firm 1 chooses quantity qı > 0 and Firm...
Two profit-maximizing firms compete in a market. Firm 1 chooses quantity qı > 0 and Firm 2 chooses quantity 42 > 0. The market price is: p(91,92) = 8 - 2q1 - 42. The cost to Firm 1 of producing qi is C1 = 41. The cost to Firm 2 of producing 92 is C2 = 42 + 42. a.) * Calculate the best-response function for each firm. b.) Suppose the two firms choose their quantities simultaneously. What is the...
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'...
3. Cournot model: Quantity competition in simultaneous move homogeneous product duopoly explain in words. The market...
3. Cournot model: Quantity competition in simultaneous move homogeneous product duopoly explain in words. The market for bricks consists of two firms that produce identical products. Competition in the market is such that each of the firms simultaneously and independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 has a patented technology that provides it with a...
2. Consider a Cournot dupoly, but assume that demand is p(q) = 12 – 9 (ignoring...
2. Consider a Cournot dupoly, but assume that demand is p(q) = 12 – 9 (ignoring non-negativity) and and unit cost c= 3. Again, firms simultaneously pick quantities qı > 0 and q2 > 0 and the price is set to clear the market given the quantities chosen. 1. Write down the optimization problems that define the best responses, solve explicitly for the best response functions, and find all Nash equilibria. 2. Formulate the problem for a cartel that maximizes...
5. Consider two firms selling differentiated varieties of a product, e.g., Coke and Pepsi. Each firm...
5. Consider two firms selling differentiated varieties of a product, e.g., Coke and Pepsi. Each firm j chooses a price pj for its own variety. Since these varieties are close substitutes, the demand that each firm faces depends not only on its own price, but also the price of its competitor. Specifically, the demand for j’s variety is given by Dj (pj , p−j ) = max 0, 60 + p−j − 2pj Suppose that both firms can produce any...
2. Cournot competition: P1 and P2 (independently and simultaneously) choose quantities, qi and q2. The cost...
2. Cournot competition: P1 and P2 (independently and simultaneously) choose quantities, qi and q2. The cost of producing q units is c(ai)i and the demand curve is given by P(O) 10 Q: (i.e., if P1 produces qi and P2 produces q2; each sells all his units at price 10 1 92 (a) Find all NE. b) Now suppose that the game is played twice. Each firm chooses both a production quantity, and, firm 2 can choose to donate some of...
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...
Mathematical Question 3 (30pts) 3. Consider two firms are performing Cournot price competition in two differentiated...
Mathematical Question 3 (30pts) 3. Consider two firms are performing Cournot price competition in two differentiated goods markets. Firm 1 produces goods 1, and firm 2 produces goods 2, and two market demand functions are given by 91 (P1,P2) = 12-2p1 + P2 and 921,P2) = 12-2p2 + P 1. Furthermore, assume that the two firms have the same cost function such that fixed cost is $20 and variable cost is zero. a. (10pts) Calculate the equilibrium prices, quantities and...
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...
Two profit-maximizing firms compete in a market. Firm 1 chooses quantity qı > 0 and Firm 2 chooses quantity 42 > 0. The market price is: p(91,92) = 8 - 2q1 - 42. The cost to Firm 1 of producing qi is C1 = 41. The cost to Firm 2 of producing 92 is C2 = 42 + 42. a.) * Calculate the best-response function for each firm. b.) Suppose the two firms choose their quantities simultaneously. What is the...
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'...
3. Cournot model: Quantity competition in simultaneous move homogeneous product duopoly explain in words. The market for bricks consists of two firms that produce identical products. Competition in the market is such that each of the firms simultaneously and independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 has a patented technology that provides it with a...
2. Consider a Cournot dupoly, but assume that demand is p(q) = 12 – 9 (ignoring non-negativity) and and unit cost c= 3. Again, firms simultaneously pick quantities qı > 0 and q2 > 0 and the price is set to clear the market given the quantities chosen. 1. Write down the optimization problems that define the best responses, solve explicitly for the best response functions, and find all Nash equilibria. 2. Formulate the problem for a cartel that maximizes...
2. Cournot competition: P1 and P2 (independently and simultaneously) choose quantities, qi and q2. The cost of producing q units is c(ai)i and the demand curve is given by P(O) 10 Q: (i.e., if P1 produces qi and P2 produces q2; each sells all his units at price 10 1 92 (a) Find all NE. b) Now suppose that the game is played twice. Each firm chooses both a production quantity, and, firm 2 can choose to donate some of...
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...
Mathematical Question 3 (30pts) 3. Consider two firms are performing Cournot price competition in two differentiated goods markets. Firm 1 produces goods 1, and firm 2 produces goods 2, and two market demand functions are given by 91 (P1,P2) = 12-2p1 + P2 and 921,P2) = 12-2p2 + P 1. Furthermore, assume that the two firms have the same cost function such that fixed cost is $20 and variable cost is zero. a. (10pts) Calculate the equilibrium prices, quantities and...
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