Nash equilibrium in price model of duopoly
In the price model duopoly, the firms 1 and 2 produce quantities d1 and d2 as a functions of their prices p1, p2.
In this case:
d1 = max {0; 5 - p1 + 3p2} and d2 = max {0; 10 - 2p1 + p2}.
The firms have no production cost and they choose the prices at the same time and
independent of what the other chooses.
Solve for the Nash equilibrium and write down the best response functions of the firms.
Homework Answers
Suppose there are two firms in a market producing differentiated products. Both firms have MC=0. The...
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Please answer the following question fully and in detail! Consider a Bertrand duopoly with two firms...
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Please answer the following question fully and in detail! Consider a Bertrand duopoly with two firms...
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6. Entry Deterrence 2: Consider the Cournot duopoly game with demand p= 100 - (qı+q2) and...
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1 (Bertrand Model with sequential move) Consider a Bertrand duopoly model with two firms, Fi and...
1 (Bertrand Model with sequential move) Consider a Bertrand duopoly model with two firms, Fi and Fa selling two varieties of a product. The demand curve for Fi's product is 91 (pi,P2) = 10-Pl + 0.5p2: and the demand for F's product is where p is the price charged by F). Both firms have a constant marginal cost of (a) Write down the profits of F1 and F2 as a function of prices P1 and P2. You have b) Derive...
Suppose that identical duopoly firms have constant marginal costs of $16 per unit. Firm 1 faces...
Suppose that identical duopoly firms have constant marginal costs of $16 per unit. Firm 1 faces a demand function of q1 130-2p1+1p2 where q1 is Firm 1's output, p1 is Firm 1's price, and p2 is Firm 2's price. Similarly, the demand Firm 2 faces is 2 130-2P2+ 1p1 Solve for the Bertrand equilibrium. Note that OTI _-130-2p1 + 1p2-2p1 +32-0 op1 and oP2 p 130-2p2+ 1p1-2p2+320 In equilibrium, p1 equals $and p2 eqs (Enter numeric responses using integers.)
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...
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...
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...
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...
1 (Bertrand Model with sequential move) Consider a Bertrand duopoly model with two firms, Fi and Fa selling two varieties of a product. The demand curve for Fi's product is 91 (pi,P2) = 10-Pl + 0.5p2: and the demand for F's product is where p is the price charged by F). Both firms have a constant marginal cost of (a) Write down the profits of F1 and F2 as a function of prices P1 and P2. You have b) Derive...
Suppose that identical duopoly firms have constant marginal costs of $16 per unit. Firm 1 faces a demand function of q1 130-2p1+1p2 where q1 is Firm 1's output, p1 is Firm 1's price, and p2 is Firm 2's price. Similarly, the demand Firm 2 faces is 2 130-2P2+ 1p1 Solve for the Bertrand equilibrium. Note that OTI _-130-2p1 + 1p2-2p1 +32-0 op1 and oP2 p 130-2p2+ 1p1-2p2+320 In equilibrium, p1 equals $and p2 eqs (Enter numeric responses using integers.)
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...
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...
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...
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