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Q.3 Two firms (i 1, 2) produce differentiated products. The demand function for the product of...
Q.3 Two firms (i 1, 2) produce differentiated products. The demand function for the product of...
Q.3 Two firms (i 1, 2) produce differentiated products. The demand function for the product of firm i is given by: qiVi, pj) 4-pi + 2pj firm i and pj the price chosen by its competitor. Firm 1 chooses its price first and firm 2 chooses its price after observing the price of firm 1. The cost function of each firm is G(%) 21. Find the subgame-perfect Nash equilibrium. , where Pi is the price chosen by
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...
Q.2 Two firms (i- 1, 2) produce differentiated produets. The market-clearing price is given by: pl60-lj,...
Q.2 Two firms (i- 1, 2) produce differentiated produets. The market-clearing price is given by: pl60-lj, where is the quantity chosen by firm i and qj the quantity chosen simultaneously by its competitor. The cost function of each firm is C,(a)-10q Q.2.a Find the response functions and show the response functions graphically. Q.2.b Identify the Nash equilibrium. Q.2.c Calculate each firm's equilibrium profit.
2. Two firms produce homogeneous products. Market demand is given by Q = 40-P, and each firm face...
2. Two firms produce homogeneous products. Market demand is given by Q = 40-P, and each firm faces a marginal cost of production of 4 per unit The timing of the game is as follows. In Period 1, firm 1 chooses the quantity q it will sell. In Period 2, firm 2 (who observed firm 1s choice in period 1) chooses whether or not to enter the market. If firm 2 chooses to enter it must pay an entry fee...
Q.2 Two firms produce homogeneous products. The inverse demand function is: p(x1,x2)-a-x1- x2, where x is...
Q.2 Two firms produce homogeneous products. The inverse demand function is: p(x1,x2)-a-x1- x2, where x is the quantity chosen by firm 1, x2 the quantity chosen by firm 2, and a > 0. The cost functions are C1 (x1)-x follower. and C2(x2)- . Firm I is a Stackelberg leader and firm 2 a Stackelberg Q.2.a Find the subgame-perfect quantities. Q.2.b Calculate each firm's equilibrium profit.
2.13. Recall the static Bertrand duopoly model (with homoge- neous products) from Problem 1.7: the firms name prices si...
2.13. Recall the static Bertrand duopoly model (with homoge- neous products) from Problem 1.7: the firms name prices simul- taneously; demand for firm i's product is a - Pi if Pi < Pi, is 0 if Pi > Pi, and is (a – Pi)/2 if Pi = Pj; marginal costs are c < a. Consider the infinitely repeated game based on this stage game. Show that the firms can use trigger strategies (that switch forever to the stage-game Nash equilibrium...
3. (35 points Suppose that there are K( 3) firms operate in a market with demand...
3. (35 points Suppose that there are K( 3) firms operate in a market with demand function given by P(Q) = 100-Q, where Q=91 +92 + ... +2K, and qi is the quantity produced by firm i. Each firm has a constant marginal cost of production, c = 10, and no fixed cost. The firms choose their quantities dynamically as follows: Firm 1, which is the industry leader, chooses qı € (0, 100). All other firms i = 2,..., K...
Suppose that the inverse market demand for a commodity is given by P = 240 Q...
Suppose that the inverse market demand for a commodity is given by P = 240 Q The cost curves of the three firms which could serve this market are TC,(a) 30q +300 and TC2() (d) Suppose that firms engage in Stackelberg rather than Cournot competition. Firm 1 moves first by choosin its output level. After Firm 1 has chosen its output level, Firm 2 observes ql and chooses its output leve Find the subgame-perfect Nash equilibrium of the Stackelberg game....
2 Two firms compete in a market by selling differentiated products. The demand equations are given...
2 Two firms compete in a market by selling differentiated products. The demand equations are given by the following equations: P2 91 = 75 - Pi + P1 92 = 75 - P2 + 2 assume that each firm has a marginal cost (and average costs) of o. a. What market model do we use if each firm competes by simultaneously choosing price? b. Are the two goods substitutes? C. Solve for firm 1's best response function. d. Solve for...
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...
Q.3 Two firms (i 1, 2) produce differentiated products. The demand function for the product of firm i is given by: qiVi, pj) 4-pi + 2pj firm i and pj the price chosen by its competitor. Firm 1 chooses its price first and firm 2 chooses its price after observing the price of firm 1. The cost function of each firm is G(%) 21. Find the subgame-perfect Nash equilibrium. , where Pi is the price chosen by
Q.2 Two firms (i- 1, 2) produce differentiated produets. The market-clearing price is given by: pl60-lj, where is the quantity chosen by firm i and qj the quantity chosen simultaneously by its competitor. The cost function of each firm is C,(a)-10q Q.2.a Find the response functions and show the response functions graphically. Q.2.b Identify the Nash equilibrium. Q.2.c Calculate each firm's equilibrium profit.
2. Two firms produce homogeneous products. Market demand is given by Q = 40-P, and each firm faces a marginal cost of production of 4 per unit The timing of the game is as follows. In Period 1, firm 1 chooses the quantity q it will sell. In Period 2, firm 2 (who observed firm 1s choice in period 1) chooses whether or not to enter the market. If firm 2 chooses to enter it must pay an entry fee...
Q.2 Two firms produce homogeneous products. The inverse demand function is: p(x1,x2)-a-x1- x2, where x is the quantity chosen by firm 1, x2 the quantity chosen by firm 2, and a > 0. The cost functions are C1 (x1)-x follower. and C2(x2)- . Firm I is a Stackelberg leader and firm 2 a Stackelberg Q.2.a Find the subgame-perfect quantities. Q.2.b Calculate each firm's equilibrium profit.
2.13. Recall the static Bertrand duopoly model (with homoge- neous products) from Problem 1.7: the firms name prices simul- taneously; demand for firm i's product is a - Pi if Pi < Pi, is 0 if Pi > Pi, and is (a – Pi)/2 if Pi = Pj; marginal costs are c < a. Consider the infinitely repeated game based on this stage game. Show that the firms can use trigger strategies (that switch forever to the stage-game Nash equilibrium...
3. (35 points Suppose that there are K( 3) firms operate in a market with demand function given by P(Q) = 100-Q, where Q=91 +92 + ... +2K, and qi is the quantity produced by firm i. Each firm has a constant marginal cost of production, c = 10, and no fixed cost. The firms choose their quantities dynamically as follows: Firm 1, which is the industry leader, chooses qı € (0, 100). All other firms i = 2,..., K...
Suppose that the inverse market demand for a commodity is given by P = 240 Q The cost curves of the three firms which could serve this market are TC,(a) 30q +300 and TC2() (d) Suppose that firms engage in Stackelberg rather than Cournot competition. Firm 1 moves first by choosin its output level. After Firm 1 has chosen its output level, Firm 2 observes ql and chooses its output leve Find the subgame-perfect Nash equilibrium of the Stackelberg game....
2 Two firms compete in a market by selling differentiated products. The demand equations are given by the following equations: P2 91 = 75 - Pi + P1 92 = 75 - P2 + 2 assume that each firm has a marginal cost (and average costs) of o. a. What market model do we use if each firm competes by simultaneously choosing price? b. Are the two goods substitutes? C. Solve for firm 1's best response function. d. Solve for...
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...
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