Homework Answers
In case of Bertrand competition, firms
A) when C=2 then P1=P2=2 and P1=P2=3 Are two pure strategy Nash equilibrium
b) P1=P2=3 is the only Nash equilibrium
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Consider the following variation of the Bertrand competition model (e.g., price competition) discussed in class. Two...
consider the standard Bertrand model of price competition. There are two firms that produce a homogenous...
consider the standard Bertrand model of price competition. There
are two firms that produce a homogenous good with the same constant
marginal cost of c.
a) Suppose that the rule for splitting up cunsumers when the
prices are equal assigns all consumers to firm1 when both firms
charge the same price. show that (p1,p2) =(c,c) is a Nash
equilibrium and that no other pair of prices is a Nash
equilibrium.
b) Now, we assume that the Bertrand game in part...
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...
Problem 4. Bertrand Competition with Different Costs Suppose two firms facing a demand D(p) compete by...
Problem 4. Bertrand Competition with Different Costs Suppose two firms facing a demand D(p) compete by setting prices simultaneously (Bertrand Competition). Firm 1 has a constant marginal cost ci and Firm 2 has a marginal cost c2. Assume ci < C2, i.e., Firm 1 is more efficient. Show that (unlike the case with identical costs) p1 = C1 and P2 = c2 is not a Bertrand equilibrium.
Problem 4. Bertrand Competition with Different Costs Suppose two firms facing a demand D(p) compete by setting prices s...
Problem 4. Bertrand Competition with Different Costs Suppose two firms facing a demand D(p) compete by setting prices simultaneously (Bertrand Competition). Firm 1 has a constant marginal cost ci and Firm 2 has a marginal cost c2. Assume ci < C2, i.e., Firm 1 is more efficient. Show that (unlike the case with identical costs) p1 = (1 and p2 = c2 is not a Bertrand equilibrium.
Problem 5: Product Differentiation in a Bertrand Setting. Firms 1 and 2 face the same AC...
Problem 5: Product Differentiation in a Bertrand Setting. Firms 1 and 2 face the same AC = MC = 30 but sell differentiated products. The demands for firms 1 and 2 are given by D.(P1, P2) = 70 – P1 + P2 D2(P1, P2) = 70 – P2 +5 P1 The firms choose prices Pı and P2 simultaneously. a) For each firm, represent profits as a function of both prices p and p2. b) Find the best response function for...
Please answer the following question fully and in detail! Consider a Bertrand duopoly with two firms...
Please answer the following question fully and in detail! Consider a Bertrand duopoly with two firms 1,2 who sell the same good. The demand curve of the good is given by Q = 15 − p if p < 15 and Q = 0 if p ≥ 15. Both firms have the same constant unit cost 2. Firms 1,2 set prices p1, p2. If firms set different prices, then the firm which sets the minimum price of the two, receives...
Please answer the following question fully and in detail! Consider a Bertrand duopoly with two firms...
Please answer the following question fully and in detail! Consider a Bertrand duopoly with two firms 1,2 who sell the same good. The demand curve of the good is given by Q = 30 − p if p < 30 and Q = 0 if p ≥ 20. Both firms have the same constant unit cost 5. Firms 1,2 set prices p1, p2. If firms set different prices, then the firm which sets the minimum price of the two, receives...
QUESTION 6 Consider the Hotelling model of the competition between two firms discussed in class. Select...
QUESTION 6 Consider the Hotelling model of the competition between two firms discussed in class. Select all that apply. a.If both firms are localized in position 1/2 (i.e., center of the line), neither firm has incentives to deviate and move to a different position. D. If Firm 1 is located at position 1/2 (i.e., center of the line) and firm 2 is located somewhere else, then both firms have incentives to deviate and change their position along the line. C....
1. Consider two firms engaging in Bertrand Competition. Each firm picks a price at which to...
1. Consider two firms engaging in Bertrand Competition. Each firm picks a price at which to charge for their good. All of the demand for the good goes to the firm with the lowest price, where the quantity demanded = 1000-P. If the firms’ prices are the same, firm 1 gets all of the demand. The cost-per-product produced by firm 1 is MC=2, and the costper-product produced by firm 2 is MC=5. Suppose that the firms can charge any continuous...
Suppose there are two firms in a market producing differentiated products. Both firms have MC=0. The...
Suppose there are two firms in a market producing differentiated products. Both firms have MC=0. The demand for firm 1 and 2’s products are given by: q1(p1,p2) = 5 - 2p1 + p2 q2(p1,p2) = 5 - 2p2 + p1 a. First, suppose that the two firms compete in prices (i.e. Bertrand). Compute and graph each firm’s best response functions. What is the sign of the slope of the firms’ best-response functions? Are prices strategic substitutes or complements? b. Solve...
consider the standard Bertrand model of price competition. There
are two firms that produce a homogenous good with the same constant
marginal cost of c.
a) Suppose that the rule for splitting up cunsumers when the
prices are equal assigns all consumers to firm1 when both firms
charge the same price. show that (p1,p2) =(c,c) is a Nash
equilibrium and that no other pair of prices is a Nash
equilibrium.
b) Now, we assume that the Bertrand game in part...
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...
Problem 4. Bertrand Competition with Different Costs Suppose two firms facing a demand D(p) compete by setting prices simultaneously (Bertrand Competition). Firm 1 has a constant marginal cost ci and Firm 2 has a marginal cost c2. Assume ci < C2, i.e., Firm 1 is more efficient. Show that (unlike the case with identical costs) p1 = C1 and P2 = c2 is not a Bertrand equilibrium.
Problem 4. Bertrand Competition with Different Costs Suppose two firms facing a demand D(p) compete by setting prices simultaneously (Bertrand Competition). Firm 1 has a constant marginal cost ci and Firm 2 has a marginal cost c2. Assume ci < C2, i.e., Firm 1 is more efficient. Show that (unlike the case with identical costs) p1 = (1 and p2 = c2 is not a Bertrand equilibrium.
Problem 5: Product Differentiation in a Bertrand Setting. Firms 1 and 2 face the same AC = MC = 30 but sell differentiated products. The demands for firms 1 and 2 are given by D.(P1, P2) = 70 – P1 + P2 D2(P1, P2) = 70 – P2 +5 P1 The firms choose prices Pı and P2 simultaneously. a) For each firm, represent profits as a function of both prices p and p2. b) Find the best response function for...
QUESTION 6 Consider the Hotelling model of the competition between two firms discussed in class. Select all that apply. a.If both firms are localized in position 1/2 (i.e., center of the line), neither firm has incentives to deviate and move to a different position. D. If Firm 1 is located at position 1/2 (i.e., center of the line) and firm 2 is located somewhere else, then both firms have incentives to deviate and change their position along the line. C....
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