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In class we examined a model of Bertrand competition in which all consumers had the same RP, i.e. $3. This corresponds to a demand curve of the following form. D(p) = 100 for 0 3. Here you will examine a model of Bertrand competition in which not all consumers have the same RP. Two firms selling the identical product compete in Bertrand fashion by setting their prices pi and P2 simultaneously. Whichever firm sets the lower price will get the entire market, whereas the other will sell zero units. If firms set the same price, then they will each get half of the market. The total demand at a unit price of p is given by D(p) = 25 – 0.5p. So, if firm l's price p1 < P2, firm l's demand will be 25 – 0.5p1 while firm 2's demand will be 0. If p1 = P2 = P, then firm l's demand will be 0.5(25 – 0.5p) and firm 2's demand will be the same. q? where q is the quantity Both firms face the same cost function, which is given by C(q) produced.

In class we examined a model of Bertrand competition in which all consumers had the same RP, i.e. $3. This corresponds to a demand curve of the following form. D(p) = 100 for 0 3. Here you will examine a model of Bertrand competition in which not all consumers have the same RP. Two firms selling the identical product compete in Bertrand fashion by setting their prices pi and P2 simultaneously. Whichever firm sets the lower price will get the entire market, whereas the other will sell zero units. If firms set the same price, then they will each get half of the market. The total demand at a unit price of p is given by D(p) = 25 – 0.5p. So, if firm l's price p1 < P2, firm l's demand will be 25 – 0.5p1 while firm 2's demand will be 0. If p1 = P2 = P, then firm l's demand will be 0.5(25 – 0.5p) and firm 2's demand will be the same. q? where q is the quantity Both firms face the same cost function, which is given by C(q) produced.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In class we examined a model of Bertrand competition in which all consumers had the same RP, i.e. $3. This corresponds to a demand curve of the following form. D(p) = 100 for 0 <p < 3 and D(p) = 0 for all p > 3. Here you will examine a model of Bertrand competition in which not all consumers have the same RP. Two firms selling the identical product compete in Bertrand fashion by setting their prices pi and p2 simultaneously. Whichever firm sets the lower price will get the entire market, whereas the other will sell zero units. If firms set the same price, then they will each get half of the market. The total demand at a unit price of p is given by D(p) = 25 – 0.5p. So, if firm l's price pi < P2, firm l's demand will be 25 – 0.5p1 while firm 2's demand will be 0. If pi = P2 = P, then firm l's demand will be 0.5(25 – 0.5p) and firm 2's demand will be the same. Both firms face the same cost function, which is given by C(q) : produced. q where q is the quantity 1a) Is p1 = p2 = 150/11 a Nash equilibrium? b)Identify another price (not mentioned above) which is a Nash Equilibrium.
Transcribed Image Text:In class we examined a model of Bertrand competition in which all consumers had the same RP, i.e. $3. This corresponds to a demand curve of the following form. D(p) = 100 for 0 <p < 3 and D(p) = 0 for all p > 3. Here you will examine a model of Bertrand competition in which not all consumers have the same RP. Two firms selling the identical product compete in Bertrand fashion by setting their prices pi and p2 simultaneously. Whichever firm sets the lower price will get the entire market, whereas the other will sell zero units. If firms set the same price, then they will each get half of the market. The total demand at a unit price of p is given by D(p) = 25 – 0.5p. So, if firm l's price pi < P2, firm l's demand will be 25 – 0.5p1 while firm 2's demand will be 0. If pi = P2 = P, then firm l's demand will be 0.5(25 – 0.5p) and firm 2's demand will be the same. Both firms face the same cost function, which is given by C(q) : produced. q where q is the quantity 1a) Is p1 = p2 = 150/11 a Nash equilibrium? b)Identify another price (not mentioned above) which is a Nash Equilibrium.
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