Consider the following 2–firm (firm 1 and 2) model of Bertrand duopoly with differen- tiated products. Demand for firm i is q:(Pi, Pj) = a – Pi – bi.Pj costs are zero for both firms. The sensitivity of firm i's demand to firm j's price is measured by b;. (a) First suppose b1 # b2. Find the equilibrium prices pi and p2. (b) Deduce that if the two firms are identical, they choose the same price p where b = b, = bɔ. а 2+6

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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Chapter12: Price And Output Determination: Oligopoly
Section: Chapter Questions
Problem 1E
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Consider the following 2-firm (firm 1 and 2) model of Bertrand duopoly with differen-
tiated products. Demand for firm i is
q:(Pi, P;) = a – Pi – bi.Pj
costs are zero for both firms. The sensitivity of firm i's demand to firm j's price is
measured by bị.
(a) First suppose b1 # b2. Find the equilibrium prices p1 and p2.
(b) Deduce that if the two firms are identical, they choose the same price p = 216)
where b = b1 = b2.
а
Transcribed Image Text:Consider the following 2-firm (firm 1 and 2) model of Bertrand duopoly with differen- tiated products. Demand for firm i is q:(Pi, P;) = a – Pi – bi.Pj costs are zero for both firms. The sensitivity of firm i's demand to firm j's price is measured by bị. (a) First suppose b1 # b2. Find the equilibrium prices p1 and p2. (b) Deduce that if the two firms are identical, they choose the same price p = 216) where b = b1 = b2. а
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