aps7x313_s06

aps7x313_s06 - Econ 313 - Wissink Spring 2006 PS#7 XtraQ...

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1. Suppose the airline industry consists of only two firms: Firm1=American and Firm2 =Texas Air Corp. Let the two firms have identical cost functions: tc i (x i ) = 40x i . Assume the demand curve for the industry is given by P = 100 – X where X = x 1 +x 2 , and that each firm expects the other to behave as a Cournot competitor. a. American: Π A = (100 – x A – x T )x A – 40x A FOC: 100 – 2x A – x T – 40 = 0. So American’s reaction function is x A = 30 – (1/2)x T . Texas Air: Π T = (100 – x A – x T )x T – 40x T FOC: 100 – 2x T – x A – 40 = 0. So Texas Air’s reaction function is x T = 30 – (1/2)x A . Solving simultaneously yields: x A CN = 20 = x T CN ; p CN = 60; Π A CN = 400 = Π T CN . b. American’s reaction function is still x A = 30 – (1/2)x T . Texas Air: Π T = (100 – x A – x T )x T – 25x T FOC: 100 – 2x T – x A – 25 = 0. So Texas Air’s reaction function is x T = 37.5 – (1/2)x A . Solving simultaneously yields: x T CN = 30; x A CN = 15; p CN = 55. Texas Air’s profits with the lower costs are Π T CN = (55)30 – (25)30 = 900. With the higher costs, Texas Air’s profits are 400 [see (a)].
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This note was uploaded on 10/29/2009 for the course ECON 3130 taught by Professor Masson during the Fall '06 term at Cornell.

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aps7x313_s06 - Econ 313 - Wissink Spring 2006 PS#7 XtraQ...

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