Consider a strategic interaction between firms 1 and 2. In Stage 1, firm 1 chooses the level of advertising a > 0. In stage 2, firm 2 learns about firm 1's amount of advertising a. Subsequently, firms 1 and 2 compete in a Cournot fashion. That is, firms 1 and 2 simultaneously and independently choose their outputs: q1 and q2,

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter15: Imperfect Competition
Section: Chapter Questions
Problem 15.8P
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Consider a strategic interaction between firms 1
and 2. In Stage 1, firm 1 chooses the level of
advertising a > 0. In stage 2, firm 2 learns about
firm 1's amount of advertising a. Subsequently,
firms 1 and 2 compete in a Cournot fashion. That
is, firms 1 and 2 simultaneously and
independently choose their outputs: q1 and q2,
where qi denotes the output of firm i = 1,2. The
price that the consumers are willing to pay for
the product produced by the two firms, or the
inverse aggregate demand function, is given by
6a - q1 - q2. Firm 1's advertising cost is a3. Both
firms have zero production costs. Both firms
maximize their individual profits (equal to the
total revenue minus total cost).
In the unique subgame perfect equilibrium of
the game, the two firms will choose the
following strategies:
a. Firm 1 will choose strategy (a = 3, q1 = a/3)
while firm 2 will choose strategy q2 = a/3
b. Firm 1 will choose strategy (a = 1, q1 = 16/3 )
while firm 2 will choose strategy q2 = 16/3
c. Firm 1 will choose strategy (a = 32/3 , q1 = 2a)
while firm 2 will choose strategy q2 = 2a
d. Firm 1 will choose strategy (a = 8/3 , q1 = 2a)
while firm 2 will choose strategy q2 = 2a
e. None of the above
Transcribed Image Text:Consider a strategic interaction between firms 1 and 2. In Stage 1, firm 1 chooses the level of advertising a > 0. In stage 2, firm 2 learns about firm 1's amount of advertising a. Subsequently, firms 1 and 2 compete in a Cournot fashion. That is, firms 1 and 2 simultaneously and independently choose their outputs: q1 and q2, where qi denotes the output of firm i = 1,2. The price that the consumers are willing to pay for the product produced by the two firms, or the inverse aggregate demand function, is given by 6a - q1 - q2. Firm 1's advertising cost is a3. Both firms have zero production costs. Both firms maximize their individual profits (equal to the total revenue minus total cost). In the unique subgame perfect equilibrium of the game, the two firms will choose the following strategies: a. Firm 1 will choose strategy (a = 3, q1 = a/3) while firm 2 will choose strategy q2 = a/3 b. Firm 1 will choose strategy (a = 1, q1 = 16/3 ) while firm 2 will choose strategy q2 = 16/3 c. Firm 1 will choose strategy (a = 32/3 , q1 = 2a) while firm 2 will choose strategy q2 = 2a d. Firm 1 will choose strategy (a = 8/3 , q1 = 2a) while firm 2 will choose strategy q2 = 2a e. None of the above
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