Question

Two firms in a homogeneous-product duopoly market (firm 1 and firm 2) have the following cost and demand functions: TC1=4q1; TC2=4q2 and Q=40-P; Q=q1+q2. a) Derive the reaction function/best-response function for each firm. b) Assume that the firms play a simultaneous move game. Characterize the Nash Equilibrium. c) Suppose the two firms play game is a sequential game with the following timing of events: 1. Firm 1 chooses output 2. Firm 2 observes firm 1’s output and then chooses output Characterize the Nash equilibrium of this sequential move game. 

Answer 1

a.

$q_1+q_2=40-p\\4Q=40-P\\P=40-Q\\4Q-40=40-Q\\5Q=80\\Q=16\\P=24$

b.

simultaneous move game

Q of firm1 followed by firm 2

Optimal quantity is (16,16)

Nash equilibria quantity (16,16)

pyoff(24,24)

c.