How the two firms have the same market share

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Consider a Stackelberg duopoly game of quantity competition. Firm #1 is the "Leader" and firm #2 is the "Follower." Market demand is given by the inverse demand function p=100-4Q.where Q=q1+q2 is the total output of the two firms. The firms have constant unit cost of productionc1 and c2, respectively. That is, the cost function of firm #1 isC(q1)=c1q1 and that of firm #2 is C(q2)=c2q2.

(a) Initially suppose that c1=c2=20. Use backward induction to solve for the subgame perfect Nash equilibrium (SPNE) of this game.
(b) Now suppose that firm #1 still has unit cost c1=20, but firm #2 has a lower production cost, that is c2<20. What value wouldc2 have to be so that, in the SPNE, the two firms have the same market share?

Reference no: EM13190791

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