Consider a market with two horizontally differentiated products. The system of de mands is given by

Q1(p1, p2) = 3 − 2p1 + p2

and

Q2(p1, p2) = 3 − 2p2 + p1.

Suppose firm 1 has cost a marginal cost of c1 = 0 and firm 2 has marginal cost of c2 = 1. The two

firms compete in prices. [Note: I apologize for the fact the numbers in this example is very difficult

to get to be simple. You will have to use a calculator at some points of this exercise.]

(a) Compute the firms? profits at the Nash equilibrium of the simultaneous Bertrand game, that

is when they set their prices simultaneously.

(b) Compute the firms? profits at the subgame perfect Nash equilibrium of the sequential game in

two cases

i. with firm 1 being the leader, and

ii. with firm 2 being the leader.

(c) Solve for the Nash equilibria of the endogenous timing game in which firms simultaneously

choose whether to play ?early? or to play ?late? assuming price competition takes place after

they have made their timing choices which are observed by both firms. If they both make the

same choice (either ?early? or ?late?), the simultaneous Bertrand game follows; if they make

different choices, a sequential game follows with the firm having chosen ?early? being the leader.

Comment on the qualitative properties of the equilibria you find.

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