DSE 2010

[Rahul]

consider a bertrand duopoly with firms 1 and 2 that produce a homogenous good and set prices p1 and p2.demand function is (5-p).Firm 1 has constant average cost of 5/2 and firm 2 has constant average cost of 3/2.In equilibrium
a)p1=2=p2
b)p1=3=p2
c)p1=3 and p2=2
d)p1=3 and p2 is 2 or 3

As per solution ans is "d".Should not firm 2 sell at a price just below firm 1's marginal price??

[Amit Goyal]

Write the game in normal form (Its easy to write it because prices are positive integers which is also given in the problem) and then check that you will get two Nash Equilibrium (3,2) and (3,3).

[Rahul]

I still can't get it.Amit sir I would be thankful if you can provide me a solution.Not much time is left and i can't go back to books now.

[Amit Goyal]

Rahul this how you are going to put entries in the game box:
For example p1 = 3 and p2 = 2, then firm 2 will get the entire market so profit of firm 1 will be 0 and firm 2 will be TR-TC = pq-cq= 2(5-2) - 1.5(5-2)= 6-4.5=1.5.
Just do this exercise and compute all entries, in particular, for prices between 1 and 4 and then solve for Nash equilibrium.