DSE-2010 solution wrong

[Arun]

For DSE-2010 Ques -9 your solution provides answer as "both firms produce positive outputs with firm 2 producing more than firm 1" which doesn't appear correct to me.

For both firms producing positive quantities with Q2>Q1 the total quantity produced would be >=3.At Q=3 price would be 2.Given firm 1 has constant average cost of 2.5 it would be in loss and better off shutting down.So its not a Nash equilibrium.

If we solve for cournot equilib we get Q1=.5,Q2=1.5.Both (1,1) and (0,2) are nash equilibrium.Whats the answer??

[PRIYANKA]

profit for firm 1  (f1)= 1/2(5-q1-q2) - 5/2 q1
= 1/2(5-0.50- 1.5)- 5/2*1/2
>0
so,no loss

[Amit Goyal]

In this problem there is a unique equilibrium (q_1, q_2)=(0.5, 1.5). Hence the answer that is provided is correct. Please recheck what have you done.

[Arun]

Even my answer is (.5,1.5) but is fractional answer possible.A firm manufacturing .5 units?

[PRIYANKA]

yeah its possible

[Arun]

Thanks for your prompt reply at this odd time.That solves my problem