Discussion Problem Of the Day ( 19/06/2011)

[varsha]

Consider an industry with 3 firms each having MC as 0 with the following inverse demand function:

p(q1,q2,q3)   = 60 - ( q1+ q2 + q3 )

1)calculate cournot equilibrium.

2)now consider that firms 2 and 3 decide to merge and form single firm (mc still 0 ). calculate new industry equilibrium. Is firm 1 better or worse off as a result. Are combined profits of firms 1 and 2 greater or less than before? Would you suggest forming a cartel of all 3 firms ?

3)Suppose firm 1 can commit to some output level in advance.  If the choice of firm 1 is q1,  what is the optimal choices of outputs for firm 2 and 3 ?

[poonam]

Hi varsha

finding cournot rquilibrium-
I got my reaction curves as follows:

q1=30-(q2+q3)/2
q2=30-(q1+q3)/2
q3=30-(q1+q2)/2

and on solving these , i got the cournot equilibrium as follows:
q1=7.5
q2=37.5
q3=7.5

P=7.5

kindly let me know if i am going right.
thank you.

[barkha]

check your calculations