http://discussion-forum.276.s1.nabble.com/ISI-ME-II-2014-tp7587168p7589287.html
Shefali copy pasting Amit sir's answer to q5 which he posted on another thread.. hope it helps..
5 In what follows q(i) denotes firm i's output:
(a)
Firm 1 maximizes wrt q(1)
(10-q(1)-q(2))q(1) -q(1)
and firm 1's reaction function will be
q(1) = (9-q(2))/2
Similarly firm 2's reaction function is
q(2) = (9-q(1))/2
Solving the above two,
we get the equilibrium as q(1) = q(2) = 3.
(b)
Firm 1 maximizes wrt q(1)
(10-q(1)-q(2))q(1) -q(1) s.t. q(1) <= 2
and firm 1's reaction function will be
q(1) = min{(9-q(2))/2, 2}
Similarly firm 2's reaction function is
q(2) = min{(9-q(1))/2, 2}
Solving the above two,
we get the equilibrium as q(1) = q(2) = 2.