ME 2,,,ISI 2014..PLS HELPP

[The Villain]

PLS help me with part b..thankzz

[The Villain]

Someone pls helpp!!!

[Ridhika]

5a) Profit of firm 1 (call it P1) = q1(10-q1-q2)-q1
dp1/dq1 = 9 - 2q1-q2=0 -- Eq1
q1= (9-q2)/2 = Best response of firm 1 to q2 [BR1(q2)]
similarly BR2(q1)= q2 = (9-q1)/2 -- Eq2

Substitute eq 2 in eq 1 and u will get q1=3 and by symmetry q2=3

for part b i think they'll produce til their max op as 2<3 .. so for all level of output below 3 MR>MC.. so firms will find it profitable to produce

[The Villain]

Thnxx ridhika..bt will the reaction curves be in part b

[Amit Goyal]

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.

[Dreyfus]

Thank you so much sir

[The Villain]

Thank you Sir :)