Cournot equillibrium-ISI 2010

[kangkan]

Hi....cant figure out how to get statrted with this

an economy has 2 firms with cost functions c(q)=48q q>0.Inverse demand function for firm 1 is P(q1,q2)=a-q1-sq2 and for firm 2 it is P(q1,q2)=a-q2-sq1. 0<s<1 and a>m>0.

Find the cournot equillibrium for the two firms

[bhavya jain]

we are given-
c1=48q1 & c2=48q2
p1=a-q1-sq2 & p2=a-q2-sq1
we have pi(firm 1)=(p1-mc)q1= (a-q1-sq2-48)q1
diff pi1 wrt q1. we'll get a-2q1-sq2-48=0...(1)
sly, pi(firm 2)= (a-q2-sq1-48)q2
dpi/dq2= a-2q2-sq1-48=0....(2)
solving (1) & (2), we'll get
q1*= (a-48)(s-2)/s^2+4
q2*= s(a-48)(s-2)/s(s^2+4)

[kangkan]

Got it..thanks :)