Equilibrium and Profit Levels in Cournot Duopoly

1a) Note: We will assume the subscripts for typing cases.
Response function= (a-c-bQ2)/2b
Q1 and Q2 rep the quantities of either output and a b c are the intercepts of the demand
function K= a-bQ
C= marginal cost
For cournot firms, we get our Q1 and Q2 as follows
P= 12-Q
MC1=3
MC2=3
Q1= (12-3-3Q2)/3X3
= (9-3Q2)/4
=9/4-3Q2/4
Since MC1 and MC2 are equal, then Q1=Q2
Thus the response function is
12-Q= 9/4-3Q2/4
9.75=1/4Q
Hence Q= 39
b)

The equilibrium is at b1(0)
c) From a) it is clear that the output levels of the equilibrium cluster at Q=39. Since the MCI
and MC2 are on same response function
d) Equilibrium:12-Q=Q
Assumption, Q1=Q2=Q
Thus P=12
e) Profit level
The two firms are operating in the same market structure. In my case, I assume the duopoly
situation
Profit =TR-TC
12-Q =3
Q=9
2a) MCA=1, and