Ihave the following question
For part (a) my solution is
Since the question says that the two firms compete by simulatanously offering price, this is Bertrand competition
Then the profit function of firm (i) is as follows for all i=1,2
From the definition of Nash equilibrium
$$p*^*=(200,200) $$ if $$\pi_i(200,200)\ge \pi (p_i,200)$$ for all i
Case 1:
$P^*=(200,200)$ then $\pi^*=0$
Case 2 :
$p^*(p,200)$ where $p<200$ then $0\ge (p-200)(1000-p)$
Case 3 :
$p^*(p,200)$ where $p>200$ then $0\ge (p-200)(1000-p)=0$
So this is Nash equilibrium for $p^*=MC=200$.
I hope so far my solution is true?
My real question is how can I proceed the part b? I am stuck at this point.
All helps are appreciated. Thanks a lot.