# How to work out Price with only the Derivative of Profit Function?

Best response functions are obtained by differentiating a profit function and solving for q.

In equilibrium, the firms produce 30. But, there's no inverse demand function, so how would equilibrium price be determined?

This question seems to be unanswerable. Even assuming a linear inverse demand function $p(Q) = a - bQ$ and a linear cost function $C_i(Q_i) = cQ_i$ the best response function will take the form $$q_i = \frac{a-c}{2b} - \frac{1}{2}q_j.$$ From the information given, you cannot know if say $c=10$ and $a=55$ or $c = 0$ and $a = 45$, so it is impossible to infer the inverse demand function and the price. (And this is assuming linear functions everywhere.)

Also, notice that the exact market structure (Cournot or Stackelberg) is only given in question c). Yet this would also affect market price. Hence, the question is unfortunately just of bad quality and cannot be answered.