<p>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.)</p>

<p>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 <strong>just of bad quality</strong> and cannot be answered.</p>

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2018-05-19T19:37:50.000Z
2018-05-20T09:42:09.703Z
2018-05-20T09:42:09.703Z
Giskard
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<p>Best response functions are obtained by differentiating a profit function and solving for q.</p>

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

<supply-and-demand><profit-maximization>
How to work out Price with only the Derivative of Profit Function?
Dominic
# How to work out Price with only the Derivative of Profit Function?

(Asked by: username_0 on 2018-05-19)

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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?

**Tags:** supply-and-demand, profit-maximization

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## 1 answers

### Answer by username_1 on 2018-05-19. Score: 2

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.


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