Scenario 12.2:
Suppose a stream is discovered whose water has remarkable healing powers. You decide to bottle the liquid and sell it. The market demand curve is linear and is given as follows:
P = 30 - Q
The marginal cost to produce this new drink is $3.
-Refer to Scenario 12.2. What will be the price of this new drink in the long run if the firms in the industry collude with one another to maximize joint profit?
A) $3
B) $9
C) $12
D) $16.50
E) none of the above

Question

Quizplus · Accepted Answer

To maximize joint profit, firms will act like a monopolist and produce where marginal revenue (MR) equals marginal cost (MC). The demand curve is P = 30 - Q, so the total revenue (TR) is P*Q = (30 - Q)Q = 30Q - Q^2. The marginal revenue (MR) is the derivative of TR with respect to Q, which is MR = 30 - 2Q. Setting MR equal to MC (which is $3) to find the quantity: 30 - 2Q = 3, solving for Q gives Q = 13.5. Plugging Q back into the demand equation to find P: P = 30 - 13.5 = $16.50.

Scenario 12.2: Suppose a Stream Is Discovered Whose Water Has Remarkable Healing