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Scenario: Monopolist
The demand curve for a monopolist is P = 75 -- 0.5Q,and the monopolist's marginal cost curve is defined using the equation MC = 2Q.Assume also that ATC at the profit-maximizing level of production is equal to $12.50.
-(Scenario: Monopolist)Use Scenario: Monopolist.The profit-maximizing output is _____ units,and the profit-maximizing price is _____.
A) 25;$75.00
B) 20;$62.50
C) 25;$75.50
D) 25;$62.50

Question

Quizplus · Accepted Answer

To find the profit-maximizing output, we need to set MR (marginal revenue) equal to MC (marginal cost). Since the monopolist faces the entire market demand curve, MR is equal to the slope of the demand curve multiplied by quantity, which gives us:

MR = 75 - Q

Setting MR equal to MC and solving for Q, we get:

75 - Q = 2Q

Q = 25

So the profit-maximizing output is 25 units.

To find the profit-maximizing price, we can plug this value of Q back into the demand curve:

P = 75 - 0.5Q
P = 75 - 0.5(25)
P = $62.50

So the profit-maximizing price is $62.50.

Therefore, the best choice is D.

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