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Question: What is the monopolist's profit maximized optimal price, based on the demand curve? (Use calculus...

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What is the monopolist's profit maximized optimal price, based on the demand curve? (Use calculus to solve this problem)

Demand curve : Q = 450 - 10p

Note: Marginal cost was not given in this question and that's why I am struggling. The answer should be price of $30 but I don't know how to solve this problem. Can you please explain to me how to calculate it?

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Homework Answers

Answer #1

For the market price to be $30, the marginal cost must be $15

This implies that while quantity is Q = 450 - 10P, Revenue is PQ = 450P - 10P^2 and total cost is 15Q or 15(450 - 10P). This gives cost = 6750 - 150P

Profit = Revenue - cost

= 450P - 10P^2 - 6750 + 150P

= 600P - 10P^2 - 6750

Profit is maximum when its derivative is 0

600 = 20P

P = 600/20 = 30

Hence monopolist's profit maximized optimal price, based on the demand curve is $30

A reference figure is shown below with inverse demand P = 45 - 0.1Q and MR = 45 - 0.2Q. MC is $15.

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