A monopolist faces the following demand curve, marginal revenue curve, total cost curve and marginal cost curve for its product: Q = 200 - 2P MR = 100 - Q TC = 5Q MC = 5 Refer to Scenario 10.2. What is the profit maximizing level of output?

Question

Mathematics

Deanna Bauer

25 June, 10:39

A monopolist faces the following demand curve, marginal revenue curve, total cost curve and marginal cost curve for its product: Q = 200 - 2P MR = 100 - Q TC = 5Q MC = 5 Refer to Scenario 10.2. What is the profit maximizing level of output?

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Answers (1)

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Sean Cruz · Answer 1

Q=95, P = 52.5

Step-by-step explanation:

The profit maximizing level of output in monopolies is reached when the marginal cost is equal to the marginal revenue. This is also the profit maximizing rule in perfect competition, the difference between both is that is perfect competition the marginal revenue is equal to the price while in monopolies, the demand curve is often above the marginal revenue curve, then the actual price (defined by the demand curve) is often higher than the marginal revenue price.

For this problem the profit maximizing level of output is:

MC=MR

5=100-Q

Q=95

Because monopolies decide the selling price based on the demand curve, you should replace this quantity in the demand curve equation:

95=200-2P

95-200/2=-P

P = 52.5