(Scenario: A Monopolist) A monopolist faces a demand curve given by P = 20 Q and has total costs given by TC = Q2. By using a bit of calculus, you should be able to determine that the firm's marginal revenue is MR = 20 2Q and its marginal cost is MC = 2Q. What is its profit-maximizing output level?

The correct option is a.5.

Explanation:

Note: This question is not complete as some important signs are committed from it. The complete question is therefore provided before answering the question as follows:

A monopolist faces a demand curve given by P = 20 - Q and has total costs given by TC = Q2. By using a bit of calculus, you should be able to determine that the firm's marginal revenue is MR = 20 - 2Q and its marginal cost is MC = 2Q. What is its profit-maximizing output level?

a.5

b.6

c.7

d.8

The explanation of the answer to the question is now provided as follows:

A monopolist refers to the a person or company who is the only supplier of a commodity in the market.

For a monopolist, profit is maximized when marginal revenue (MR) is equal to the marginal cost (MC). That is, where MR = MC. This implies that the profit-maximizing output level of a mopolist can be obtained by setting MR equal to MC.

Since in the question, we are given the following:

MR = 20 - 2Q ………………………………………. (1)

MC = 2Q ……………………………………………… (2)

We can therefore equate equations (1) and (2) and solve for Q as follows:

MR = MC

20 – 2Q = 2Q

20 = 2Q + 2Q

4Q = 20

Q = 20 / 4

Q = 5. This is the profit maximizing output level.

Therefore, the correct option is a.5.

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