Suppose a firm\'s marginal cost is MC = 80 + 2 Q and its marginal revenue is MR

Question

Suppose a firm's marginal cost is MC = 80 + 2Q and its marginal revenue is MR = 200 – Q. Which of the following statements is TRUE?

I.

The profit-maximizing price is $180.

II.

If Q = 20, MR > MC, so the firm should expand output to increase profits.

III.

If Q = 50, MR < MC, so the firm should reduce output to increase profits.

I.

The profit-maximizing price is $180.

II.

If Q = 20, MR > MC, so the firm should expand output to increase profits.

III.

If Q = 50, MR < MC, so the firm should reduce output to increase profits.

Explanation / Answer

Ans. The profit maximizing condition is, MR=MC

200 – Q = 80+2Q

Q=40

If we integrate the MR function, then we get the TR function, so

TR = 200Q - 0.5Q2

Now, we know that AR = Price, then dividing TR by Q

AR= P(Q) = 200 - 0.5Q

So, put the value of Q=40 in P(Q), we would get the profit maximizing price is:

P = 200 - 0.5x40

P= $180.

Hence, option (i) is right.

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