Question

In: Economics

monopoly profit function Π=-Q^3+48×Q^2-180×Q-800 (0≤Q≤100) Which of the following is true? a.The total profit function is...

monopoly profit function Π=-Q^3+48×Q^2-180×Q-800 (0≤Q≤100)

Which of the following is true?

a.The total profit function is U-shaped because its second derivative is always positive.

b.The total profit function is an inverted-U because its second derivative is always negative.

c.The total profit function has two output levels at which marginal profit is equal to zero.

d. The total profit function is maximised when the monopolist is producing the maximum level of output possible.

e. None of the above is necessarily true.

Expert Solution

First derivative :

Second derivative

Second derivative is positive when Q < 16 and negative when Q > 16

The graph of the profit function is given below:

Option a is wrong because the second derivative is not always positive.

Option b) is wrong because the second derivative is not always negative.

Option c) is correct because The total profit function has two output levels (2 and 30 ) at which marginal profit is equal to zero.

Option d) is incorrect The total profit function is maximised when the monopolist is producing 30 units of output.

Therefore, option c) The total profit function has two output levels at which marginal profit is equal to zero is the correct answer.

Please upvote if this answer helped you. Thank you

Rahul Sunny answered 1 year ago

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