If the demand function is P = 3000 − 2√Q find expressions for TR and MR. Calculate the marginal revenue when Q = 9 and give an interpretation of this result.

Question

If the demand function is P = 3000 − 2√Q find expressions for TR and MR. Calculate the marginal revenue when Q = 9 and give an interpretation of this result.

Answer 1

Hi Isfaar,

Total Revenue (TR) = P(Q) * Q

In this case, we get...

TR = (3000 - 2√Q) * Q

TR = 3000Q - 2Q^3/2

To find the Marginal Revenue, we can just take the derivative of our TR.

MR = 3000 - 3Q^1/2

We can plug in Q = 9 to into the equation above and get

MR = 3000 - 3(9)^1/2 = 2991

This means that the additional revenue for the 9th unit bought and sold is $2991.