Question

The demand function of a monopolist is given by $p = 30 + 5x - 3x^2$, where $x$ is quantity and $p$ is price. The marginal revenue when 2 units are sold is

• A. ₹ 28
• B. ₹ 23
• C. ₹ 1
• D. ₹ 14

Hint:

To find marginal revenue, always express TR as a function of $x$ and then differentiate it.

Answer 1

The Correct Option is D

Marginal revenue (MR) is the derivative of total revenue (TR) with respect to quantity $x$.
First, find total revenue: $TR = p.x = (30 + 5x - 3x^2).x = 30x + 5x^2 - 3x^3$.
Now, differentiate $TR$ with respect to $x$ to get MR:
$MR = \frac{d(TR)}{dx} = 30 + 10x - 9x^2$
Now substitute $x = 2$:
$MR = 30 + 10(2) - 9(4) = 30 + 20 - 36 = 14$
So, the marginal revenue when 2 units are sold is ₹14.