Question

The demand function of a monopolist is given by $p=1500-2x-x^2$. Find the marginal revenue when $x=10$.

• A. $1170$
• B. $1160$
• C. $1150$
• D. None of these

Answer 1

The correct option is B $1160$

$\Rightarrow$ We have, $p=1500-2x-x^2$

$\Rightarrow$ Revenue Function $R=p\times x$

$\therefore$ $R=1500x-2x^2-x^3$.

$\Rightarrow$ Marginal revenue = $\frac{d}{dx}R$

$\Rightarrow$ Marginal revenue = $\frac{d}{dx}(1500x-2x^2-x^3)$

$\Rightarrow$ Marginal revenue = $1500-4x-3x^2$

$\Rightarrow$ Now, substitute $x=10$.

$\Rightarrow$ Marginal revenue = $1500-2\left(100\right)-3(100{)}^2=1160$

$\therefore$ Marginal revenue is $1160$.