MCQ 11 Mark
Assertion (A): If the demand function of a product is $p=200-\frac{x^2}{3}$, then the marginal revenue (MR) of selling 10 units is ₹ 120.
Reason (R): $MR =\frac{d}{d x}( R )$
Reason (R): $MR =\frac{d}{d x}( R )$
- ABoth A and R are true and R is the correct explanation of A.
- BBoth A and R are true but R is not the correct explanation of A.
- CA is true but R is false.
- ✓A is false but R is true.
Answer
View full question & answer→Correct option: D.
A is false but R is true.
(d) A is false but R is true.
Explanation: Given $P =200-\frac{x^2}{3}$
$\Rightarrow R ( x )= P \cdot x \Rightarrow R ( x )=200 x -\frac{x^3}{3}$
Now, Marginal Revenue $( MR )=\frac{d}{d x} R =\frac{d}{d x}\left(200 x -\frac{x^3}{3}\right)$
$\Rightarrow MR =200- x ^2$
$=[ MR ]_{ x =10}=₹\left(200-10^2\right)=₹ 100$
Assertion is false.
Reason is true.
Explanation: Given $P =200-\frac{x^2}{3}$
$\Rightarrow R ( x )= P \cdot x \Rightarrow R ( x )=200 x -\frac{x^3}{3}$
Now, Marginal Revenue $( MR )=\frac{d}{d x} R =\frac{d}{d x}\left(200 x -\frac{x^3}{3}\right)$
$\Rightarrow MR =200- x ^2$
$=[ MR ]_{ x =10}=₹\left(200-10^2\right)=₹ 100$
Assertion is false.
Reason is true.