A company is selling a certain commodity 'x'. The demand function for the commodity is linear. The company can sell 2000 units when the price is ₹8 per unit and it can sell 3000 units when the price is ₹4 per unit. The Marginal revenue at x = 5 is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹15.96
Let demand function be $p=ax+b$.
Given points on demand curve: $(x,p)=(2000,8)$ and $(3000,4)$.
Slope:
$a=\frac{4-8}{3000-2000}=\frac{-4}{1000}=-\frac{1}{250}$
So $p=-\frac{x}{250}+b$.
Substitute $(2000,8)$:
$8=-\frac{2000}{250}+b$
$8=-8+b$
$b=16$
Thus $p=16-\frac{x}{250}$.
Revenue $R=xp=x\left(16-\frac{x}{250}\right)=16x-\frac{x^{2}}{250}$.
Marginal revenue:
$MR=\frac{dR}{dx}=16-\frac{2x}{250}$
$=16-\frac{x}{125}$
At $x=5$:
$MR=16-\frac{5}{125}=16-\frac{1}{25}=\frac{399}{25}$
final answer: $\frac{399}{25}$