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 Rs. 8 per unit and it can sell 3000 units when the price is Rs. 4 per unit. The Marginal revenue at x = 5 is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 15.96
Let the price be p when x units are sold. The demand line passes through (x, p) = (2000, 8) and (3000, 4):
\( \displaystyle \text{slope} = \frac{4 - 8}{3000 - 2000} = -\frac{1}{250} \)
\( \displaystyle p - 8 = -\frac{1}{250}(x - 2000) \)
\( \displaystyle p = 16 - \frac{x}{250} \)
Revenue is price times quantity:
\( \displaystyle R = xp = 16x - \frac{x^2}{250} \)
Marginal revenue is the derivative of revenue:
\( \displaystyle MR = \frac{dR}{dx} = 16 - \frac{2x}{250} = 16 - \frac{x}{125} \)
At x = 5:
\( \displaystyle MR = 16 - \frac{5}{125} = 16 - 0.04 = 15.96 \)