Question

XYZ Co. Ltd. is a costless monopoly from suburban Mumbai producing and selling exotic mushrooms. The demand for mushrooms is given by \[ Q = 700 - 100P. \text{ Do you agree that XYZ will have a maximum possible total revenue of ₹1500?} \]

• A. Yes, the maximum possible total revenue is ₹1500.
• B. No, the maximum possible total revenue is less than ₹1500.
• C. No, the maximum possible total revenue is more than ₹1500.
• D. No, the maximum possible total revenue cannot be estimated.

Hint:

To find the maximum total revenue, differentiate the total revenue function and solve for \( P \). Then substitute \( P \) into the demand function to find \( Q \), and calculate \( TR \).

Answer 1

The Correct Option is B

Step 1: Total Revenue Formula.
The total revenue (TR) is given by: \[ TR = P \times Q = P \times (700 - 100P) = 700P - 100P^2. \] Step 2: Find the Maximum Total Revenue.
To find the maximum total revenue, we first differentiate TR with respect to \( P \): \[ \frac{d(TR)}{dP} = 700 - 200P. \] Set the derivative equal to zero to find the critical point: \[ 700 - 200P = 0 \quad \Rightarrow \quad P = 3.5. \] Step 3: Calculate Total Revenue at \( P = 3.5 \).
Substitute \( P = 3.5 \) back into the demand equation: \[ Q = 700 - 100(3.5) = 350. \] Thus, the total revenue is: \[ TR = 3.5 \times 350 = ₹1225. \] Step 4: Conclusion.
The maximum total revenue is ₹1225, which is less than ₹1500. Therefore, the correct answer is (B).