Suppose a firm's demand curve is linear and given by P = a - bQ, where P is price and Q is quantity. What is the formula for marginal revenue (MR) for this firm?

• A. MR = a - 2bQ
• B. MR = a - bQ
• C. MR = aQ - b
• D. MR = bQ

Answer: (A)

Verified step by step guidance

1. Start with the demand function given: \(P = a - bQ\), where \(P\) is price and \(Q\) is quantity demanded.
2. Recall that total revenue (TR) is price times quantity: \(TR = P \times Q\). Substitute the demand function into this to get \(TR = (a - bQ)Q\).
3. Simplify the total revenue expression: \(TR = aQ - bQ^2\).
4. Marginal revenue (MR) is the derivative of total revenue with respect to quantity, so calculate \(MR = \frac{d(TR)}{dQ}\).
5. Differentiate \(TR = aQ - bQ^2\) with respect to \(Q\) to get \(MR = a - 2bQ\).