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

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

Answer: (B)

Verified step by step guidance

1. Start with the given linear demand function: \(P = a - bQ\), where \(P\) is price, \(Q\) is quantity, and \(a\), \(b\) are positive constants.
2. Recall that total revenue (TR) is the product of price and 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 \(Q\). Differentiate \(TR\) with respect to \(Q\) to find \(MR = \frac{d(TR)}{dQ}\).
5. Perform the differentiation: \(MR = \frac{d}{dQ}(aQ - bQ^2) = a - 2bQ\). This is the formula for marginal revenue for the firm.