Given a revenue function r = r(q), what is the marginal revenue (MR)?

• A. The derivative of the revenue function with respect to quantity, dr/dq
• B. The total revenue divided by the quantity, r(q)/q
• C. The derivative of the cost function with respect to quantity, dC/dq
• D. The difference between total cost and total revenue, r(q) - C(q)

Answer: (A)

Verified step by step guidance

1. Understand that marginal revenue (MR) measures the additional revenue generated from selling one more unit of a good or service.
2. Recall that the total revenue function is given by \(r = r(q)\), where \(q\) is the quantity sold.
3. Marginal revenue is mathematically defined as the rate of change of total revenue with respect to quantity, which means taking the derivative of the revenue function with respect to \(q\).
4. Express this derivative as \(\frac{d r}{d q}\), which represents how total revenue changes when quantity changes by a small amount.
5. Note that other options like \(\frac{r(q)}{q}\) (average revenue), \(\frac{d C}{d q}\) (marginal cost), or \(r(q) - C(q)\) (profit) do not represent marginal revenue.