Given the demand schedule of a monopolist, which of the following statements is correct regarding marginal revenue (MR) compared to price (P) as output increases?

• A. Marginal revenue is always greater than price for each additional unit sold.
• B. Marginal revenue and price are unrelated for a monopolist.
• C. Marginal revenue is always equal to price for each additional unit sold.
• D. Marginal revenue is always less than price for each additional unit sold.

Answer: (D)

Verified step by step guidance

1. Recall the relationship between price (P) and marginal revenue (MR) for a monopolist. Unlike a perfectly competitive firm, a monopolist faces a downward-sloping demand curve, meaning it must lower the price to sell additional units.
2. Understand that because the monopolist must reduce the price to sell one more unit, the marginal revenue from selling that additional unit is less than the price at which the unit is sold. This is due to the price reduction applying not only to the additional unit but also to all previous units sold.
3. Express the marginal revenue mathematically: if the demand function is \(P(Q)\), then total revenue is \(TR = P(Q) \times Q\). Marginal revenue is the derivative of total revenue with respect to quantity, so \(MR = \frac{d(TR)}{dQ} = P(Q) + Q \times \frac{dP}{dQ}\).
4. Note that since the demand curve is downward sloping, \(\frac{dP}{dQ} < 0\), which makes \(Q \times \frac{dP}{dQ}\) negative. Therefore, \(MR < P(Q)\) for each additional unit sold.
5. Conclude that for a monopolist, marginal revenue is always less than price as output increases, which explains why the correct statement is: 'Marginal revenue is always less than price for each additional unit sold.'