If a monopolist has a straight-line demand curve, its marginal revenue curve (LOI) a) will be the same as the demand curve b) will fall twice as quickly as the demand curve c) will lie below the demand curve at all points d) will cross the demand curve

Statement (a) suggests that the marginal revenue (MR) curve will be the same as the demand curve. This statement is incorrect because, for a monopolist, the MR curve will always lie below the demand curve.

Statement (b) suggests that the marginal revenue curve will fall twice as quickly as the demand curve. This statement is accurate because, when a monopolist's demand curve is a straight line, its change in quantity with respect to its price will be twice as fast for its marginal revenue curve. Let's consider the linear demand curve, represented as \(P = a - bQ\), where \(P\) is price and \(Q\) is quantity demanded. The total revenue can be represented as \(TR = PQ = aQ - bQ^2\). Then, the marginal revenue will be the derivative of the total revenue with respect to quantity \(Q\). So, \(MR = \frac{d(TR)}{dQ} = a - 2bQ\). Comparing the demand curve and the MR curve, we can see that the slope of the MR curve is twice the slope of the demand curve.

Statement (c) suggests that the marginal revenue curve will lie below the demand curve at all points. This statement is also correct because the slope of the MR curve is twice the slope of the demand curve, creating a steeper decline. Therefore, the MR curve will always lie below the demand curve when the demand curve is a straight line.

Statement (d) suggests that the marginal revenue curve will cross the demand curve. This statement is incorrect. Although the MR curve has twice the slope of the demand curve, it does not guarantee that they will cross each other. So, the correct answers are statements (b) and (c). The marginal revenue curve of a monopolist with a straight-line demand curve will fall twice as quickly as the demand curve and lie below the demand curve at all points.