If a monopolist has a straight-line demand curve, its marginal revenue curve (LO1) 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

The demand curve represents the relationship between the quantity of a product demanded and its price, whereas the marginal revenue curve shows the additional revenue a monopolist receives when they sell one more unit of a product. For a monopolist with a straight-line demand curve, the marginal revenue curve has a specific relationship with the demand curve.

We will now analyze each of the given options in order to determine the correct relationship between the demand curve and the marginal revenue curve for a monopolist with a straight-line demand curve. a) Will be the same as the demand curve: This statement is incorrect, as the marginal revenue curve is not the same as the demand curve for a monopolist. In perfect competition, the demand curve is equal to the marginal revenue curve. However, for a monopolist, the two curves are different. b) Will fall twice as quickly as the demand curve: This statement is correct. For a straight-line demand curve, the marginal revenue curve indeed falls twice as fast as the demand curve. We can derive the marginal revenue curve from the demand curve, and we will notice that the slope of the marginal revenue curve will be twice as steep as the slope of the demand curve. c) Will lie below the demand curve at all points: Although it is true that the marginal revenue curve lies below the demand curve for a monopolist, this statement is not as specific as option (b). The marginal revenue curve does lie below the demand curve, but option (b) gives more precise information about the relationship between the two curves. Thus, we can eliminate this option. d) Will cross the demand curve: The marginal revenue curve does not cross the demand curve for a monopolist. The demand curve represents the price that consumers are willing to pay, while the marginal revenue curve indicates the additional revenue that the monopolist obtains from selling one more unit of a product. These two concepts are distinct; hence, the two curves do not intersect.

Based on the analysis of the given options, the correct answer is option (b): the marginal revenue curve for a monopolist with a straight-line demand curve will fall twice as quickly as the demand curve. This relationship can be derived by calculating the marginal revenue from the demand curve equation, where we will see that the slope of the marginal revenue curve will be twice as steep as the slope of the demand curve.