Question

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

Short answer

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 is due to the fact that the slope of the marginal revenue curve is twice as steep as the slope of the demand curve.

Step-by-step solution

1. Understanding Demand Curve and Marginal Revenue 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.

2. Evaluating the Options

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.

3. Conclusion

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.

Key concepts

Demand Curve

The demand curve illustrates how many units of a product consumers are willing to purchase at various price points. For a monopolist, this curve is particularly crucial because it dictates the highest price that can be charged for each quantity. A critical aspect of a monopolist's demand curve is its downward slope. This slope indicates that as the price decreases, the quantity demanded increases, and vice versa. For example, if a monopolist wants to sell more units, they must lower the price of their product. This trade-off between price and quantity is a fundamental characteristic of the demand curve in monopoly markets. Unlike in perfect competition, where firms perceive the demand curve as horizontal due to price-taking behavior, a monopoly has a unique downward-sloping demand curve. In the case of a straight-line demand curve, the slope is consistent, meaning a specific price change will always result in a definite quantity change. This linear relationship makes it simpler to predict how price adjustments will impact demand.

Marginal Revenue

Marginal Revenue (MR) is the additional income that a firm receives from selling one additional unit of a good or service. In a monopolistic market, the relationship between the demand curve and the marginal revenue curve is essential for profit maximization. The key insight about MR in monopoly is that it is always less than the price of the product. Unlike firms in perfect competition, a monopolist's marginal revenue curve lies beneath its demand curve and falls twice as quickly. This occurs because the monopolist must reduce the price of all units sold, not just the additional unit, to sell more. Therefore, the MR curve will be steeper than the demand curve, meaning it has a greater negative slope. Let's consider an example: if a monopolist has a straight-line demand curve with a slope of -1, the marginal revenue curve will have a slope of -2. This steeper slope reflects the fact that the monopolist loses some revenue on existing sales when prices are lowered to increase quantity sold, thus making the MR less than the price.

Perfect Competition

Perfect competition represents a market structure where numerous small firms compete against each other, and no single firm has significant pricing power. One of the defining features of perfect competition is the horizontal or perfectly elastic demand curve that individual firms face. In perfect competition, the price a firm charges is dictated by the market, and every unit sold contributes the same revenue. Consequently, for a firm in perfect competition, the demand curve coincides with the marginal revenue curve. This alignment results because the sale of an additional unit directly translates into additional revenue without necessitating a change in price. It’s crucial to understand the distinction between monopoly and perfect competition regarding these curves. While a monopolist manipulates price to manage quantity sold, perfect competitors are price takers accepting the market price. This fundamental difference is vital for comprehending how monopolists structure their production and pricing strategies differently from firms in a perfectly competitive market.