Question

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

Short answer

The correct answers are statements (b) and (c). When a monopolist has a straight-line demand curve, its marginal revenue curve will fall twice as quickly as the demand curve and lie below the demand curve at all points.

Step-by-step solution

Examine statement (a)

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.

Examine statement (b)

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.

Examine statement (c)

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.

Examine statement (d)

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.

Key concepts

Understanding Marginal Revenue in a Monopoly

Marginal revenue (MR) is a key concept in understanding how monopolies forge their pricing strategies. Simply put, marginal revenue refers to the additional income a firm receives from selling one extra unit of a good or service. For monopolies, this concept behaves in a unique manner due to their market power.
In a competitive market, the marginal revenue matches the price since firms can sell additional units without needing to lower the price. However, a monopolist faces a different reality. Since it is the only supplier, it can set the price at a point that maximizes profit.

• The marginal revenue curve for a monopolist is always below its demand curve.
• This is because, under monopoly, to sell more units, the price for all units must be lowered, not just the extra one being sold.
• As a result, each additional unit sold contributes less to total revenue than the previous one did, making the MR grow at a declining rate.

Thus, a monopoly experiences a steeper decline in marginal revenue compared to the rate of decrease in the demand curve.

Deciphering the Demand Curve

The demand curve is a fundamental economic tool that illustrates the relationship between the price of a good and the quantity demanded by consumers. For a monopolist, this curve looks quite different than for firms in competitive markets.
In monopoly, the demand curve is downwards sloping, indicating that as prices fall, quantity demanded increases. This downward slope implies a negative relationship between price and the quantity consumers wish to purchase.

• A straight-line demand curve can be represented by the equation: \( P = a - bQ \), where \(P\) is price, \(Q\) is quantity, \(a\) is the y-intercept, and \(b\) is the slope of the demand curve.
• The demand curve essentially sets the maximum price that consumers are willing to pay for a given quantity of goods.
• In a monopoly, this demand curve is critical since the firm uses it to find out how much they can sell at various price points.

Understanding the demand curve helps the monopolist determine optimal pricing strategies and how different prices may affect its overall revenue and sales volume.

Exploring Economic Concepts of Monopolies

Monopolies bring about unique economic dynamics that are crucial to comprehend. These businesses wield significant control over entire markets and can influence conditions in ways that competitive firms cannot. Here's how they fit into broader economic concepts:

• Monopolies lead to market inefficiencies since competition is absent, resulting in higher prices and reduced output compared to a perfectly competitive market.
• The concept of barriers to entry is pivotal, as monopolists often benefit from high barriers which prevent new firms from entering and challenging their market position.
• Monopolies have the power to be price setters rather than price takers, deciding the optimal price where marginal costs meet marginal revenues for maximum profit.

These economic realities mean that monopolies can often cause reduced consumer surplus and potential welfare losses for society. Understanding these concepts helps in evaluating the wider implications of monopolies within the economy.