For A Monopolist Marginal Revenue Is

For a Monopolist, Marginal Revenue is Less Than Price

For a monopolist, the relationship between marginal revenue (MR) and price (P) is a crucial aspect of understanding their market power and decision-making process. Unlike perfectly competitive firms that are price takers, monopolists are price makers, meaning they have the power to influence the price of their product. This power, however, comes with a trade-off: to sell more units, they must lower the price not only on the additional units but also on all the units they were already selling. This fundamental characteristic leads to the key principle: for a monopolist, marginal revenue is always less than price (MR < P).

Understanding Marginal Revenue

Marginal revenue is the additional revenue a firm receives from selling one more unit of output. In a perfectly competitive market, the firm can sell as many units as it wants at the prevailing market price. Therefore, marginal revenue equals the price. But for a monopolist, this is not the case.

A monopolist faces the entire market demand curve. To sell an extra unit, they must lower the price not just on that extra unit but on all the units they were previously selling at a higher price. This price reduction leads to a decrease in revenue on the units previously sold, offsetting the revenue gained from the extra unit sold. This is why the marginal revenue curve for a monopolist lies below the demand curve.

Calculating Marginal Revenue for a Monopolist

Let's illustrate this with a simple example. Suppose a monopolist faces a demand curve given by:

P = 10 - Q

Where:

• P = Price
• Q = Quantity

To find the total revenue (TR), we multiply price by quantity:

TR = P * Q = (10 - Q) * Q = 10Q - Q²

Marginal revenue (MR) is the derivative of the total revenue function with respect to quantity:

MR = d(TR)/dQ = 10 - 2Q

Notice that the marginal revenue curve (MR = 10 - 2Q) has twice the slope of the demand curve (P = 10 - Q). This demonstrates the crucial point: the marginal revenue curve always lies below the demand curve for a monopolist. For every unit sold, the monopolist loses some revenue on the previously sold units due to the price reduction necessary to sell the additional unit.

The Implications of MR < P

The fact that MR < P for a monopolist has several important implications for their profit maximization strategy:

• Profit Maximization: Monopolists, like all firms, aim to maximize profits. They do this by producing the quantity where marginal revenue equals marginal cost (MR = MC). Since MR < P, the price they charge will be higher than their marginal revenue. This allows them to extract economic profits in the long run, a stark contrast to perfectly competitive firms that earn zero economic profit in the long run.

• Deadweight Loss: Because a monopolist restricts output to maximize profits (producing where MR = MC, not where P = MC as in perfect competition), they create a deadweight loss. This is the loss of economic efficiency that results from the monopolist producing less than the socially optimal quantity. Consumers are willing to pay more than the marginal cost for additional units, but the monopolist restricts output to maintain higher prices.

• Price Discrimination: The relationship between MR and P provides the rationale for price discrimination. If a monopolist can separate consumers into different groups with different price elasticities of demand, they can charge higher prices to those with less elastic demand and lower prices to those with more elastic demand, thereby increasing their total revenue. This is a way for the monopolist to capture some of the consumer surplus that would otherwise be lost due to the MR < P constraint.

• Regulation and Antitrust Laws: The inherent inefficiency caused by monopolist behavior is the reason for government intervention through regulation and antitrust laws. These laws aim to prevent monopolies from forming or to break them up, promoting competition and efficiency in the market. By promoting competition, the price is brought closer to the marginal cost, reducing deadweight loss and benefiting consumers.

Illustrative Examples and Real-World Applications

Let's explore some examples to further solidify the understanding of this concept.

Example 1: A Simple Linear Demand Curve

Consider a monopolist with a demand curve: P = 20 - 2Q

• Total Revenue (TR): TR = P * Q = 20Q - 2Q²
• Marginal Revenue (MR): MR = d(TR)/dQ = 20 - 4Q

If the monopolist's marginal cost (MC) is constant at 4, they will produce where MR = MC:

20 - 4Q = 4 16 = 4Q Q = 4

Substituting Q = 4 into the demand equation:

P = 20 - 2(4) = 12

Therefore, the monopolist will produce 4 units and charge a price of 12. Note that MR (8) is less than P (12).

Example 2: Non-Linear Demand Curve

The relationship between MR and P also holds true for non-linear demand curves. The only difference is that calculating MR becomes more complex, often requiring calculus. Consider a demand curve like P = 100 - Q². Finding the MR would involve finding the derivative of the total revenue function, demonstrating that MR will still be less than P at every quantity.

Real-World Applications

Numerous real-world scenarios illustrate the MR < P principle:

• Pharmaceutical Companies: Pharmaceutical companies often hold patents on life-saving drugs, granting them significant market power. They can charge prices significantly higher than their marginal cost, exploiting their monopoly power.

• Utility Companies: In many regions, utility companies like electricity providers or water suppliers enjoy a degree of monopoly power due to high barriers to entry. They can set prices higher than their marginal costs, leading to potential regulatory intervention.

• Software Companies: Companies developing proprietary software with unique features can exert some degree of monopoly power. They can charge premium prices, acknowledging that their marginal revenue will always be less than their price.

• Diamond Mines: De Beers, historically, had significant control over the global diamond market, enabling them to influence prices and restrict supply, ensuring that their marginal revenue remained below the price they set for diamonds.

Advanced Considerations

While the fundamental relationship MR < P holds for all monopolists, several advanced considerations can further refine our understanding:

• Elasticity of Demand: The difference between MR and P is directly related to the price elasticity of demand. The more inelastic the demand, the smaller the difference between MR and P. Conversely, the more elastic the demand, the larger the difference. This is because with inelastic demand, price changes have a smaller effect on quantity demanded, thus reducing the revenue loss from lowering the price to sell more.

• Multiple Products: If a monopolist sells multiple products, the analysis becomes more complex. The marginal revenue for each product will depend on the demand for both products and the cross-price elasticity of demand between them.

Conclusion

The principle that for a monopolist, marginal revenue is less than price (MR < P) is fundamental to understanding their market behavior. This relationship dictates their profit-maximizing output, leads to deadweight loss, justifies the use of price discrimination, and provides the rationale for government regulation. While the examples and explanations provided here focus on simpler scenarios, the core principle remains valid even with more complex market structures and demand functions. Understanding this crucial relationship allows for a deeper appreciation of the economic implications of monopoly power and its impact on consumers and the economy as a whole. Further exploration of the concepts of elasticity, cost functions, and market dynamics provides a more comprehensive understanding of monopolist behavior and the policies designed to mitigate its inefficiencies.