Why Is Marginal Revenue Less Than Price In A Monopoly

Why is Marginal Revenue Less Than Price in a Monopoly?

A fundamental characteristic of a monopoly is its ability to influence the market price of its product. Unlike firms in perfectly competitive markets that are price takers, monopolies are price makers. This power, however, comes with a trade-off: to sell more units, a monopolist must lower the price of all units sold, not just the additional ones. This leads to a crucial economic relationship: marginal revenue (MR) is always less than price (P) in a monopoly. This article delves deep into the reasons behind this phenomenon, exploring the underlying economic principles and illustrating the concept with examples.

Understanding Marginal Revenue and Price

Before examining why MR < P in a monopoly, let's clarify these key terms:

• Price (P): The price a monopolist charges per unit of its product. This price is determined by the demand curve the monopolist faces. The demand curve shows the relationship between the price of a good and the quantity demanded at that price. In a monopoly, the demand curve for the firm is the market demand curve – there are no other producers.

• Marginal Revenue (MR): The additional revenue a monopolist earns from selling one more unit of its product. It's the change in total revenue (TR) resulting from a one-unit increase in quantity sold. Mathematically, MR = ΔTR/ΔQ.

The Downward-Sloping Demand Curve: The Root Cause

The core reason why MR < P in a monopoly stems from the downward-sloping demand curve. Because the monopolist is the sole provider, it faces the entire market demand. To sell more, it must lower the price not just for the additional unit but for all units it sells. This price reduction eats into the revenue earned from the previously sold units, causing MR to fall below P.

Consider this scenario:

Suppose a monopolist is initially selling 10 units at a price of $10 per unit. Its total revenue is $100. If it wants to sell one more unit (11 units), it must lower the price to, say, $9.50 per unit. The total revenue now becomes $104.50 ($9.50 x 11). The marginal revenue from selling the 11th unit is $4.50 ($104.50 - $100). Notice that the marginal revenue ($4.50) is significantly less than the price of the 11th unit ($9.50). This illustrates the core principle: the price reduction on the existing units reduces the marginal revenue gained from selling an additional unit.

Graphical Representation

The relationship between MR and P can be visually represented through a graph:

• Demand Curve (D): This curve slopes downward, reflecting the inverse relationship between price and quantity demanded.

• Marginal Revenue Curve (MR): This curve lies below the demand curve and also slopes downward. It always has twice the slope of the demand curve (assuming a linear demand curve).

The distance between the demand curve and the marginal revenue curve represents the revenue lost from lowering the price on previously sold units. This distance increases as quantity increases, showcasing the increasingly smaller marginal revenue gained from selling each extra unit.

Mathematical Derivation (Linear Demand)

Let's assume a linear demand function: P = a - bQ, where:

• P = Price
• Q = Quantity
• a = The price intercept (the price when Q = 0)
• b = The slope of the demand curve (a negative value)

Total Revenue (TR) = P * Q = (a - bQ) * Q = aQ - bQ²

Marginal Revenue (MR) is the derivative of TR with respect to Q:

MR = d(TR)/dQ = a - 2bQ

Comparing the demand curve (P = a - bQ) and the marginal revenue curve (MR = a - 2bQ), we can see that for any given Q, MR will always be less than P because of the -2bQ term in the MR equation which is twice the magnitude of -bQ in the demand equation.

Implications for Monopoly Pricing and Output

The fact that MR < P has significant implications for a monopolist's decisions regarding price and output:

• Lower Output: Because marginal revenue diminishes with each additional unit sold, a monopolist will produce a lower quantity of output compared to a perfectly competitive market. This is because the monopolist will continue to produce only as long as the marginal revenue is greater than or equal to its marginal cost.

• Higher Price: By restricting output, the monopolist creates scarcity and maintains a higher price than would prevail under perfect competition. This allows the monopolist to earn economic profits (profits above normal profits).

• Deadweight Loss: The lower output and higher price result in a deadweight loss, which represents a loss of efficiency in the market. This is because some mutually beneficial trades do not take place due to the monopolist's restriction of output.

Non-Linear Demand Curves

While the linear demand example provides a clear illustration, the principle of MR < P holds true for all downward-sloping demand curves, regardless of their shape. The intuition remains the same: to sell more, the monopolist must lower the price of all units, leading to marginal revenue being less than the price. The mathematical derivation will, however, be more complex depending on the specific form of the demand function.

Elasticity and Marginal Revenue

The relationship between price elasticity of demand and marginal revenue is also important. When demand is elastic (percentage change in quantity demanded is greater than the percentage change in price), marginal revenue is positive. However, when demand is inelastic (percentage change in quantity demanded is less than the percentage change in price), marginal revenue is negative. A monopolist will always operate in the elastic portion of the demand curve, as producing where demand is inelastic would lead to lower total revenue.

Conclusion

The fact that marginal revenue is less than price in a monopoly is a fundamental concept in microeconomics. It arises directly from the downward-sloping demand curve faced by the monopolist. The monopolist's ability to control the price means it must lower its price to sell more units; this price reduction impacts revenue from all units sold, leading to MR < P. This relationship has profound implications for the monopolist's pricing strategy, output decision, and overall market efficiency. Understanding this fundamental principle is crucial for comprehending the behavior of monopolies and their impact on the economy. The analysis of this concept helps in understanding the inefficiencies associated with monopoly power and its implications for social welfare. Further, understanding the relationship between price elasticity and marginal revenue is key to understanding the profit-maximizing behavior of a monopolist.