The Profit-Maximising Equilibrium of a Monopoly

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The profit-maximising equilibrium of a monopoly is one of the most fundamental concepts in microeconomic theory. It describes the point at which a monopolist chooses its level of output and the corresponding price to achieve the highest possible economic profit. Unlike firms in perfectly competitive markets, monopolists face downward-sloping demand curves, allowing them to influence prices directly. However, this pricing power introduces inefficiencies and prompts regulatory scrutiny. This article explores the economic logic behind profit-maximising behavior in monopolies, including graphical and mathematical derivations, cost and revenue relationships, and real-world implications.

Key Characteristics of Monopoly

Before analyzing the equilibrium condition, it is important to understand what defines a monopoly:

  • Single Seller: The firm is the only producer in the market
  • No Close Substitutes: Consumers cannot switch to alternatives
  • High Barriers to Entry: Legal, technological, or strategic obstacles deter new entrants
  • Price Maker: The firm determines the price-output combination

These features provide the monopolist with the ability to maximize profit by adjusting output and price simultaneously.

Revenue and Cost Functions

To understand monopoly equilibrium, we must examine how revenue and costs behave.

Total Revenue (TR):

TR = P × Q

Since the monopolist faces a downward-sloping demand curve, selling more units requires lowering the price. As a result, marginal revenue (MR) is less than price.

Marginal Revenue (MR):

MR = d(TR)/dQ

Total Cost (TC):

TC = Fixed Costs (FC) + Variable Costs (VC)

Marginal Cost (MC):

MC = d(TC)/dQ

Profit Maximisation Condition

The monopolist maximizes profit where:

MR = MC

At this point:

  • If MR > MC, the firm can increase profit by increasing output
  • If MR < MC, the firm should reduce output
  • At MR = MC, profit is maximized

Graphical Illustration

The monopoly equilibrium can be illustrated with the following curves:

  • Demand curve (D)
  • Marginal revenue curve (MR), which lies below demand
  • Marginal cost curve (MC)
  • Average total cost curve (ATC)
Price
|
|         ATC
|          /\
|         /  \
|        /    \       D
|       /      \_____/‾‾‾
|------/------------------\---------- Quantity
|     MR                   \
|                            MC

Equilibrium Output:

  • At MR = MC, output is Q*
  • Price is determined from the demand curve at Q*, which is P*
  • Profit = (P* – ATC) × Q*

Mathematical Derivation

Assume the following linear demand function:

P = a - bQ

Then:

TR = P × Q = aQ - bQ²
MR = d(TR)/dQ = a - 2bQ

Let marginal cost be constant:

MC = c

Set MR = MC:

a - 2bQ = c
→ Q* = (a - c) / (2b)

Find price:

P* = a - bQ* = a - b((a - c)/(2b)) = (a + c)/2

Thus:

  • Profit-maximising output: (a – c)/2b
  • Profit-maximising price: (a + c)/2

Profit and Welfare Implications

1. Supernormal Profit

Monopolists typically earn profits greater than zero in the short and long run due to barriers to entry.

2. Deadweight Loss

The monopolist restricts output below the socially optimal level (where P = MC), creating a deadweight loss.

3. Consumer Surplus Reduction

Consumers pay more and receive less compared to competitive markets.

Comparison to Perfect Competition

Feature Perfect Competition Monopoly
Number of Firms Many One
Price Control None High
Output Level Higher Lower
Price Level Lower Higher
Profit in Long Run Zero Positive

Limitations and Real-World Deviations

1. Uncertainty in Demand

Monopolists may not know the exact demand curve, making marginal revenue estimation difficult.

2. Cost Fluctuations

Variable costs can change due to supply chain constraints or inflation.

3. Strategic Goals

Firms may maximize long-term market share or reputation, not just short-term profit.

4. Regulatory Constraints

Governments may cap prices, mandate service levels, or break up monopolies.

Real-World Examples

1. De Beers

Controlled global diamond supply, setting prices through output restriction and market segmentation.

2. Microsoft

Maintained dominance in operating systems, leveraging bundling strategies to maintain equilibrium above competitive levels.

3. Google

Monetizes search dominance through algorithmic ad placement and personalized pricing—raising questions about where equilibrium lies in a zero-price market.

Equilibrium in Theory and Practice

The profit-maximising equilibrium of a monopoly is a powerful model that reveals the trade-offs between private gain and public loss. In reality, monopolies face strategic complexity, evolving market conditions, and regulatory oversight that shift the practical equilibrium. Yet, the MR = MC framework remains a central tool for understanding how and why monopolists choose output and price—and why such decisions often demand careful economic and legal scrutiny.

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