Monopoly
Market Power and Pricing

Explore how a single seller controls an entire market: from price-setting behavior to deadweight loss and the profit-maximizing rule $ MR = MC $.

AP Microeconomics

What Is a Monopoly?

A monopoly is a market structure in which a single firm is the sole producer of a good or service with no close substitutes. Unlike a perfectly competitive firm, a monopolist is a price maker: it faces the entire market demand curve and chooses the quantity (and thus price) that maximizes its profit.

Sources of Monopoly Power

Legal Barriers

Patents, copyrights, licenses, and government franchises grant exclusive rights to produce.

Natural Monopoly

Economies of scale so large that one firm can supply the entire market at a lower cost than two or more firms.

Control of Resources

A single firm owns or controls an essential input (e.g., De Beers and diamonds historically).

Demand, $ MR $, and the Price-Maker

For a monopolist with a linear demand curve $ P = a - bQ $, total revenue is $ TR = PQ = aQ - bQ^2 $. Marginal revenue is the derivative:

The Profit-Maximizing Rule

A monopolist maximizes profit by producing at the quantity where marginal revenue equals marginal cost:

1

Find $ Q^* $: Set $ MR = MC $ and solve for the profit-maximizing quantity.

2

Find $ P^* $: Plug $ Q^* $ into the demand curve to find the price.

3

Calculate profit: $ \pi = (P^* - ATC) \times Q^* $. If $ P^* > ATC $, the firm earns economic profit.

The Monopoly Graph

Monopoly vs. Perfect Competition

	Monopoly	Perfect Competition
Number of Firms	One	Many
Price	Price maker	Price taker
Demand Curve	Downward-sloping	Perfectly elastic (horizontal)
$ MR $ vs. $ P $	$ MR < P $	$ MR = P $
Long-Run Profit	Possible (barriers)	Zero (free entry)
Efficiency	Allocatively inefficient	Allocatively efficient

Deadweight Loss of Monopoly

Because a monopolist restricts output below the competitive level and charges a higher price, society loses surplus. The triangle between the demand curve, the $ MC $ curve, and the monopoly quantity represents deadweight loss (DWL).

The Natural Monopoly

A natural monopoly arises when the minimum efficient scale is so large relative to market demand that a single firm can produce the total output at a lower average total cost than multiple firms could. Think utilities: water, electricity, rail networks.

How to Solve Monopoly Problems

1

Write down demand and cost functions. Identify $ P(Q) $ (inverse demand), $ TC(Q) $, or individual cost curves ($ MC $, $ ATC $).

2

Derive $ MR $. If demand is linear $ P = a - bQ $, then $ MR = a - 2bQ $. Otherwise, use $ MR = \frac{dTR}{dQ} $.

3

Set $ MR = MC $. Solve for $ Q^* $.

4

Find $ P^* $. Substitute $ Q^* $ back into the demand equation (not the $ MR $ equation).

5

Calculate profit. $ \pi = (P^* - ATC(Q^*)) \times Q^* $, or $ \pi = TR - TC $.

6

Find DWL (if asked). Compare monopoly outcome ($Q_m, P_m$) to competitive outcome ($Q_c$) where $ P = MC $. $$ DWL = \frac{1}{2}(P_m - MC)(Q_c - Q_m) $$

Worked Example: Finding $ Q^* $ and $ P^* $

1

Derive $ MR $: $ MR = 100 - 4Q $

2

Set $ MR = MC $: $ 100 - 4Q = 20 $ $\rightarrow$ $ 4Q = 80 $ $\rightarrow$ $ Q^* = 20 $

3

Find $ P^* $ from demand: $ P = 100 - 2(20) = $ $ \$60 $

Worked Example: Calculating Profit

1

Total Revenue: $ TR = P^* \times Q^* = 60 \times 20 = $ $ \$1{,}200 $

2

Total Cost: $ TC = ATC \times Q^* = 30 \times 20 = $ $ \$600 $

3

Economic Profit: $ \pi = TR - TC = 1{,}200 - 600 = $ $ \$600 $

Worked Example: Deadweight Loss

1

Find competitive $ Q_c $: Set $ P = MC $: $ 100 - 2Q = 20 $ $\rightarrow$ $ Q_c = 40 $

2

Compute $ DWL $ triangle: Base = $ Q_c - Q_m = 40 - 20 = 20 $. Height = $ P_m - MC = 60 - 20 = 40 $.

3

$ DWL $: $ \frac{1}{2} \times 20 \times 40 = $ $ \$400 $

Price Discrimination

A monopolist with market power may charge different prices to different consumers for the same product. This requires the ability to segment the market and prevent resale.

First Degree

Charge each consumer their maximum willingness to pay. Captures all consumer surplus. Eliminates DWL.

Second Degree

Quantity discounts: different prices for different quantities purchased (e.g., bulk pricing).

Third Degree

Different prices for different groups (student vs. adult tickets). Most common in practice.

Regulating a Monopoly

Marginal-Cost Pricing

Set $ P = MC $. Allocatively efficient, but if $ MC < ATC $, the firm incurs losses and needs a subsidy.

Fair-Return Pricing

Set $ P = ATC $. Firm earns zero economic profit. Not fully efficient but sustainable without subsidies.

Common Mistakes

✕ Pricing off MR

Students set $ P^* = MR $ at $ Q^* $. The price comes from the demand curve, not the $ MR $ curve.

✕ Assuming Max Revenue = Max Profit

Revenue is maximized where $ MR = 0 $. Profit is maximized where $ MR = MC $. These are different quantities.

✕ Ignoring ATC for Profit

A monopolist can incur losses if $ P^* < ATC $. Market power does not guarantee positive economic profit.

Monopoly Summary

Concept	Key Formula / Rule
Profit-Max Rule	$ MR = MC $
Linear $ MR $	If $ P = a - bQ $, then $ MR = a - 2bQ $
Monopoly Price	Read $ P^* $ from demand curve at $ Q^* $
Economic Profit	$ \pi = (P^* - ATC) \times Q^* $
Deadweight Loss	$$ \frac{1}{2}(P_m - MC)(Q_c - Q_m) $$
Allocative Efficiency	Requires $ P = MC $ (monopoly fails this)
Perfect Price Disc.	All $CS$ captured; $DWL = 0$; $ Q = Q_c $

Question 1 of 5

A profit-maximizing monopolist determines its price by finding the quantity where $ MR = MC $ and then:

The monopolist finds $ Q^* $ where $ MR = MC $, then reads the price consumers are willing to pay from the demand curve, not the $ MR $ or cost curves.

Question 2 of 5

A monopolist faces demand $ P = 80 - Q $ and has constant marginal cost $ MC = 20 $. What is the profit-maximizing price?

$ MR = 80 - 2Q $. Set $ MR = MC $: $ 80 - 2Q = 20 $ $\rightarrow$ $ Q^* = 30 $. Then $ P^* = 80 - 30 = \$50 $.

Question 3 of 5

Which of the following is true about a natural monopoly?

A natural monopoly exists when economies of scale are so extensive that $ATC$ declines over the entire range of market demand. One firm can serve the market more cheaply than multiple firms.

Question 4 of 5

Compared to the perfectly competitive outcome, a single-price monopolist produces ___ output at a ___ price.

A monopolist restricts output below the competitive level ($ Q_m < Q_c $) and charges a higher price ($ P_m > P_c $). This creates deadweight loss.

Question 5 of 5

Under perfect (first-degree) price discrimination, which of the following is true?

With perfect price discrimination, the monopolist charges each consumer their maximum willingness to pay. Output expands to the competitive quantity ($ Q_c $), eliminating DWL. However, all consumer surplus is captured by the producer.

Monopoly
Market Power and Pricing

What Is a Monopoly?

Sources of Monopoly Power

Demand, \( MR \), and the Price-Maker

The Profit-Maximizing Rule

The Monopoly Graph

Monopoly vs. Perfect Competition

Deadweight Loss of Monopoly

The Natural Monopoly

How to Solve Monopoly Problems

Worked Example: Finding \( Q^* \) and \( P^* \)

Worked Example: Calculating Profit

Worked Example: Deadweight Loss

Price Discrimination

Regulating a Monopoly

Common Mistakes

Monopoly Summary

Question 1 of 5

Question 2 of 5

Question 3 of 5

Question 4 of 5

Question 5 of 5

Concept	Key Formula / Rule
Profit-Max Rule	\( MR = MC \)
Linear \( MR \)	If \( P = a - bQ \), then \( MR = a - 2bQ \)
Monopoly Price	Read \( P^* \) from demand curve at \( Q^* \)
Economic Profit	\( \pi = (P^* - ATC) \times Q^* \)
Deadweight Loss	$$ \frac{1}{2}(P_m - MC)(Q_c - Q_m) $$
Allocative Efficiency	Requires \( P = MC \) (monopoly fails this)
Perfect Price Disc.	All \(CS\) captured; \(DWL = 0\); \( Q = Q_c \)

MonopolyMarket Power and Pricing

What Is a Monopoly?

Sources of Monopoly Power

Demand, \( MR \), and the Price-Maker

The Profit-Maximizing Rule

The Monopoly Graph

Monopoly vs. Perfect Competition

Deadweight Loss of Monopoly

The Natural Monopoly

How to Solve Monopoly Problems

Worked Example: Finding \( Q^* \) and \( P^* \)

Worked Example: Calculating Profit

Worked Example: Deadweight Loss

Price Discrimination

Regulating a Monopoly

Common Mistakes

Monopoly Summary

Question 1 of 5

Question 2 of 5

Question 3 of 5

Question 4 of 5

Question 5 of 5

Monopoly
Market Power and Pricing