Introduction to Imperfectly Competitive Markets

AP Microeconomics· AP Microeconomics CED — Imperfect Competition· 14 min read

1. Core Definition of Imperfect Competition★★☆☆☆⏱ 3 min

Imperfectly competitive markets are any market structure that deviates from the strict assumptions of perfect competition. At least one firm has market power: the ability to set price above marginal cost, rather than taking the market price as given.

This foundational topic for AP Microeconomics Unit 4 (which counts for 16-22% of total AP exam score) introduces core tools that apply to all three main imperfect competition structures: monopoly, monopolistic competition, and oligopoly. These tools are also used for antitrust analysis of market power.

📘 Definition

Market Power

A firm's ability to set price above marginal cost, resulting from facing a downward-sloping demand curve rather than being a price-taker.

Example:

A local utility company has enough market power to set prices well above its marginal cost of production.

2. Downward-Sloping Demand and Marginal Revenue★★★☆☆⏱ 4 min

Unlike perfectly competitive firms, which face horizontal (perfectly elastic) demand at the market price, all imperfectly competitive firms face a downward-sloping demand curve. To sell additional output, a firm with market power must lower its price for all units sold, not just the extra unit. This means marginal revenue (additional revenue from selling one more unit) is always less than price, or $M R < P$ for all $Q > 0$ .

For a linear inverse demand curve of the form $P = a - b Q$ , we derive marginal revenue by first calculating total revenue, then finding its derivative:

TR = P \times Q = (a - bQ)Q = aQ - bQ^2 \\ MR = \frac{dTR}{dQ} = a - 2bQ

For linear demand, MR has the same vertical intercept as the inverse demand curve but twice the slope, so it is always below the demand curve and crosses the horizontal axis at half the quantity where demand crosses the horizontal axis. We can also relate MR to price elasticity of demand:

MR = P\left(1 - \frac{1}{|E_d|}\right)

This relationship means: $M R > 0$ when demand is elastic ( $∣ E_{d} ∣ > 1$ ), $M R = 0$ when demand is unit elastic ( $∣ E_{d} ∣ = 1$ ), and $M R < 0$ when demand is inelastic ( $∣ E_{d} ∣ < 1$ ).

📐 Worked Example

A local bakery sells custom cakes and faces the linear inverse demand $P = 30 - 1.5 Q$ , where $P$ is price per cake and $Q$ is number of cakes sold per week. (1) Derive the marginal revenue curve, (2) find the quantity where $M R = 0$ , (3) state what this implies about the elasticity of demand at $Q = 8$ .

1
First calculate total revenue:
2
$TR = PQ = (30 - 1.5Q)Q = 30Q - 1.5Q^2$
3
Take the derivative of $T R$ to get $M R$ , which matches the twice-the-slope rule:
4
$MR = \frac{dTR}{dQ} = 30 - 3Q$
5
Set $M R = 0$ to find where marginal revenue crosses the horizontal axis:
6
$30 - 3Q = 0 \implies Q=10$
7
Calculate $M R$ at $Q = 8$ and interpret elasticity:
8
$MR = 30 - 3(8) = 6 > 0$
9
A positive marginal revenue means demand is elastic ( $∣ E_{d} ∣ > 1$ ) at this quantity.

Exam tip:

On AP graph questions, always draw MR below the demand curve for any imperfectly competitive firm. If you draw MR on the same line as demand, you will lose points even if your profit-maximizing quantity is correct.

3. The Lerner Index of Market Power★★★☆☆⏱ 3 min

Market power is formally defined as a firm’s ability to set price above marginal cost. The Lerner Index is a standardized measure of the degree of market power a firm has, derived directly from the profit-maximizing condition $M R = M C$ .

P\left(1 - \frac{1}{|E_d|}\right) = MC \\ L = \frac{P - MC}{P} = \frac{1}{|E_d|}

The Lerner Index ranges from 0 (no market power, $P = M C$ , which describes perfect competition) to 1 (maximum market power, where $∣ E_{d} ∣ = 1$ and $M C$ approaches 0). The more inelastic the firm’s demand, the higher the Lerner Index, and the greater the firm’s market power. Barriers to entry allow firms to maintain market power in the long run.

📐 Worked Example

A regional natural gas provider charges a profit-maximizing price of $12 per thousand cubic feet, and has a constant marginal cost of $3 per thousand cubic feet. Calculate the Lerner Index, then find the price elasticity of demand for the provider’s output.

1
Apply the Lerner Index formula using the given price and marginal cost:
2
$L = \frac{P-MC}{P} = \frac{12 - 3}{12} = 0.75$
3
Use the relationship between Lerner Index and elasticity to solve for $∣ E_{d} ∣$ :
4
$|E_d| = \frac{1}{L} = \frac{1}{0.75} \approx 1.33$
5
Since demand is downward-sloping, the price elasticity of demand is $E_{d} = - 1.33$ . A Lerner Index of 0.75 indicates the provider has a high degree of market power, consistent with being a regulated monopoly.

Exam tip:

Always remember the Lerner Index only applies to profit-maximizing firms where $M R = M C$ holds. If a question asks for the Lerner Index at a non-profit-maximizing quantity, you cannot use the $1/∣ E_{d} ∣$ shortcut—you have to calculate $(P - M C) / P$ directly.

4. Market Concentration Measures★★★☆☆⏱ 4 min

To measure the degree of market power across an entire market (rather than just one firm), two common concentration measures are regularly tested on the AP exam: the 4-firm concentration ratio (CR4) and the Herfindahl-Hirschman Index (HHI).

📘 Definition

4-Firm Concentration Ratio (CR4)

CR_4

The sum of the percentage market shares of the 4 largest firms in a market. Ranges from 0% (perfect competition) to 100% (monopoly), with higher values indicating more concentrated markets.

📘 Definition

Herfindahl-Hirschman Index (HHI)

HHI = \sum_{i=1}^n s_i^2

The sum of the squares of the percentage market shares of all firms in the market. Ranges from near 0 (perfect competition) to 10,000 (monopoly), and accounts for the size distribution of all firms, unlike simple concentration ratios.

Markets with HHI above 2500 are classified as highly concentrated by U.S. antitrust regulators.

📐 Worked Example

The craft beer market in a small state has 5 firms with market shares: 45%, 25%, 15%, 10%, 5%. Calculate the 4-firm concentration ratio (CR4) and the HHI for this market.

1
CR4 is the sum of the market shares of the top 4 firms:
2
$CR4 = 45 + 25 + 15 + 10 = 95\%$
3
HHI is the sum of the squares of all 5 firms' percentage market shares:
4
$HHI = 45^2 + 25^2 + 15^2 + 10^2 + 5^2 = 2025 + 625 + 225 + 100 + 25 = 3000$
5
Interpretation: A CR4 of 95% and HHI of 3000 confirms this market is highly concentrated and clearly imperfectly competitive.

Exam tip:

When calculating HHI, always use market shares in percentage points (e.g., 45 for 45%, not 0.45) to get the standard 0-10000 range AP expects. Using decimals will give you a result 10,000 times too small and cost you points.

5. 6. Common Pitfalls

Wrong move:

Drawing the marginal revenue curve on the same line as the downward-sloping demand curve for an imperfectly competitive firm

Why:

Students confuse the perfect competition case (where $M R = P =$ demand) with imperfect competition, carrying over the wrong graph convention

Correct move:

Always draw MR below the demand curve for any downward-sloping demand, with MR crossing the horizontal axis at half the quantity where demand crosses the horizontal axis

Wrong move:

Calculating marginal revenue for $P = a - b Q$ as $M R = a - b Q$ (same slope as demand)

Why:

Students forget to multiply price by quantity to get total revenue before taking the derivative

Correct move:

Always derive $T R = P Q$ first, then take the derivative, or remember the 'twice the slope' rule for linear demand to get MR directly

Wrong move:

Claiming all imperfectly competitive markets earn positive economic profit in the long run

Why:

Students group all non-perfect competition into one category, ignoring differences in barriers to entry

Correct move:

Remember that monopolistic competition has low barriers to entry, so it earns zero economic profit in the long run, same as perfect competition

Wrong move:

Arguing that $M R < P$ for imperfect competition because marginal cost is upward-sloping

Why:

Students confuse the reason for MR < P with properties of cost curves

Correct move:

$M R < P$ only because the firm faces a downward-sloping demand curve, so cutting price to sell an extra unit reduces revenue on all previous units, regardless of the shape of MC

Wrong move:

Calculating HHI by squaring decimal market shares (e.g., 0.45 for 45% gives $0.4 5^{2} = 0.2025$ )

Why:

Confusion over the standard scaling of HHI for the AP exam

Correct move:

Always use percentage point values for market share when calculating HHI, resulting in a 0-10000 range

7. Quick Reference Cheatsheet

Category	Formula	Key AP Exam Notes
Marginal Revenue (Linear Inverse Demand)	If $P = a - b Q$ , then $M R = a - 2 b Q$	Same intercept as demand, twice the slope, always below demand for $Q > 0$
MR and Elasticity Relationship	$M R = P (1 - \frac{1}{∣ E _{d} ∣})$	$M R > 0 ⟺ ∣ E_{d} ∣ > 1$ ; $M R = 0 ⟺ ∣ E_{d} ∣ = 1$ ; $M R < 0 ⟺ ∣ E_{d} ∣ < 1$
Lerner Index (Profit-Maximizing Firm)	$L = \frac{P - M C}{P} = \frac{1}{∣ E _{d} ∣}$	Ranges 0 (no market power) to 1 (maximum market power)
4-Firm Concentration Ratio	$C R_{4} = \sum_{i = 1}^{4} s_{i}$	$s_{i}$ = % market share of top 4 firms; ranges 0-100%
Herfindahl-Hirschman Index (HHI)	$H H I = \sum_{i = 1}^{n} s_{i}^{2}$	$s_{i}$ = % market share of all firms; ranges ~0 to 10,000
Core Rule for All Imperfect Competition	$M R < P$ for all $Q > 0$	Always true for any firm with downward-sloping demand

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · MCQ
Calculate HHI for given market
2022 · FRQ
Derive MR for linear demand

What's Next

This topic establishes the core shared properties of all non-perfectly competitive markets, laying the critical foundation for the rest of Unit 4, which counts for 16-22% of your total AP Microeconomics exam score. All tools you learned here—deriving marginal revenue for downward-sloping demand, measuring market power with the Lerner Index, and calculating market concentration—are applied directly to each specific imperfectly competitive market structure in the coming topics. Without mastering these basics, you will struggle to correctly draw profit-maximization graphs, calculate equilibrium outcomes, and analyze deadweight loss for all other imperfect competition topics. This topic also introduces the core concept of market power, which underpins all microeconomics policy analysis around regulation and antitrust.