Introduction to Imperfectly Competitive Markets — AP Microeconomics Study Guide

For: AP Microeconomics candidates sitting AP Microeconomics.

Covers: Characteristics of imperfect competition, marginal revenue for downward-sloping demand, the relationship between MR and elasticity, the Lerner Index of market power, 4-firm concentration ratios, and the Herfindahl-Hirschman Index (HHI) of market concentration.

You should already know: Profit maximization rule $MR=MC$, price elasticity of demand, demand curve properties for perfectly competitive firms.

A note on the practice questions: All worked questions in the "Practice Questions" section below are original problems written by us in the AP Microeconomics style for educational use. They are not reproductions of past College Board / Cambridge / IB papers and may differ in wording, numerical values, or context. Use them to practise the technique; cross-check with official mark schemes for grading conventions.

1. What Is Introduction to Imperfectly Competitive Markets?

Imperfectly competitive markets are any market structure that deviates from the strict assumptions of perfect competition, meaning at least one firm has market power: the ability to set price above marginal cost rather than taking the market price as given. This topic is the foundational introduction to Unit 4 (Imperfect Competition) of the AP Microeconomics CED, which counts for 16-22% of the total AP exam score; this introductory component makes up roughly 2-4% of the total exam. It appears in both multiple-choice (MCQ) questions testing core characteristics and as a lead-in concept in free-response (FRQ) questions analyzing specific market structures. The three main types of imperfect competition (monopoly, monopolistic competition, oligopoly) all share the core properties covered in this chapter, which we will expand on in later topics. This topic also introduces key tools to measure the degree of market power and market concentration, which are used for antitrust analysis.

2. Core Properties: Downward-Sloping Demand and Marginal Revenue

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 that the marginal revenue (additional revenue from selling one more unit) is always less than the price of that unit, or $MR<P$ for all $Q>0$.

For a linear inverse demand curve of the form $P=a-bQ$, we can derive marginal revenue directly:

1. Total revenue is $TR=P\times Q=(a-bQ)Q=aQ-b{Q}^2$
2. Marginal revenue is the derivative of $TR$ with respect to $Q$, giving $MR=a-2bQ$

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: $$MR=P\left(1+\frac{1}{E_d}\right)=P\left(1-\frac{1}{|E_d|}\right)$$ This means $MR>0$ when demand is elastic ($|E_d|>1$), $MR=0$ when demand is unit elastic ($|E_d|=1$), and $MR<0$ when demand is inelastic ($|E_d|<1$).

Worked Example

A local bakery sells custom cakes and faces the linear inverse demand $P=30-1.5Q$, 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 $MR=0$, (3) state what this implies about the elasticity of demand at $Q=8$.

1. First calculate total revenue: $TR=PQ=(30-1.5Q)Q=30Q-1.5Q^2$
2. Take the derivative of $TR$ to get $MR$: $MR=\frac{dTR}{dQ}=30-3Q$. This matches the "twice the slope" rule for linear demand, as expected.
3. Set $MR=0$ to find the quantity where marginal revenue crosses the x-axis: $30-3Q=0⟹Q=10$.
4. At $Q=8$, $MR=30-3(8)=6>0$, so 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. Market Power and the Lerner Index

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 $MR=MC$. Starting from $MR=P\left(1-\frac{1}{|E_d|}\right)$, set equal to $MC$: $$P\left(1-\frac{1}{|E_d|}\right)=MC$$ Rearranging gives the Lerner Index: $$L=\frac{P-MC}{P}=\frac{1}{|E_d|}$$ The Lerner Index ranges from 0 (no market power, $P=MC$, which is perfect competition) to 1 (maximum market power, where $|E_d|=1$ and $MC$ 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 (legal restrictions, economies of scale, control of key inputs, network effects) allow firms to maintain market power in the long run, unlike perfect competition where free entry drives economic profit to zero and $P=MC$ in equilibrium.

Worked Example

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

1. First apply the Lerner Index formula using price and marginal cost: $L=\frac{P-MC}{P}=\frac{12-3}{12}=\frac{9}{12}=0.75$.
2. Use the Lerner-elasticity relationship $L=\frac{1}{|E_d|}$ to solve for elasticity: $|E_d|=\frac{1}{L}=\frac{1}{0.75}\approx 1.33$.
3. Since demand is downward-sloping, $E_d=-1.33$.
4. Interpretation: A Lerner Index of 0.75 indicates the provider has a high degree of market power, consistent with its status as a regulated monopoly (an imperfectly competitive market structure).

Exam tip: Always remember the Lerner Index only applies to profit-maximizing firms where $MR=MC$ 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 $(P-MC)/P$ directly.

4. Market Concentration Measures

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

The N-firm concentration ratio (CR${}_N$) is the sum of the market shares (usually expressed as percentage points) of the N largest firms in the market. The most common is the 4-firm concentration ratio (CR4), which ranges from 0% (perfect competition, all firms are tiny) to 100% (monopoly, one firm controls the entire market). Higher CR values mean more concentrated markets with more overall market power.

The Herfindahl-Hirschman Index (HHI) improves on the CR by accounting for all firms in the market, not just the top N. It is calculated as the sum of the squares of the market shares (in percentage points) of all firms in the market: $$HHI=\sum _{i=1}^n{s}_i^2$$ HHI ranges from near 0 (perfect competition) to 10,000 (monopoly: $100^2=10,000$). The U.S. Department of Justice uses HHI to evaluate mergers: markets with HHI above 2500 are classified as highly concentrated.

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: $CR4=45+25+15+10=95\%$.
2. HHI is the sum of the squares of all 5 firms’ market shares: $$HHI=45^2+25^2+15^2+10^2+5^2=2025+625+225+100+25=3000$$
3. Interpretation: A CR4 of 95% and HHI of 3000 means this market is highly concentrated, which confirms it is imperfectly competitive rather than perfectly 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. Common Pitfalls (and how to avoid them)

• 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 $MR=P=$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 $P=a-bQ$ as $MR=a-bQ$ (same slope as demand). Why: Students forget to multiply price by quantity to get total revenue before taking the derivative. Correct move: Always derive $TR=PQ$ 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 $MR<P$ for imperfect competition because marginal cost is upward-sloping. Why: Students confuse the reason for MR < P with properties of cost curves. Correct move: $MR<P$ 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% gets $0.45^2=0.2025$). Why: Confusion over the standard scaling of HHI for AP. Correct move: Always use percentage point values for market share when calculating HHI, resulting in a 0-10000 range.

6. Practice Questions (AP Microeconomics Style)

Question 1 (Multiple Choice)

Which of the following statements is true for all imperfectly competitive markets? A) Firms earn positive economic profit in the long run B) Firms produce where marginal revenue equals marginal cost at the profit-maximizing quantity C) The Herfindahl-Hirschman Index of the market is less than 1500 D) Firms set price equal to marginal cost at the profit-maximizing quantity

Worked Solution: Eliminate incorrect options one by one. Option A is wrong because monopolistic competition has free entry, so firms earn zero economic profit in the long run. Option C is wrong because a pure monopoly has an HHI of 10,000, which is far higher than 1500. Option D is wrong because all imperfectly competitive firms have $MR<P$, so profit maximization $MR=MC$ implies $P>MC$, not $P=MC$. Option B is correct: all profit-maximizing firms, regardless of market structure, produce where $MR=MC$. Correct answer: B

Question 2 (Free Response)

A private golf club faces the inverse demand curve $P=200-4Q$, where $P$ is the annual membership fee in dollars and $Q$ is the number of members. The marginal cost of adding an additional member is constant at $40. (a) Derive the marginal revenue curve for the golf club. (b) Calculate the profit-maximizing quantity and price for the golf club, then calculate the Lerner Index at this outcome. (c) What is the value of the price elasticity of demand at the profit-maximizing quantity?

Worked Solution: (a) Total revenue is $TR=PQ=(200-4Q)Q=200Q-4Q^2$. Marginal revenue is the derivative of $TR$, so: $$MR=\frac{dTR}{dQ}=200-8Q$$ (b) Set $MR=MC$ to find profit-maximizing quantity: $200-8Q=40⟹8Q=160⟹Q=20$. Substitute $Q=20$ back into demand to get price: $P=200-4(20)=\$120$. Lerner Index: $L=\frac{P-MC}{P}=\frac{120-40}{120}=\frac{80}{120}\approx 0.67$. (c) Using $L=1/|E_d|$, we get $|E_d|=1/0.67\approx 1.5$. For downward-sloping demand, $E_d=-1.5$.

Question 3 (Application / Real-World Style)

The mobile phone service market in Canada has 4 major carriers with the following market shares: 33%, 30%, 22%, 15%. Calculate the HHI for this market, and state whether it would be classified as highly concentrated per the DOJ standard of HHI > 2500. What does this HHI value tell you about the nature of competition in this market?

Worked Solution: Calculate HHI as the sum of squared percentage market shares: $$HHI=33^2+30^2+22^2+15^2=1089+900+484+225=2698$$ The HHI of 2698 is greater than the 2500 threshold for high concentration. In context, this means the Canadian mobile phone service market is highly concentrated, with significant overall market power held by the four large firms, so it is clearly an imperfectly competitive market rather than a perfectly competitive one.

7. Quick Reference Cheatsheet

8. What's Next

This chapter establishes the core shared properties of all non-perfectly competitive markets, laying the critical foundation for the rest of Unit 4. All tools you learned here—deriving marginal revenue for downward-sloping demand, measuring the degree of 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.

Monopoly Monopolistic Competition Oligopoly and Game Theory