# COURSE: AP MICROECONOMICS

# UNIT 4: IMPERFECT COMPETITION

# 1. INTRODUCTION

In our study of economics thus far, we have often operated under the "ideal" conditions of Perfect Competition. In that world, thousands of identical firms sell identical products, and no single buyer or seller has the power to influence the market price. However, if you look around at the actual economy, you will notice that this model is the exception, not the rule. From the social media platform you use, to the electricity powering your home, to the specific brand of cereal you eat, most markets are Imperfectly Competitive.

In Unit 4, we dive into the reality of Market Power. We will explore how firms behave when they have the ability to set their own prices rather than simply accepting a market-determined price. We will examine why some companies, like local water utilities, face no competition at all (Monopoly), why others like Nike and Adidas compete through branding rather than just price (Monopolistic Competition), and how giants like Boeing and Airbus engage in complex strategic "games" to outmaneuver one another (Oligopoly).

By the end of this unit, you will understand why prices are higher and quantities are lower in the real world compared to the theoretical ideal, why your airline ticket costs a different price than the person sitting next to you, and why "big business" behaves the way it does.

# 2. KEY CONCEPTS, TERMS, AND PRINCIPLES

To master Imperfect Competition, you must become fluent in the following terminology:

1. Market Power (Price-Making Ability): The ability of a firm to raise its price without losing all of its customers. This occurs because the firm's product is unique or because competitors are few.
2. Barrier to Entry: Any constraint that prevents new firms from entering an industry. Examples include patents, high start-up costs (economies of scale), and control of strategic resources.
3. Monopoly: A market structure where a single seller provides a unique product with no close substitutes.
4. Natural Monopoly: A situation where a single firm can produce the entire market quantity at a lower cost than two or more firms could, typically due to massive economies of scale (e.g., local power lines).
5. Monopolistic Competition: A market structure with many firms selling differentiated products and low barriers to entry.
6. Oligopoly: A market structure dominated by a few large firms whose decisions are interdependent.
7. Product Differentiation: The process of making a product distinct from others through quality, service, location, or advertising.
8. Price Discrimination: The practice of selling the same good at different prices to different customers based on their willingness to pay.
9. Game Theory: The study of strategic decision-making where the outcome for one player depends on the actions of others.
10. Dominant Strategy: A strategy that is best for a player regardless of the strategy chosen by the other players.
11. Nash Equilibrium: A situation where no player can improve their outcome by changing their own strategy, given the strategies of others.
12. Collusion / Cartel: An agreement among firms to limit output and keep prices high, acting effectively as a monopoly.
13. Excess Capacity: The difference between the profit-maximizing output and the output at minimum Average Total Cost (ATC). This is a hallmark of monopolistic competition.
14. Allocative Efficiency: Occurs when $P = MC$. In imperfect competition, usually $P > MC$, leading to Deadweight Loss (DWL).
15. Productive Efficiency: Occurs when a firm produces at the minimum of its ATC curve ($P = \text{min } ATC$).

# 3. IN-DEPTH EXPLANATION

# 4.1 – Imperfectly Competitive Markets

In Perfect Competition, the firm's demand curve is perfectly elastic (horizontal) because the firm is a price taker. In Imperfect Competition, the firm faces a downward-sloping demand curve.

# The Price-Marginal Revenue Relationship

Because the firm must lower its price to sell an additional unit, the Marginal Revenue (MR) for an imperfectly competitive firm is always less than the Price (P) for all units after the first.
Mathematically, if Total Revenue $TR = P \times Q$, then:
$$MR = \frac{\Delta TR}{\Delta Q}$$
For a linear demand curve $P = a - bQ$, the Total Revenue is $TR = aQ - bQ^2$.
The Marginal Revenue is the derivative of $TR$ with respect to $Q$:
$$MR = \frac{d(TR)}{dQ} = a - 2bQ$$
Notice that the slope of the MR curve ($2b$) is twice as steep as the slope of the Demand curve ($b$).

{
  "type": "line",
  "title": "Demand vs. Marginal Revenue for a Price Maker",
  "subtitle": "P = 20 - Q, MR = 20 - 2Q",
  "xLabel": "Quantity (units)",
  "yLabel": "Price/Revenue ($)",
  "labels": ["0", "2", "4", "6", "8", "10"],
  "datasets": [
    { "label": "Demand (Price)", "data": [20, 18, 16, 14, 12, 10], "tension": 0 },
    { "label": "Marginal Revenue", "data": [20, 16, 12, 8, 4, 0], "tension": 0 }
  ]
}

# Barriers to Entry

Firms maintain market power through barriers:

• Economies of Scale: High fixed costs make it difficult for small firms to compete.
• Legal Barriers: Patents, copyrights, and government licenses.
• Control of Resources: Owning the only mine for a specific mineral.

# 4.2 – Monopoly

A Monopoly is the purest form of imperfect competition.

# Profit Maximization

Like all firms, a monopolist maximizes profit where:
$$MR = MC$$

1. Find the quantity ($Q_m$) where $MR$ intersects $MC$.
2. Go up to the Demand curve to find the price ($P_m$).
3. Profit is calculated as: $\text{Profit} = (P_m - ATC) \times Q_m$.

{
  "type": "line",
  "title": "Monopoly Profit Maximization",
  "subtitle": "Profit-Max where MR=MC; Price found on Demand Curve",
  "xLabel": "Quantity (units)",
  "yLabel": "Price/Cost ($)",
  "labels": ["0", "10", "20", "25", "30", "40", "50"],
  "datasets": [
    { "label": "Demand", "data": [100, 90, 80, 75, 70, 60, 50], "tension": 0.1 },
    { "label": "MR", "data": [100, 80, 60, 50, 40, 20, 0], "tension": 0.1 },
    { "label": "MC", "data": [0, 20, 40, 50, 60, 80, 100], "tension": 0.1 },
    { "label": "ATC", "data": [100, 70, 45, 40, 36.6, 32.5, 30], "tension": 0.4 }
  ]
}

# Efficiency and Welfare

• Allocative Inefficiency: Since $P_m > MC$ at the profit-maximizing quantity, the value to society of the last unit produced is greater than the cost to produce it. This creates Deadweight Loss (DWL).
• Productive Inefficiency: The monopolist does not produce at the minimum of the ATC curve.

# Natural Monopoly

In some industries, the $ATC$ is still declining at the point where it crosses the market demand. This happens when fixed costs are very high and marginal costs are very low.

• If the government regulates a natural monopoly at $P = MC$ (Socially Optimal Price), the firm will likely suffer an economic loss because $MC < ATC$.
• If regulated at $P = ATC$ (Fair Return Price), the firm earns zero economic profit (normal profit).

{
  "type": "line",
  "title": "Natural Monopoly Costs and Regulation",
  "subtitle": "Declining ATC throughout the relevant range of demand",
  "xLabel": "Quantity (units)",
  "yLabel": "Price/Cost ($)",
  "labels": ["1", "2", "4", "6", "8", "10"],
  "datasets": [
    { "label": "Demand", "data": [15, 13, 11, 9, 7, 5], "tension": 0 },
    { "label": "ATC (Continuous Economies of Scale)", "data": [12, 7, 4.5, 3.6, 3.25, 3], "tension": 0.4 },
    { "label": "MC (Constant Low Cost)", "data": [2, 2, 2, 2, 2, 2], "tension": 0 }
  ]
}

# 4.3 – Price Discrimination

Price discrimination allows a firm to capture more Consumer Surplus.

# Requirements for Price Discrimination

1. The firm must have Market Power.
2. The firm must be able to Segregate Customers based on their willingness to pay (price elasticity of demand).
3. The firm must be able to Prevent Resale (arbitrage).

# Perfect Price Discrimination (First-Degree)

In this theoretical extreme, the monopolist charges every single customer exactly what they are willing to pay.

• Result: The Demand curve becomes the MR curve.
• Output: The firm produces where $D (MR) = MC$, which is the socially optimal quantity.
• Efficiency: There is no Deadweight Loss and no Consumer Surplus. All surplus is converted into Producer Surplus.

# 4.4 – Monopolistic Competition

This structure blends elements of Perfect Competition and Monopoly. Examples: Restaurants, clothing brands, hair salons.

# Characteristics

• Differentiated Products: Non-price competition (advertising).
• Low Barriers: Firms can enter or exit easily.

# Short Run vs. Long Run

• Short Run: Firms can earn economic profits or losses.
• Long Run: If there are profits, new firms enter, shifting the existing firms' demand curves to the left until $\text{Profit} = 0$.
• Long-Run Equilibrium: The demand curve is tangent to the ATC curve ($P = ATC$).

{
  "type": "line",
  "title": "Monopolistic Competition: Long-Run Equilibrium",
  "subtitle": "Zero Economic Profit (P = ATC) and Excess Capacity",
  "xLabel": "Quantity (units)",
  "yLabel": "Price/Cost ($)",
  "labels": ["5", "10", "15", "20", "25", "30"],
  "datasets": [
    { "label": "Demand (D)", "data": [45, 40, 35, 30, 25, 20], "tension": 0 },
    { "label": "MR", "data": [40, 30, 20, 10, 0, -10], "tension": 0 },
    { "label": "ATC", "data": [60, 45, 35, 30, 35, 45], "tension": 0.4 },
    { "label": "MC", "data": [10, 10, 10, 10, 10, 10], "tension": 0 }
  ]
}

# The Cost of Variety (Inefficiency)

1. Excess Capacity: The firm produces at a quantity $Q_{mc}$ which is less than $Q_{atc}$ (where ATC is minimized).
2. Markup: $P > MC$, meaning it is allocatively inefficient.

# 4.5 – Oligopoly and Game Theory

Oligopolies consist of a few "players" who must anticipate each other's moves.

# The Payoff Matrix

Consider two firms, A and B, choosing between High Price and Low Price. The values in the cells represent (Profit A, Profit B).

# Dominant Strategy

A player has a dominant strategy if one choice is always better regardless of what the opponent does.

• In the table above, if B chooses High, A's best is Low (150 > 100). If B chooses Low, A's best is Low (50 > 20).
• Firm A's dominant strategy is Low Price.

# Nash Equilibrium

A Nash Equilibrium occurs when both players choose their best response to the other's choice.

• In the example above, the Nash Equilibrium is (Low Price, Low Price) with payoffs (50, 50).

# Prisoner's Dilemma

This is a specific game where the Nash Equilibrium results in a lower total payoff than if the players had cooperated. In the table above, both firms would be better off at (High Price, High Price), but the incentive to "cheat" leads them to the lower-profit (Low Price, Low Price) outcome.

# 4. EXAMPLES

# 1. Marginal Revenue Calculation

A monopolist faces demand $P = 20 - Q$.

• $TR = 20Q - Q^2$
• $MR = \frac{d(TR)}{dQ} = 20 - 2Q$
  If $Q=5, P=15, TR=75, MR=10$. If $Q=6, P=14, TR=84, MR=8$.
  Notice $MR < P$ (8 < 14).

# 2. Profit Maximization Steps

A firm has $MC = 2Q$ and faces $P = 100 - Q$.

• Find MR: $MR = 100 - 2Q$.
• Set $MR = MC$: $100 - 2Q = 2Q \implies 4Q = 100 \implies Q^* = 25$.
• Find Price: $P = 100 - 25 = $75$.
• If $ATC$ at $Q=25$ is $$40$, Profit $= (75 - 40) \times 25 = $875$.

# 3. Natural Monopoly: Utilities

A water company has high fixed costs ($FC = $1,000,000$) and low constant marginal cost ($MC = $2$).
$$ATC = \frac{1,000,000}{Q} + 2$$
As $Q$ increases, $ATC$ continues to fall. One firm can serve 100,000 people cheaper than two firms serving 50,000 each.

# 4. Deadweight Loss Calculation

In the example from #2 ($Q^=25, P^=75$), the socially optimal quantity is where $P = MC$.
$100 - Q = 2Q \implies 3Q = 100 \implies Q_{so} \approx 33.3$.
The DWL is the triangle area between Demand and MC from $Q=25$ to $Q=33.3$.
$$\text{DWL} = \frac{1}{2} \times (75 - 50) \times (33.3 - 25) \approx $103.75$$

# 5. Perfect Price Discrimination: Tuition

A private university knows exactly what every student can pay. Student A can pay $$50k$, Student B can pay $$20k$. The university charges A $$50k$ and B $$20k$. The university's MR for the second student is $$20k$, not $$20k$ minus the "loss" from lowering A's price. Thus, $D = MR$.

# 6. Airline Ticket Pricing (Price Discrimination)

Airlines charge more for last-minute business travelers (inelastic demand) and less for vacationers who book months in advance (elastic demand). This segments the market to maximize profit.

# 7. Monopolistic Competition: Coffee Shops

A local coffee shop raises its price by $$0.50$. Unlike perfect competition, it doesn't lose all customers because people like its specific atmosphere or "brand" of beans. However, it still faces a downward-sloping demand curve.

# 8. Excess Capacity in Monopolistic Competition

A boutique clothing store's long-run equilibrium output is 50 shirts a day. However, its $ATC$ is minimized at 80 shirts a day. The 30-shirt difference is Excess Capacity. The store is "too small" to be productively efficient but exists to provide variety.

# 9. Game Theory: Advertising War

Coke and Pepsi are deciding whether to advertise.

• If both advertise, they split the market but have high costs.
• If one advertises and the other doesn't, the advertiser takes the whole market.
• If neither advertises, they split the market and save money.
  The incentive to steal market share usually leads both to advertise (the Nash Equilibrium).

# 10. The OPEC Cartel

Oil-producing countries agree to limit production to keep global oil prices high. This is Collusion. If one country (e.g., Saudi Arabia) produces more than its quota to make extra money, the cartel "cheats," and prices may collapse.

# 11. Movie Theaters: Age-Based Pricing

Theaters offer student and senior discounts. This is 3rd-degree price discrimination. Seniors have more leisure time and are more price-sensitive (elastic), while prime-age adults are less price-sensitive (inelastic).

# 12. Monopsony: The Company Town

In a small town with only one coal mine, the mine is a Monopsony (single buyer of labor). It has the power to set wages lower than the competitive rate. To hire more workers, it must raise the wage for all workers, making its Marginal Factor Cost ($MFC$) higher than the wage ($W$).

# 13. Patents as a Barrier

A pharmaceutical company spends billions developing a drug. The government grants a 20-year patent. During this time, the firm is a monopolist. Once the patent expires, "generic" firms enter, and the market becomes Monopolistically Competitive.

# 14. Network Effects

Social media sites like Facebook or X (Twitter) become more valuable as more people join. This creates a barrier to entry because a new competitor can't offer the same "network" of friends, even if their software is better.

# 15. Concentration Ratio

If the four largest firms in the breakfast cereal industry control 85% of the market, the Four-Firm Concentration Ratio is 85%. This indicates an Oligopoly.

# 16. Herfindahl-Hirschman Index (HHI)

An advanced measure of market power calculated by squaring the market share of each firm.
$$\text{HHI} = s_1^2 + s_2^2 + \dots + s_n^2$$
If 4 firms each have 25% share, $\text{HHI} = 25^2 \times 4 = 2500$. High HHI indicates low competition.

# 17. The "Fair Return" Regulation

Regulators force a local electric company to set $P = ATC$. The firm stays in business with zero economic profit, and the price is lower than the monopoly price, though not as low as the socially optimal ($P=MC$) price.

# 18. Product Differentiation: Quality

Two vacuum cleaners perform differently. Dyson differentiates through suction technology and design, allowing it to charge a premium price ($P > MC$).

# 19. Strategic Interdependence

Ford sees GM offering a 0% interest financing deal. Ford must respond by either matching the deal or losing significant market share. This back-and-forth is the essence of Oligopoly.

# 20. Couponing

Only price-sensitive consumers take the time to clip coupons. By offering coupons, a firm can charge a high price to "lazy/busy" customers and a lower price to "price-sensitive" customers.

# 21. Natural Monopoly and Subsidy

If a government forces a natural monopolist to produce at $P=MC$ (Socially Optimal), the firm will lose money ($P < ATC$). To keep the firm afloat, the government must provide a Lump-sum Subsidy equal to the loss.

# 22. Kinked Demand Curve Model

An old theory explaining why oligopoly prices are "sticky." If a firm raises prices, others don't follow (elastic demand). If a firm lowers prices, others follow (inelastic demand). This creates a "kink" in the demand curve.

# 23. Deadweight Loss in Monopolistic Competition

Even though there are many firms, the fact that products are differentiated means $P > MC$. Therefore, there is always some DWL in Monopolistic Competition, representing the "price" society pays for having variety (different colors, flavors, brands).

# 24. First-Degree Price Discrimination Efficiency

Derivation: If $P = 10 - Q$ and $MC = 2$.

• Standard Monopoly: $MR = 10 - 2Q = 2 \implies Q=4, P=6$. $\text{CS} = 0.5(10-6)4 = 8$. $\text{Profit} = (6-2)4 = 16$.
• Perfect Price Discrim: Firm produces where $P=MC \implies 10-Q=2 \implies Q=8$. Total Surplus is the entire area under demand above MC: $0.5(10-2)8 = 32$. All 32 is Producer Surplus.

# 25. Brand Loyalty as a Barrier

Apple users are often reluctant to switch to Android due to the ecosystem (iMessage, iCloud). This "switching cost" acts as a barrier to entry for competitors.

# 26. Exclusive Ownership of Resources

DeBeers historically controlled most of the world’s diamond mines. By controlling the supply, they operated as a near-monopoly for decades.

# 27. Advertising and ATC

In Monopolistic Competition, heavy advertising increases the $ATC$ curve. However, if advertising successfully increases demand, the firm might still increase profit.

# 28. Dominant Firm Model

In some oligopolies, one massive firm (like Walmart in retail) sets the price, and smaller "fringe" firms follow. This is called Price Leadership.

# 29. Tying Agreements

A monopolist sells one product only on the condition that the buyer also purchases a different product. This is often used to extend monopoly power into a second market.

# 30. Shutdown Point for a Monopolist

A monopolist will shut down in the short run if the price it can charge ($P_m$) is less than its Average Variable Cost ($AVC$). Being a monopoly does not guarantee profit!

# 31. Zero-Sum Game

A game where one player's gain is exactly equal to the other player's loss. Most market competition games are not zero-sum because total market size can grow or shrink.

# 32. Marginal Revenue and Elasticity

• When $MR > 0$, Demand is Elastic.
• When $MR = 0$, Total Revenue is maximized and Demand is Unit Elastic.
• When $MR < 0$, Demand is Inelastic.
  A monopolist will never produce in the inelastic range of its demand curve.

# 33. Profit-Sharing in Oligopolies

If two firms in an oligopoly collude perfectly, they will produce the exact same quantity as a single monopolist ($MR=MC$) and split the monopoly profits.

# 34. Natural Monopoly: High $FC$, Zero $MC$

A digital software download has a high cost to code ($FC$), but the cost to send one more copy is $$0$ ($MC$). $ATC$ will fall forever as $Q$ increases.

# 35. Long-Run Equilibrium in Monopolistic Competition (Math)

If $P = 100 - Q$ and $ATC = \frac{500}{Q} + 20$.
In the long run, $P = ATC$.
$$100 - Q = \frac{500}{Q} + 20 \implies 80 - Q = \frac{500}{Q} \implies 80Q - Q^2 = 500$$
Solving $Q^2 - 80Q + 500 = 0$ using the quadratic formula gives the equilibrium quantity where economic profit is zero.