Intermediate Microeconomics (Besanko & Braeutigam, 5th ed.) | Chapter 13: Market Structure and Competition
Difficulty: Intermediate | Prerequisites: Perfect competition (Ch. 9), monopoly (Ch. 11), basic game theory concepts
Chapter 13 sits at the heart of industrial organisation: it covers the space between the two extremes you have already studied (perfect competition and monopoly) and asks what happens when a handful of firms compete. Most real-world markets fall somewhere in this middle ground, so the models here, Cournot and Bertrand in particular, are the ones that do the heavy lifting on exams and in applied work. You should already be comfortable with profit maximisation under monopoly (MR = MC), the perfectly competitive outcome (P = MC), and the idea of a Nash equilibrium from basic game theory. If those feel shaky, revisit Chapters 9, 11, and the game theory primer before going further.
Oligopoly models predict market outcomes that lie between monopoly and perfect competition. Cournot firms choose quantities and land on a price above marginal cost but below the monopoly price; Bertrand firms choose prices and, with identical products, drive price all the way down to marginal cost. Concentration ratios and the HHI measure how close a market is to monopoly, and product differentiation (vertical or horizontal) explains why competing firms can still charge different prices.
Oligopoly
A market structure in which a small number of firms account for most or all of the output in an industry, and each firm's decisions affect the others. Think of it as the middle ground between monopoly (one seller) and perfect competition (many sellers, none with market power).
Cournot model (quantity competition)
An oligopoly model in which each firm simultaneously chooses how much to produce, taking the other firm's output as given. The resulting Nash equilibrium is called the Cournot equilibrium. In simple terms, each firm picks a quantity, and the market price is whatever the demand curve says at the total output.
Bertrand model (price competition)
An oligopoly model in which each firm simultaneously chooses a price, taking the other firm's price as given. With homogeneous products, the equilibrium price equals marginal cost, even with only two firms. In simple terms, price competition with identical goods is brutal: undercut or lose all your customers.
Reaction function (best response function)
A function that gives one firm's profit-maximising output (Cournot) or price (Bertrand) as a function of the other firm's choice. The Cournot equilibrium is where the two reaction functions intersect. Think of it as each firm's "if they do X, my best move is Y" rule.
Nash equilibrium
A set of strategies (one per player) where no player can improve their payoff by changing their own strategy alone. Both the Cournot and Bertrand equilibria are Nash equilibria of their respective games.
Four-firm concentration ratio (4CR / C4)
The sum of the market shares of the four largest firms in an industry, expressed as a percentage. A 4CR near 100% signals a highly concentrated market. In simple terms, it tells you how much of the pie the top four firms control.
Herfindahl-Hirschman Index (HHI)
The sum of the squared market shares (in percentage points) of all firms in the industry. Ranges from near 0 (many tiny firms) to 10,000 (a single firm with 100% share). The squaring gives extra weight to firms with large shares, making the HHI more sensitive to dominance than the 4CR.
Vertical product differentiation
Products differ in quality in a way that all consumers agree on: everyone prefers product A to product B if they are priced the same, though some consumers will still buy B if A is expensive enough. Think of it as a clear ranking, better versus worse.
Horizontal product differentiation
Products differ in characteristics but not in a universally agreed quality ranking. Some consumers prefer product A, others prefer product B, even at the same price. Think of it as a matter of taste: chocolate versus vanilla.
Homogeneous products
Goods that are identical across sellers. Consumers see no difference between one firm's output and another's, so they buy from whoever charges less.
Dominant firm
A firm with a very large market share in an industry that also contains much smaller competitors. The dominant firm often sets the market price, while the fringe firms are price takers.
In a Cournot oligopoly, each firm chooses its quantity to maximise its own profit, treating the rival's output as fixed.
The Cournot price sits between the monopoly price and the perfectly competitive price. This makes intuitive sense:
A monopolist restricts output to push price up. Two Cournot firms each have an incentive to produce more than half the monopoly quantity, because each firm captures all the revenue from its own extra units while only sharing part of the price reduction. Total output therefore exceeds the monopoly level, and price falls below the monopoly price.
But each Cournot firm still has market power. Unlike a perfectly competitive firm, a Cournot firm recognises that increasing its output lowers the market price. It therefore stops short of expanding output all the way to the competitive level. Price stays above marginal cost.
As the number of Cournot firms increases, the equilibrium approaches perfect competition. With infinitely many firms, each firm's impact on price vanishes, and P converges to MC.
In the Bertrand model, firms choose prices rather than quantities.
With homogeneous products (identical goods), the Bertrand equilibrium predicts P = MC, even with just two firms. This is the Bertrand paradox: two firms are enough to replicate the perfectly competitive outcome.
The logic: if Firm A prices above MC, Firm B can undercut by a tiny amount and capture the entire market. This undercutting continues until both firms price at MC, earning zero economic profit.
With differentiated products, the Bertrand result softens. Firms retain some pricing power because consumers are not indifferent between the two products, so a small price cut does not steal the entire rival market.
Cournot (quantity competition) with homogeneous products: P > MC. Firms earn positive economic profit.
Bertrand (price competition) with homogeneous products: P = MC. Firms earn zero economic profit.
The critical difference is the strategic variable. When firms commit to quantities, they implicitly soften competition (more output by one firm lowers the price for both, so there is a natural brake). When firms compete on price, competition is fierce because a tiny price cut captures everything.
Vertical differentiation: all consumers agree on the quality ranking. A BMW is "better" than a basic hatchback by any measure that matters to buyers, but the hatchback still sells because it is cheaper. Competition happens along the price-quality spectrum.
Horizontal differentiation: consumers disagree on which product is better. Pepsi versus Coca-Cola, or living in the city versus the suburbs. Each product has a natural customer base, and firms can charge above marginal cost because some customers genuinely prefer their product.
Why this matters: differentiation is a source of market power. Even in an industry with many firms, horizontal differentiation can sustain price above MC because switching to a rival means accepting a less-preferred product.
Four-firm concentration ratio (4CR): add the market shares of the top four firms. Simple to calculate, but it does not distinguish between a market where one firm has 80% and three have 1% each versus a market where four firms each have 21%.
Herfindahl-Hirschman Index (HHI): sum of squared market shares (using percentage points). Captures the asymmetry the 4CR misses. An HHI above 2,500 is considered highly concentrated by antitrust standards. A single firm with 100% share gives HHI = 10,000.
The beryllium oxide example from the homework: 4CR = 80 + 1 + 1 + 1 = 83%. HHI is at least 80² + 1² + 1² + 1² = 6,403 (higher if there are other small firms). The 4CR looks high but not extreme; the HHI reveals that the market is dominated by one firm, pointing toward a dominant-firm structure.
Cournot reaction function (symmetric, linear demand)
For demand P = a - bQ and constant marginal cost c, with two identical firms:
q_i = \frac{a - c}{2b} - \frac{1}{2} q_jEach firm's optimal quantity is a decreasing function of the rival's quantity.
Cournot equilibrium (symmetric duopoly)
q_i^* = \frac{a - c}{3b}Q^* = \frac{2(a - c)}{3b}P^* = \frac{a + 2c}{3}Monopoly output and price (for comparison)
q_m = \frac{a - c}{2b}P_m = \frac{a + c}{2}Perfectly competitive output and price
Q_{pc} = \frac{a - c}{b}P_{pc} = cFour-firm concentration ratio
4CR = s_1 + s_2 + s_3 + s_4where s_i is the market share (%) of the i-th largest firm.
Herfindahl-Hirschman Index
HHI = \sum_{i=1}^{N} s_i^2where s_i is each firm's market share in percentage points (so a monopolist gives HHI = 100² = 10,000).
OPEC is the textbook example of quantity competition in practice. Member countries negotiate production quotas (quantities), and the world oil price adjusts accordingly. The tension between the group's interest (restrict output, raise price) and each member's temptation to overproduce mirrors the Cournot logic exactly.
Airline pricing on popular routes often resembles Bertrand competition with differentiated products. Carriers match each other's fares aggressively on identical routes, but loyalty programmes, schedules, and seat quality create enough differentiation to sustain some price above cost.
Antitrust regulators (the US DOJ and FTC) use the HHI to screen proposed mergers. A post-merger HHI above 2,500 with an increase of more than 200 points triggers a closer investigation.
Students often think Bertrand competition always drives price to marginal cost. It does not. The P = MC result requires homogeneous products. With differentiated products, Bertrand firms retain pricing power and earn positive profits.
Students often confuse the 4CR and HHI as interchangeable. They are not. The 4CR ignores how market share is distributed among the top four firms. An 83% 4CR could mean four firms at roughly 21% each (moderate concentration) or one firm at 80% and three at 1% (dominant firm). The HHI captures this difference; the 4CR does not.
Students sometimes believe that two Cournot firms will produce the same total output as a monopolist. They will not. Each firm independently maximises its own profit, and the incentive to free-ride on the rival's output restriction pushes total output above the monopoly level.
Students frequently mix up the strategic variable in Cournot versus Bertrand. A useful anchor: Cournot = quantities, Bertrand = prices. Getting this backwards will lead to the wrong equilibrium prediction on an exam.
⚠️ Be prepared to explain why the Cournot price sits between the monopoly and competitive prices. This is a classic short-answer question.
⚠️ Know the Bertrand paradox cold: two firms, homogeneous products, P = MC. Exams love asking why this result is "surprising."
⚠️ You will almost certainly be asked to compute a 4CR and an HHI from a table of market shares. Remember that HHI uses the squares of market shares in percentage points (not decimals).
⚠️ Vertical versus horizontal differentiation is a common definition question. Have a crisp one-sentence distinction ready, with an example of each.
True or false: In a Cournot duopoly with identical firms, each firm produces exactly half the monopoly output. (False: each produces more than half, so total output exceeds monopoly output.)
Fill in the blank: In a Bertrand oligopoly with homogeneous products, the equilibrium price equals ________. (Marginal cost.)
True or false: The HHI for a market with four firms each holding 25% market share is 2,500. (True: 4 x 25² = 2,500.)
True or false: Horizontal product differentiation means all consumers agree that one product is better than another. (False: that describes vertical differentiation.)
Fill in the blank: The strategic variable in the Cournot model is ________, while in the Bertrand model it is ________. (Quantity; price.)
Q: Why is the Cournot equilibrium price less than the monopoly price but greater than the perfectly competitive price?
A: A monopolist restricts total output to maximise joint profits. In a Cournot duopoly, each firm maximises its own profit and has an incentive to expand output beyond half the monopoly level, because it captures all the revenue from its extra units while the price reduction is shared. Total output therefore exceeds monopoly output, pushing price below the monopoly level. However, each Cournot firm still recognises that its own output affects the market price, so it does not expand all the way to the competitive level. Price remains above marginal cost.
Q: In a homogeneous-products oligopoly, what does the Bertrand model predict about the equilibrium price? How does this differ from Cournot?
A: The Bertrand model predicts P = MC, even with only two firms (the Bertrand paradox). Cournot predicts P > MC. The difference arises because Bertrand firms compete on price: any price above MC invites undercutting. Cournot firms compete on quantity, which softens competition because expanding output lowers the price for both firms.
Q: Explain the difference between vertical and horizontal product differentiation, with an example of each.
A: Vertical differentiation means all consumers agree on the quality ranking of products (e.g. a premium laptop versus a budget one). Horizontal differentiation means consumers disagree about which product is better, based on personal preference (e.g. Coke versus Pepsi). With vertical differentiation, lower-quality products survive by being cheaper. With horizontal differentiation, firms coexist because different consumers genuinely prefer different products.
Q: A market has the following firm market shares: 80%, 1%, 1%, 1%, and many smaller firms. Calculate the 4CR and the HHI (for these four firms only). What market structure does this suggest?
A: 4CR = 80 + 1 + 1 + 1 = 83%. HHI (four firms only) = 80² + 1² + 1² + 1² = 6,400 + 1 + 1 + 1 = 6,403. The very high HHI, driven almost entirely by the dominant firm's 80% share, indicates a dominant-firm market structure. The 4CR alone would not reveal how lopsided the concentration is.
This chapter builds directly on the monopoly model from Chapter 11. The Cournot equilibrium is best understood as a relaxation of the monopoly assumption: instead of one firm maximising joint profit, multiple firms each maximise their own, and the result sits between monopoly and competition. If you go on to study game theory in more depth, the Cournot and Bertrand models are foundational examples of simultaneous-move games with continuous strategy spaces.
The concentration measures (4CR and HHI) connect to antitrust policy and regulation, which you may encounter in a public economics or law and economics course. The product differentiation material links forward to monopolistic competition (Chapter 14 in many texts), where many firms each sell a slightly different product.
Oligopoly, duopoly, Cournot equilibrium, Cournot model, Bertrand equilibrium, Bertrand model, Bertrand paradox, Nash equilibrium, reaction function, best response function, quantity competition, price competition, market concentration, four-firm concentration ratio, 4CR, C4, Herfindahl-Hirschman Index, HHI, market structure, vertical product differentiation, horizontal product differentiation, homogeneous products, differentiated products, dominant firm, market power, market share, antitrust, merger screening, oligopoly pricing, intermediate microeconomics, Besanko Braeutigam Chapter 13