Chapter 5 derived the supply curve of a competitive firm: produce where $P = MC$. But this result assumes the firm is a price taker — so small relative to the market that it cannot influence the price. Many real markets violate this assumption. A single seller (monopolist) sets its own price. A handful of large firms (oligopolists) must account for rivals' reactions. This chapter maps the spectrum of market structures and introduces game theory as the language for strategic interaction.
By the end of this chapter, you will be able to:
Characterize long-run competitive equilibrium and explain the zero-profit condition
Solve a monopolist's pricing problem and compute deadweight loss
Analyze price discrimination (first, second, and third degree)
Solve Cournot, Bertrand, and Stackelberg oligopoly models
In Chapter 5, we showed that a competitive firm maximizes profit at $P = MC$. In the long run, free entry and exit drives a further result.
Long-run competitive equilibrium.In the long run, entry occurs when existing firms earn positive economic profit (attracting new firms) and exit occurs when firms earn negative profit. Entry shifts the market supply curve right, pushing the price down; exit shifts it left, pushing the price up. The process continues until:
Economic profit vs accounting profit.Economic profit subtracts all costs, including the opportunity cost of the owner's capital and time. Accounting profit subtracts only explicit (monetary) costs. In long-run competitive equilibrium, economic profit is zero but accounting profit is positive.
Zero economic profit does not mean firms suffer. It means they earn a normal return — exactly covering all costs, including the opportunity cost of capital. Accounting profit is still positive.
6.2 Monopoly
Monopoly.A market with a single seller. The monopolist faces the entire market demand curve and chooses quantity (or equivalently, price) to maximize profit.
$$\max_Q \; \Pi = P(Q) \cdot Q - TC(Q)$$(Eq. 6.2)
where $P(Q)$ is the inverse demand function — it gives the price the monopolist must set to sell $Q$ units. Unlike the competitive firm (which takes price as given), the monopolist recognizes that selling more requires cutting the price.
Intuition
What this says: The monopolist chooses how much to produce by balancing two forces: producing more means more revenue from additional sales, but it also means lowering the price on every unit. Profit is total revenue minus total cost, and the monopolist picks the quantity where the gap is largest.
Why it matters: Unlike a competitive firm that simply takes the market price and decides how much to make, the monopolist controls the price through its output decision. This single difference -- that the firm faces the entire demand curve rather than a flat price line -- is what generates all of monopoly theory: restricted output, higher prices, and deadweight loss.
What changes: If costs rise, the monopolist produces less and charges more. If demand shifts outward (more consumers, higher willingness to pay), the monopolist produces more but also charges more -- pocketing much of the increase as profit rather than passing it through as lower prices.
In Full Mode, Eq. 6.2 states the formal optimization problem.
Marginal Revenue
Marginal revenue.The additional revenue from selling one more unit. For a price-taking firm, $MR = P$. For a firm with market power, $MR < P$ because increasing output requires lowering the price on all units sold.
$$MR = \frac{dTR}{dQ} = P + Q\frac{dP}{dQ}$$(Eq. 6.3)
This has two terms:
$P$: the revenue gained from selling one more unit at the current price (the output effect)
$Q \cdot dP/dQ$: the revenue lost because the price must fall on all units, not just the marginal one (the price effect)
Output effect and price effect.The output effect is the gain from selling one additional unit at the current price. The price effect is the loss from reducing the price on all inframarginal units. Marginal revenue is the net of these two forces: $MR = \underbrace{P}_{\text{output effect}} + \underbrace{Q \cdot dP/dQ}_{\text{price effect}}$.
For a downward-sloping demand curve, $dP/dQ < 0$, so $MR < P$. For linear demand $P = a - bQ$: $TR = aQ - bQ^2$, so $MR = a - 2bQ$. The MR curve has the same intercept as the demand curve but twice the slope.
A monopolist never produces where $MR < 0$ (she could raise revenue by producing less), so she always operates on the elastic portion of the demand curve.
The profit-maximizing condition:
$$MR = MC$$(Eq. 6.4)
Intuition
What this says: Marginal revenue is the extra revenue from selling one more unit. For a monopolist facing a downward-sloping demand curve, MR is always less than price because lowering the price to sell one more unit reduces revenue on all existing units.
Why it matters: The gap between price and MR is why monopolists restrict output — they stop producing before the competitive quantity because each additional unit erodes revenue on previous sales. The firm maximizes profit by producing until MR exactly equals MC.
What changes: When demand becomes more elastic (consumers more price-sensitive), MR gets closer to price and the monopolist behaves more like a competitive firm. When demand is inelastic, MR is actually negative — the monopolist would never produce in the inelastic portion of demand.
In Full Mode, Eqs. 6.3–6.4 derive MR from the revenue function and show the profit-maximization condition.
What this says: A monopolist faces a dilemma that competitive firms do not: to sell one more unit, it must lower the price on every unit, not just the last one. So the extra revenue from selling one more unit (marginal revenue) is always less than the price. The monopolist produces where MR = MC and charges a markup. The Lerner Index measures that markup: it equals the inverse of demand elasticity. If customers have few alternatives (inelastic demand), the monopolist charges a bigger markup.
Why it matters: This is why monopolies restrict output and raise prices — not out of villainy, but because the math of facing a downward-sloping demand curve makes it profitable to sell less at a higher price. The deadweight loss comes from units that consumers value more than they cost to produce, but the monopolist withholds because selling them would require cutting the price on all other units.
What changes: When demand becomes more elastic (consumers have more substitutes), the Lerner index falls and the monopolist's markup shrinks — the price moves closer to marginal cost. When demand is very inelastic (few alternatives), the monopolist can charge a much larger markup. This is why pharmaceutical companies with patented drugs charge far more above cost than, say, a local cable company facing satellite competition.
In Full Mode, Eq. 6.5 derives the Lerner index from the MR = MC condition.
The markup over marginal cost equals the inverse of the (absolute) price elasticity of demand. More elastic demand means less market power.
Adjust the marginal cost to see how the monopolist's optimal price, quantity, profit, and deadweight loss change. Toggle the competitive outcome overlay to compare.
Figure 6.2. The monopolist restricts output to where MR = MC, charging above marginal cost. The blue rectangle is monopoly profit; the yellow triangle is deadweight loss. Toggle the competitive overlay to see the efficient outcome.
Take
"Amazon is a monopoly even though prices are low" — Lina Khan, Yale Law Journal, 2017
Lina Khan was a 28-year-old law student when she published "Amazon's Antitrust Paradox" — an argument so influential it got her appointed chair of the FTC. Her claim: the consumer welfare standard that has governed antitrust since the 1980s is blind to Amazon's power because it only looks at prices. Amazon keeps prices low, so the standard says there's no problem. Khan says the standard is broken. By the Lerner index you just learned, she's making a radical claim — that market power can exist even when $(P - MC)/P$ is near zero.
Intermediate
The popular version
Khan's article spawned a movement — "New Brandeis" antitrust — and a popular version that's weaker than her actual argument. The popular anti-tech line: "They're monopolies — break them up!" This pattern-matches on market share (high share = monopoly = bad) without engaging with the mechanism: how are consumers being harmed? The textbook monopoly from section 6.2 harms consumers through higher prices and lower output, but Google doesn't charge consumers a price and Amazon's prices are often the lowest available. Saying "break them up" without specifying consumer harm is diagnosing a disease by looking at one symptom. The popular pro-tech counter is equally weak: "If they were monopolies, prices would be high — Google is free!" This treats zero price as proof of no market power, missing that "free" services are paid for with data and attention, that Google's monopoly power operates in advertising (where it sets prices very effectively), and that consumer welfare includes dimensions beyond price — privacy, choice, innovation. Khan's actual argument is more sophisticated than either side. But the popular versions dominate the debate.
Khan's argument at its strongest
Here's what Khan's framework looks like when you push it to its analytical limit. First, market power in adjacent markets. Amazon Marketplace may offer low prices to consumers, but Amazon charges sellers 30-50% of revenue through fees, advertising, and logistics requirements — and sellers can't leave because that's where the customers are. Google Search is free to users, but Google Ads is not free to advertisers — Google's sustained 50%+ operating margins in advertising suggest substantial market power. The Lerner index, computed on the seller-facing or advertiser-facing market, is far from zero. Second, network effects create durable barriers that reduce future competition. Platform monopolies may reduce dynamic efficiency — innovation that would occur under competition never happens because entrants can't overcome the incumbent's data and network advantage. This is Khan's deepest insight: the harm is not to today's consumers but to tomorrow's competitors. Third, the predatory pricing cycle. Amazon can sustain below-cost pricing in new markets (diapers, books, groceries) funded by AWS profits, drive competitors out, then raise fees once it dominates. Traditional antitrust acquits this because consumer prices stay low. Khan says that's exactly the blind spot.
The strongest case against
Three compelling objections to Khan's framework. First, consumer welfare is demonstrably enormous. Brynjolfsson et al. (2019) estimated the median consumer surplus from search engines at \$17,500 per year. These are not exploited consumers. Breaking up platforms would likely reduce this surplus — a fragmented social network is less useful than a unified one, and Amazon's logistics network delivers real cost savings. The traditional monopoly framework exists to protect consumers, and by consumer-outcome measures, Big Tech is delivering. Second, market dominance is contestable. IBM dominated mainframes, then lost to Microsoft; Microsoft dominated PCs, then lost to Google in search; MySpace lost to Facebook; TikTok exploded against Instagram. If barriers to entry were as durable as Khan claims, these disruptions shouldn't happen — but they keep happening. Third, Khan's framework has no limiting principle. If low prices can coexist with monopoly power, and future harm counts even without present harm, almost any large firm could be labeled a monopolist. An antitrust standard that can convict anyone is a standard that convicts no one — it becomes industrial policy disguised as competition law.
The judgment
Was Khan right that the consumer welfare standard is blind to platform monopoly? Yes — and that's her lasting contribution. The DWL framework from section 6.2 — where a monopolist restricts output and raises price above marginal cost — doesn't map cleanly onto platforms that charge zero, produce unlimited digital output, and generate massive consumer surplus. The Lerner index $(P - MC)/P$ literally returns zero for free products. This is a framework limitation, not evidence the firms are competitive. But Khan's proposed alternative remains underdeveloped. The real monopoly concerns are in three areas the textbook underweights: (1) market power in adjacent markets (advertising, seller fees, app distribution) where these firms do charge and do extract rents; (2) reduction of dynamic competition — not harm to today's consumers, but reduced probability that better products get built tomorrow; and (3) data extraction under extreme information asymmetry. The EU's Digital Markets Act moves in Khan's direction by regulating "gatekeeper" platforms based on structural position rather than consumer prices. Whether this works is an open question. Khan diagnosed a real disease in the antitrust framework. The cure is still being written.
6.3 Price Discrimination
Price discrimination.Charging different prices to different consumers (or for different units) based on willingness to pay, not cost differences.
First-Degree (Perfect) Price Discrimination
The firm charges each consumer their maximum willingness to pay. This extracts all consumer surplus. Output is efficient ($Q = Q_C$) — no DWL — but all surplus goes to the firm.
Second-Degree Price Discrimination
The firm offers different pricing schemes (quantity discounts, bundling, versioning) and lets consumers self-select. Examples: airline tickets (business vs. economy), software (basic vs. pro edition), bulk pricing.
Third-Degree Price Discrimination
The firm identifies groups with different elasticities and charges each group a different price:
$$MR_1 = MR_2 = MC$$(Eq. 6.6)
Since $MR = P(1 - 1/|\varepsilon|)$ (from the MR-elasticity relation), equal MR across markets implies the group with less elastic demand (fewer alternatives, higher switching costs) must be charged a higher price. The optimal price ratio satisfies $P_1/P_2 = (1 - 1/|\varepsilon_2|)/(1 - 1/|\varepsilon_1|)$.
Intuition
What this says: A price-discriminating firm sets marginal revenue equal across all markets and equal to marginal cost. This means the firm charges higher prices to customers who are less price-sensitive (more inelastic demand) and lower prices to those who are more price-sensitive.
Why it matters: This is the logic behind student discounts, senior pricing, regional pricing, and surge pricing. The firm is not being charitable to students -- it is extracting more total revenue by charging different prices to groups with different willingness to pay. Airlines do this with extraordinary precision: business travelers pay more because they have less flexibility.
What changes: If the elasticity gap between markets narrows (both groups become equally price-sensitive), the optimal prices converge and discrimination becomes unprofitable. If arbitrage becomes possible (students resell to adults), the price discrimination collapses to a single price.
In Full Mode, the MR-elasticity relation shows exactly how the price ratio depends on the elasticity ratio.
The group with more inelastic demand pays the higher price.
Two markets with different demand elasticities. Adjust MC to see how optimal prices and quantities change in each market.
\$1\$1\$10
Market A (Adults): Q = 9.0, P = \$11.00, Profit = \$11.00 |
Market B (Students): Q = 5.0, P = \$1.00, Profit = \$15.00 |
Total Profit = \$106.00
Market A (Adults): $P_A = 20 - Q_A$
Market B (Students): $P_S = 12 - Q_S$
6.4 Monopolistic Competition
Monopolistic competition.A market with many firms selling differentiated products. Each firm has some market power (downward-sloping demand due to product differentiation) but faces free entry.
Short run: Firms may earn positive or negative profit. Long run: Entry and exit drive economic profit to zero.
In long-run equilibrium, each firm produces where its demand curve is tangent to its AC curve. The tangency condition imposes two simultaneous requirements:
$$P = AC \quad \text{(zero profit)} \quad \text{and} \quad MR = MC \quad \text{(profit maximization)}$$(Eq. 6.8)
Because the firm faces a downward-sloping demand curve, the tangency point occurs to the left of the AC minimum — firms produce below the efficient scale.
Intuition
What this says: In the long run, monopolistic competition produces a distinctive outcome: firms earn zero economic profit (free entry competed away the profits), but they still charge above marginal cost (product differentiation gives each firm a small monopoly on its particular variety). The firm operates below the scale that minimizes average cost.
Why it matters: This is the "price of variety." Having 50 different restaurants instead of 50 identical cafeterias means each restaurant serves fewer customers and operates below its most efficient scale. Whether this is truly inefficient depends on how much consumers value the differentiation itself.
What changes: If products become less differentiated (more substitutable), each firm's demand curve becomes more elastic, the markup shrinks, and the outcome approaches perfect competition. If entry barriers increase, firms can sustain positive profit in the long run — moving the outcome toward monopoly.
In Full Mode, Eq. 6.8 shows the tangency condition that pins down the long-run equilibrium.
This means monopolistic competition has two "inefficiencies" relative to perfect competition:
Markup: $P > MC$ (market power from differentiation)
Excess capacity: Firms produce below the scale that minimizes AC
Whether these are truly inefficient is debatable. The Dixit-Stiglitz framework shows that consumers value variety — having 50 different restaurants is worth more than 50 identical ones, even if the identical ones are cheaper. The markup above MC is the "price of variety."
Big Question #5
Is free trade always good?
In Chapter 2, comparative advantage made a clean case for free trade under perfect competition. You now have monopolistic competition and strategic interaction. Here's how imperfect competition complicates that story.
What the model says
Under monopolistic competition (Krugman 1980), trade allows more product variety and exploits economies of scale — gains from trade that go beyond comparative advantage. Countries trade not because they're different, but because consumers value variety and firms benefit from larger markets. But under Cournot oligopoly (Brander-Spencer 1985), a government subsidy to a domestic firm can shift the Nash equilibrium in its favor, capturing rents from the foreign rival. The infant industry argument also gets a formal foundation: if production involves learning-by-doing (costs fall with cumulative output), temporary protection can move a firm down the cost curve and make it competitive in the long run. Strategic trade theory says that with imperfect competition, trade policy can shift profits between countries — free trade is no longer automatically optimal.
The strongest counter
Against strategic trade: It requires the government to pick winners — to identify which industries have the right market structure and learning curves for intervention to work. Government failure (lobbying, corruption, information problems) makes this dangerous in practice. The theoretical conditions for beneficial strategic trade are knife-edge: the government must know demand elasticities, cost structures, and the rival government's response. Against infant industries: The historical record is mixed — many "infant" industries never grow up. Protection creates rents for politically connected firms rather than genuine learning. And once protection is granted, the political economy of removing it is brutal — the beneficiaries lobby to keep it forever.
How the mainstream responded
The mainstream view shifted after the China shock literature. Pre-2010, the consensus was strongly pro-free-trade with redistribution as a side policy. Post-2010, the profession acknowledged that adjustment costs from trade are larger, longer-lasting, and more geographically concentrated than previously assumed (Autor, Dorn & Hanson 2013, 2016). The trade adjustment assistance programs that were supposed to compensate the losers have been small and ineffective. Krugman himself — who won the Nobel partly for showing gains from trade under imperfect competition — acknowledged that the distributional effects were understated for decades.
The judgment (at this level)
Free trade remains net positive for most countries most of the time — the comparative advantage logic from Chapter 2 is robust, and Krugman's monopolistic competition model adds further gains from variety and scale. But the unconditional case has weakened. The distributional effects are larger than the profession acknowledged for decades, and compensation mechanisms have failed. Strategic trade and infant industry arguments have theoretical merit but are dangerous in practice — government failure is the binding constraint. The honest answer: free trade is the right default, strategic intervention can work but usually doesn't, and the losers from trade need real compensation, not promises.
What you can't resolve yet
The models here are static — they compare one equilibrium to another. How should we think about trade in a world with supply chain dependencies (semiconductors, rare earths, energy)? Economic security arguments for protection are different from efficiency arguments. And the macroeconomic dimension is missing entirely: trade deficits, capital flows, and exchange rates all affect the story. Come back in Chapter 17 (§17.1–17.7), where the open-economy macro framework adds balance-of-payments accounting, the impossible trinity, and global imbalances to the picture.
Related Takes
Take
"I am a Tariff Man" — Donald Trump, and why he says tariffs are "the greatest thing ever invented"
Strategic trade theory says subsidies and tariffs can shift oligopoly profits to domestic firms. But the theory requires governments to know more than they usually do — and retaliation changes everything.
Oligopoly.A market with a few large firms, each aware that its actions affect others. Strategic interaction is the defining feature.
Cournot Model
Cournot competition.An oligopoly model in which firms simultaneously choose quantities. Each firm selects the quantity that maximizes its profit given its belief about the other firms' quantities.
Firms choose quantities simultaneously. Each firm's optimal quantity depends on the other firms' quantities.
Setup. Two firms, demand $P = a - b(q_1 + q_2)$, constant marginal cost $c$ for both.
Best response (reaction) function.Firm $i$'s optimal quantity as a function of the rival's quantity: $q_i^*(q_j)$. It solves $\max_{q_i} \Pi_i = (P(q_i + q_j) - c) q_i$. In Cournot equilibrium, every firm is on its best response function simultaneously.
What this says: Each firm picks its quantity by asking: "Given what my rival produces, what quantity maximizes my profit?" The best response function captures this strategic interdependence -- if my rival produces more, I should produce less (since total output drives the price down). The equilibrium is where both firms are simultaneously best-responding: neither wants to change. Each duopolist produces one-third of the competitive output; together they produce two-thirds.
Why it matters: Cournot shows that oligopoly outcomes fall between monopoly and perfect competition. More firms push the market closer to the competitive outcome. This is the formal basis for antitrust intuitions about market concentration: fewer firms means higher prices and more deadweight loss.
What changes: When a rival expands production, the best response is to contract -- the reaction functions slope downward. Adding more firms to the market shrinks each firm's share and pushes the price toward marginal cost. With 2 firms, the industry produces 2/3 of competitive output; with 5 firms, 5/6; with 20 firms, the market is essentially competitive. Higher marginal costs shift the equilibrium toward lower output and higher prices for all firms.
In Full Mode, Eqs. 6.7-6.10 derive the best response functions and solve for the Cournot-Nash equilibrium.
$n$-firm generalization: With $n$ symmetric firms, each produces $q_i = (a-c)/((n+1)b)$, total output is $Q = n(a-c)/((n+1)b)$, and the Cournot price is $P^C = (a + nc)/(n+1)$. As $n \to \infty$, $P \to c$ — the market converges to perfect competition.
Intuition
What this says: As the number of firms grows, each firm's share of the market shrinks, and the total output rises. With enough firms, the oligopoly outcome becomes indistinguishable from perfect competition: price equals marginal cost, economic profit vanishes, and deadweight loss disappears.
Why it matters: This is the Cournot convergence result -- it provides the bridge between monopoly (one firm, maximum market power) and perfect competition (many firms, zero market power). It gives precise meaning to the idea that "more competition is better": each additional firm moves the price closer to cost.
What changes: With 2 firms, the markup is substantial. With 5 firms, it is much smaller. With 20 firms, the market is essentially competitive. The speed of convergence depends on cost structure: when marginal costs are high relative to demand, fewer firms suffice to drive the market toward competition.
In Full Mode, the n-firm Cournot formula shows the exact relationship between the number of firms and the market outcome.
Slide the number of firms from 1 (monopoly) to 20. Watch total output rise, price fall, and deadweight loss shrink toward zero as the market approaches perfect competition.
Figure 6.3a. As N increases, the Cournot outcome converges to perfect competition. At N=1, this is monopoly. The bar chart shows how key outcomes change with market structure.
Interactive: Cournot Reaction Functions
Adjust each firm's marginal cost to see how their reaction functions shift and the equilibrium moves. Asymmetric costs lead to asymmetric output.
Figure 6.3b. Each firm's reaction function is downward-sloping: more output by the rival reduces the optimal response. The intersection is the Cournot-Nash equilibrium. Drag the cost sliders to see how asymmetric costs shift the reaction functions and move the equilibrium.
Big Question #3
Do minimum wages cause unemployment?
In Chapter 2, the competitive model gave a clean answer: a minimum wage above equilibrium creates unemployment. You now have monopoly, oligopoly, and the tools to model market power. Here's what happens when the labor market isn't competitive.
What the model says
Apply the monopoly framework from §6.2 to a labor market, but flip the direction: instead of a single seller with market power, consider a single buyer of labor — a monopsonist. The firm faces an upward-sloping labor supply curve $w(L)$ with $w' > 0$. The marginal cost of labor exceeds the wage: $MC_L = w + w' \cdot L$. The firm hires where $MC_L = MRP_L$, at a wage below the competitive level and employment below the competitive level. Now impose a minimum wage between the monopsony wage and the competitive wage. The firm's marginal cost of labor becomes flat at the minimum wage (up to a point), which means it hires more workers, not fewer. A minimum wage can increase both employment and earnings simultaneously. Above the competitive wage, the standard unemployment prediction returns.
The strongest counter
Even if individual firms have some labor market power, workers can move between employers, industries, and cities. Labor mobility limits monopsony power in the long run. The empirically relevant question is how much monopsony power exists in practice — and this varies enormously by sector, geography, and worker type. Fast food in a small rural town may approximate monopsony; tech hiring in San Francisco is close to competitive. The "new monopsony" literature (Manning 2003) argues that search frictions and moving costs create monopsony power even with many employers — but the degree of that power, and therefore the employment effect of minimum wages, remains an empirical question that theory alone cannot settle.
How the mainstream responded
The mainstream absorbed monopsony as a theoretical possibility early on — Joan Robinson formalized it in 1933. But before Card and Krueger's landmark 1994 study, the profession treated monopsony as empirically rare and the competitive model's unemployment prediction as the dominant result. The "new monopsony" literature broadened the concept from "one employer in a company town" to "employers have some wage-setting power due to search frictions, moving costs, and information asymmetries" — which is much more common than the textbook monopsony suggests.
The judgment (at this level)
The theory is now clear: the effect of minimum wages depends on the degree of monopsony power. Both "always causes unemployment" and "never causes unemployment" are wrong as general claims. The correct theoretical answer is "it depends on market structure" — and market structure varies across labor markets. The Cournot model from §6.5 offers an analogy: just as the welfare effects of oligopoly depend on the number of firms and the degree of market power, the employment effects of minimum wages depend on the structure of the labor market. The competitive model and the monopsony model are two ends of a spectrum.
What you can't resolve yet
Theory gives a conditional prediction: the employment effect depends on market structure. But which market structure is empirically relevant? We need data to adjudicate. Come back in Chapter 10 (§10.4), where Card and Krueger's natural experiment is analyzed using difference-in-differences — the econometric method that launched a 30-year empirical war between the competitive and monopsony predictions.
Related Takes
Take
"A \$7.25 minimum wage is a starvation wage" — AOC on the House floor, 2019
The monopsony model says moderate increases can raise employment. But \$15 in San Francisco is very different from \$15 in rural Mississippi. The answer depends on the local wage bite — and the local degree of employer market power.
Comparative advantage says yes. But with monopolistic competition and Cournot oligopoly, strategic trade theory says: it depends on market structure. Governments may be able to shift profits — if they can pick winners.
Bertrand competition.An oligopoly model in which firms simultaneously choose prices. Consumers buy from the lowest-price firm; if prices are equal, demand is split evenly.
In the Bertrand model, firms choose prices simultaneously (rather than quantities). With identical products and equal marginal costs:
$$P^B = c \quad \text{(Bertrand paradox)}$$(Eq. 6.11)
Bertrand paradox.With two firms selling identical products at equal marginal cost, the unique Nash equilibrium is $P = MC$ — the perfectly competitive outcome. The paradox is that just two firms suffice to eliminate all market power, contradicting the Cournot prediction that market power persists with few firms.
With just two firms, price competition reproduces the perfectly competitive outcome. This is the Bertrand paradox: the Cournot model says you need many firms for competition; the Bertrand model says two suffice. The logic: if one firm charges any price above $MC$, the other can undercut by an infinitesimal amount and capture the entire market. This undercutting continues until neither firm can profitably go lower — which occurs at $P = MC$.
Intuition
What this says: When two firms sell identical products and compete on price, a relentless undercutting logic drives the price all the way down to marginal cost. If Firm A charges $50 and Firm B charges $49.99, every customer goes to Firm B. So Firm A cuts to $49.98, then Firm B cuts to $49.97 -- and this continues until neither can go lower without losing money. The result: the competitive outcome with just two firms.
Why it matters: This is the Bertrand paradox -- it says the number of firms is not what determines market power. What matters is how firms compete. Quantity competition (Cournot) preserves market power with few firms; price competition (Bertrand) destroys it immediately. The real-world question is which model better fits a given industry.
What changes: The paradox dissolves when products are differentiated (a small price cut does not steal the entire market), when firms have capacity constraints (they cannot serve everyone), when firms interact repeatedly (enabling tacit collusion), or when consumers face search costs (they do not instantly switch). Most real markets have some combination of these frictions, which is why we rarely see pure Bertrand outcomes.
In Full Mode, the undercutting argument is stated precisely: any P > MC is not a Nash equilibrium because a rival can profitably deviate.
When the paradox dissolves:
Product differentiation: A price cut doesn't steal the entire market
Capacity constraints: Firms cannot serve the whole market at once
With differentiated products, equilibrium price (\$10$) exceeds marginal cost (\$10$). The Bertrand paradox dissolves because a small price cut no longer captures the entire market.
6.7 Stackelberg Competition
Stackelberg competition.A sequential oligopoly model in which one firm (the leader) chooses its quantity first, and the other firm (the follower) observes the leader's choice before selecting its own quantity.
In the Stackelberg model, one firm (the leader) moves first, choosing its quantity. The follower observes the leader's choice and then optimizes. The leader internalizes the follower's reaction function.
Step 1 (Follower's problem): The follower observes $q_1$ and maximizes $\Pi_2 = [a - b(q_1 + q_2) - c] \cdot q_2$. This yields the same best-response function as Cournot: $q_2^*(q_1) = \frac{a - c}{2b} - \frac{q_1}{2}$.
Step 2 (Leader's problem): The leader substitutes the follower's best response into its own profit function: $\Pi_1 = [a - b(q_1 + q_2^*(q_1)) - c] \cdot q_1$. Maximizing gives:
What this says: When one firm moves first, it can commit to a large quantity, forcing the follower to accommodate by producing less. The leader produces half the competitive output (the monopoly quantity); the follower produces only half of what the leader does. Total output exceeds Cournot, so the price is lower.
Why it matters: Commitment has strategic value. By going first and locking in a large quantity, the leader effectively says "I am flooding the market -- adjust accordingly." This is the formal logic behind first-mover advantages in industries where capacity decisions are hard to reverse (factories, infrastructure, spectrum licenses).
What changes: If the leader's cost advantage grows, it produces even more and squeezes the follower further. If commitment becomes less credible (the leader can easily reverse its decision), the game reverts toward the Cournot outcome because the follower no longer needs to accommodate. The asymmetry depends entirely on the irreversibility of the leader's move.
In Full Mode, Eqs. 6.12-6.13 derive the Stackelberg quantities via backward induction.
First-mover advantage.The strategic benefit of committing to an action before rivals can respond. In the Stackelberg model, the leader commits to a large quantity, forcing the follower to accommodate by producing less. The leader earns higher profit than in the simultaneous (Cournot) game.
The leader produces the monopoly quantity, and the follower produces half of that. Total output exceeds Cournot; the price is lower. The first-mover advantage comes from committing to a large quantity before the follower chooses.
Figure 6.4. Compare Cournot (symmetric) and Stackelberg (leader advantage). The Stackelberg equilibrium is below-right of Cournot on the reaction function diagram: the leader produces more, the follower less.
6.8 Introduction to Game Theory
Game in normal (strategic) form.Consists of: (1) Players $i = 1, 2, \ldots, n$; (2) Strategies $S_i$ for each player; (3) Payoffs $u_i(s_1, \ldots, s_n)$ for each strategy combination.
Nash Equilibrium
Nash equilibrium.A strategy profile $(s_1^*, s_2^*, \ldots, s_n^*)$ such that no player can increase their payoff by unilaterally changing their strategy. Every player is best-responding to the strategies of all other players.
What this says: A Nash equilibrium is a situation where every player is doing the best they can, given what everyone else is doing. Nobody can improve their outcome by changing their own strategy alone. Think of it as a "no regrets" outcome -- once you see what everyone else chose, you would not change your choice.
Why it matters: Nash equilibrium is the central solution concept in game theory and applies far beyond economics -- to politics, biology, and any situation with strategic interaction. It does not mean the outcome is good for society (the Prisoner's Dilemma shows it can be terrible), just that it is self-enforcing: no individual has an incentive to deviate.
What changes: When payoffs change, equilibria shift. If the penalty for defection increases (stronger enforcement, higher fines), cooperation becomes easier to sustain. If a new strategy becomes available, old equilibria may dissolve. Some games have multiple Nash equilibria (coordination games), some have exactly one (Prisoner's Dilemma), and some have none in pure strategies -- requiring randomization (mixed strategies).
In Full Mode, Eq. 6.14 states the formal condition: no player can improve their payoff by unilateral deviation.
Each player is best-responding to the others. No one has a reason to deviate, given what everyone else is doing.
The Prisoner's Dilemma
Dominant strategy.A strategy that yields a weakly higher payoff than any alternative, regardless of what other players do. If $s_i^*$ is dominant, then $u_i(s_i^*, s_{-i}) \geq u_i(s_i, s_{-i})$ for all $s_i$ and all $s_{-i}$.
Prisoner's dilemma.A two-player game in which each player has a dominant strategy to defect, yet mutual cooperation yields a higher payoff for both. The Nash equilibrium (Defect, Defect) is Pareto-dominated by (Cooperate, Cooperate), illustrating the tension between individual rationality and collective welfare.
Player 2: Cooperate
Player 2: Defect
Player 1: Cooperate
(3, 3)
(0, 5)
Player 1: Defect
(5, 0)
(1, 1)
Dominant strategy: Defect is best regardless of the other's choice. Nash equilibrium: (Defect, Defect) with payoffs (1, 1). Both are worse off than mutual cooperation (3, 3), but neither can unilaterally improve.
Intuition
What this says: The Prisoner's Dilemma captures a fundamental tension: what is rational for each individual leads to a bad outcome for everyone. Each player reasons: "No matter what the other does, I am better off defecting." But when both think this way, they end up with (Defect, Defect) -- worse for both than if they had cooperated.
Why it matters: This structure appears everywhere in economics and beyond. Firms in a cartel each have an incentive to secretly increase output. Countries each want to free-ride on others' carbon reductions. Arms race participants each prefer to build weapons while the other disarms. The core insight: markets, institutions, and enforcement mechanisms exist precisely to solve Prisoner's Dilemmas -- converting individual incentives toward socially better outcomes.
What changes: If the temptation payoff (defecting while the other cooperates) shrinks -- through penalties, reputation effects, or social norms -- cooperation becomes easier. If the game is repeated, future punishment can sustain cooperation (see repeated games below). If communication is allowed, players can coordinate -- but only if commitments are enforceable.
Why the prisoner's dilemma matters:
Oligopoly pricing: Each firm wants to undercut cartel agreements
Arms races: Each country fears the other will cheat on limits
Tragedy of the commons: Individual incentives deplete shared resources
Climate change: Each country wants to free-ride on others' reductions
Interactive: 2×2 Game Payoff Explorer
Enter any payoffs for a 2×2 game. The tool auto-identifies dominant strategies, Nash equilibria, and Pareto-optimal outcomes. Green cells are Nash equilibria; blue borders mark Pareto-optimal outcomes.
Player 2: L
Player 2: R
Player 1: U
(,
)
(,
)
Player 1: D
(,
)
(,
)
Blue = Player 1 payoff |
Red = Player 2 payoff
Analyzing...
Other Classic Games
Coordination game:
B: Left
B: Right
A: Left
(2, 2)
(0, 0)
A: Right
(0, 0)
(1, 1)
Two Nash equilibria: (Left, Left) and (Right, Right). The challenge is coordination, not conflict.
Battle of the sexes:
B: Opera
B: Football
A: Opera
(3, 1)
(0, 0)
A: Football
(0, 0)
(1, 3)
Two pure-strategy Nash equilibria with different preferred outcomes for each player.
Example 6.5 — Nash Equilibria in an Advertising Game
Two firms choose whether to Advertise (A) or Not Advertise (N):
Firm 2: A
Firm 2: N
Firm 1: A
(4, 4)
(7, 2)
Firm 1: N
(2, 7)
(5, 5)
Step 1 — Check for dominant strategies.
Firm 1: If Firm 2 plays A, Firm 1 gets 4 (A) vs 2 (N) → A is better. If Firm 2 plays N, Firm 1 gets 7 (A) vs 5 (N) → A is better. So A is a dominant strategy for Firm 1. By symmetry, A is dominant for Firm 2.
Step 2 — Find Nash equilibria.
The unique Nash equilibrium is (A, A) with payoffs (4, 4). Both firms advertise, even though (N, N) = (5, 5) Pareto-dominates. This is a prisoner's dilemma: individual incentives to advertise lead to a collectively worse outcome.
Repeated Games
Repeated game.A game in which the same stage game is played multiple (or infinitely many) times by the same players. Repeated interaction allows strategies to condition on history (e.g., "cooperate until someone defects"), potentially sustaining cooperation that is impossible in a one-shot game.
When the prisoner's dilemma is played repeatedly (and players are patient), cooperation can be sustained. The threat of future punishment (reversion to defection) makes current cooperation self-enforcing. This is the folk theorem.
Under the grim trigger strategy (cooperate until the other defects, then defect forever), cooperation is sustainable if:
where $\pi_C$ is the per-period cooperation payoff, $\pi_D$ is the one-shot deviation payoff, and $\pi_N$ is the Nash (punishment) payoff. With standard prisoner's dilemma payoffs (CC=3, DC=5, DD=1): $\delta \geq (5-3)/(5-1) = 1/2$.
Intuition
What this says: Cooperation in a repeated game is a cost-benefit calculation: the short-run temptation to cheat (the one-time gain from defecting while the other cooperates) versus the long-run punishment (being stuck in mutual defection forever). If players are patient enough (high discount factor), the future punishment outweighs the immediate gain, and cooperation is self-enforcing.
Why it matters: This explains why cartels, arms agreements, and trade deals can work even without external enforcement. The threat of retaliation (price wars, tariff escalation, arms races) sustains cooperation -- as long as the relationship is expected to continue. It also explains why cooperation breaks down when firms are impatient, when the game has a known end date, or when cheating is hard to detect.
What changes: Higher discount factor (more patience) makes cooperation easier. Larger temptation payoff makes it harder. If the punishment is mild (Nash payoff close to cooperation payoff), cooperation requires more patience. This is why OPEC struggles to maintain output quotas: the temptation to overproduce is large, detection is slow, and punishment is weak.
In Full Mode, Eq. 6.15 derives the critical discount factor from the grim trigger strategy.
The intuition: cooperating today sustains the relationship. Cheating gives a short-run gain but triggers punishment forever. If the discount factor $\delta$ is high enough, the long-run cost of punishment outweighs the short-run gain.
Interactive: Repeated Game — Cooperation Threshold
In the standard prisoner's dilemma (payoffs: CC=3, CD=0, DC=5, DD=1), cooperation via grim trigger requires the discount factor $\delta$ to exceed a threshold. Slide $\delta$ to see whether cooperation is sustainable.
Impatient (0)0.50Very patient (1)
Calculating...
Figure 6.5. The horizontal line shows the minimum discount factor $\delta^*$ required for cooperation. When $\delta > \delta^*$, the long-run value of cooperation exceeds the one-shot temptation to defect. The chart compares the present value of perpetual cooperation vs defecting once then being punished forever.
Comparing Market Structures
Market structure
# of firms
Price
Output
Profit
DWL
Strategic?
Perfect competition
Many
$P = MC$
Highest
Zero (LR)
None
No
Monopolistic competition
Many
$P > MC$
Below comp.
Zero (LR)
Small
No
Cournot oligopoly
Few
$MC < P < P_M$
Between
Positive
Moderate
Yes (Q)
Stackelberg
Few
Lower than Cournot
Higher
Leader > Cournot
Less
Yes (seq.)
Bertrand (identical)
Two
$P = MC$
Competitive
Zero
None
Yes (P)
Monopoly
One
Highest
Lowest
Highest
Largest
No
Thread Example: Maya's Enterprise
A rival, Nate, opens a lemonade stand across the street. Both have the same cost structure. The neighborhood demand is $P = 5 - (Q_M + Q_N)/20$, with $MC = 1.50$.
Nash equilibrium: No player can improve by unilateral deviation. The prisoner's dilemma shows how individual rationality leads to collective inefficiency. Repeated games can sustain cooperation.
Key Equations
Label
Equation
Description
Eq. 6.1
$P = MC = AC_{min}$, $\Pi = 0$
Long-run competitive equilibrium
Eq. 6.2
$\max \Pi = P(Q)Q - TC(Q)$
Monopolist's problem
Eq. 6.3
$MR = P + Q(dP/dQ)$
Marginal revenue
Eq. 6.4
$MR = MC$
Monopoly profit max condition
Eq. 6.5
$(P-MC)/P = 1/|\varepsilon_d|$
Lerner index
Eq. 6.6
$MR_1 = MR_2 = MC$
Third-degree price discrimination
Eq. 6.7–7.8
Best response functions
Cournot reaction functions
Eq. 6.9
$q_i^C = (a-c)/(3b)$
Cournot symmetric equilibrium
Eq. 6.10
$P^C = (a+2c)/3$
Cournot price
Eq. 6.11
$P^B = c$
Bertrand equilibrium (identical products)
Eq. 6.12–7.13
$q_1^S = (a-c)/(2b)$, $q_2^S = (a-c)/(4b)$
Stackelberg quantities
Eq. 6.14
$u_i(s_i^*, s_{-i}^*) \geq u_i(s_i, s_{-i}^*)$ for all $s_i$
Nash equilibrium
Eq. 6.15
$\delta \geq (\pi_D - \pi_C)/(\pi_D - \pi_N)$
Cooperation threshold (grim trigger)
Exercises
Practice
A monopolist faces $P = 50 - Q$ and has $MC = 10$. Find the monopoly price, quantity, profit, and DWL. Compute the Lerner index and verify it equals \$1/|\varepsilon_d|$.
A monopolist sells in two markets: $P_1 = 24 - Q_1$ and $P_2 = 16 - 2Q_2$, with $MC = 4$. Find the profit-maximizing price and quantity in each market. Which market has more elastic demand?
Two Cournot duopolists face $P = 80 - Q$, with $c_1 = c_2 = 8$. Find: (a) each firm's output, (b) the market price, (c) each firm's profit. Compare total industry output and profit to the monopoly case.
Repeat Exercise 3 as a Stackelberg game with firm 1 as leader.
Find all pure-strategy Nash equilibria:
B: X
B: Y
A: X
(3, 3)
(1, 4)
A: Y
(4, 1)
(2, 2)
Is this a prisoner's dilemma? Why or why not?
Apply
Why doesn't the Bertrand paradox hold for Coca-Cola and Pepsi? Identify three specific features of the real soft drink market that prevent price from falling to marginal cost.
Two gas stations sit on opposite corners of an intersection. They sell identical gasoline and observe each other's prices daily. Explain why the Bertrand model predicts $P = MC$, and then explain why in practice gas stations can maintain prices above MC.
A pharmaceutical company holds a patent (monopoly) on a drug. When the patent expires, generic competitors enter. Using the perfect competition model, predict what happens to: price, quantity, producer surplus, consumer surplus, and deadweight loss. Is the patent system efficient?
Consider a market with one incumbent firm and a potential entrant. The incumbent can set a "limit price" — a low price that makes entry unprofitable — or a high monopoly price. Analyze this as a sequential game. Under what conditions is limit pricing credible?
Challenge
Derive the Cournot equilibrium for $n$ symmetric firms with demand $P = a - bQ$ and constant marginal cost $c$. Show that as $n \to \infty$, $P \to c$ and the outcome converges to perfect competition. At what $n$ does the Cournot price reach within 10% of the competitive price?
In a Cournot duopoly, firms consider forming a cartel. (a) Find the cartel output and profit. (b) Show that each firm has an incentive to cheat. (c) What discount factor $\delta$ makes cooperation sustainable in an infinitely repeated game with Cournot reversion?
Prove that a monopolist never operates on the inelastic portion of the demand curve. (Hint: Show that if $|\varepsilon_d| < 1$, the monopolist can increase profit by reducing output.)
You’ve Completed Part II — Micro
You can now evaluate:
Whether Big Tech is a monopoly problem
Strategic trade arguments beyond simple S/D
Big Questions you can now engage with:
BQ #4: Are people rational? (now that you know what rational choice formally requires)
BQ #5: Is free trade always good? (with market power)
Coming in Part III: macroeconomics changes the scale from firms to countries.
