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.
Prerequisites: Chapter 5 (cost curves, profit maximization, Lagrangians).
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.
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.
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.
This has two terms:
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:
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.
See Full Mode for the derivation.The markup over marginal cost equals the inverse of the (absolute) price elasticity of demand. More elastic demand means less market power.
Demand: $P = 100 - 2Q$. Cost: $TC = 20Q$ (constant $MC = 20$).
$TR = 100Q - 2Q^2$, $MR = 100 - 4Q$.
$MR = MC$: \$100 - 4Q = 20 \implies Q_M = 20$, $P_M = 60$.
$\Pi = (60 - 20)(20) = 800$.
Competitive outcome: $P = MC = 20$, $Q_C = 40$.
$DWL = \frac{1}{2}(60 - 20)(40 - 20) = 400$.
Lerner index: $(60 - 20)/60 = 2/3$. Check: $\varepsilon_d = (dQ/dP)(P/Q) = (-1/2)(60/20) = -1.5$, so \$1/|\varepsilon_d| = 2/3$. ✓
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.
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.
IntermediateThe 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.
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.
The firm identifies groups with different elasticities and charges each group a different price:
The group with more inelastic demand pays the higher price.
A theater faces two markets. Adult demand: $P_A = 20 - Q_A$. Student demand: $P_S = 12 - Q_S$. $MC = 2$.
Adults: $MR_A = 20 - 2Q_A = 2 \implies Q_A = 9$, $P_A = 11$.
Students: $MR_S = 12 - 2Q_S = 2 \implies Q_S = 5$, $P_S = 7$.
Total profit: $(11-2)(9) + (7-2)(5) = 81 + 25 = 106$.
Two markets with different demand elasticities. Adjust MC to see how optimal prices and quantities change in each market.
Market A (Adults): $P_A = 20 - Q_A$
Market B (Students): $P_S = 12 - Q_S$
Short run: Firms may earn positive or negative profit. Long run: Entry and exit drive economic profit to zero. Each firm produces where its demand curve is tangent to its AC curve — not at the minimum of AC.
This means monopolistic competition has two "inefficiencies" relative to perfect competition:
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."
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.
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.
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.
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.
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.
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.
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.
IntermediateFirms 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 function for firm 1:
Cournot-Nash equilibrium (solving 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 -- 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.
See Full Mode for the derivation.With $n$ symmetric firms, $q_i = (a-c)/((n+1)b)$ and $P \to c$ as $n \to \infty$.
Demand: $P = 100 - Q$, $c = 10$. Best responses: $q_i^* = 45 - q_j/2$.
Equilibrium: $q_1^C = q_2^C = 30$. $Q^C = 60$, $P^C = 40$. $\Pi_i = 900$.
| Structure | Output | Price | Industry Profit | DWL |
|---|---|---|---|---|
| Competition | 90 | 10 | 0 | 0 |
| Cournot duopoly | 60 | 40 | 1,800 | 450 |
| Monopoly | 45 | 55 | 2,025 | 1,012.5 |
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.
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.
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.
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.
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.
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 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.
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.
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.
IntermediateIn the Bertrand model, firms choose prices simultaneously (rather than quantities). With identical products and equal marginal costs:
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.
When the paradox dissolves:
Two firms sell differentiated goods. Demand for firm $i$: $q_i = 100 - 2p_i + p_j$ (products are substitutes but not identical). Marginal cost: $c = 10$.
Firm 1 maximizes: $\Pi_1 = (p_1 - 10)(100 - 2p_1 + p_2)$.
FOC: \$100 - 4p_1 + p_2 + 20 = 0 \implies p_1^*(p_2) = \frac{120 + p_2}{4} = 30 + p_2/4$.
By symmetry: $p^* = 30 + p^*/4 \implies p^* = 40$.
Each firm: $q^* = 100 - 80 + 40 = 60$. $\Pi^* = 30 \times 60 = 1{,}800$.
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.
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.
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.
See Full Mode for the derivation.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.
$P = 100 - Q$, $c = 10$:
$q_1^S = 45$, $q_2^S = 22.5$. $Q^S = 67.5$, $P^S = 32.5$.
$\Pi_1 = 1{,}012.5$ (leader), $\Pi_2 = 506.25$ (follower).
Leader's profit exceeds Cournot (\$1{,}012.5 > 900$). Follower is worse off (\$106.25 < 900$).
Toggle between simultaneous (Cournot) and sequential (Stackelberg) to compare quantities and profits using $P = 100 - Q$, $c = 10$.
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.
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.
See Full Mode for the derivation.Each player is best-responding to the others. No one has a reason to deviate, given what everyone else is doing.
| 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.
Why the prisoner's dilemma matters:
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
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.
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.
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.
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.
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.
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.
| 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 |
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 $MC = 1.50$.
Cournot equilibrium: $Q_M^* = Q_N^* = 23.3$ cups. $P = 2.67$. Maya's profit: \$17.2/day (materials only).
Stackelberg (Maya leads): $Q_M^S = 35$, $Q_N^S = 17.5$. $P = 2.375$. Maya's profit: \$10.6/day — slightly better due to first-mover advantage.
With Nate in the market, Maya's output drops from 45 to 23.3 cups, and the price drops from \$1.75 to \$1.67.
| 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 |
| B: X | B: Y | |
|---|---|---|
| A: X | (3, 3) | (1, 4) |
| A: Y | (4, 1) | (2, 2) |
Coming in Part III: macroeconomics changes the scale from firms to countries.