# Market Structure Concept Card: [Your industry, course or case] > A concept card for the MBA core microeconomics course: perfect competition, monopoly, monopolistic competition and > oligopoly (Cournot, Bertrand and Stackelberg), with every equilibrium computed, plus entry barriers, contestable > markets and the Herfindahl-Hirschman Index (HHI) as competition authorities use it. It is for MBA students preparing > cases and exams, admitted students who finished the pre-MBA economics primer, and managers who need to explain why > margins in one industry hold up while they collapse in another. Source basis: Cournot (1838), Bertrand (1883), > Chamberlin (1933), Robinson (1933), Lerner (1934), von Stackelberg (1934), Bain (1956), Baumol, Panzar and Willig > (1982), and the US Department of Justice and Federal Trade Commission 2023 Merger Guidelines, all written up in > original words with fictional examples. Replace every [bracketed] value and every row marked *Example*. This is a > learning aid, not legal or competition-law advice. ## Document control | Field | Value | |---|---| | Learner | [Your name] | | Course and session | [Microeconomics for managers, session 6 to 8] | | Market analysed | [Example: regional market for technical outdoor jackets] | | Data source and date for shares | [Industry report, company filings, YYYY-MM-DD] | | Spreadsheet used | [Excel / Google Sheets / LibreOffice Calc] | | Reviewed by | [Study partner, teaching assistant or mentor] | | Version | [0.1] | | Last updated | YYYY-MM-DD | ## Contents - When to use it - The idea in plain language - Formulas and notation - The four structures side by side - Oligopoly: Cournot, Bertrand and Stackelberg - Entry barriers and contestable markets - Concentration and the HHI - Assumptions and limits - How managers use it - Worked example A (fully solved) - Worked example B (half solved) - Exercise C (unsolved) - Connections to other cards - Common mistakes and misconceptions - Self-test questions - My notes and next steps - Sources and further reading - Answer key - Revision history - Standard and licence note ## When to use it Use this card when you need to answer any of these questions in a case, an exam or a real decision: - Why does this industry earn high (or near-zero) returns, and will that last when someone new enters? - What price and output should we expect if the few large firms compete on quantity, on price, or with one firm moving first? - Will a proposed acquisition raise concentration enough to attract a competition authority's attention? - Is a market really protected by barriers, or could a hit-and-run entrant discipline prices anyway? Market structure is the economic foundation under the strategy frameworks you meet later in the core. Porter's five forces (mba/mba-five-forces-card) organises the same ideas (rivalry, entry, substitutes, buyer and supplier power) into a checklist; this card gives you the mechanics underneath it so that you can compute a price, a margin and a concentration index rather than only list forces. ## The idea in plain language How much a firm can price above its marginal cost depends on three things: how many rivals it has, how close their products are to its own, and how easy it is for new firms to enter. With many firms selling identical products and free entry, no one can raise price without losing every customer, so price is driven down to marginal cost and, in the long run, to the minimum of average cost: economic profit is zero. With a single seller protected by barriers, the firm chooses the point on the demand curve that maximises profit, which means a higher price, lower output and a deadweight loss to society. Between those extremes sit two structures that describe most real markets. Monopolistic competition (Chamberlin 1933; Robinson 1933) has many firms with differentiated products and easy entry: each has a little pricing power from brand or location, but entry erodes profit toward zero. Oligopoly has a few interdependent firms: each firm's best choice depends on what it expects rivals to do, which is why oligopoly is the natural home of game theory (mba/mba-game-theory-card). A useful way to hold the whole card in your head: **price above marginal cost is the reward for being hard to replace.** Fewer rivals, more differentiation and higher barriers each make a firm harder to replace. ## Formulas and notation **Profit maximisation (every structure):** produce where marginal revenue equals marginal cost. $$\pi(q) = P(q)\,q - C(q), \qquad \frac{d\pi}{dq} = MR - MC = 0$$ **Linear inverse demand and marginal revenue:** with $P = a - bQ$, total revenue $PQ = aQ - bQ^2$, so $$MR = a - 2bQ$$ **Lerner index** (Lerner 1934) and the inverse-elasticity rule for a profit-maximising monopolist: $$L = \frac{P - MC}{P} = \frac{1}{|\varepsilon|}$$ **Perfect competition, long run:** $P = MC = \min AC$, with average cost $AC = C(q)/q$. **Cournot duopoly** (Cournot 1838), identical marginal cost $c$, demand $P = a - b(q_1 + q_2)$. Firm 1's best response and the symmetric equilibrium: $$q_1^{BR}(q_2) = \frac{a - c - b q_2}{2b}, \qquad q_i^{*} = \frac{a - c}{3b}, \qquad P^{*} = \frac{a + 2c}{3}$$ **N-firm symmetric Cournot:** $$q_i^{*} = \frac{a - c}{(N + 1)b}, \qquad P^{*} = \frac{a + Nc}{N + 1}, \qquad \frac{P - c}{P} = \frac{s_i}{|\varepsilon|}$$ where $s_i$ is firm $i$'s market share as a fraction. Summed over firms weighted by share, the industry's average Lerner index equals $HHI/(10{,}000 \times |\varepsilon|)$ when the HHI uses shares in percent. **Bertrand duopoly** (Bertrand 1883), identical products, identical constant cost $c$, no capacity limits: $$P^{*} = c, \qquad \pi_i^{*} = 0$$ **Stackelberg leader-follower** (von Stackelberg 1934): the leader chooses $q_1$ knowing the follower will play its best response. $$q_1^{*} = \frac{a - c}{2b}, \qquad q_2^{*} = \frac{a - c}{4b}$$ **Asymmetric Cournot duopoly** (costs $c_1$, $c_2$): $$q_1^{*} = \frac{a - 2c_1 + c_2}{3b}, \qquad q_2^{*} = \frac{a - 2c_2 + c_1}{3b}$$ **Herfindahl-Hirschman Index** (Hirschman 1945; Herfindahl 1950), shares $s_i$ in percent, and the change from a merger of firms $j$ and $k$: $$HHI = \sum_{i=1}^{n} s_i^2, \qquad \Delta HHI = (s_j + s_k)^2 - s_j^2 - s_k^2 = 2\,s_j s_k$$ **Deadweight loss** with linear demand and constant marginal cost: $$DWL = \tfrac{1}{2}\,(P^{m} - c)\,(Q^{c} - Q^{m})$$ | Symbol | Meaning | |---|---| | $P$, $Q$, $q_i$ | Market price, market quantity, quantity of firm $i$ | | $a$, $b$ | Intercept and slope of linear inverse demand $P = a - bQ$ | | $c$, $c_i$, $MC$ | Constant marginal cost (of firm $i$) | | $C(q)$, $AC$ | Total cost, average cost $C(q)/q$ | | $MR$ | Marginal revenue | | $\pi$ | Profit | | $\varepsilon$ | Price elasticity of demand (negative), $\varepsilon = (dQ/dP)(P/Q)$ | | $L$ | Lerner index, the price-cost margin as a share of price | | $N$ | Number of symmetric firms | | $s_i$ | Market share of firm $i$ (percent in the HHI, fraction in the Lerner formula) | | $HHI$, $\Delta HHI$ | Herfindahl-Hirschman Index and its change | | $Q^{m}$, $P^{m}$, $Q^{c}$ | Monopoly quantity and price, competitive quantity | | $DWL$ | Deadweight loss (surplus lost because units worth more than their cost are not produced) | ## The four structures side by side | Feature | Perfect competition | Monopolistic competition | Oligopoly | Monopoly | |---|---|---|---|---| | Number of sellers | Many, each tiny | Many | Few, interdependent | One | | Product | Identical | Differentiated | Identical or differentiated | No close substitute | | Entry | Free | Easy | Barriers | Blocked | | Firm's demand curve | Horizontal at market price | Downward sloping, elastic | Depends on rivals' choices | Market demand curve | | Pricing rule | $P = MC$ | $MR = MC$, $P > MC$ | Strategic (Cournot, Bertrand, Stackelberg, collusion) | $MR = MC$, $P > MC$ | | Long-run economic profit | Zero | Zero (entry erodes it) | Can persist | Can persist while barriers hold | | Efficiency | Allocatively efficient | Excess capacity, variety benefit | Between the extremes | Deadweight loss | | *Example* | Spot commodities, foreign exchange | Restaurants, independent gear shops | Airlines, cloud platforms, technical fabrics | A patented drug before generics | ```mermaid flowchart TD A["Define the relevant market: product and geography"] --> B{"How many sellers matter?"} B -->|"One"| M["Monopoly: MR = MC, check barriers"] B -->|"Few, each reacts to the others"| O{"What do they compete on?"} B -->|"Many"| C{"Are products differentiated?"} C -->|"No, identical"| PC["Perfect competition: P = MC = min AC in the long run"] C -->|"Yes, brand or location"| MC2["Monopolistic competition: short-run margin, zero long-run profit"] O -->|"Quantity or capacity, set first"| CO["Cournot"] O -->|"Price, identical products, spare capacity"| BE["Bertrand: price falls to cost"] O -->|"One firm commits first"| ST["Stackelberg leader-follower"] M --> E{"Is the market contestable?"} CO --> E BE --> E ST --> E E -->|"Yes: free entry and exit, no sunk costs"| K["Prices pushed toward average cost"] E -->|"No: sunk costs, scale, legal barriers"| H["Margins can persist: measure concentration with HHI"] ``` **Perfect competition in numbers.** Suppose each Northfield private-label supplier of basic cotton socks *(Example)* has total cost $C(q) = 64 + 4q + q^2$ (thousand pairs, USD thousand). Average cost $AC = 64/q + 4 + q$ is lowest where $64/q^2 = 1$, at $q = 8$ with $AC = 20$. In the long run the price settles at USD 20 per unit. If market demand is $Q = 2000 - 50P$, the market buys 1,000 at that price, which supports $1000/8 = 125$ firms. If demand jumps and the short-run price rises to 26, each firm sets $P = MC = 4 + 2q$, so $q = 11$, average cost is 20.82 and profit is $26 \times 11 - (64 + 44 + 121) = 57$ per firm: exactly the signal that attracts entry until price returns to 20. **Monopoly in numbers.** A single licensed maker of a patented waterproof membrane *(Example)* faces $P = 120 - 2Q$, has $MC = 20$ and fixed cost 200. $MR = 120 - 4Q = 20$ gives $Q^m = 25$ and $P^m = 70$; profit $= (70 - 20) \times 25 - 200 = 1{,}050$. At $P = MC$ the market would buy $Q^c = 50$, so the deadweight loss is $\tfrac{1}{2} \times 50 \times 25 = 625$. The elasticity at the monopoly point is $\varepsilon = -0.5 \times 70/25 = -1.4$ and the Lerner index is $50/70 = 0.714 = 1/1.4$, confirming the inverse-elasticity rule. Consumer surplus falls from 2,500 at the competitive point to 625. A monopolist never prices in the inelastic part of the demand curve, because there MR is negative. **Monopolistic competition.** The same MR = MC rule applies to each firm's own (fairly elastic) demand curve, so a boutique outdoor shop prices a little above marginal cost. But because entry is easy, profits attract copycats that shift each incumbent's demand curve left until it is tangent to the average cost curve: price equals average cost, profit is zero, and each shop operates below its minimum efficient scale (the "excess capacity" result). The social cost is partly offset by variety, which customers value. ## Oligopoly: Cournot, Bertrand and Stackelberg Take one market and three ways of competing. Two makers of technical shell fabric, the duopoly that supplies Northfield's premium jackets *(Example)*, face market demand $P = 120 - Q$ (thousand metres, USD per metre) and the same marginal cost $c = 20$. | Model | How firms compete | $q_1$ | $q_2$ | $Q$ | $P$ | $\pi_1$ | $\pi_2$ | Industry profit | |---|---|---|---|---|---|---|---|---| | Cartel (joint monopoly) | Maximise joint profit | 25.00 | 25.00 | 50.00 | 70.00 | 1,250.00 | 1,250.00 | 2,500.00 | | Cournot | Choose quantities (capacity) simultaneously | 33.33 | 33.33 | 66.67 | 53.33 | 1,111.11 | 1,111.11 | 2,222.22 | | Stackelberg | Firm 1 commits to quantity first | 50.00 | 25.00 | 75.00 | 45.00 | 1,250.00 | 625.00 | 1,875.00 | | Bertrand | Choose prices simultaneously, identical product | 50.00 | 50.00 | 100.00 | 20.00 | 0.00 | 0.00 | 0.00 | | Perfect competition | Price-taking | n/a | n/a | 100.00 | 20.00 | 0.00 | 0.00 | 0.00 | Under Bertrand the two firms split the 100 units demanded at $P = 20$, which is the same output as perfect competition. **Cournot (1838).** Each firm picks its quantity taking the rival's quantity as given. Firm 1's best response is $q_1 = (100 - q_2)/2$. At the equilibrium both best responses hold at once: $q = (100 - q)/2$, so $q = 33.33$. The Cournot price, 53.33, sits between the monopoly price (70) and marginal cost (20). The intuition: each firm ignores the fact that its extra output lowers the price its rival earns, so together they over-produce relative to a cartel. **Why cartels are unstable.** If firm 2 keeps to the cartel quantity of 25, firm 1's best response is $q_1 = (100 - 25)/2 = 37.5$, the price falls to 57.5 and firm 1 earns 1,406.25 instead of 1,250, while firm 2 drops to 937.5. Each firm has an incentive to cheat, which is the prisoner's dilemma treated in mba/mba-game-theory-card. Collusion is also illegal in most jurisdictions; the analysis explains why tacit coordination is fragile, not how to achieve it. **Bertrand (1883).** Bertrand objected that firms in practice set prices, not quantities. With identical products and enough capacity, any price above the rival's price wins no customers and any price slightly below wins them all, so the only equilibrium is $P = c = 20$. Two firms are enough for the competitive outcome. The "Bertrand paradox" is resolved in real markets by capacity limits (Kreps and Scheinkman 1983 show that capacity choice followed by price competition can reproduce the Cournot outcome), product differentiation, and repeated interaction. **Stackelberg (1934).** If firm 1 can commit first (it builds a plant before firm 2 decides), it chooses $q_1$ knowing firm 2 will respond with $q_2 = (100 - q_1)/2$. Firm 1's profit $(100 - q_1 - (100 - q_1)/2)\,q_1$ is maximised at $q_1 = 50$, so $q_2 = 25$, $P = 45$. The leader earns 1,250 against 1,111.11 under Cournot: commitment is valuable when it is credible and visible. This is first-mover advantage in its cleanest form. **More firms, lower prices.** With $N$ symmetric Cournot firms the price falls toward marginal cost as $N$ grows. | N firms | $q_i$ | $Q$ | $P$ | Lerner index | Profit per firm | HHI | |---|---|---|---|---|---|---| | 1 | 50.00 | 50.00 | 70.00 | 0.714 | 2,500.00 | 10,000 | | 2 | 33.33 | 66.67 | 53.33 | 0.625 | 1,111.11 | 5,000 | | 3 | 25.00 | 75.00 | 45.00 | 0.556 | 625.00 | 3,333 | | 4 | 20.00 | 80.00 | 40.00 | 0.500 | 400.00 | 2,500 | | 5 | 16.67 | 83.33 | 36.67 | 0.455 | 277.78 | 2,000 | | 6 | 14.29 | 85.71 | 34.29 | 0.417 | 204.08 | 1,667 | | 8 | 11.11 | 88.89 | 31.11 | 0.357 | 123.46 | 1,250 | | 10 | 9.09 | 90.91 | 29.09 | 0.313 | 82.64 | 1,000 | Excel, with $a$ in B1, $c$ in B2, $b$ in B3 and $N$ in A6: quantity per firm `=($B$1-$B$2)/((A6+1)*$B$3)`, price `=($B$1+A6*$B$2)/(A6+1)`, Lerner `=(C6-$B$2)/C6` where C6 holds the price. ```vega-lite { "$schema": "https://vega.github.io/schema/vega-lite/v5.json", "description": "Symmetric Cournot price as the number of firms rises, demand P = 120 - Q, marginal cost 20 (fictional example)", "width": 380, "height": 220, "data": {"values": [ {"N": 1, "Price": 70.0, "Series": "Cournot price"}, {"N": 2, "Price": 53.33, "Series": "Cournot price"}, {"N": 3, "Price": 45.0, "Series": "Cournot price"}, {"N": 4, "Price": 40.0, "Series": "Cournot price"}, {"N": 5, "Price": 36.67, "Series": "Cournot price"}, {"N": 6, "Price": 34.29, "Series": "Cournot price"}, {"N": 7, "Price": 32.5, "Series": "Cournot price"}, {"N": 8, "Price": 31.11, "Series": "Cournot price"}, {"N": 9, "Price": 30.0, "Series": "Cournot price"}, {"N": 10, "Price": 29.09, "Series": "Cournot price"}, {"N": 1, "Price": 20.0, "Series": "Marginal cost (Bertrand price)"}, {"N": 10, "Price": 20.0, "Series": "Marginal cost (Bertrand price)"} ]}, "mark": {"type": "line", "point": true}, "encoding": { "x": {"field": "N", "type": "quantitative", "title": "Number of firms", "scale": {"domain": [1, 10]}}, "y": {"field": "Price", "type": "quantitative", "title": "Price (USD per metre)", "scale": {"domain": [0, 80]}}, "color": {"field": "Series", "type": "nominal", "title": null} } } ``` ## Entry barriers and contestable markets Bain (1956) defined barriers to entry as the advantages of established sellers over potential entrants that let them price above the competitive level without attracting entry. The main sources: | Barrier | Mechanism | *Example* | |---|---|---| | Economies of scale | Minimum efficient scale is large relative to market demand, so an entrant must win a big share or produce at high cost | Fabric mills, cloud data centres | | Absolute cost advantages | Incumbent has cheaper inputs, patents, know-how or locations | A patented membrane, prime retail sites | | Product differentiation and switching costs | Brand loyalty, learning costs, contracts | Outdoor brands with loyal climbers | | Network effects | Value to each user rises with the number of users | Marketplaces, payment networks | | Legal and regulatory barriers | Licences, standards, trade restrictions | Medical devices, telecoms spectrum | | Strategic behaviour | Excess capacity, limit pricing, exclusive contracts (lawful only within competition law) | Long-term exclusive supply deals | **Contestable markets** (Baumol, Panzar and Willig 1982; Baumol 1982). A market is perfectly contestable if entry is free and exit is costless: an entrant faces no sunk costs and can use the same technology as the incumbent. Then even a single firm must price at average cost, because any profit would invite "hit-and-run" entry that undercuts and leaves before the incumbent reacts. The lesson for managers is that **sunk costs, not the number of firms, are what protect margins.** A route served by one airline with leasable aircraft may be more contestable than a market with three firms that each sank capital in specialised plants. The theory is a benchmark: few markets are perfectly contestable, and incumbents that can cut price faster than entrants can enter weaken the result. ## Concentration and the HHI The HHI squares each firm's share (in percent) and adds them up. It ranges from close to 0 (many tiny firms) to 10,000 (one firm). Squaring gives large firms more weight than the simple concentration ratio (for example CR4, the sum of the four largest shares), so two markets with the same CR4 can have very different HHIs. **Current US screening thresholds (dated fact).** As of October 2026, the US Department of Justice and Federal Trade Commission 2023 Merger Guidelines (December 2023, announced in February 2025 as remaining in effect) treat a post-merger HHI above 1,800 with an increase above 100 as raising a presumption of harm. They also treat a merger that creates a firm with a share above 30 percent with an increase above 100 as raising a presumption of harm, and they call a market with an HHI above 1,800 highly concentrated. The presumption is rebuttable, and market definition comes first. Other authorities (for example the European Commission) use their own thresholds. These numbers change with policy: check the current guidelines at justice.gov and ftc.gov before you rely on these numbers. ## Assumptions and limits - **Linear demand and constant marginal cost** keep the algebra clean. Real demand curves bend and costs change with scale, so use the models for direction and order of magnitude, then check with data. - **Homogeneous products** drive the Bertrand result. Differentiated products give each firm a downward-sloping demand curve and positive margins even under price competition. - **One-shot interaction.** All three oligopoly models describe a single period. Firms that meet repeatedly can sustain higher prices (mba/mba-game-theory-card covers repeated games). - **Static market definition.** The HHI depends entirely on which products and regions count as "the market". A narrow definition inflates concentration, a broad one dilutes it. - **Concentration is not conduct.** A high HHI is consistent with fierce Bertrand competition; a low HHI is consistent with tacit collusion in a local sub-market. Look at margins, entry history and pricing behaviour too. - **Contestability needs zero sunk cost**, which is rare. Treat it as a direction (lower sunk cost, more discipline), not a prediction that prices equal average cost. ## How managers use it 1. **Margin diagnosis.** Compare the observed price-cost margin with the Lerner benchmark $1/|\varepsilon|$ and the Cournot benchmark $s_i/|\varepsilon|$. A margin far above both suggests differentiation, barriers or coordination; far below suggests Bertrand-style rivalry or excess capacity. 2. **Capacity and commitment decisions.** Stackelberg shows why a visible, irreversible capacity investment can deter or shrink a rival. It also shows the risk: if the rival does not believe you, you have sunk the cost anyway. 3. **Pricing in concentrated markets.** If rivals compete on price with spare capacity, price cuts are matched instantly and destroy margin for everyone. Compete on differentiation, service or cost instead. 4. **Entry decisions.** An entrant should estimate the post-entry price, not today's price: with $N + 1$ Cournot firms instead of $N$, the price falls, and the entrant must still cover its sunk cost. 5. **Mergers and acquisitions.** Corporate development teams compute pre- and post-merger HHI as a first screen before counsel looks at a deal (link the result to finance/m-and-a-integration-100-day-plan if the deal proceeds). 6. **Supplier strategy.** Northfield buys technical fabric from a duopoly: understanding Cournot pricing explains why second-sourcing or qualifying a third mill can lower prices more than tough negotiation. ## Worked example A (fully solved) **Setting** *(Example)*. Northfield is weighing whether to acquire a regional outdoor retailer. In its definition of the relevant market (specialist outdoor retail in one metropolitan region), seven firms hold these shares: 30, 25, 15, 10, 10, 5 and 5 percent. Northfield holds 15 percent and the target holds 10 percent. **Step 1: pre-merger HHI.** $30^2 + 25^2 + 15^2 + 10^2 + 10^2 + 5^2 + 5^2 = 900 + 625 + 225 + 100 + 100 + 25 + 25 = 2{,}000$. Excel with shares in B2:B8: `=SUMSQ(B2:B8)` returns 2,000. **Step 2: change and post-merger HHI.** $\Delta HHI = 2 \times 15 \times 10 = 300$, so the post-merger HHI is 2,300. Excel: `=2*B4*B5` returns 300. **Step 3: screen against the 2023 Merger Guidelines.** Post-merger HHI 2,300 is above 1,800 and the increase of 300 is above 100, so the deal would fall under the structural presumption (the combined share of 25 percent is below the 30 percent test, but one test is enough). Compare two alternatives: buying a 5 percent firm gives $\Delta HHI = 2 \times 15 \times 5 = 150$, still above 100 at a post-merger HHI of 2,150; a merger of the two 5 percent firms with each other would add only $2 \times 5 \times 5 = 50$ (post-merger 2,050) and falls below the increase test. **Step 4: what the presumption means for the business case.** A presumption is not a prohibition. It means the parties must expect a detailed review and must be able to show, for example, that the market is wider than defined (online sellers compete for the same customers), that entry is easy, or that efficiencies benefit customers. The manager's task is to price that delay and risk into the deal: timeline, possible remedies (store divestitures) and the probability the deal does not close. **Step 5: what the economics predicts.** Under Cournot logic, the margin of each firm is proportional to its share divided by demand elasticity. If local demand elasticity is about 2, a firm with 25 percent share would have a Lerner index near $0.25/2 = 0.125$; the merged firm's incentive to raise price is exactly what the reviewer will test. **Interpretation.** The acquisition raises concentration enough to trigger a presumption under the current US guidelines. Before spending on due diligence, Northfield should test a broader market definition with data on cross-shopping between stores and e-commerce, and model divestiture scenarios. This is a planning screen, not legal advice: competition counsel decides how a filing is approached. ## Worked example B (half solved) **Setting** *(Example)*. The two technical-fabric mills compete à la Cournot with demand $P = 120 - Q$. Mill 1 has modernised and its marginal cost is $c_1 = 20$; mill 2 still has $c_2 = 35$. 1. Mill 1's best response: $q_1 = (120 - 20 - q_2)/2$. Mill 2's best response: $q_2 = (120 - 35 - q_1)/2$. 2. Solve: $q_1^{*} = (a - 2c_1 + c_2)/3 = (120 - 40 + 35)/3 = 38.33$. $q_2^{*} = (a - 2c_2 + c_1)/3 =$ [ ]. 3. Market quantity $Q = $ [ ] and price $P = 120 - Q =$ [ ]. 4. Profits: $\pi_1 = (P - 20) \times 38.33 = 1{,}469.44$. $\pi_2 = (P - 35) \times q_2 =$ [ ]. 5. Shares: mill 1 holds $38.33/61.67 = 62.16$ percent; mill 2 holds [ ] percent. HHI $=$ [ ]. 6. Lerner indices: $L_1 = (58.33 - 20)/58.33 = 0.657$; $L_2 =$ [ ]. 7. In one sentence: why does a cost advantage translate into both a higher share and a higher margin? Excel: `=(B1-2*B2+B3)/(3*B4)` for $q_1$ with $a$, $c_1$, $c_2$, $b$ in B1:B4. ## Exercise C (unsolved) **Setting** *(Example)*. A single operator runs the only gear-rental kiosk at a national park entrance. Demand is $P = 100 - 2Q$ (rentals per day, USD), marginal cost is 10 and the daily fixed cost of the kiosk is 400. 1. Find the profit-maximising quantity, price and daily profit. 2. Compute the Lerner index and the price elasticity of demand at that point. 3. What quantity would $P = MC$ give, and what would the operator's profit be? Why is that not sustainable? 4. Suppose the park re-tenders the kiosk concession every season and any operator can bring in movable rental stock with no sunk cost. Under perfect contestability, what price and quantity would you expect? (Hint: set $P = AC$ and take the larger root.) 5. Name two features of the real situation that would weaken the contestability prediction. ## Connections to other cards | Card or template | Connection | |---|---| | mba/mba-demand-elasticity-card | Elasticity sets the monopoly margin through $L = 1/\lvert\varepsilon\rvert$ | | mba/mba-pricing-card | Price discrimination and value-based pricing extend the monopoly analysis | | mba/mba-game-theory-card | Nash equilibrium underlies Cournot and Bertrand; repeated games explain tacit collusion | | mba/mba-five-forces-card | Rivalry, entry and buyer and supplier power restate this card as a strategy checklist | | mba/mba-competitive-advantage-card | Sustained above-average returns need barriers that rivals cannot copy | | mba/mba-resource-based-view-card | Firm-specific resources as the source of absolute cost and differentiation advantages | | mba/mba-microeconomics-guide | Course roadmap: where this card sits in the micro sequence | | mba/pre-mba-economics-primer | Section 5 introduces structures and the HHI at primer level | ## Common mistakes and misconceptions 1. **Mixing fractions and percents in the HHI.** Shares of 0.30 and 0.25 give an HHI of 0.2 on a 0 to 1 scale; multiply by 10,000 before comparing with the 1,800 threshold. 2. **Treating "few firms" as "monopoly".** A duopoly that competes on price with spare capacity can price at cost. 3. **Setting price where demand is inelastic.** A profit-maximising monopolist always operates where $|\varepsilon| > 1$, because MR is negative where demand is inelastic. 4. **Using MR = price.** Only a price-taker has MR equal to price. For linear demand, MR has twice the slope of demand. 5. **Confusing accounting profit with economic profit.** Zero long-run economic profit still pays the normal return on capital. 6. **Assuming high concentration proves market power.** The HHI is a screen; conduct, margins and entry evidence decide. 7. **Calling all capital requirements barriers.** Capital that can be recovered on exit is not a barrier in the contestable-markets sense; sunk cost is. 8. **Forgetting credibility in Stackelberg.** First-mover advantage needs a commitment rivals observe and believe; an announcement that can be reversed does not move the follower. 9. **Defining the market after computing the HHI.** Choose and document the market definition first, otherwise the index can be made to say anything. 10. **Ignoring that cartel members want to cheat.** Collusive prices are fragile because each member's best response to the cartel quantity is to expand. ## Self-test questions 1. In one sentence, what three features of a market decide a firm's pricing power? 2. A monopolist faces $P = 200 - 4Q$ and $MC = 40$. Find $Q^m$, $P^m$ and the deadweight loss. 3. A firm's margin is $(P - MC)/P = 0.20$. If it maximises profit, what is the elasticity of demand it faces? 4. Find the error in this statement: "Under Bertrand with $P = 120 - Q$ and $c = 20$, each firm sells 40." 5. In symmetric Cournot with $P = 120 - Q$ and $c = 20$, what are the price and the Lerner index with 4 firms? 6. Why does the Stackelberg leader earn more than a Cournot firm, and what does it need for that to happen? 7. Shares are 40, 30, 20 and 10 percent. Compute the HHI and the change if the 20 and 10 percent firms merge. 8. Under the 2023 US Merger Guidelines as described in this card, does the merger in question 7 trigger the structural presumption? Show both tests. 9. What exactly must be true for a market to be perfectly contestable? 10. Why does monopolistic competition end with zero economic profit even though each firm has pricing power? ## My notes and next steps | Item | My note | |---|---| | Market I analysed and its structure | [One line] | | Model that best fits how rivals compete there | [Cournot / Bertrand / Stackelberg / differentiated] | | Most important barrier and whether it is sunk | [One line] | | HHI and data source | [Value, source, date] | | Self-test score and misses logged | [x / 10, logged in mba/mba-error-log on YYYY-MM-DD] | | Next card | [mba/mba-game-theory-card / mba/mba-five-forces-card] | ## Sources and further reading Primary works: - Bain, J. S. (1956). *Barriers to New Competition*. Harvard University Press. - Baumol, W. J. (1982). Contestable markets: an uprising in the theory of industry structure. *The American Economic Review*, 72(1), 1-15. - Baumol, W. J., Panzar, J. C., and Willig, R. D. (1982). *Contestable Markets and the Theory of Industry Structure*. Harcourt Brace Jovanovich. - Bertrand, J. (1883). Review of Walras, *Théorie mathématique de la richesse sociale*, and Cournot, *Recherches sur les principes mathématiques de la théorie des richesses*. *Journal des Savants*, 67, 499-508. - Chamberlin, E. H. (1933). *The Theory of Monopolistic Competition*. Harvard University Press. - Cournot, A. (1838). *Recherches sur les principes mathématiques de la théorie des richesses*. Hachette. - Herfindahl, O. C. (1950). *Concentration in the Steel Industry*. Doctoral dissertation, Columbia University. - Hirschman, A. O. (1945). *National Power and the Structure of Foreign Trade*. University of California Press. - Kreps, D. M., and Scheinkman, J. A. (1983). Quantity precommitment and Bertrand competition yield Cournot outcomes. *The Bell Journal of Economics*, 14(2), 326-337. - Lerner, A. P. (1934). The concept of monopoly and the measurement of monopoly power. *The Review of Economic Studies*, 1(3), 157-175. - Robinson, J. (1933). *The Economics of Imperfect Competition*. Macmillan. - von Stackelberg, H. (1934). *Marktform und Gleichgewicht*. Springer, Vienna. English translation (2011), *Market Structure and Equilibrium*, Springer. Official page (checked October 2026): US Department of Justice and Federal Trade Commission, *Merger Guidelines* (December 2023), and the February 2025 FTC and DOJ statements to staff confirming they remain in effect (ftc.gov, justice.gov). Textbooks (further reading, any recent edition): Besanko, Dranove, Shanley and Schaefer, *Economics of Strategy*; Pindyck and Rubinfeld, *Microeconomics*; Carlton and Perloff, *Modern Industrial Organization*. Open resource: OpenStax, *Principles of Economics* (3rd edition, CC BY-NC-SA 4.0), chapters on monopoly, monopolistic competition and oligopoly, openstax.org. ## Answer key **Worked example B.** (2) $q_2^{*} = (120 - 70 + 20)/3 = 23.33$. (3) $Q = 61.67$, $P = 58.33$. (4) $\pi_2 = (58.33 - 35) \times 23.33 = 544.44$. (5) Mill 2 holds 37.84 percent; $HHI = 62.16^2 + 37.84^2 = 5{,}296$. (6) $L_2 = (58.33 - 35)/58.33 = 0.400$. (7) The low-cost mill's best response is to produce more at any rival quantity, so it ends with more output; in Cournot each firm's margin is its share over the elasticity, so the larger share and the lower cost both show up as a higher margin. **Exercise C.** (1) $MR = 100 - 4Q = 10$, so $Q = 22.5$, $P = 55$, profit $= 45 \times 22.5 - 400 = 612.5$. (2) $L = 45/55 = 0.818$; $dQ/dP = -0.5$, so $\varepsilon = -0.5 \times 55/22.5 = -1.22$, and $1/1.22 = 0.818$. (3) $P = MC = 10$ gives $Q = 45$ and a loss equal to the fixed cost, 400: with fixed costs, marginal-cost pricing cannot cover total cost. (4) $P = AC$: $100 - 2Q = 10 + 400/Q$, so $2Q^2 - 90Q + 400 = 0$, roots 5 and 40; take $Q = 40$, $P = 20$, profit zero. Excel check: `=10+400/40` returns 20. (5) Any two of: rental stock and kiosk fit-out are partly sunk; the incumbent can cut price faster than a challenger can enter within a season; switching operators mid-season is impossible, so contestability works only at tender time; brand and reviews favour the incumbent. **Self-test.** 1. The number of rivals, how close their products are, and how easy it is to enter (barriers and sunk costs). 2. $MR = 200 - 8Q = 40$, so $Q^m = 20$, $P^m = 120$; $Q^c = 40$; $DWL = \tfrac{1}{2} \times 80 \times 20 = 800$. 3. $|\varepsilon| = 1/0.20 = 5$, so $\varepsilon = -5$. 4. At $P = c = 20$ the market buys $120 - 20 = 100$, so each firm sells 50 if they split demand equally, not 40. The statement confused the Bertrand output with a quantity between Cournot and competition. 5. $P = (120 + 4 \times 20)/5 = 40$; $L = 20/40 = 0.50$. 6. The leader commits to a large quantity first, and the follower's best response is to produce less, which raises the price the leader receives. It needs a commitment that is observable and irreversible (a built plant, a signed contract). 7. $HHI = 1600 + 900 + 400 + 100 = 3{,}000$; $\Delta HHI = 2 \times 20 \times 10 = 400$; post-merger 3,400. 8. Yes. Post-merger HHI 3,400 is above 1,800 and the increase of 400 is above 100. The merged share is 30 percent, which is not above 30, so the share test is not met, but the HHI test alone suffices. 9. Entry is free (entrants have access to the same technology and demand) and exit is costless, which requires that no costs are sunk; entrants can come in, undercut and leave before the incumbent reacts. 10. Profits attract entrants with close substitutes, which shifts each firm's demand left until price equals average cost at the profit-maximising output. ## Revision history | Version | Date | Author | Change summary | |---|---|---|---| | 0.1 | YYYY-MM-DD | [Your name] | First pass through the card | | 0.2 | YYYY-MM-DD | [Your name] | *Example:* Replaced HHI example with shares from my case industry | ## Standard and licence note Based on the standard treatment of market structure in industrial organisation, drawing on the primary works listed above (Cournot 1838, Bertrand 1883, Chamberlin 1933, Robinson 1933, Lerner 1934, von Stackelberg 1934, Bain 1956, Baumol, Panzar and Willig 1982) and on the US Department of Justice and Federal Trade Commission 2023 Merger Guidelines as checked in October 2026. The text, the worked examples and the questions are original; no textbook text is copied or paraphrased, and the fictional companies are not real businesses. The template is independent and not affiliated with or endorsed by any business school or competition authority. Check the current official guidelines before you rely on any threshold. Template licence: MIT.