Oligopoly and monopolistic competition

In perfect competition a firm is too small to matter: it takes the price as given and sells what it likes. A monopolist has no rivals. Oligopoly sits between the two. There are few enough firms that each one’s output or price visibly moves the market, so what is best for you depends on what your rivals do. The examiners call this interdependence, and CUET asks for it by name as the defining feature of oligopoly.

That makes oligopoly a game. The players are the firms, the moves are quantities or prices, the payoffs are profits, and the answer is a Nash equilibrium: a pair of choices where neither firm wants to change its own, given the other’s. If Nash equilibrium is new to you, the game theory guide comes first. Every model in this guide is one particular answer to the question “what does each firm assume its rivals will do?”.

The simplest way to say how few “few” is takes the market shares in per cent, squares each and adds them up:

Cournot (1838) studied two firms that each pick an output. The price falls as the total rises, P = a − bQ, and each firm’s cost is c per unit. Firm 1 looks at firm 2’s output as something it cannot change and asks: “what output gives me the highest profit?”. That is its reaction function.

The reaction function slopes down: if your rival makes more, the price will be lower, so you make less. The Cournot–Nash equilibrium is where the two reaction functions cross, because there each firm is already doing its best given the other. With equal costs the crossing is easy:

With n identical firms the same steps give a clean pair of formulas. One firm (n = 1) is the monopolist. As n grows, the price falls towards marginal cost, but it never reaches it.

Look at the second box in the lab. For a Cournot industry the Lerner index of firm i is its market share divided by the elasticity of demand, because the first-order condition says P − c_i = b q_i. So the share-weighted average Lerner index is the Herfindahl index divided by the elasticity: concentration and market power are the same fact seen from two sides.

Put c₁ and c₂ into the reaction functions and solve the pair. Each firm’s output rises with the rival’s cost and falls with its own. If a firm’s cost is too high compared with the rival’s, its best output is zero and it leaves the market (try raising firm 2’s cost in the lab).

In von Stackelberg’s version one firm, the leader, commits to its output first. The follower sees it and then picks her best reply, which is just her Cournot reaction function. The leader knows this, so she does not treat the follower’s output as fixed. She puts the follower’s reaction function into her own profit and maximises along it.

Open the lab from chapter 2 and press “Stackelberg: one leads”. The gold curve is the leader’s isoprofit curve: every output pair that gives her the same profit. She is moving along the follower’s reaction curve and stops where her isoprofit curve just touches it. That tangency is the picture the Delhi School keeps asking about.

Price leadership is a different arrangement in the same spirit. In the dominant-firm model one big firm sets the price and the many small firms take it as given, supplying what suits them at that price. Sequential play is the common thread: UoH calls price leadership “a sequential action game”.

Bertrand (1883) replied that firms in real markets name prices, not quantities. Take two firms selling the same good with the same constant cost c. Buyers go to whoever is cheaper. Suppose both charge a price above c. Either firm can undercut by a hair, win the whole market and do better. So neither price can be an equilibrium. Going the other way, below c would lose money. The only stable pair of prices is p₁ = p₂ = c. Two firms are enough to wipe out all profit: the Bertrand paradox.

With unequal costs the cheaper firm wins. It can set its price up to just below the dearer firm’s cost (the limit price) without being undercut. If its own monopoly price is lower than that, it simply charges the monopoly price. So the price is the smaller of the two. Try costs of 0 and 30 in the lab with a = 50: the monopoly price is 25, below 30, so 25 is the answer.

If the goods are differentiated, a small price cut does not take away all the rival’s customers. Each firm’s demand is of the form q_i = α − βp_i + γp_j, and the best price rises when the rival’s does, so the price reaction curves slope up and the equilibrium is where they cross, above cost. If prices must be whole numbers, undercutting by a hair is impossible; a cut of a whole rupee can cost more than it gains, and several price pairs can be equilibria (JAM 2021).

Edgeworth (1897) saw the weak point of the undercutting argument. It works only if a firm can serve everyone who comes to it. If each firm has a limit on how much it can make, undercutting stops paying, and the simple answer p = c no longer holds. DSE 2012 asks one such case; it is in the Delhi School section below.

Sweezy’s paper and Hall and Hitch’s were both published in 1939, and the idea is the same. An oligopolist at a going price believes two things. If she raises her price, her rivals will not follow, and she will lose many customers: demand above the going price is flat (elastic). If she cuts her price, her rivals will match it, and she gains few customers: demand below is steep. UoH asks the assumption directly: rivals follow a price decrease but not an increase.

The demand curve has a kink at the going price. A straight line has marginal revenue that falls steadily with output; a kinked one has marginal revenue that drops suddenly at the kink, as the curve changes slope. In that vertical stretch marginal revenue takes every value between the two ends. If marginal cost moves up or down but stays inside the gap, the profit-maximising output and price do not move at all.

Firms do better together than apart. A cartel gets the members to act as one monopolist: they choose the total output that maximises industry profit, then share it out. Compare the numbers in the chapter 2 lab. Joint output is (a − c)/2b, the price is the monopoly price, and total profit is higher than in Cournot. UoH asks both statements: a cartel acts like a monopoly, and its members earn more than at the Cournot equilibrium.

The trouble is that each member is tempted. Given that the others keep to their quotas, one firm that quietly makes more sells at the cartel’s high price and earns more still. Every member reasons the same way, so cartels are unstable. The lab puts numbers on the temptation.

The threshold in the lab uses a simple punishment: if anyone cheats, everyone goes back to Cournot for ever. Cheating then wins a one-off gain and loses the cartel’s extra profit in every later period. This is a step beyond what the past papers ask, but it explains why cartels last when members are patient and break up when they are not, and why a large cartel is harder to hold than a small one. It also explains the OPEC question in the practice set: a high price attracts cheating and new supply, and in the long run demand and supply are more elastic, not less.

Two related terms come up in CUET. Price leadership is a pattern in which one firm regularly announces price changes and the others match them. Price signalling is implicit collusion in which a firm announces a price increase in the hope that others will follow it. Both are ways to coordinate without a written agreement.

Chamberlin (1933) described a market that mixes the two extremes. There are many sellers and free entry, as in perfect competition. But each firm sells its own variety (a brand, a location, a recipe), so it faces a downward-sloping demand curve, as a monopolist does. Close substitutes keep the demand quite elastic; selling costs such as advertising try to shift it. Chamberlin called the set of close-substitute firms a group. Because the rivals are so many, each firm ignores their reactions: there are no dependent actions, which is why UoH lists “dependent actions” as not a feature.

In the short run a firm sets marginal revenue equal to marginal cost, as any firm with some market power does, and may make a profit or a loss. A profit invites entrants, who take customers away: each firm’s demand moves in. Entry stops when the demand curve just touches the average cost curve. Profit is zero, and price equals average cost. But the touching point is on the falling part of the average cost curve, so the firm is smaller than the output that would minimise average cost.

A related theory, Baumol’s, supposes that managers aim to maximise sales revenue rather than profit, subject to a minimum acceptable profit. UoH asks for the basic goal: revenue maximisation. Chapter 2’s lab lets you switch firm 1 to a revenue maximiser and watch its reaction curve move out; the Delhi School section uses this.

Work through the sets in order. Foundation is definitions and who-said-what. Standard is the calculations (Cournot with n firms and unequal costs, Stackelberg, Bertrand) and the statements to sort. The Delhi School sets are below in their own chapter.

All 20 foundation questions · all 53 standard questions

The Delhi School entrance sets the hardest oligopoly questions: unequal costs with comparative statics, choosing your own cost before competing, a revenue-maximising rival, and the geometry of reaction curves and isoprofit curves. There are 24 questions here, from 2004 to 2018, in two sets. Each of the ideas below is a short extension of the chapters above.

Read on 24 October 2026 from the sources below. Where this guide sets out a result, the formulas were solved again and every worked answer and exercise on this page was recomputed against the question’s key before it was published. A small number of questions with an answer key that is wrong or open to dispute were left out of the sets; the reasons are listed at the top of lib/oligopoly.ts.

• Joseph Bertrand, profile at cruel.org (the 1883 review in the Journal des Savants, vol. 67, and the duopoly with prices)
• Kinked demand: Wikipedia (Sweezy, and Hall and Hitch, Oxford Economic Papers no. 2, 1939)
• The Herfindahl–Hirschman index: Orris C. Herfindahl and the Conversable Economist on its history
• Heinrich von Stackelberg, Marktform und Gleichgewicht (Springer, Vienna, 1934)