Difficulty: Intermediate | Prerequisites: Supply, Demand, and Market Equilibrium notes (Part 1)
This set of notes covers the three market structures you will be tested on: perfect competition, monopoly, and oligopoly (Cournot and Bertrand models). Understanding how firms behave under each structure, and how outcomes differ, is the centrepiece of intermediate microeconomics. You need to be comfortable with the P = MC equilibrium from Part 1, because every structure is compared against it.
In perfect competition, many firms drive price down to marginal cost and earn zero economic profit. A monopolist restricts output to push price above marginal cost, earning positive profit at the expense of efficiency. Oligopoly models (Cournot and Bertrand) sit between these extremes: Cournot firms compete on quantity and land between monopoly and competitive outcomes, while Bertrand firms compete on price and, with homogeneous products, replicate the competitive result.
Perfect competition
A market with many small firms selling an identical product, where no single firm can influence the market price. Each firm is a price taker and sets output where P = MC.
Monopoly
A market with a single seller. The monopolist faces the entire market demand curve and has the power to set price above marginal cost by restricting output.
Marginal revenue (MR)
The additional revenue from selling one more unit. For a monopolist facing a linear demand curve P = a - bQ, marginal revenue is MR = a - 2bQ (the slope is twice as steep as the demand curve).
Profit-maximising rule
All firms maximise profit by producing where MR = MC. For a competitive firm, MR = P, so this simplifies to P = MC.
Market power
The ability of a firm to set price above marginal cost. A perfectly competitive firm has none. A monopolist has the most. Cournot firms have some.
Cournot model (Cournot duopoly)
An oligopoly model where firms compete by simultaneously choosing quantities. Each firm picks its output level to maximise its own profit, taking the rival's output as given. Think of it as a quantity-setting game.
Reaction function (best-response function)
A function that gives one firm's profit-maximising output as a function of its rival's output. In a symmetric Cournot duopoly with demand P = a - bQ and marginal cost c, the reaction function for firm i is q_i = (a - c)/(2b) - 0.5 x q_j.
Cournot-Nash equilibrium
The pair of quantities where each firm is on its reaction function simultaneously. Neither firm has an incentive to change its output given the other's choice.
Bertrand model
An oligopoly model where firms compete by simultaneously choosing prices. With homogeneous products and identical costs, the equilibrium price is driven down to marginal cost (the Bertrand paradox).
Bertrand paradox
The surprising result that just two firms competing on price are enough to replicate the perfectly competitive outcome (P = MC) when products are identical. In simple terms, any price above MC invites undercutting, so neither firm can sustain a price above cost.
Deadweight loss (from monopoly)
The reduction in total surplus caused by the monopolist producing less than the competitive quantity. Units where consumers value the good more than it costs to produce go unproduced.
Many firms, identical products, free entry and exit.
Each firm is a price taker: it faces a horizontal demand curve at the market price.
Equilibrium condition: P = MC.
In the long run, economic profit is zero (P = ATC).
This is the benchmark for allocative efficiency: every unit where the consumer's marginal benefit exceeds the marginal cost gets produced.
One firm, no close substitutes, significant barriers to entry.
The monopolist faces the downward-sloping market demand curve.
To sell more, the monopolist must lower the price on all units, so MR < P.
For linear demand P = a - bQ, MR = a - 2bQ.
Profit-maximising output: set MR = MC and solve for Q. Then substitute back into the demand curve to find P.
Profit = (P - MC) x Q, or equivalently (P - ATC) x Q when ATC differs from MC.
Compared to perfect competition: the monopolist produces less (Q_m < Q_c), charges more (P_m > P_c), and creates deadweight loss.
Two (or more) firms choose quantities simultaneously.
Each firm maximises its own profit, taking the rival's quantity as given.
To derive a reaction function:
Write firm i's profit as a function of q_i and q_j: profit_i = (P - c) x q_i, where P depends on total Q = q_i + q_j.
Take the first-order condition: differentiate profit with respect to q_i and set equal to zero.
Solve for q_i as a function of q_j. This is the reaction function.
The Cournot equilibrium is where both reaction functions intersect.
With symmetric firms (same MC), both produce the same quantity.
The Cournot price sits between the monopoly price and the competitive price. This is because Cournot firms produce more than a monopolist (they ignore the negative externality their output has on the rival's revenue) but less than competitive firms (they still have some market power).
When firms have different marginal costs, the lower-cost firm produces more.
If the high-cost firm's MC is at or above the demand intercept (the price at Q = 0), that firm cannot profitably produce anything and is priced out of the market.
The surviving firm then acts as a monopolist.
Worked example from the exam: demand Q = 40 - P (so P = 40 - Q), MC_1 = 20, MC_2 = 40. Firm 2's marginal cost equals the demand intercept, so q_2 = 0 and Firm 1 produces q_1 = 10 at P = 30.
Two firms set prices simultaneously.
With homogeneous products and identical costs, the logic is simple: if one firm charges above MC, the other can steal the entire market by undercutting. This process continues until both firms charge P = MC.
The result is the perfectly competitive outcome, even with only two firms. This is the Bertrand paradox.
Key contrast with Cournot: Cournot competition yields prices above MC; Bertrand competition yields P = MC.
For the same demand curve P = 70 - 2Q and MC = 10:
Structure | Price | Total Quantity | Firm Profit |
|---|---|---|---|
Perfect competition | 10 | 30 | 0 |
Cournot duopoly (symmetric) | 30 | 20 (10 each) | 200 each |
Monopoly | 40 | 15 | 450 |
Bertrand duopoly | 10 | 30 | 0 |
The pattern: as the number of firms increases or competition intensifies, price falls toward MC, quantity rises toward the competitive level, and individual profit falls.
Marginal revenue for linear demand
If demand is P = a - bQ, then:
MR = a - 2bQThe MR curve has the same intercept as demand but twice the slope.
Monopoly profit maximisation
Worked example: P = 70 - 2Q, MC = 10.
MR = 70 - 4Q
Set MR = MC: 70 - 4Q = 10, so Q = 15
P = 70 - 2(15) = 40
Profit = (40 - 10) x 15 = 450
Cournot reaction function derivation
Demand: P = 70 - 2(q_A + q_B). Firm A's profit:
\pi_A = [70 - 2(q_A + q_B)] \times q_A - 10 \times q_A = 60q_A - 2q_A^2 - 2q_Aq_BFirst-order condition (differentiate with respect to q_A, set to zero):
60 - 4q_A - 2q_B = 0
q_A = 15 - 0.5q_B (Amy's reaction function)
By symmetry, q_B = 15 - 0.5q_A.
Substitute: q_A = 15 - 0.5(15 - 0.5q_A) = 15 - 7.5 + 0.25q_A, so 0.75q_A = 7.5, q_A = 10.
Equilibrium: q_A = q_B = 10, Q = 20, P = 70 - 40 = 30.
Profit per firm: (30 - 10) x 10 = 200.
Cournot with asymmetric costs
Demand: P = 40 - Q, MC_1 = 20, MC_2 = 40.
Firm 1's reaction function: q_1 = 10 - 0.5q_2.
Firm 2's FOC gives: q_2 = (40 - MC_2)/(2) - 0.5q_1 = 0 - 0.5q_1. Since the numerator (40 - 40) = 0, Firm 2's best response is never positive.
Equilibrium: q_2 = 0, q_1 = 10, P = 30. Firm 1 acts as a monopolist.
Cournot competition is a reasonable model for industries where firms commit to production levels before observing the market (e.g. oil production by OPEC members, semiconductor fabrication capacity). Bertrand competition fits markets where firms can adjust prices quickly and products are nearly identical (e.g. petrol stations on the same road, generic pharmaceuticals).
Monopoly analysis applies wherever a single firm dominates due to patents, network effects, or natural monopoly conditions (e.g. a local water utility, a pharmaceutical under patent protection).
Students often think the Cournot model involves firms setting prices. It does not. Cournot firms set quantities; Bertrand firms set prices. Getting this backwards is a common exam error.
Students sometimes believe that two firms in a market always means prices above MC. Under Bertrand competition with homogeneous products, two firms are enough to drive price to MC.
Students often forget that the monopolist's MR curve has twice the slope of the demand curve (for linear demand). Using the demand curve as MR is a frequent calculation mistake.
Students sometimes confuse the Cournot equilibrium with collusion. Cournot firms do not cooperate. Each firm maximises its own profit independently. The resulting output is higher than the collusive (monopoly) output.
⚠️ The Cournot reaction function derivation is a multi-step calculation that appears as a long-answer question (7 marks). Practise it until you can do it without notes.
⚠️ The asymmetric-cost Cournot problem tests whether you can spot that a firm with MC equal to (or above) the demand intercept produces zero. This is not a standard result, so many students miss it.
⚠️ Expect a comparison question asking you to rank outcomes across structures: monopoly vs Cournot vs competition. Know the table of P, Q, and profit for each.
⚠️ The Bertrand model's key result (P = MC with homogeneous products) is a common multiple-choice question. Remember: Bertrand = price competition = competitive outcome.
True or false: In the Cournot model, firms set prices simultaneously. (False. They set quantities.)
True or false: A monopolist's marginal revenue curve lies below the demand curve for all positive quantities. (True.)
Fill in the blank: In the Bertrand model with homogeneous products, the equilibrium price equals ________. (Marginal cost.)
True or false: If a Cournot competitor's marginal cost equals the demand intercept, it will produce a positive quantity. (False. It is priced out of the market.)
Fill in the blank: The Cournot equilibrium price is ________ than the monopoly price and ________ than the competitive price. (Lower; higher.)
Q: Two firms, Amy and Beau, compete as Cournot duopolists. Market demand is P = 70 - 2Q (Q = q_A + q_B), MC = 10, zero fixed costs. Derive Amy's reaction function and find the equilibrium quantities, price, and profit.
A: Amy's profit = (70 - 2q_A - 2q_B)q_A - 10q_A = 60q_A - 2q_A^2 - 2q_Aq_B. FOC: 60 - 4q_A - 2q_B = 0, so q_A = 15 - 0.5q_B. By symmetry, q_B = 15 - 0.5q_A. Substituting: q_A = 10, q_B = 10, Q = 20, P = 30, profit = 200 each.
Q: A monopolist faces P = 70 - 2Q with MC = 10. Find the profit-maximising price, quantity, and profit. Compare to the competitive outcome (P = 10, Q = 30).
A: MR = 70 - 4Q. Set MR = MC: Q = 15, P = 40, profit = 450. Compared to competition: the monopolist charges a higher price (40 vs 10), produces less (15 vs 30), and earns positive profit (450 vs 0). The gap represents deadweight loss from output restriction.
Q: In a Cournot market, demand is Q = 40 - P. Firm 1 has MC = 20, Firm 2 has MC = 40. Find the equilibrium. Does Firm 2 produce?
A: Rewrite demand as P = 40 - q_1 - q_2. Firm 1's reaction function: q_1 = 10 - 0.5q_2. Firm 2's MC equals the demand intercept (40), so any positive output would sell at or below its cost. Firm 2 produces zero. Firm 1 produces q_1 = 10, P = 30.
Q: In the Bertrand model with homogeneous products, what is the equilibrium price? Why?
A: P = MC. With homogeneous products, any firm charging above MC is undercut by its rival, who captures the entire market. This undercutting continues until both firms charge exactly MC.
The competitive equilibrium (P = MC, Q = 30) from Part 1 is the welfare benchmark throughout this material. Consumer surplus and deadweight loss (Part 1) are the tools you use to evaluate monopoly and oligopoly outcomes.
Market concentration measures (HHI, CR4) from Part 3 of these notes quantify how close an industry is to monopoly or competition. Product differentiation (also Part 3) is one factor that determines whether Bertrand competition yields P = MC or something higher.
Perfect competition, monopoly, monopolist, oligopoly, duopoly, Cournot model, Cournot duopoly, Cournot-Nash equilibrium, reaction function, best response function, Bertrand model, Bertrand paradox, marginal revenue, MR = MC, profit maximisation, market power, deadweight loss, allocative efficiency, price taker, quantity competition, price competition, asymmetric costs, homogeneous products, ECO3101, FIU, intermediate microeconomics