Difficulty: Intermediate | Prerequisites: Consumer theory, basic calculus, cost concepts.
This material covers how firms decide what to produce and at what price, across different market structures. Perfect competition is the baseline: many firms, no market power, price equals marginal cost in the long run. Monopoly and oligopoly introduce market power, strategic interaction, and deadweight loss. You should already be comfortable with cost functions, marginal cost, and average cost before working through this.
In perfect competition, firms produce where P = MC and earn zero economic profit in the long run (P = min ATC). A monopolist restricts output and charges above MC, creating deadweight loss; the Lerner Index measures the markup. In Cournot oligopoly, firms choose quantities simultaneously, each firm's best response depends on the rival's output, and the Nash equilibrium lies between the competitive and monopoly outcomes.
Perfect competition
A market structure with many small firms, a homogeneous product, complete information, no transaction costs, and free entry and exit. Each firm is a price taker.
Think of it as a market where no single firm can move the needle on price.
Marginal cost (MC)
The additional cost of producing one more unit of output. MC = dTC/dq.
In simple terms, it is what the next unit costs you to make.
Average total cost (ATC)
Total cost divided by quantity: ATC = TC/q. It includes both fixed and variable costs per unit.
Think of it as the per-unit cost when you spread everything evenly across output.
Average variable cost (AVC)
Variable cost divided by quantity. The shutdown condition compares price to minimum AVC.
In simple terms, it is the per-unit cost of just the inputs you can vary in the short run.
Long-run equilibrium (perfect competition)
The state where P = MC = min ATC. Firms earn zero economic profit, and there is no incentive for entry or exit.
Think of it as the point where the market has settled and nobody wants in or out.
Monopoly
A market with a single seller who faces the entire market demand curve. The monopolist has pricing power and sets MR = MC to maximise profit.
In simple terms, one firm, no competition, higher price and lower output than a competitive market.
Marginal revenue (MR)
The additional revenue from selling one more unit. For a linear demand P = a - bQ, MR = a - 2bQ (same intercept, twice the slope).
Think of it as revenue from the next unit sold, accounting for the fact that selling more requires lowering the price on all units.
Lerner Index
A measure of market power: L = (P - MC) / P. Ranges from 0 (perfect competition, no markup) to 1 (extreme market power). The higher L, the greater the firm's ability to price above cost.
In simple terms, it tells you what fraction of the price is pure markup.
Cournot oligopoly
A model of oligopoly where firms simultaneously choose quantities, taking the rival's output as given. The equilibrium is a Nash equilibrium in quantities.
Think of it as a quantity-setting game where each firm asks, "given what my rival produces, how much should I produce?"
Reaction function (best response function)
An equation giving one firm's profit-maximising quantity as a function of the other firm's quantity. In Cournot with linear demand, it is typically a downward-sloping line.
In simple terms, it is each firm's answer to the question, "if they produce that much, what should I do?"
Nash equilibrium
A set of strategies (one per player) where no player can improve their payoff by unilaterally changing their strategy. In Cournot, it is the intersection of the two reaction functions.
Think of it as the point where everyone is doing their best given what everyone else is doing.
Herfindahl-Hirschman Index (HHI)
A measure of market concentration: HHI = s1^2 + s2^2 + ... + sn^2, where s_i is each firm's percentage market share. Higher HHI means more concentrated. The FTC uses HHI thresholds to evaluate mergers.
In simple terms, it is a single number that summarises how concentrated a market is.
Diminishing marginal returns
In the short run, with at least one fixed input, adding more of a variable input eventually produces smaller and smaller increases in output.
Think of it as cramming more workers into a fixed-size kitchen: eventually each additional cook adds less output.
Returns to scale
How output responds when all inputs are scaled proportionally. Constant returns: doubling inputs doubles output. Increasing returns: output more than doubles. Decreasing returns: output less than doubles.
In simple terms, it is what happens to output when you photocopy the entire operation at a larger size.
Many small firms, each a price taker.
Homogeneous product.
Complete information among buyers and sellers.
Free entry and exit (no significant barriers).
No transaction costs.
The firm produces where P = MC (as long as P >= min AVC).
If P < min AVC, the firm shuts down: it loses less by paying only fixed costs than by producing.
Entry and exit drive economic profit to zero.
Each firm produces where MC = ATC (the minimum of ATC).
The market price equals min ATC.
TC(q) = 100 + q^2.
ATC = 100/q + q. MC = 2q.
Set MC = ATC: 2q = 100/q + q, so q = 100/q, giving q^2 = 100, q = 10.
P = MC(10) = 2(10) = 20. The break-even price is $20 and each firm produces 10 units.
Agricultural commodity markets approximate perfect competition: many small farmers sell identical wheat at a price none of them individually controls. The long-run zero-profit prediction explains why farms consolidate or exit when costs rise above the market price.
The monopolist faces the entire downward-sloping market demand.
Total revenue TR = P * Q. For linear demand P = a - bQ: TR = aQ - bQ^2.
Marginal revenue MR = a - 2bQ (same vertical intercept as demand, twice the slope).
Profit maximisation: set MR = MC, solve for Q, then read P off the demand curve.
L = (P - MC) / P.
For a competitive firm, P = MC, so L = 0.
The monopolist's L is positive and related to the price elasticity of demand: L = 1 / |Ed|.
Demand: P = 100 - Q. MC = 20 (constant).
MR = 100 - 2Q. Set MR = MC: 100 - 2Q = 20, so Q = 40.
P = 100 - 40 = 60.
Lerner Index = (60 - 20)/60 = 40/60 = 2/3 = 0.667.
The monopolist marks up by two-thirds of the price.
Pharmaceutical companies with patent protection behave as monopolists for the duration of the patent. The Lerner Index helps regulators gauge just how far above cost a drug is priced, which informs decisions about patent policy and generic entry.
Two (or more) firms choose quantities simultaneously.
Market price depends on total quantity: P = a - Q, where Q = q1 + q2.
Each firm takes the rival's output as given and maximises its own profit.
Firm 1's profit: pi_1 = (a - q1 - q2) * q1 - MC * q1.
First-order condition: d(pi_1)/dq1 = a - 2q1 - q2 - MC = 0.
Rearrange to get Firm 1's reaction function: q1 = (a - MC - q2) / 2.
By symmetry (if costs are equal), Firm 2's reaction function is: q2 = (a - MC - q1) / 2.
Substitute one reaction function into the other and solve.
With symmetric costs, each firm produces q* = (a - MC) / 3 in a two-firm Cournot model.
Total output Q = 2(a - MC)/3, which lies between the competitive output (a - MC) and monopoly output (a - MC)/2.
Demand: P = 120 - Q. MC1 = MC2 = 0.
Firm 1's reaction function: q1 = (120 - 0 - q2)/2 = 60 - 0.5q2.
By symmetry: q2 = 60 - 0.5q1.
Substituting: q1 = 60 - 0.5(60 - 0.5q1) = 60 - 30 + 0.25q1, so 0.75q1 = 30, q1 = 40.
q2 = 40. Total Q = 80. P = 120 - 80 = 40.
Cournot-style competition describes markets with a small number of large producers choosing production levels, such as OPEC oil producers deciding output quotas. The model predicts that prices fall and total output rises as the number of firms increases, converging toward the competitive outcome.
\text{Profit maximisation: } MR = MC\text{MR for linear demand } P = a - bQ: \quad MR = a - 2bQ\text{Lerner Index: } L = \frac{P - MC}{P}\text{ATC} = \frac{TC}{q}, \quad MC = \frac{dTC}{dq}\text{Long-run equilibrium: } P = MC = \min(ATC)\text{Shutdown condition (short run): } P < \min(AVC)\text{Cournot reaction function: } q_1 = \frac{a - MC - q_2}{2}\text{HHI} = s_1^2 + s_2^2 + \ldots + s_n^2Students often think diminishing marginal returns and decreasing returns to scale are the same thing. Diminishing marginal returns is a short-run concept (one input fixed). Returns to scale is a long-run concept (all inputs scaled together).
Students often think the shutdown condition is P < ATC. The short-run shutdown condition is P < min AVC. If P is between min AVC and min ATC, the firm loses money but is better off producing than shutting down, because it covers some fixed costs.
Students often think Nash equilibrium requires dominant strategies. A Nash equilibrium only requires that no player wants to deviate given the other players' strategies. Dominant strategies are sufficient but not necessary.
Students often forget that the monopolist's MR curve has twice the slope of the demand curve (for linear demand). Writing MR = P or MR = demand is a common algebraic error.
⚠️ The long-run equilibrium condition MC = min ATC is heavily tested. Practise finding min ATC by setting MC = ATC.
⚠️ Monopoly profit maximisation (derive MR, set MR = MC, find Q, find P, compute Lerner Index) is a standard 10-mark problem.
⚠️ Deriving reaction functions and solving for Cournot Nash equilibrium quantities is a core exam skill. Be fluent with the algebra.
⚠️ The shutdown condition (P < min AVC) versus break-even (P = min ATC) distinction is a favourite short-answer question.
⚠️ HHI formula and the FTC merger-challenge thresholds (HHI > 1800 and change >= 50) appear in multiple-choice sections.
⚠️ Constant returns to scale (doubling inputs doubles output) versus diminishing marginal returns is tested as a conceptual distinction.
True or False: In long-run competitive equilibrium, firms earn positive economic profit. (False. Economic profit is zero.)
Fill in the blank: The Lerner Index for a perfectly competitive firm is ______. (Zero.)
True or False: Doubling all inputs and getting exactly double the output is constant returns to scale. (True.)
Fill in the blank: A firm should shut down in the short run if P < ______. (min AVC.)
True or False: In a Nash equilibrium, each player must be playing a dominant strategy. (False. A Nash equilibrium only requires that no player wants to unilaterally deviate.)
Q: A firm has TC(q) = 100 + q^2. Find the break-even price and quantity in long-run equilibrium.
A: ATC = 100/q + q, MC = 2q. Set MC = ATC: 2q = 100/q + q, so q = 10. P = MC(10) = 20.
Q: A monopolist faces P = 100 - Q with MC = 20. Find Q, P, and the Lerner Index.
A: MR = 100 - 2Q. Set MR = MC: 100 - 2Q = 20, Q = 40. P = 60. L = (60 - 20)/60 = 2/3.
Q: In a Cournot duopoly with P = 120 - Q and MC = 0, derive Firm 1's reaction function and find equilibrium quantities.
A: q1 = 60 - 0.5q2. By symmetry, q2 = 60 - 0.5q1. Solving: q1 = q2 = 40.
Q: Which of the following is NOT an assumption of perfect competition: (a) homogeneous product, (b) complete information, (c) significant barriers to entry, (d) no transaction costs?
A: (c) Significant barriers to entry. Perfect competition assumes free entry and exit.
Q: If the post-merger HHI is 2000 and the change in HHI is 75, will the FTC likely challenge the merger?
A: Yes. HHI > 1800 and the change (75) exceeds the 50-point threshold.
Perfect competition provides the benchmark against which monopoly and oligopoly outcomes are measured, and it connects to general equilibrium and the First Welfare Theorem (competitive equilibria are Pareto efficient). The Cournot model is a stepping stone to other oligopoly models (Bertrand, Stackelberg) and to game theory more broadly. Cost curves underpin tax-incidence and welfare analysis.
Perfect competition, monopoly, oligopoly, Cournot, duopoly, Nash equilibrium, reaction function, best response, marginal cost, average total cost, average variable cost, shutdown condition, break-even price, long-run equilibrium, zero economic profit, Lerner Index, market power, marginal revenue, HHI, Herfindahl-Hirschman Index, FTC merger guidelines, diminishing marginal returns, constant returns to scale, increasing returns to scale, decreasing returns to scale, price taker, ECON 302, intermediate microeconomics