How to Calculate the Cournot Equilibrium
With inverse demand P = a − bQ and n identical firms at marginal cost c, each Cournot firm makes (a − c) ÷ [(n + 1)b] and the price settles at (a + nc) ÷ (n + 1).
The Cournot Competition formula
Calculator
Enter demand, marginal cost and the number of firms to get Cournot output per firm, market price and profit.
The price at which buyers would take nothing at all.
How much the price falls for each extra unit the industry sells.
Constant cost per unit, identical across the firms.
Set this to one to see the monopoly outcome, then raise it.
Each firm's best answer to the others is 20 units, and no firm can do better by moving alone.
- Total industry output
- 40
- Market price
- $60
- Profit per firm
- $800
- Industry profit
- $1,600
- Monopoly price for comparison
- $80
All the firms together supply 40 units, short of what a competitive industry would produce.
That output puts the price at $60, above marginal cost because each firm holds back to protect the price.
Each firm keeps $800, the margin over marginal cost times its own output.
The firms earn $1,600 between them, less than a single seller would take from the same market.
One firm alone would charge $80, so the gap to the Cournot price is what rivalry is worth to buyers here.
How to calculate Cournot Competition, step by step
- 1Write inverse demand and marginal cost. Put price as P = a − bQ, where Q is total industry output, and let every firm make a unit for the same constant c.
- 2Set marginal revenue equal to marginal cost for one firm. Holding rivals' output fixed at Q_rest, a firm's marginal revenue is a − b × Q_rest − 2b × q. Setting that equal to c gives its reaction function.
- 3Impose symmetry. Identical firms end up producing the same amount, so replace Q_rest with (n − 1) × q and solve. The result is q = (a − c) ÷ [(n + 1)b].
- 4Add up and price the market. Total output is n × q, and price comes straight off demand: P = a − bQ, which tidies up to (a + nc) ÷ (n + 1).
- 5Check the limits. Setting n to one reproduces the monopoly answer, and raising the number of firms slides price down toward marginal cost.
Worked example: Cournot Competition
Take P = 140 − 2Q with two firms, each able to make a unit for $20, so a − c = 120. Each firm produces 120 ÷ (3 × 2) = 20 units, industry output is 40 and price is 140 − 2(40) = $60. Each firm earns (60 − 20) × 20 = $800, so the industry earns $1,600. A single firm would hold output to 30 units and charge $80, and every firm added past the second pushes price nearer the $20 marginal cost.
Cournot Competition questions
What is a Cournot reaction function?
It is one firm's best output given what the rest produce: q = (a − c − b × Q_rest) ÷ (2b). Equilibrium sits where every firm is on its own reaction function at the same time, which makes it a Nash equilibrium in quantities.
Why does the Cournot price stay above marginal cost?
Each firm still faces a downward sloping residual demand curve, so an extra unit drags the price down on everything it sells. That restraint holds output below the competitive level and keeps price above c.
What happens as the number of firms rises?
Output per firm shrinks, industry output climbs toward (a − c) ÷ b, and price falls toward marginal cost. That limit is why the model is used to show entry disciplining an oligopoly.
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