Cournot Model | Econ Academy

The Cournot model (1838) is the foundational model of oligopoly. Two firms simultaneously choose quantities, and the market price comes from total output through the demand curve. Each firm’s profit depends on both its own quantity and the rival’s, creating strategic interdependence. The solution concept is Nash Equilibrium — each firm’s quantity is a best response to the other’s.

Key Term

Cournot Duopoly Setup

Players: 2 firms (duopoly)
Strategy: Each firm chooses a quantity ( $Q_{1}$ , $Q_{2}$ ) simultaneously
Market price: Determined by total output, $P = a - b (Q_{1} + Q_{2})$
Costs: Typically $M C = c$ (constant)
Solution: Find reaction functions, then solve for Nash Equilibrium

Classic Cournot example: linear demand with zero marginal cost

To solve the Cournot model, derive each firm’s reaction function (or best response function). This tells us how much Firm 1 wants to produce as a function of Firm 2’s output, and vice versa. Graphically, the Nash Equilibrium is where the two reaction functions intersect. At that point, each firm is producing its best response to the other’s actual output — neither wants to change.

Worked Example

Two firms face $P = 30 - Q$ where $Q = Q_{1} + Q_{2}$ . Both have $M C = 0$ . Find the Cournot Nash Equilibrium quantities, price, and profits.

Interactive — Cournot, Collusion, and Free Market

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Cournot reaction functions with the active equilibrium highlighted. Click Next to cycle between Cournot, collusion, and the free-market benchmark.

Only the Cournot dot lies on both reaction functions. Collusion is more profitable for the firms but unstable — at those quantities each firm could deviate and earn more. The free-market dot is more efficient (highest output, lowest price) but yields zero profit. Cournot sits between the two — more output than collusion, less than competition — and is the only outcome where neither firm wants to move.

Multistep Problem0/4 · +20 XP

Two firms compete in quantities. Market demand is $P = 90 - Q$ where $Q = Q_{1} + Q_{2}$ . Each firm has $M C = 0$ . Walk through the Cournot Nash equilibrium step by step.

Find Firm 1's reaction function. Firm 1's profit is $π_{1} = (90 - Q_{1} - Q_{2}) Q_{1}$ . Taking $d π_{1} / d Q_{1}$ and setting it to zero gives a reaction function of the form $Q_{1} = a - Q_{2} /2$ . Enter the value of $a$ (the intercept — the quantity Firm 1 produces when $Q_{2} = 0$ ).

Solve for the equilibrium quantity. The firms are identical, so by symmetry $Q_{1} = Q_{2} = Q^{*}$ in equilibrium. Substitute this into the reaction function $Q_{1} = 45 - Q_{2} /2$ and solve. What is $Q^{*}$ ?

Find the market price. With $Q_{1} = Q_{2} = 30$ , total industry output is $Q = 60$ . Plug this into the demand curve $P = 90 - Q$ to find the price.

Find each firm's profit. Use $π_{i} = (P - M C) \cdot Q_{i}$ with $P = 30$ , $M C = 0$ , and $Q_{i} = 30$ .

Check yourself · no marks

What happens to the Cournot equilibrium as the number of firms increases?

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Practice · 1 / 4

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The Cournot model:

In the Cournot model, firms compete by simultaneously choosing:

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