Cournot Duopoly Nash Equilibrium Calculator
Calculate Nash equilibrium output, market price, and firm profits for a two-firm Cournot duopoly with linear demand and constant marginal costs.
In the Cournot duopoly model, two firms choose quantities simultaneously, each taking the other’s output as given. The inverse demand curve is linear:
P = a - b(Q1 + Q2)
where a is the demand intercept and b is the slope. Each firm i has constant marginal cost c_i.
Nash equilibrium quantities. Each firm maximizes its own profit given the other’s output. Solving the simultaneous best-response functions gives:
Q1* = (a - 2c1 + c2) / (3b) Q2* = (a - 2c2 + c1) / (3b)
Market price. P* = a - b(Q1* + Q2*)
Profits. pi_i = (P* - c_i) * Qi*
Comparing market structures:
- Perfect competition: P = min(c1, c2), zero profit
- Cournot duopoly: intermediate price and quantity, positive profit
- Monopoly (if c1 = c2 = c): Q_m = (a - c)/(2b), P_m = (a + c)/2
Cournot sits between these extremes. As the number of firms grows, Cournot equilibrium approaches the competitive outcome — this is the Cournot convergence result.
Interpretation. If one firm has lower cost, it produces more and earns higher profit, but both firms earn positive economic profit in equilibrium. A firm with sufficiently high cost may find its Nash equilibrium quantity is negative — in that case, it exits the market and the remaining firm acts as a monopolist.
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