Cournot Duopoly Calculator

Problem → model → reason → result

What problem does this model solve?

Solve quantities, market price and operating profits for two Cournot competitors with linear demand and constant marginal costs.

Why does the model apply?

Each firm chooses quantity while treating its rival's quantity as fixed. The closed-form solution assumes simultaneous choice, homogeneous output and no capacity constraints.

What assumptions does it make?

The variables must describe the same market, firm, period or decision context and use consistent units. Any behavioural condition implied by the formula—such as other factors remaining unchanged—must be reasonable for the question being asked.

Formula

For P = a − b(q1 + q2): q1 = (a − 2c1 + c2) ÷ 3b and q2 = (a − 2c2 + c1) ÷ 3b

Calculation and working

The calculator substitutes your inputs locally and displays the numerical result. Change one input at a time to test which relationship drives the result.

What does the result mean?

Interpret the result in the economic context named above, including its sign, magnitude, units and time period. A calculated relationship is not by itself evidence that one variable caused another.

Worked example

With P = 100 − Q, firm costs $10 and $20, equilibrium quantities are 33.33 and 23.33, price is $43.33, and profits are about $1,111.11 and $544.44.

When does this model not apply?

Do not use the result when the input definitions, units or formula assumptions do not match the real situation. This is an educational model, not financial, investment, tax or policy advice; verify material decisions against primary data and professional guidance.