Monopoly Price, Quantity and Profit Calculator

Problem → model → reason → result

What problem does this model solve?

Solve the profit-maximising price, output and profit for linear demand and constant marginal cost.

Why does the model apply?

A single-price monopolist with linear demand maximises profit where marginal revenue equals marginal cost, provided the resulting price covers relevant costs.

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

Demand P = a − bQ; set MR = a − 2bQ equal to MC; Profit = (P − MC)Q − Fixed cost

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

For P = 100 − 0.1Q, marginal cost of $20 and fixed cost of $5,000, optimal output is 400, price is $60 and operating profit is $11,000.

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.