Microeconomics
Monopoly Price, Quantity and Profit Calculator
Solve the profit-maximising price, output and profit for linear demand and constant marginal cost.
Inputs and results stay in this browser. Currency symbols are illustrative; use any consistent currency.
Positive economic profit in this model
Understand Monopoly analysis
One idea, three depths
Choose how deeply to explain Monopoly analysis
Monopoly analysis: Solve the profit-maximising price, output and profit for linear demand and constant marginal cost.
Age 5Explain it to a 5-year-oldStart with a picture
Imagine using Monopoly analysis to answer this question: solve the profit-maximising price, output and profit for linear demand and constant marginal cost? Enter Demand price intercept (a), Demand slope (b), Constant marginal cost, and 1 other input; the calculator shows Profit-maximising quantity. For 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. The answer tells you Profit-maximising quantity.
Age 15Explain it to a 15-year-oldConnect it to the formula
A single-price monopolist with linear demand maximises profit where marginal revenue equals marginal cost, provided the resulting price covers relevant costs. The rule is Demand P = a − bQ; set MR = a − 2bQ equal to MC; Profit = (P − MC)Q − Fixed cost. Its input values are Demand price intercept (a), Demand slope (b), Constant marginal cost, Fixed cost, and the main result is Profit-maximising quantity. For 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.
CollegeExplain it at college levelState the model precisely
This calculator evaluates a microeconomics relationship while holding unmodelled conditions constant. The implemented relation is Demand P = a − bQ; set MR = a − 2bQ equal to MC; Profit = (P − MC)Q − Fixed cost, evaluated from Demand price intercept (a), Demand slope (b), Constant marginal cost, Fixed cost to produce Profit-maximising quantity. A single-price monopolist with linear demand maximises profit where marginal revenue equals marginal cost, provided the resulting price covers relevant costs. The result depends on comparable definitions, units, populations and time periods. It estimates a relationship; it does not establish causation or replace current primary data.
The economic question
Solve the profit-maximising price, output and profit for linear demand and constant marginal cost.
Why this relationship is useful
A single-price monopolist with linear demand maximises profit where marginal revenue equals marginal cost, provided the resulting price covers relevant costs.
Inputs that must be comparable
- Demand price intercept (a) (minimum 0).
- Demand slope (b) (minimum 0).
- Constant marginal cost (minimum 0).
- Fixed cost (minimum 0).
Use one market, firm, population and time period throughout; mixing definitions can make a correctly calculated number economically meaningless.
The model
Demand P = a − bQ; set MR = a − 2bQ equal to MC; Profit = (P − MC)Q − Fixed cost
From inputs to output
The calculator combines Demand price intercept (a), Demand slope (b), Constant marginal cost, Fixed cost and reportsProfit-maximising quantity together with Monopoly price, Operating profit, Competitive benchmark quantity. Change one assumption at a time to identify what actually drives the estimate.
How to read Profit-maximising quantity
Read the sign, magnitude, unit and period together. The result quantifies the relationship in “solve the profit-maximising price, output and profit for linear demand and constant marginal cost”; it does not by itself prove that one input caused another.
A worked economic 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.
Where interpretation can fail
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.
Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations
Standards, reading and academic references
Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.
Principles of Economics 3e
Read the free OpenStax economics textbookCite this book
- APA 7
- Greenlaw, S. A., Shapiro, D., & MacDonald, D. (2022). Principles of economics 3e. OpenStax. https://openstax.org/books/principles-economics-3e/pages/1-introduction
- MLA 9
- Greenlaw, Steven A., et al. Principles of Economics 3e. OpenStax, 2022, https://openstax.org/books/principles-economics-3e/pages/1-introduction.
- Chicago author-date
- Greenlaw, Steven A., David Shapiro, and Daniel MacDonald. 2022. Principles of Economics 3e. Houston, TX: OpenStax. https://openstax.org/books/principles-economics-3e/pages/1-introduction.
OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.
Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS
These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.
APA 7
MW SysArc. (2026, July 21). Monopoly Price, Quantity and Profit Calculator. MW SysArc Tools. https://economics.mwsysarc.com/micro/monopoly-price-quantity-profit
MLA 9
MW SysArc. “Monopoly Price, Quantity and Profit Calculator.” MW SysArc Tools, 21 July 2026, https://economics.mwsysarc.com/micro/monopoly-price-quantity-profit. Accessed 31 Aug. 2026.
Chicago 17
MW SysArc. “Monopoly Price, Quantity and Profit Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://economics.mwsysarc.com/micro/monopoly-price-quantity-profit.
Harvard
MW SysArc (2026) ‘Monopoly Price, Quantity and Profit Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://economics.mwsysarc.com/micro/monopoly-price-quantity-profit (Accessed: 31 August 2026).
BibTeX and RIS records
BibTeX
@misc{mwsysarc_monopoly_analysis_2026,
author = {{MW SysArc}},
title = {Monopoly Price, Quantity and Profit Calculator},
howpublished = {MW SysArc Tools},
year = {2026},
url = {https://economics.mwsysarc.com/micro/monopoly-price-quantity-profit},
note = {Published July 21, 2026; accessed August 31, 2026}
}RIS
TY - ELEC
AU - MW SysArc
TI - Monopoly Price, Quantity and Profit Calculator
T2 - MW SysArc Tools
PY - 2026
DA - 2026-07-21
Y2 - 2026-08-31
UR - https://economics.mwsysarc.com/micro/monopoly-price-quantity-profit
N1 - Published July 21, 2026
ER -Clear answers
Frequently asked questions
What does the Monopoly analysis do?
Solve the profit-maximising price, output and profit for linear demand and constant marginal cost.
How does the Monopoly analysis work?
The calculator applies this formula: Demand P = a − bQ; set MR = a − 2bQ equal to MC; Profit = (P − MC)Q − Fixed cost. A single-price monopolist with linear demand maximises profit where marginal revenue equals marginal cost, provided the resulting price covers relevant costs.
What can I learn from the Monopoly analysis?
It helps you explore the relationship described by this tool: Solve the profit-maximising price, output and profit for linear demand and constant marginal cost. Change one input at a time to observe how it affects the result.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the result as an estimate or educational aid. Check important financial, business or policy decisions with qualified sources and current data.
Last reviewed . Calculations tested .