Monopoly Profit Maximization
Imagine you are the only seller in the market — a monopolist. You can pick any price you want. But you face a constraint: the higher you set the price, the fewer units customers buy. That trade-off is captured by the demand curve.
So where do you stop? Two ideas settle it. Marginal costis what it costs to make one more unit — the extra cost of the next bottle, kilowatt-hour, or app license. Marginal revenue is the extra money you get from selling that one more unit. The rule is simple: keep producing as long as the next unit brings in more than it costs. Stop when the two are equal. Economists write that condition .
This rule works for any firm. What makes a monopolist different is that marginal revenue is less than the price. To sell one more unit, the monopolist has to drop the price on every unit, not just the new one. So the MR curve sits below the demand curve, the firm stops well short of the quantity a competitive market would produce, and consumers pay more than they would under competition.
One tile of the full monopoly unit.
The course teaches monopoly interactively — drag the graphs, practice with feedback, and spaced reviews bring it back before you forget. Free.
Interactive monopoly graph
What you are looking at
- Horizontal axis: quantity — units the firm produces.
- Vertical axis: dollars (price and cost on the same scale).
- Blue solid line (D) — the demand curve. How much customers will pay for each quantity.
- Indigo dashed line (MR) — marginal revenue. Sits below the demand curve because the monopolist must drop price on every unit to sell more.
- Red solid line (MC) — marginal cost. The cost of one more unit.
- Gray dashed line (ATC) — average total cost. Used to measure profit: price minus ATC, times quantity.
- The dot where MR meets MC marks the profit-maximizing quantity, . The monopoly price is read off the demand curve directly above that dot.
What to try
- Toggle Profit to see the rectangle between price and ATC at — total monopoly profit.
- Toggle DWLto see the welfare-loss triangle — trades that disappear because output is restricted.
- Toggle Competitive to overlay the outcome you would see with perfectly competitive firms instead ().
Worked example
Suppose demand is and marginal cost is constant at .
Total revenue:
Marginal revenue: — the slope of $TR$ with respect to $Q$.
Set :
Monopoly price (read off demand at ):
Compare with perfect competition: , so , .
The monopolist deliberately produces half what a competitive industry would. Those missing 40 units are the trades that no longer happen — the basis of the deadweight loss triangle.
Common mistake
“The monopolist sets price by reading off the marginal cost curve at .” No — quantity comes from , but price comes from the demand curve at that quantity. The monopolist charges what consumers are willing to pay, which sits above . The gap between and is the monopoly markup.
Five practice questions
Pick an answer, then click Check answer to see the explanation.
Question 1 of 5
A monopolist faces demand and constant marginal cost . What quantity does it produce, and at what price?
Question 2 of 5
Why is a monopolist's marginal revenue strictly below the price it charges (for every unit after the first)?
Question 3 of 5
Compared to a perfectly competitive market with the same demand and marginal cost, a monopoly will produce:
Question 4 of 5
Which condition describes a profit-maximizing monopolist?
Question 5 of 5
Two monopolists have the same marginal cost. One sells to a market with elastic demand, the other to a market with inelastic demand. Which one charges a higher markup over marginal cost?
What the course adds
Beyond this one page
The monopoly unit walks you through price discrimination, natural monopoly with average-cost pricing, and the Lerner markup formula — with interactive graphs and adaptive practice that catches the misconceptions students keep making.
Spaced reviews
FSRS brings every concept back right before you'd forget. ~50% better retention than re-reading.
Per-concept mastery
Performance Factor Analysis tracks each sub-skill separately — you see which version of the idea is still wobbly.
Diagnostic placement
A short test skips you past what you already know. No re-learning the basics.
For instructors
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Want the full story on monopoly?
The Econ Academy monopoly unit covers price discrimination, natural monopoly, regulation, and the Lerner index — with interactive graphs and spaced reviews.