Single-Price Monopoly: Output, Profit and Deadweight Loss
A single-price monopoly can leave valuable trades unmade even while earning profit. Compare the profit-maximizing quantity with the efficient-output benchmark, separate profit from deadweight loss, and try three original interactive questions.
The efficient units between the monopoly quantity and the efficient quantity are not sold.
Check Two Output Comparisons
Use the standard static comparison: one uniform price, downward-sloping demand, the same aggregate cost curve, no externalities and a feasible interior profit maximum. Hold those assumptions fixed for the two cases below. They do not establish that every large firm, patent holder or cost-saving merger reduces welfare.
Relative to the efficient output, a single-price monopoly stops production where
- marginal benefit is below marginal cost
- marginal benefit still exceeds marginal cost
- price equals marginal cost
- consumer surplus is maximized
- average total cost is minimized
marginal benefit still exceeds marginal cost The monopoly quantity is below the P=MC quantity, so excluded units have willingness to pay above marginal cost.
Compared with a competitive market with the same demand and cost, a single-price monopoly generally produces
- less output at a higher price
- more output at a lower price
- the efficient output at a higher price
- the same output at the same price
- less output at a lower price
less output at a higher price Because monopoly chooses where MR=MC rather than P=MC, it restricts output and raises price relative to competition.
Video Lesson: Monopoly and Efficiency
A focused video lesson from Economics in Many Lessons.
Compare Marginal Revenue and Benefit
Efficient output equates demand’s marginal benefit with marginal cost. A single-price seller also considers the price reduction on earlier units when it expands sales, so marginal revenue is below price. In the standard model, its profit-maximizing output leaves some units with benefit above cost unmade. Their unrealized gains are deadweight loss; the seller’s profit is a different measure.
Find the Two Quantities
Compare two intersections on the same graph. Q_m comes from MR and MC at the feasible interior profit maximum. Q_e comes from demand and MC because efficiency compares marginal benefit with marginal cost. For the downward-sloping demand and increasing MC used below, Q_m<Q_e. Check the model’s shape and boundary conditions rather than relying on the vague phrase “ordinary MC.”
Locate the Missing Beneficial Trades
At units between Q_m and Q_e, demand lies above MC. Buyers value each unit more than the resources needed to produce it, but the single-price policy withholds it. The area between demand and MC over that interval is deadweight loss. It is not the entire monopoly profit rectangle.
Read the Diagram’s Four Measures
| Benchmark | Equality | Meaning |
|---|---|---|
| Monopoly quantity | MR=MC |
Interior profit choice under the stated model and feasibility checks |
| Efficient quantity | P=MB=MC |
Efficient output absent externalities and other distortions |
| Monopoly markup | P_m-MC |
Price above marginal cost at Q_m |
| Deadweight loss | Area for Q_m to Q_e |
Unrealized gains from trade |
Keep the Efficiency Tests Separate
Monopoly pricing does not force output to occur at minimum average total cost. But it does not rule that coincidence out either, as the example below shows. Also distinguish the minimum-ATC output benchmark from using the least-cost method to produce a given quantity; monopoly status alone does not prove avoidable input waste.
The allocative test asks whether more beneficial trades remain. In this model, P>MC, specifically P_m>MC at monopoly output, means that expanding output would create gains. Zero economic profit would not repair this markup. Profit and efficiency are different measures.
Separate a Transfer from a Lost Trade
Suppose a comparison reports competitive output of 100 units at $10 and monopoly output of 70 at $16. That is 30 fewer units and a $6 higher price on the 70 still sold: $420 of extra payments on those retained trades. That transfer is not automatically the change in total profit, since costs and quantity differ. Measuring deadweight loss on the 30 missing units requires the demand and MC paths; these four numbers alone do not give its area.
State the Wider Policy Tradeoffs
A patent can create static output restriction while encouraging research by allowing a temporary return. A natural monopoly can use one network at lower cost than duplicated networks. These considerations can affect policy, but they do not change how the standard single-price graph is read. Answer the model stated, then note broader tradeoffs only when asked.
Check Whether the Cost Curve Changed
A lower cost curve can change the market-structure comparison: a cost-saving monopolist may produce more, charge less or create more total surplus than a higher-cost alternative while P>MC still holds. The standard common-cost graph isolates pricing power; it does not settle every institutional comparison.
Shade Profit and Deadweight Loss Separately
On a diagram, shade profit and deadweight loss separately. Profit uses the gap between price and ATC across Q_m. Deadweight loss uses the gap between demand and MC from Q_m to Q_e. Different boundaries answer different questions.
When a question changes technology, entry or innovation incentives, identify those changes before transferring the static result to the new setting. If it holds cost and demand fixed, compare the marginal conditions and lost-trade area within that stated model.
Within the stated graph, however, the test is exact: if demand lies above MC for missing units, total surplus can rise by expanding. The monopolist does not expand because the price-cut effect makes MR lower than those buyers’ willingness to pay.
Read the Revenue and Cost Definitions
OpenStax’s monopoly output lesson explains the marginal-revenue choice. Its short-run cost lesson distinguishes total, variable, fixed, average and marginal costs. The following model and questions are original examples, not copied textbook exercises.
Calculate Output, Profit and Lost Gains
For a separate fictional example, use inverse demand P = 42 − Q and total economic cost TC = 98 + 0.5Q². Fixed cost is $98, variable cost is 0.5Q², and marginal cost is Q. Quantity is continuous; amounts are dollars. Compare outputs with the same costs, no externalities and the firm operating. The efficient-output price is a static benchmark, not a prediction about long-run entry.
Marginal revenue is MR = 42 − 2Q. Equating it to MC = Q gives monopoly quantity Q = 14 and price P = $28. Revenue is $392. Variable cost is $98, so producer surplus is $294. Total cost includes another $98 of fixed cost, making economic profit $196. Consumer surplus is ½ × 14 × ($42 − $28) = $98.
Efficient output equates demand and MC: 42 − Q = Q, giving Q = 21 and P = $21. At this benchmark, consumer surplus is ½ × 21 × ($42 − $21) = $220.50. Revenue of $441 minus variable cost of $220.50 leaves producer surplus of $220.50. Consumer plus producer surplus is $441, compared with $392 at monopoly output. Subtract the same fixed $98 once from either total if measuring net benefit after fixed cost; the difference is still $49.
The seven missing units run from Q = 14 to Q = 21. At Q = 14, their marginal-benefit-minus-cost gap is $28 − $14 = $14, shrinking linearly to zero at Q = 21. Deadweight loss is therefore ½ × 7 × $14 = $49. It is neither the $196 profit nor the $294 producer surplus.
Can Minimum ATC Coincide with Monopoly Output?
Here ATC = 98/Q + 0.5Q. Check its value at Q = 14, and decide whether reaching minimum ATC also eliminates the markup over marginal cost.
Check your reasoning
ATC at Q = 14 is $98/14 + $7 = $14. It is the minimum for positive Q: ATC − 14 = (Q − 14)²/(2Q), which is never negative. The seller happens to choose its minimum-ATC output in this model.
Yet its $28 price is still above $14 marginal cost at Q = 14, and output is below the efficient quantity of 21. The $49 lost-trade area remains. This coincidence is a counterexample to the claim that every monopoly must miss minimum ATC; it does not make monopoly pricing allocatively efficient.
Finally, profit requires the full cost calculation: $392 revenue minus $98 variable cost minus $98 fixed cost equals $196. Keeping profit, producer surplus and deadweight loss separate prevents three different areas from being treated as the same number.
Try Three Monopoly Questions
Choose one answer, then check your reasoning. These are short learning checks, not an exam score. If the controls are unavailable, the explanations remain readable below each question.
Answer D. Set 42 − 2Q = Q to obtain Q = 14. The demand curve then gives P = 42 − 14 = $28. The efficient-output comparison uses demand = MC and gives Q = 21, a different test.
Answer A. The lost gains form a triangle with quantity base 7 and per-unit value gap 14. Its area is $49. Profit, producer surplus and quantity are different measurements and cannot replace that area.
Answer C. Producer surplus is revenue minus variable cost: $392 − $98 = $294. Economic profit subtracts fixed cost as well: $294 − $98 = $196. The independently computed deadweight loss is $49, not the seller’s profit.
Connect Output, Surplus and Pricing
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