Why Monopoly Has No Supply Curve: Demand and Cost
A monopoly has no independent supply curve because its output choice depends on demand as well as cost. The same marginal-cost curve can support different quantities at the same selling price when demand changes. Compare three calculated examples, distinguish fixed fees from per-unit taxes, and try three original interactive questions.
Quantity depends on both demand and cost.
Review Three Monopoly Decisions
The examples concern a single-price, profit-maximizing seller facing downward-sloping demand. For an interior continuous optimum, compare MR with MC and then read price from demand; also check boundaries and whether operating is worthwhile. A fixed fee leaves the operating output unchanged only while the firm remains in the market and other conditions stay fixed.
A monopoly has no independent supply curve because
- it never changes output when cost conditions change
- it always produces at minimum average total cost
- its price is fixed independently by government
- its marginal cost cannot be measured
- price-output choices depend jointly on demand and cost
price-output choices depend jointly on demand and cost A monopolist’s output at a given price cannot be inferred from marginal cost alone. Demand and marginal revenue also matter.
Why does marginal revenue lie below demand for a single-price monopolist?
- A price cut on the extra unit also lowers revenue on earlier units.
- Marginal cost rises each time the firm expands output.
- Fixed cost is excluded when marginal revenue is calculated.
- Demand becomes perfectly inelastic once price is chosen.
- The monopolist cannot choose both a price and an output.
A price cut on the extra unit also lowers revenue on earlier units. The added unit brings in its price but the necessary price cut reduces revenue on units that would otherwise sell at the higher price.
A monopolist faces a fixed annual license fee. If the fee rises but marginal cost and demand do not change, the profit-maximizing
- quantity rises while price falls
- quantity and price both remain unchanged
- quantity falls while price rises
- price rises while quantity remains unchanged
- price falls while quantity remains unchanged
quantity and price both remain unchanged Conditional on continued operation, a fixed fee changes total profit but not marginal cost, so it does not change the optimizing quantity or the price read from demand. An avoidable renewal fee can instead make exit preferable.
Video Lesson: Why Monopoly Has No Supply Curve
A focused video lesson from Dave Anderson.
Compare Monopoly with Price Taking
For a price-taking firm, the usual short-run supply curve follows the rising portion of MC above the shutdown price, subject to the model’s cost assumptions. A monopolist faces a downward-sloping demand curve: its price is part of its own choice, not an independently given market price. MC still matters, but MC alone does not provide its supply curve.
At a given market price, a competitive firm compares that price with MC, then checks shutdown. For monopoly, changing demand also changes MR. The same cost curve can accompany different quantities at the same price across demand conditions. That is a direct counterexample to a quantity supplied determined by price and cost alone. It does not mean the monopolist can ignore demand or choose price and sales independently.
Specify How Demand Changes
If demand and MR both move outward under the usual single-crossing assumptions, unchanged MC can meet the new MR at a larger output. Read the resulting price from the new demand curve; do not infer it from quantity alone. A general statement that demand is “stronger” needs a specified change in its level and slope. The numerical comparisons below make those changes explicit.
Check the Elastic-Demand Result
For a positive-price, interior choice on smooth downward-sloping demand, a monopolist with nonnegative MC does not maximize profit on a strictly inelastic segment. Reducing quantity there raises total revenue while weakly reducing variable cost. Demand is elastic at an interior optimum with positive MC; with zero MC, a unit-elastic revenue maximum can be relevant.
Using the positive magnitude e of demand elasticity, MR = P(1 − 1/e). At an interior optimum with positive MC, MR is positive, which requires e greater than one. This conclusion assumes the seller can adjust output along that demand curve; it is not an unconditional rule for indivisible choices, capacity boundaries or regulated prices.
Separate Operating Choice from Participation
A demand change requires a new profit comparison using its new MR. A fixed-cost increase raises ATC at each positive output and lowers profit, but leaves the best operating quantity and price unchanged when MC and demand remain fixed. Whether the fixed payment is unavoidable or can be escaped by leaving the market matters for participation.
Identify Which Cost Changes
A lower variable input price can lower MC. With unchanged demand and a stable interior solution where MR crosses MC from above, this can increase output and lower price; a discrete schedule may keep the same row. A lump-sum subsidy does not change MC if it is independent of output, while a per-unit subsidy lowers effective marginal cost. Classify the payment and participation conditions before predicting the choice.
Read the Conditional Cost Comparisons
| Change | Quantity-price step | Profit effect |
|---|---|---|
| Fixed cost rises | Q and P unchanged |
Profit falls |
| Marginal cost rises | Under the stated interior assumptions, new MR-MC at lower Q. Read higher P |
Profit generally falls |
| Demand shifts | Both demand and MR change | Recompute. No fixed supply response |
| Lump-sum tax | MC unchanged | Profit falls by tax |
| Per-unit tax | MC rises | Recompute quantity and price; a discrete choice may stay unchanged |
Describe the Cost Shift Precisely
Do not say “monopoly supply shifts left” when MC rises. The cost curve shifts, but monopoly choice is still determined jointly with demand. Reserve supply-curve language for a valid price-quantity relationship.
The absence of a supply curve does not mean the monopolist ignores cost. MC remains essential in MR=MC. It means cost alone cannot pair an externally given price with a unique quantity because the monopolist selects a price-output combination jointly with demand.
Use the Stronger Same-Price Test
The same quantity at different prices also shows that demand matters, but that observation alone does not rule out a supply function: a perfectly inelastic competitive supply curve can be vertical. The stronger test here holds cost and selling price fixed and obtains different optimal quantities after changing demand. Compare cases A and B below.
Read the Demand and Cost Explanation
OpenStax’s monopoly lesson explains the quantity-first, price-from-demand method. Kansas State’s monopoly chapter, especially sections 3.3–3.4, discusses elasticity, taxes and why demand matters to the output decision. The calculations below are original examples, with a direct same-price comparison rather than relying on an informal one-to-one definition of a function.
Hold Cost Fixed and Change Demand
Suppose continuous output Q is nonnegative, total cost is TC = Q² + $90, and MC = 2Q. The $90 is unavoidable over this operating period. In each separate demand case, restrict output to prices at or above zero. Set MR = MC and read price from the stated demand curve:
| Case and demand | MR | Best Q | Price | Profit |
|---|---|---|---|---|
| A: P = 60 − Q | 60 − 2Q | 15 | $45 | $360 |
| B: P = 54 − 0.5Q | 54 − Q | 18 | $45 | $396 |
| C: P = 90 − 2Q | 90 − 4Q | 15 | $60 | $585 |
For A, 60 − 2Q = 2Q gives Q = 15, so P = 60 − 15 = $45. Revenue is $675 and total cost is $315, leaving $360 profit. For B, 54 − Q = 2Q gives Q = 18, P = $45, and profit $810 − $414 = $396. The same price and cost curve produce different quantities because the demand slope and MR differ. A price of $45 alone therefore cannot identify the monopolist’s chosen output.
Cases A and C keep Q = 15 while price changes from $45 to $60. This is another illustration of demand dependence, but the A–B comparison is the direct contradiction to a demand-independent quantity supplied at a given price. These cases change the whole demand schedule; they are not movements along a single demand curve.
Try a Fee and a Per-Unit Tax
Keep case A’s demand and variable cost. First, raise the fixed cost from $90 to $390, leaving it unavoidable during the operating period. Then, in a separate comparison with fixed cost back at $90, impose a $12 tax on every unit sold. Which change affects the best operating quantity?
Check your reasoning
The larger fixed cost leaves MR and MC unchanged. Q stays 15 and P stays $45; profit falls from $360 to $60. If a $500 fixed fee instead must be paid only when renewing permission to operate, the best operating profit is $450 − $500 = −$50. With exit worth $0 and no other consequences, the firm declines to renew. Unchanged marginal incentives do not guarantee continued participation.
For the separate $12 per-unit tax, effective MC is 2Q + 12. Solve 60 − 2Q = 2Q + 12 to get Q = 12 and P = $48. Profit after the tax is $576 − $144 variable cost − $90 fixed cost − $144 tax = $198. Here price rises by $3, not by the full $12 tax. This pass-through result belongs to these demand and cost equations; it is not a universal monopoly tax fraction.
Each reported operating choice is a global maximum over its feasible demand range: profits in A, B and C equal their stated maximum minus 2(Q − 15)², 1.5(Q − 18)² and 3(Q − 15)², respectively. With the tax, profit is $198 − 2(Q − 12)². These strictly concave expressions also rule out a second, more profitable interior choice in the examples.
Try Three Monopoly Supply 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 C. Set marginal revenue 60 − 2Q equal to marginal cost 2Q: Q = 15. Return to demand for P = 60 − 15 = $45. At this output MR and MC are $30, which is not the selling price.
Answer A. The cost curve and observed selling price are the same, yet optimal quantities differ because demand and MR differ. A demand-independent quantity supplied cannot be inferred from this price and cost alone.
Answer D. Among operating choices, fixed fees leave Q = 15 and P = $45 unchanged. But the best operating profit is $450 − $500 = −$50. Because the fee can be avoided and exit is worth zero, exit wins. Distinguish participation from conditional output choice.
Connect Demand, Output and Costs
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