Skip to content
Marlbridge

AP® Microeconomics · Unit 4 · Topic 4.2

Monopoly: Study Guide (Microeconomics 4.2)

Learn how a monopoly chooses output where MR = MC, reads its price from demand, and how to calculate its profit, consumer surplus, producer surplus and deadweight loss, including natural monopoly.

What a monopoly is

A monopoly is a market with one seller of a product that has no close substitutes. The firm is the industry, so the demand curve it faces is the market demand curve. It is a price maker: it chooses a price (or a quantity), but it cannot escape the demand curve. A higher price always means fewer sales.

A monopoly exists only because of barriers to entry (Topic 4.1). If entry were free, its profit would attract rivals and the monopoly would disappear. The usual barriers are:

  • legal barriers: a patent, copyright or government licence (sometimes called a licence or patent monopoly);
  • exclusive control of a key resource;
  • economies of scale so large that one firm can supply the whole market more cheaply than any group of smaller firms (a natural monopoly, covered below).

How a monopoly chooses its output

A monopoly follows the same rule as every profit-maximising firm: keep producing while an extra unit adds more to revenue than to cost.

  1. Find the quantity where MR = MC. If MR > MC, one more unit raises profit; if MR < MC, it lowers profit. With a table, choose the last unit for which MR ≥ MC.
  2. Find the price on the demand curve directly above that quantity. This is the highest price buyers will pay for that amount. Do not read the price from the MR or MC curve.
  3. Compare price with ATC at that quantity. Profit = (P − ATC) × Q. If P < ATC, the monopoly makes a loss; in the short run it still produces if P ≥ AVC, as in Topic 3.6.

Because MR is below price, the quantity where MR = MC always has P > MC. The gap between price and marginal cost is the sign of market power, and it is why monopoly output is inefficient.

Two more facts help in exams:

  • Revenue-maximising quantity: where MR = 0 (the top of the total revenue curve). A profit-maximiser stops earlier, because MC is positive.
  • Elastic range: since MC > 0, MR must be positive at the monopoly’s quantity. From Topic 2.3, positive MR means demand is elastic. A monopoly that maximises profit never produces on the inelastic part of its demand curve.

Reading a monopoly graph

Voltaris Labs: a monopoly with profit, consumer surplus and deadweight loss Graph with quantity in thousand batteries per month on the horizontal axis from 0 to 80 and price and cost in dollars on the vertical axis from 0 to 80. A straight demand line D falls from 80 dollars at zero to zero at 80 thousand. A straight marginal revenue line MR starts at 80 dollars and reaches zero at 40 thousand. An upward-sloping marginal cost line MC starts at 5 dollars and rises. A U-shaped average total cost curve ATC has its lowest point of about 31 dollars near 52 thousand. MR meets MC at 30 thousand batteries and 20 dollars. Directly above, demand gives the monopoly price of 50 dollars, and ATC is 35 dollars. The rectangle from 0 to 30 thousand between 35 and 50 dollars is hatched and labelled profit. The triangle above the 50 dollar price and below demand, from 0 to 30 thousand, is labelled consumer surplus. A dotted triangle between demand and MC from 30 thousand to 50 thousand, with its point at 50 thousand and 30 dollars where demand meets MC, is labelled deadweight loss. 0 30 50 80 0 20 30 35 50 80 Quantity (thousand batteries per month) Price and cost ($ per battery) CS Profit DWL (dotted) D MR MC ATC monopoly point
Figure 1. Voltaris Labs. MR = MC at 30 thousand batteries; the price, $50, is read from demand above that quantity. Hatched rectangle: profit. Plain shaded triangle: consumer surplus (CS). Dotted triangle: deadweight loss (DWL), the value lost because output is 30 rather than 50 thousand. Solid lines: D and MC; dashed line: MR; dotted curve: ATC.

Every monopoly graph shows the same features. Learn to draw them in this order:

  1. Demand (D) sloping down, and MR below it with the same price intercept.
  2. MC, rising (or flat for constant cost), and ATC, U-shaped with MC through its lowest point.
  3. Quantity Qm where MR = MC; price Pm on D above Qm.
  4. ATC at Qm. If Pm > ATC, the rectangle between them is profit; if Pm < ATC, it is a loss.
  5. The socially efficient quantity where D meets MC (P = MC). The triangle between D and MC from Qm to that quantity is the deadweight loss.

Monopoly compared with perfect competition

If the same market were perfectly competitive, the MC curve would be the market supply curve, and output would be where demand meets MC.

Outcome Perfect competition Monopoly
Price lower: P = MC higher: P > MC
Quantity higher lower
Consumer surplus larger smaller: part becomes the monopoly’s surplus, part is lost
Producer surplus smaller larger
Deadweight loss none yes
Long-run economic profit zero can be positive (barriers block entry)
Allocative efficiency (P = MC) yes no
Productive efficiency (output at minimum ATC) yes, in the long run usually no

Because the price signal is above marginal cost, buyers and seller stop trading before all the mutually beneficial trades have happened. This is why prices in a monopoly cannot be relied on to coordinate everyone in the market efficiently.

Natural monopoly

A natural monopoly exists when long-run economies of scale continue over the whole range of market demand. The long-run ATC curve is still falling where it meets demand, so one firm can produce any quantity the market wants more cheaply than two or more firms sharing it. Water pipes, electricity grids and railway tracks are typical cases: the network costs a huge amount, and each extra customer costs little.

On the graph, the difference from a licence or patent monopoly is the cost curves:

  • ATC slopes down across the whole demand curve;
  • MC lies below ATC across the whole demand curve (an average falls when the marginal value is below it).

The profit-maximising rule is unchanged: MR = MC, price from demand.

Brenmouth Water: a natural monopoly Graph with quantity of water in million cubic metres per year on the horizontal axis from 0 to 350 and price and cost in dollars per cubic metre on the vertical axis from 0 to 16. A straight demand line D falls from 14 dollars at zero to zero at 350. A dashed MR line starts at 14 dollars and reaches zero at 175. Marginal cost is a horizontal line at 2 dollars. The long-run average total cost curve falls steadily from 14 dollars at 50 million cubic metres to about 3.7 dollars at 350 and stays above MC throughout. MR meets MC at 150 million cubic metres, where demand gives a price of 8 dollars and average cost is 6 dollars; the hatched rectangle between 6 and 8 dollars from 0 to 150 is profit. At 300 million cubic metres, demand meets MC at 2 dollars, but average cost there is 4 dollars, so pricing at marginal cost would mean a loss. 0 150 300 350 0 2 4 6 8 14 Quantity (million cubic metres per year) Price and cost ($ per cubic metre) monopoly: P = $8 Profit ATC = $4 at 300 D MR MC LRATC
Figure 2. Brenmouth Water. Long-run ATC (dotted curve) is still falling where it meets demand, so one firm is the cheapest way to supply the market. The firm chooses 150 million cubic metres, where MR = MC, and charges $8 (hatched rectangle: profit). At the efficient quantity of 300, where demand meets MC, price ($2) would be below ATC ($4).

Worked example 1: Sorrel Diagnostics’ patented test kit

Question. Sorrel Diagnostics (fictional) holds a patent on a home test kit. Quantity is in thousand kits per month; price, MR and MC are in $ per kit; revenue and cost are in $ thousand per month. Fixed cost is $50 thousand per month.

Q 1 2 3 4 5 6
Price 90 80 70 60 50 40
MC 10 15 20 25 40 55

(a) Find TR and MR, and the profit-maximising quantity and price. (b) Calculate the maximum profit. (c) Find the revenue-maximising quantity. (d) Find the allocatively efficient quantity and the deadweight loss.

(a) TR = P × Q; MR = change in TR.

Q 1 2 3 4 5 6
TR 90 160 210 240 250 240
MR 90 70 50 30 10 −10
MC 10 15 20 25 40 55

MR ≥ MC up to the 4th thousand kits (30 > 25). For the 5th, MR = 10 < MC = 40. So Q = 4 thousand kits and, from the demand row, P = $60. Note P ($60) > MC ($25).

(b) TC at Q = 4 is fixed cost + all the marginal costs: 50 + 10 + 15 + 20 + 25 = 120. Profit = TR − TC = 240 − 120 = $120 thousand per month. Check with averages: ATC = 120 ÷ 4 = $30, so profit = (60 − 30) × 4 = 120. Profit at Q = 3 is 210 − 95 = 115 and at Q = 5 is 250 − 160 = 90, both lower.

(c) TR is largest ($250 thousand) at Q = 5, where MR is last positive. Sorrel produces less than this because the 5th thousand kits adds more to cost (40) than to revenue (10).

(d) Efficiency needs every unit for which price ≥ MC. The 5th thousand kits is worth $50 to buyers and costs $40; the 6th is worth $40 but costs $55. So the efficient quantity is 5 thousand kits. Deadweight loss = value lost on the 5th thousand kits = (50 − 40) × 1 thousand = $10 thousand per month.

Worked example 2: areas on Voltaris Labs’ graph

Question. Voltaris Labs (fictional) holds a patent on a fast-charging battery. Its demand is P = 80 − Q, so MR = 80 − 2Q, and MC = 5 + 0.5Q (Q in thousand batteries per month, P in $). At its chosen output, ATC = $35. Use Figure 1. (a) Find Qm and Pm. (b) Calculate profit, consumer surplus and producer surplus. (c) Find the competitive outcome and the deadweight loss.

(a) MR = MC: 80 − 2Q = 5 + 0.5Q, so 75 = 2.5Q and Qm = 30. Price from demand: P = 80 − 30 = $50. MC at 30 is 5 + 15 = $20, so P > MC.

(b) All values in $ thousand per month:

  • Profit = (P − ATC) × Q = (50 − 35) × 30 = 450.
  • Consumer surplus = triangle under D above Pm = ½ × (80 − 50) × 30 = 450.
  • Producer surplus = area above MC and below Pm from 0 to 30. MC runs from $5 to $20, so it is a trapezium (trapezoid): ½ × [(50 − 5) + (50 − 20)] × 30 = 1,125.

Producer surplus is larger than profit because it ignores fixed cost. Here fixed cost is 1,125 − 450 = 675.

(c) Competitive outcome: D = MC, so 80 − Q = 5 + 0.5Q, giving Q = 50 and P = $30.

Deadweight loss = triangle between D and MC from 30 to 50 = ½ × (50 − 20) × (50 − 30) = 300.

Check. Under competition, CS = ½ × 50 × 50 = 1,250 and PS = ½ × (30 − 5) × 50 = 625: total surplus 1,875. Under monopoly, total surplus is 450 + 1,125 = 1,575. The difference, 300, is the deadweight loss.

Worked example 3: is Brenmouth Water a natural monopoly?

Question. Brenmouth Water’s (fictional) long-run total cost is TC = 600 + 2Q ($ million; Q in million cubic metres per year), and market demand is P = 14 − 0.04Q. Use Figure 2. (a) Show that one firm is cheaper than two at any quantity in the market. (b) Find the unregulated monopoly’s quantity, price and profit. (c) What would happen if the firm had to charge P = MC?

(a) ATC = 600 ÷ Q + 2, which keeps falling as Q rises, and demand reaches zero price at Q = 350. To supply 300 million cubic metres: one firm costs 600 + 2 × 300 = $1,200 million (ATC $4); two firms of 150 each cost 2 × (600 + 300) = $1,800 million (ATC $6). Splitting the market repeats the big fixed cost, so one firm is cheaper: a natural monopoly.

(b) MR = 14 − 0.08Q. MC = 2. MR = MC: 0.08Q = 12, so Q = 150. Price: 14 − 0.04 × 150 = $8. ATC = 600 ÷ 150 + 2 = $6. Profit = (8 − 6) × 150 = $300 million.

(c) P = MC = $2 gives 14 − 0.04Q = 2, so Q = 300. ATC there is $4, so the firm would lose (4 − 2) × 300 = $600 million, which is exactly its fixed cost. No private firm would do this unaided. How governments deal with this belongs to Unit 6.

Common misconceptions

  • “A monopoly produces where MR = MC and charges a price equal to MC.” The price comes from the demand curve above Qm, and it is above MC.
  • “A monopoly charges the highest possible price.” It chooses the price that maximises profit, which is limited by demand.
  • “A monopoly always makes a profit.” If demand is weak or costs are high, P can be below ATC.
  • “A monopoly produces where demand is inelastic.” With positive MC, MR must be positive at Qm, so demand is elastic there.
  • “Deadweight loss is the monopoly’s profit.” Profit is a transfer from buyers to the seller; the deadweight loss is surplus that nobody gets.
  • “Profit and producer surplus are the same.” Producer surplus ignores fixed cost, so it is larger than profit unless fixed cost is zero.
  • “A natural monopoly is any monopoly that occurs naturally.” It means economies of scale across the whole market, not just owning a natural resource.

Where this leads

Next, Topic 4.3, Price Discrimination, shows how a monopoly can charge different buyers different prices and what that does to surplus and deadweight loss. In Unit 6 you will see how price regulation and antitrust policy respond to monopoly. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate.

Quick questions

Does a monopoly charge the highest price it can?

No. A higher price means selling fewer units. The monopoly picks the quantity where MR = MC and charges the highest price buyers will pay for that quantity, which is read from the demand curve.

Can a monopoly make a loss?

Yes, in the short run, if the price at its best quantity is below average total cost. It keeps producing if price covers average variable cost; otherwise it shuts down. With no profit possible in the long run, it leaves the market.

AP® and Advanced Placement® are trademarks registered by the College Board, which is not affiliated with, and does not endorse, this website. Marlbridge is an independent tuition provider. It is not an authorized AP course provider, an AP school or an exam centre, and these resources are not official College Board materials. Reading them or doing simulations does not meet the laboratory requirement of an AP science course.