Natural Monopoly Explained: Graph, Regulation and Deadweight Loss

A natural monopoly is an industry where one firm can supply the entire market at a lower average total cost than two or more firms could, because ATC keeps falling over the whole range of output that buyers demand. Left alone, the firm sets MR = MC and charges a high price, so governments regulate it. The three outcomes to know are the unregulated price (MR = MC), the fair-return price (P = ATC) and the socially optimal price (P = MC), which causes a loss that needs a subsidy.

Water systems, electricity distribution, natural gas pipelines and local sewer networks are the usual examples. Each needs an enormous network before it can serve a single customer, and very little extra cost to serve one more. This guide explains why that makes ATC fall, works through all three pricing outcomes with one set of numbers, compares the deadweight loss in each, and covers how AP Micro topics 4.2 and 6.4 test it. For monopoly in general, start with the monopoly guide.

Why ATC falls over the relevant range

Average total cost is average fixed cost plus average variable cost: ATC = AFC + AVC. A natural monopoly has two cost features that push ATC down at every output the market buys.

Huge fixed costs. Pipes, wires, treatment plants and rights of way must be built before the first customer is served, and once built they cost the same whether the network carries a little water or a lot. Spreading that fixed cost over more units makes AFC fall steadily.

Low and roughly constant marginal cost. Once the pipes are in the ground, delivering another gallon of water costs very little. AVC and MC stay low and flat.

Put those together and ATC slopes downward across the whole demand curve. This is a case of economies of scale that never run out before the market does. In the language of cost curves, the market demand curve crosses ATC before ATC reaches its minimum. The natural monopoly vs minimum efficient scale comparison explains why the size of the market relative to that minimum decides how many firms an industry can support.

One more fact follows from the marginal-average rule. Whenever an average is falling, the marginal value must be below it. Since ATC falls over the whole relevant range, MC lies below ATC the entire way. That single fact is the reason marginal-cost pricing causes a loss, as the example below shows.

The worked example

A regional water utility faces:

• Market demand: P = 120 - Q, so MR = 120 - 2Q
• Constant marginal cost: MC = $30
• Fixed cost: $1,800
• ATC = 30 + 1,800/Q, which falls at every quantity

Q is thousands of gallons per day and prices are dollars per thousand gallons.

Why one firm is cheaper. Suppose the market buys 60 units. One firm produces all 60 at ATC = 30 + 1,800/60 = $60, for a total cost of $3,600. Two firms splitting the market each produce 30 at ATC = 30 + 1,800/30 = $90, for a combined total cost of 2 x 2,700 = $5,400. Duplicating the network wastes $1,800 a day. That is what makes the monopoly "natural": the cost structure, not a patent or a law, keeps rivals out.

Outcome 1: Unregulated, where MR = MC

The unregulated monopolist maximizes profit. Setting MR = MC gives 120 - 2Q = 30, so Q = 45. The price comes from demand: P = 120 - 45 = $75. ATC at 45 units is 30 + 1,800/45 = 30 + 40 = $70.

• Economic profit: (75 - 70) x 45 = $225
• The allocatively efficient quantity is where demand meets MC: 120 - Q = 30, so Q = 90
• Deadweight loss: 0.5 x (90 - 45) x (75 - 30) = 0.5 x 45 x 45 = $1,012.50

Price is far above MC, output is half the efficient level, and the firm earns profit. This is the case regulation tries to fix.

Outcome 2: Socially optimal price, where P = MC

A regulator who wants the efficient quantity sets the price where demand crosses MC. That gives Q = 90 and P = $30.

• Deadweight loss: zero, because P = MC at the last unit
• ATC at 90 units: 30 + 1,800/90 = 30 + 20 = $50
• Economic loss: (50 - 30) x 90 = $1,800

The firm sells every unit for $30 while each unit costs $50 on average. Because MC is constant, a price of $30 covers only the variable cost, so the loss equals the entire $1,800 fixed cost. Without a subsidy of $1,800 a day, the firm would leave the industry in the long run. This is the socially optimal price, and its loss is the reason it cannot work without public funding.

Outcome 3: Fair-return price, where P = ATC

A regulator who wants the firm to cover its costs without a subsidy sets the price where demand crosses ATC:

120 - Q = 30 + 1,800/Q

Multiply both sides by Q and rearrange: Q² - 90Q + 1,800 = 0, which factors to (Q - 30)(Q - 60) = 0. Demand crosses ATC twice, at 30 units and at 60 units. The regulator chooses the larger output, Q = 60, so P = 120 - 60 = $60.

• ATC at 60 units: 30 + 1,800/60 = $60, so economic profit is zero
• The firm earns a normal profit and stays in business with no subsidy
• Deadweight loss: 0.5 x (90 - 60) x (60 - 30) = 0.5 x 30 x 30 = $450

The fair-return price cuts the deadweight loss by more than half compared with no regulation, but it does not remove it, because P = $60 is still above MC = $30.

The three outcomes side by side

Consumer surplus is the triangle under demand and above price: 0.5 x 45 x (120 - 75) = $1,012.50, then 0.5 x 60 x (120 - 60) = $1,800, then 0.5 x 90 x (120 - 30) = $4,050. Moving from no regulation toward P = MC lowers price, raises output and raises consumer surplus at every step. You can check any of the triangles with the deadweight loss calculator, and the socially optimal vs fair-return price comparison sets out the regulator's choice in one table.

How regulators choose in practice

Regulators often aim close to the fair-return price, because it lets the firm cover its costs without an ongoing payment from taxpayers. A common version is rate-of-return regulation, where the regulator lets the firm charge enough to cover its costs plus a normal return on its capital.

Each approach has a cost of its own:

• Fair-return pricing leaves some deadweight loss, and a firm guaranteed to cover its costs has a weak reason to cut them.
• Marginal-cost pricing with a subsidy reaches the efficient quantity, but the subsidy has to be raised through taxes, and taxes create deadweight loss of their own.
• Any regulated price requires the regulator to know the firm's costs, which the firm knows better than the regulator does.

Breaking a natural monopoly into several competitors is usually the wrong fix, since the example shows that splitting the market raises the cost of every unit.

Natural monopoly vs ordinary monopoly

Both face market demand and set MR = MC when unregulated. The difference is on the cost side. An ordinary monopoly is protected by a barrier such as a patent, a license or control of a resource, and its ATC is U-shaped with MC crossing it at the minimum. A natural monopoly is protected by its own cost curve: ATC is still falling where it meets demand, and MC stays below ATC. The natural monopoly vs monopoly comparison lists the differences row by row, and the natural monopoly graph explainer shows how to draw it.

How it shows up on the AP exam

Natural monopoly appears under monopoly in topic 4.2 and under government intervention in topic 6.4. Students are usually asked to:

• Draw the graph with a downward-sloping ATC above MC across the range of demand.
• Identify the quantity and price for the unregulated, fair-return and socially optimal outcomes.
• Explain why the socially optimal price produces a loss, and shade that loss.
• Identify which outcome has deadweight loss and compare its size.
• Explain why one firm can serve the market more cheaply than several.

Common mistakes:

• Drawing a U-shaped ATC with its minimum inside the demand curve. That is an ordinary monopoly graph.
• Reading the fair-return price where MR meets ATC. It is where demand meets ATC.
• Calling the fair-return price efficient. P = ATC is still above MC, so some deadweight loss remains.
• Forgetting the subsidy. Under P = MC, the firm needs one to stay in business.
• Reading the socially optimal quantity at MR = MC. It is where demand meets MC.

The AP Micro 6.4 topic page covers the other interventions in the same topic, and the monopoly sandbox lets you practice reading price and quantity off the monopoly graph.

See it move

Make it move

A monopoly's price, quantity, profit and deadweight loss. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.