Some industries are monopolies because one firm really is cheapest: economies of scale (Economies and Diseconomies of Scale) run across the whole market. Breaking them up would raise costs, but leaving them alone brings the deadweight loss of Monopoly and Deadweight Loss. Regulators look for a middle path.
Key idea
A natural monopoly has average total cost falling over the whole range of market demand, usually because of a big fixed cost. Two common price rules: $P = MC$ is allocatively efficient but, since MC is below ATC, the firm loses money and needs a subsidy; $P = ATC$ (average-cost pricing) lets the firm break even with a small deadweight loss.
Why it works
When average cost is falling, each extra unit costs less than the average so far: $MC < ATC$. So a price equal to MC is below the cost per unit, and the firm loses $(ATC - MC) \times Q$, which with a constant MC is exactly its fixed cost. Setting the price at ATC covers every cost, including a normal return, so the firm can stay in business without a subsidy, at the cost of producing a bit less than the efficient amount.
Worked example: Unregulated, and P = MC
A water utility faces demand $P = 20 - Q$, has a constant marginal cost of \$4 and a fixed cost of \$48. Find its outcome unregulated and under a $P = MC$ rule.
- Unregulated: $MR = 20 - 2Q = 4$ gives $Q = 8$ and $P = \$12$; profit $= (12 - 4)(8) - 48 = \$16$.
- $P = MC$: $20 - Q = 4$ gives $Q = 16$ and $P = \$4$.
- At \$4 the price covers each unit's marginal cost but none of the \$48 fixed cost: a loss of \$48, which a subsidy would have to cover.
Answer: Unregulated: 8 units at \$12. $P = MC$: 16 units at \$4, losing \$48.
Worked example: Average-cost pricing
For the same utility, find the price and quantity under a $P = ATC$ rule.
- $ATC = \dfrac{48}{Q} + 4$. Set it equal to demand: $20 - Q = \dfrac{48}{Q} + 4$.
- Multiply by $Q$ and rearrange: $Q^2 - 16Q + 48 = 0$, so $(Q - 4)(Q - 12) = 0$.
- Take the larger root, $Q = 12$ (more output at a lower price): $P = 20 - 12 = \$8$, and $ATC = 48/12 + 4 = \$8$. Zero economic profit.
Answer: 12 units at \$8: the firm breaks even.
Common mistake
Expecting a $P = MC$ rule to let the firm break even. With average cost falling, MC is below ATC, so price equal to MC can't cover the average cost. Check: compare MC and ATC at the regulated quantity; if MC is lower, the firm loses $(ATC - MC) \times Q$.
Real regulators also worry that a firm guaranteed to cover its costs has little reason to cut them. Rules that cap prices for several years at a time try to keep that incentive; which approach works best is debated.