Surplus and deadweight loss: Single price monopolies have both consumer and producer surplus. But since they do not produce the allocatively efficient quantity (where P=MC), they create deadweight loss and are inefficient. 

Natural Monopolies and Regulation: A natural monopoly is an industry which captures economies of scale at the allocatively efficient quantity resulting in much lower average costs when there is a large single provider. These businesses usually have extremely high start-up costs but have a very low marginal cost of production. Electricity providers are a prime example of natural monopolies. The most expensive part of providing homes in a city with electricity is putting up wires and cables all over town to carry the electricity. If electric service was not a monopoly and consumers had multiple choices regarding who to purchase electricity from, the costs of production would be dramatically higher (as multiple sets of cables and wires would need to be strung) and price would likely be higher as a result. So, the natural monopoly may actually benefit consumers. 

Governments will often regulate natural monopolies by imposing price ceilings which may be more efficient than the unregulated price. The socially optimal price is allocatively efficient and creates no deadweight loss where price equals marginal cost, but the firm may suffer economic losses at this price. If forced to earn economic losses, the firm will eventually exit the market so the government must provide the firm with a lump sum subsidy (equal to its loss) to eliminate deadweight loss.

A fair return price is one which enforces a price ceiling where economic profits are zero (P=ATC). At the fair return price, there is less deadweight loss than an unregulated monopoly and the firm breaks even.