Electric utilities are often natural monopolies. Due to the extensive and costly infrastructure needed to generate, transmit, and deliver electricity, one firm can produce the total output of the market at a lower cost than could several firms. Regulatory authorities such as the Central Electricity Regulatory Commission in India and the Australian Energy Regulator oversee the operation of electric utilities, and many limit their market power by setting electricity rates for residential, commercial, and industrial customers. If the marginal cost of production for a monopoly is upward sloping and the linear market demand curve is downward sloping, draw a diagram indicating the socially optimal price. If the regulatory authority sets a price ceiling that is above the socially optimal price but below the monopoly's profit-maximizing price, how do the price, quantity, and welfare compare to those under optimal regulation?