Answer to Question 1
The statement is true. For example, in the case of a private good such as a hamburger, a consumer either reveals her willingness to pay by purchasing the good at the market price or goes without it. This is not the case with a public good. Once produced, individuals cannot be excluded from consuming the good even if they have not paid for the good. Therefore, it is in a consumer's interest not to reveal her true preferences for the good.
Answer to Question 2
Regulating the actions of a natural monopoly to achieve an efficient outcome implies setting the level of output at the quantity where MB = MC, and the monopoly must set its price equal to marginal cost. This type of regulation is called the marginal cost pricing rule. A marginal cost pricing rule maximizes total surplus. However, when the monopoly price equals marginal cost, average total cost exceeds price and the monopoly incurs an economic loss. A monopoly that is required to use a marginal cost pricing rule will not stay in business because it is not covering its costs. Two possible ways of enabling the firm to cover its costs are by price discrimination and by using a two-part price (called a two-part tariff). The government might also grant the firm a subsidy. But this subsidy must be raised through imposing taxes on other economic activity, which creates deadweight loss and prevents efficient resource allocation in the markets affected by the tax.