A monopoly firm has an incentive to increase the price and decrease the produced quantity in order to increase its revenues. But this decreases the social welfare. The government can intervene in several ways, one of which is to set a maximum price for the product.
Ideally, the price set by the government should be equal to the equilibrium price, because then the social welfare is maximized. However, in order to know this socially-optimal price, the government must know the cost curve of the seller. A monopolist seller might decide to hide the true cost curve and claim that the cost is higher than it is, in order to make the government raise the maximum price.
MY QUESTION IS: what can a government do in order to approximate the socially-optimal price? I am interested in references to both theoretical suggestions and practical case-studies.
NOTE: I am interested even in a very simple case, in which the monopolist's price per unit can be assumed to be constant, so that the only hidden information is that constant.