A water supply company faces the following inverse demand function: P = 100 - 2Q. Its cost function is C = 100+2Q. Note P is the water rate per thousand litres of water and Q is the quantity measured in thousand liters of water.

1. Calculate the firm's profit-maximizing output and price. What profit it will make? Will there be a deadweight loss to the society? How much?
2. Suppose a government regulator regulates the price following the marginal cost pricing rule. What price and water consumption will result? How much profit the monopoly will now make? What cost will the regulator incur? What deadweight loss will result due to this regulation?
3. Now suppose the regulator wants the monopoly to follow the average cost pricing rule. What price and quantity will result? What will be the deadweight loss?