A natural monopolist company has $1000 in fixed costs on basic scientific research and a constant marginal cost of $10 per unit produced. It faces a demand curve of P=90-0.5Q, where Q is the quantity consumed by an individual. The company's marginal revenue is 90-Q. There are 10000 equal individuals in the market.

a. Without regulation, what price would be set and what quantity (per household) will it produce.

b. Say the government forces the utility company to set prices equal to marginal cost. What quantity will it produce now? Is socially efficient? Can the natural monopolist stay in business in the long run?

c. Design a two-part tariff (i.e. a two-part price) per individual to allow the utility company to stay in business in the long run while maintaining social efficiency.

d. Can you make an argument for the government to allow the utility company to charge above marginal cost in a dynamic setting?