The market demand for a monopoly is given by

P = 90 - 2Q,

where Q is the number of the product demanded at price P. The total cost function is given by

TC = 90 + 20Q +0.5Q2.

1. If the firm is a single-price monopoly, what are the equilibrium quantity and price? What are the resultant consumer surplus, producer surplus and social welfare?
2. If the government forced the firm to behave as if it were a perfect competitor, what are the equilibrium quantity and price? What are the resultant consumer surplus, producer surplus and social welfare?
3. How much does social welfare increase when the firm moves from monopoly to competition?