A monopolist faces the following demand function for its product: Q = 45 - 5P

The fixed costs of the monopolist are $12 and the variable costs are $5 per unit.
a) What are the profit-maximizing price and quantity? What will be the profits at these price and output levels?

b) If the government imposes an annual tax on the firm of $10, what will be the profit-maximizing price, output, and profits? Who bears the burden of the tax? Why? (Distinguish short run and long run).

c) If, instead of the annual tax, the government imposes an excise tax of 50 cents per unit of output sold, what is the impact on the profit-maximizing price, output, and profits? Who bears the burden of tax? Why?

c) If, instead of the annual tax, the government imposes a ceiling $6 on the price of the firm's product, what output will the firm produce, and what will be the total profits? What is the impact of the price ceiling on 'market efficiency'? (Hint: Compare the quantity produced under monopoly without price ceiling with quantity produced with price ceiling, and with quantity that would be produced by a perfectly-competitive firm).

e) Calculate the consumer surplus under each of the following alternatives:
* Monopoly without tax and without price ceiling
* Monopoly with tax of 50 cents per unit
* Monopoly without tax, but with price ceiling of $6
* Perfectly competitive inudstry

Illustrate your answers with diagrams whenever appropriate.