A monopolist faces the following demand curve and cost function:
P = 50 - 0.5Q TC = 2Q + 1000

a) Find the following equations: Marginal Cost: Marginal Revenue: Aver. Total Cost: Now carefully graph them, along with the demand curve on the same graph.

b) What is the otimal price and quantity if the firm can only set one price for all units?

c) Calculate the elasticity of demand at the profit maximizing price.

d) If the government forced the firm to produced the socially efficient level of output, and set a pair unit subsidy in order to compensate for any losses, what would the per unit subsidy be? (Assume the firm can still set only one price per unit).

e) What would be the total amount of the subsidy assuming nothing else changes?

Note: Please help as much as possible!!