Chegg a monopolist with cost function c(q) = f + q serves a market with demand d(p) = 5 − p. note that the average cost function of the monopolist is decreasing. this corresponds to the "natural monopoly" case we mentioned in class.

(a) what quantity would the monopolist sell in the market and what would be the market price if f = 3? what if f = 5? how much profit does the monopolist make when f = 3 or when f = 5?
(b) assume f = 5. the government is considering to offer a subsidy s per unit to the monopolist. what is the optimal value of s if the government wants to maximize total surplus?