A natural monopoly exists in an industry with a demand schedule P = 100 - Q. The marginal revenue schedule is then MR = 100 - 2Q. The monopolist operates with a fixed cost F, and a total variable cost TVC = 20Q. The corresponding marginal cost is thus constant and equal to 20.
a) Suppose the firm sets a uniform price to maximize profit. What is the largest value of F for which the firm could earn zero profit?
b) Suppose the firm is able to engage in perfect first degree price discrimination. What is the largest value of F for which the firm could earn zero profit?