Suppose that the cost function curve for a natural monopoly is \(C(Q)=48+6 Q\) and the inverse demand function it faces is \(p=38-2 Q\). What are the firm's maximum profits if it cannot price discriminate? Compare that result with the firm's profits if it can price discriminate perfectly. Does the perfectly price-discriminating monopoly produce a level of output where price is less than average cost? Show your results for perfect price discrimination in a diagram.