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Page a > of2 O ZOOM + Suppose the rm Vintage Muggle Inc., has a monopoly in the product of recliners due to having proprietary muggle recliner technology. The inverse demand function for recliners in the market is: P=2003Q Suppose the rm's cost function is: C(Q) = 202 +6562 Part a) Find the prot maximizing price and quantity of recliners as well as the prot the rm would make at this price and quantity. Sketch a graph representing the monopoly, including the demand curve, marginal revenue curve, marginal cost curve, and average cost curves. Label the monopoly price PM , the monopoly quantity QM , and the area that represents the monopoly's prot. Part b) Suppose antitrust regulations require that Vintage Muggle, Inc., charges the socially eicient price. What is the socially eicient price? What quantity would they produce at this price? In your graph in part a) label the point representing the socially eicient price and quantity with P* and Q*. Part c) What is the deadweight loss at monopoly price and quantity? Find it mathematically and illustrate it in your graph from Part a. Part d) Suppose the rm could perfectly price discriminate. What quantity would they produce? What would their prot be? What is the deadweight loss'.7