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A firm is originally operating as a single-price monopolist that faces a market demand curve P (Q) = 198 %Q and total cost curve equal to TC (q) = 10, 500 + 32Q, with constant MC equal to M C(Q) = 32 for all units produced. Part (a): How much output does the firm produce and at what price is each unit sold for? Part (b): Calculate the firm's profit. The firm now realizes there are actually two distinct groups of consumers that purchase their product, with the following demand functions: 13011) = 242 - 41 Pm) = 176 %42 Their total and marginal cost curves have not changed. If the firm wanted to successfully practice third-degree price discrimination: Part (c): How many units of output would they sell to group 1 and how much will each consumer in group 1 pay? Part (d): How many units of output would they sell to group 2 and how much will each consumer in group 2 pay? Part (e): How much profit is earned by the firm when they practice third-degree price discrimination? Part (f): How much did profits rise by when the firm switched to using price discrimination