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Fill in all the blanks and determine the optimal output and

Question: A monopolist's demand curve and total costs are given by:

Q is the quantity demanded at each price P, TC is total cost, TR is total revenue, MR is marginal revenue, MC is marginal cost, and π is profit. Fill in all the blanks and determine the optimal output and price.

a. If marginal cost falls by $5, find the new profit-maximizing output.

b. Since the firm is a monopolist and can set any price it wants, why does price fall at all?

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