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4. (20 points). Teddy bears are supplied by a monopoly with a production technology that is described by the total cost function TC (Q) =400 . The market for teddy bears into two segments with the following demand functions: q, =100-p, , q, =50-p, . These are the only two markets for teddy bears, so O =q, +q, . The firm can identify which customer belongs to which market segment. The consumers in the two markets are unable to trade with each other. a) Derive the profit-maximizing quantities and prices in the two markets. Confirm that they are a unique global maximum. b) Show that the firm charges a higher price where demand is less elastic. Explain why