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econ145b-PS2solutions-corr - Econ 145b Problem Set 2(Spring...

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Econ 145b. Problem Set 2 (Spring 2009) (with solutions) Please type your solutions or write legibly. Always provide arguments. Each question 1, 2(a), 2(b), 3(a), 3(b) is worth 20 points (100 points total) A monopolistic seller with zero cost of producing a good maximizes expected profits. Given a pricing schedule T that determines the transfer to the seller as the function of quantity bought, a buyer buys quantity q 0 that maximizes the net utility equal to gross utility U ( q ) minus transfer T ( q ) . The buyer’s gross utility from buying quantity q is U ( q ) = θ (1 - exp ( - q )) where θ equals θ L with probability λ and θ H with probability 1 - λ . Assume that θ H > θ L > 0 and that the seller needs to o ff er the same pricing scheme to both buyer types. The buyers are not coerced to buy; they will buy only if their net utility from buying is nonnegative. We will allow the seller to produce and sell an infinite quantity of good to any buyer θ ; in line with the above formulas, the buyer’s gross utility from buying an infinite quantity is θ . (1) Assuming the seller is constrained to uniform pricing, T ( q ) = pq , compute the profit maximizing price p m .
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