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##### 4. Assume that demand for services per period is P...

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4. Assume that demand for services per period is Pt = 1000 ? Qt where Qt is the stock of the durable consumed. Let the discount factor for both consumers and the firm be one. Suppose that the monopolist has a choice: she can either produce a product that is durable at zero marginal cost or she can produce a nondurable product?it provides consumption services for only one period?at marginal cost c. Assume that there are only two periods. (a) For what values of c would a monopolist that sells its output and cannot commit to prices choose the nondurable product? (b) For what values of c would a monopolist that leases its output introduce the nondurable product? (c) What is the efficient solution? How is this related to planned obsolescence? 2. Suppose that a monopolist?s product could be either high quality (H) or low quality (L). There are 10 identical consumers, each of whom values a low-quality product at vL and a high-quality product at vH = 85 vL . (So if consumers believe that a good is of quality i , then the monopolist can sell 10 units at any price p ? vi .) The cost of producing q units of a good of quality i is 1 10 ciq2. If vH/cH = vL/cL = 25/16, how much would a high-quality producer have to restrict his supply to convince consumers that his product was actually of quality H? [Hint: Quantity for a high-quality firm must be sufficiently small that a low-quality producer would prefer to sell all 10 units and openly reveal them as low quality, rather than disguising these goods as high-quality items.] 6. (Requires calculus.) A monopolist produces a product whose demand price and production costs vary with quality s and quantity q according to P(s, q) = s(1 ? q) C(s, q) = s2q. (a) Calculate the price and quality levels that a monopolist would choose, and the corresponding quantity sold. (b) Consumer surplus at any {s, q} combination can be derived as 12 sq2. The corresponding value for profits is (p(s, q)?s2)q = (s?sq?s2)q. Substitute the monopolist?s profit-maximizing quantity from (a) and then derive optimal quality for that quantity choice (the level of quality that maximizes consumer plus producer surplus). Show that the monopolist?s actual quality choice is lower than optimal quality, given the quantity chosen. 6. Consider the game in Figure 7.13: L R T a,?a 0, 0 B c, c 1,?1 Figure 7.13 Problem 6 (a) Solve for a and c such that there is a mixed-strategy equilibrium in which Player 1 plays T with probability 2/3, B with probability 1/3, and Player 2 plays L with probability 1/3, R with probability 2/3. (b) Are there any pure-strategy equilibria?,Only need help with Chapter 6 question 2(pg.203) and 6(pg.204), chapter 7 question 6(pg.229). Thank you!

Paper#11818 | Written in 18-Jul-2015

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