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Unformatted text preview: Econ 121 – Fall 2010 UC Berkeley Professor Cristian Santesteban Problem Set 8 Due: Thursday, December 2 by 11:15am Problem 1 (35 points) Suppose demand is p = 80 – q and marginal cost for each firm is 20. There are two firms competing. a) Find the Cournot equilibrium price and quantity. b) Find the equilibrium if there is a hypothetical monopolist. By how much is price raised? c) Show that for linear demand p = a – bq that εii(p0) = p0/(a – p0). d) Find the critical elasticity of demand for an SSNIP equal to 5%. How does this compare to the prevailing (Cournot) elasticity of demand? Determine on the basis of the critical elasticity of demand whether this market is an antitrust market. e) Suppose now that marginal cost equals 65. Redo (a), (b), and (d). Problem 2 (30 points) Consider a market with constant elasticity of demand (ε) and constant marginal cost equal to c. The gross increase in profit from increasing price by dp is dp(q + dq). The gross decrease in profit from increasing price by dp is −(m)(p)(dq) where m is the prevailing price‐cost margin (p − c)/p. [Hint: dq is negative.] a) Show that the gross increase in profits from raising price by dp equals pqt (1 − tε), where t = (dp/p). b) Show that the gross decrease in profits from raising price by dp equals mptqε. c) Use (a) and (b) to determine the maximum margin that makes a price increase of 100t% unprofitable. Problem 3 (35 points) Assume for the purposes of this problem that, contrary to its protests, Microsoft has a monopoly in providing operating systems, called “Windows,” for personal computers. Assume also that the marginal cost to Microsoft of supplying its OS for more than one computer is zero. Denote by w the price charged by Microsoft for its operating system. (Assume that Microsoft sets a single price per computer, that is, does not employ two‐part tariffs, quantity discounts, or other forms of price discrimination.) Computer Original Equipment Manufacturers (OEMs) assemble computers. Suppose that the “bill of materials” for a computer, that is, the cost to the OEM of all the parts necessary to build a computer, adds up to $900 per machine, and that assembly costs another $100 per machine. Finally, assume (contrary to the efforts of Dell, IBM, and HP) that computers are a homogeneous good, and the annual demand for computers is given by Q = 50,000,000 – 10,000 p. Suppose that the OEM business is perfectly competitive. a) For any given price, w, of operating systems, what will be the price and sales of computers? b) What price w should Microsoft set for its operating system? How much money will Microsoft make? How much money will OEMs make? What will be the price of a computer? c) How much money would a vertically integrated firm controlling both the supply of Windows and the assembly of computers make? What price would such a firm charge for computers? d) Could Microsoft make more money by integrating downstream into computer assembly? Why or why not? Suppose now (definitely contrary to reality) that a single firm, HP, has a monopoly over the assembly of computers. e) For a given price, w, for Windows, what price p would HP set for computers, and how many computers would be sold? f) What price, w, should Microsoft set for its OS? How much money will Microsoft make? How much money will HP make? What will be the price of a computer? g) Could Microsoft and HP make more money by merging? If so, how much? Would such a merger benefit or harm computer users? By how much? ...
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