Economic Analysis for Business Decisions Homework 6

HOMEWORK SET #6 Lecture 17: Transfer Pricing. 1. Acme, Inc. has a monopoly over the production of calculators. Liquid crystal displays (LCDs) are an input into calculators. Acme has the capacity to produce its own LCDs. The demand for calculators is given by: P = 135 – 2Q One LCD goes into each calculator, and the cost of producing a calculator is $10 over and above the cost of the LCD. Acme’s cost function for producing LCDs is: TCD = 25 + 5 QD + QD2 . where QD is the quantity of LCDs produced. Acme is divided into two subsidiaries: Acme Displays and Acme Calculators. Managers of each are told to maximize the profits of the subsidiary at which they work. a. If Acme cannot buy or sell LCDs, what is the optimal transfer price that Acme (headquarters) should set for LCDs? How many LCDs will Acme transfer internally? What would be the price of calculators? What will Acme’s profits be? And how will they be divided between the two subsidiaries? b. Suppose now that Acme let the subsidiaries themselves set the price of their products. Under the same assumption that subsidiaries maximize profits, what are the prices they set for LCDs and calculators? What are the profits of each subsidiary? Explain briefly why the total profits of Acme are lower than in a). Lecture 19: Asymmetric Information 2. Problem #9, p.620 in Pindyck & Rubinfeld (5th Ed), parts a, b, and c. Note: Consider whether Lew’s will or will not match Harry’s offers. 2 3. Decide whether each of the following three statements is True, False, or Uncertain, and give a brief but clear explanation why. (Note: these questions provide practice for the True, False, Uncertain section on the final exam) Lecture 15: Antitrust a. For some years, Microsoft offered original equipment manufacturers (OEM’s) a choice of methods of payment for operating system software. OEM’s could either (1) buy the software for each machine on which it was installed at a very high price, or (2) contract on the basis of the numbers of machines sold, regardless of whose operating software was installed (a so-called “per-processor” contract). This practice is not anti-competitive. Lecture 16: Auctions b. In a Dutch (descending price) auction for an object for which the bidders have independent and different valuations, participants should bid their true reservation prices. Lecture 18: Incentives & Information c. Sloan is considering the addition of theft insurance for laptop computers as a part of annual School tuition. All students have laptops, and in the past an average of 5% of these computers has been stolen over the course of a year, at an average loss of $2000 each. On the basis of that experience, the School is thinking of providing the insurance to all students and increasing the tuition by $100. This is a good insurance policy. Among other things, it allows Sloan to break even. Lectures 15 & 18: Common Property & Incentives 4. Consider two farmers and two pieces of land. We want to know what the effect is of each farmer working his own piece of land versus the farmers cooperating and jointly working on the two pieces of land. To simplify the exposition, we will denote these as ‘independent farmers’ and ‘cooperative farmers’ respectively. Assume that each farmer (whether independent or cooperative) can decide on his own how much time to spend on farming. Let farmer i’s weekly time spent on farming be denoted hi (in hours per week; so h1 for farmer 1 and h2 for farmer 2). The farmer’s productivity (expressed in bushels of grain) is directly proportional to the time he spends on farming. In particular, an independent farmer produces 80 hi bushels of grain if he works hi hours per week. Farmers in a cooperative are more productive since they can specialize: a cooperative farmer produces 90 hi bushels of grain if he works hi hours per week. Cooperative farmers share the output of their farm equally. Let bi be the bushels of grain that farmer i can take home at the end of the year, then bi = 80hi for an independent farmer, while bi = (90 h1 + 90 h2)/2 for a cooperative farmer. Farmers dislike working and more so as they work more. In particular, farmer i’s utility is u i = bi − hi2 2 We assume that a farmer i will choose hi to maximize his utility ui. a. Write out the utility functions of an independent farmer and a cooperative farmer completely in terms of h1 and h2. b. How many hours will an independent farmer work (assuming that farmers choose hi to maximize their utility)? What is his utility? c. How many hours will a cooperative farmer work? What is his utility? d. What is the problem with a cooperative farm? What would happen (qualitatively) if 100 farmers worked jointly in a cooperative farm? How could the farmers solve that problem? 3