ps7fall2000_201 - 14.03 Fall 2000 Problem Set #7:...

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14.03 Fall 2000 Problem Set #7: Asymmetric Information, Signaling, and Game Theory Due in Class #24 Theory: 1. It is known that some fraction d of all new cars is defective. Defective cars cannot be identified as such except by the people who own them. Each consumer is risk neutral and values a non-defective car at $6,000. New cars sell for $4,000 each, used ones for $1,000. If cars do not depreciate physically with use, what is d? 2. The Massachusetts Institute of Tiddlywinks (the premier institution of its kind) hires Tiddlywinks Assistants (TAs) from among a pool of available applicants. Applicants vary in quality. Some are good (G); some are excellent (E); and some are stupendous (S). Unfortunately, an applicant’s types cannot be determined until approximately 1 A.M. on the morning the first problem set is due, by which time it is too late to change assistants. Applicants who are not chosen spend the semester playing in Tiddlywinks tournaments professionally. Good players earn $50 per semester; Excellent players earn $200 per semester and Stupendous players earn $400. The applicant pool is split evenly among the three types (each of whom knows her quality), and the Institute chooses randomly among those candidates who apply at the stated wage. Regardless of quality, no TA ever agrees to do it more than once. Each Tiddlywinks class has 100 students, whose V-N-M utility depends on their wealth and their TA’s quality and is given by: U = W if they take a class and get a good TA; U = W + 5 if they take a class and get an excellent TA; U = W + 7 if they take a class and get a stupendous TA. Each student takes only 1 class. There are no costs of offering courses other than hiring TAs. (The Professors, of course, work for Love of Learning.) A. Assume that the Institute maximizes expected student utility subject to the constraint that it not lose money. What wage should it offer to pay TAs, and what price
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ps7fall2000_201 - 14.03 Fall 2000 Problem Set #7:...

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