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Rubinstein2005-page117 - a ±ormalize the two assumptions b...

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October 21, 2005 12:18 master Sheet number 115 Page number 99 Expected Utility 99 that satisfy your property and express the desired relation in a logical fashion. Problem 7. ( Difficult. Based on Miyamoto, Wakker, Bleichrodt, and Peters 1998. ) A decision maker faces a trade-off between longevity and quality of life. His preference relation ranks lotteries on the set of all certain outcomes of the form ( q , t ) , defined as “a life of quality q and length t ” (where q and t are nonnegative numbers). Assume that the preference relation satisfies von Neumann–Morgenstern assumptions and that it also satisfies Indifference between “high” and “low” quality of life when longevity is 0. Expected longevity and quality of life are desirable.
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Unformatted text preview: a. ±ormalize the two assumptions. b. Show that the preference relation derived from maximizing the expec-tation of the function v ( q ) t , where v is a strictly increasing function and v ( q ) > 0 for all q , satisFes the assumptions. c. Show that all preference relations satisfying the above assumptions can be represented by an expected utility function of the form v ( q ) t , where v is a positive and increasing function. Problem 8. ( ±ood for thought ) Consider a decision maker who systematically calculates that 2 + 3 = 6. Construct a “money pump” argument against him. Discuss the argument....
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