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Assignment:
1.) Suppose you can bet on one of two horses - Ace or Jack - in a match race. If Ace wins, you are paid $5; if he loses you must pay $2 to the track. If you bet on Jack and he loses, you pay the track $10. You judge each horse to be as likely to win as the other. Assuming you make your decision on the basis of expected monetary values, how much would a winning bet on Jack have to pay before you would be willing to risk the $10?
2.) What is the expected monetary value of the following gamble? You are to flip a fair coin. If it comes up heads you win 1 dollar, and the wager is over. If it comes up tails you lose 1 dollar, but you flip again for 2 dollars. If the coin comes up heads this time you win 2 dollars. If it comes up tails you lose 2 dollars, but flip again for 4 dollars. If it comes up heads you win 4 dollars. If it comes up tails you lose 4 dollars. But in either case, the wager is over.
3.) Suppose that you express the following preferences over fruit/fruit lotteries: Apple ? Cherry ~ {Apple, 0.5; Orange, 0.5} ? Banana ~ {Cherry, 0.75; Orange, 0.25} ? Orange. Construct a vNM utility function that represents these preferences as expected utility maximizing.
4.) Prove that Allais's preferences violate the expected utility theory.
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