Timmy Qualm\'s uncle gave him a lottery ticket. With probability 1/2 the ticket
ID: 2505976 • Letter: T
Question
Timmy Qualm's uncle gave him a lottery ticket. With probability 1/2 the ticket will be worth $100 and with probability 1/2 it will be worthless. Let x be Timmy's wealth if the lottery ticket is a winner and y his wealth if it is a loser. Timmy's preferences over alternative contingent commodity bundles are represented by the utility function U(x,y)=min{2x-y,2y-x}. He has no risks other than the ticket.
(a) Timmywould sell his lottery ticket for $25 but not for less.
(b) Timmy hates risk so much that he'd be willing to throwaway the lottery ticket rather than worry about
whether he won.
(c) Timmy satises the expected utilityhypothesis.
(d) Timmy is misnamed, he is a risk-lover.
(e) None of the above.
The correct answer is B. Please help to understand how to solve this.
Explanation / Answer
Timmy's wealth when he is a winner = x= $100
Timmy's wealth when he is a loser = y= $0
U(x,y)=min{$200,-$100}=-$100
His utility is negative which means that he is risk-averse and not risk lover. Since utility is negative means that he is not bothered about winning, he just does not qish to take any risk no matter what.
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