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(b) Jake has a current wealth of W. = 2000 and is considering two fair bets X and Y, with an equal chance of

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(b) Jake has a current wealth of W. = 2000 and is considering two fair bets X and Y, with an equal chance of winning. Jake can bet any amount of money for either X or Y to win. His utility functions of wealth and whether X or Y wins are: U(W, X) = 3W0.5 and U(W,Y)= W0.5 (i) (ii) (iii) (iv) Show that at any level of initial wealth and without any bets, Jake prefers X to win. (2 marks) If Jake bets an amount K for X to win, explain, without further calculation, what his expected wealth is. (2 marks) Find the optimal amount K, to the nearest integer, that Jake will bet on X to win. (7 marks) Jake decides to make the optimal bet. Explain whether Jake still prefers X to win. (3 marks)

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