Liam Currently Has $10,000

Essay

Liam currently has $10,000. He is offered a gamble where with one-half chance he can win $2000 but with one-half chance he can lose $2000. (a) Show that Liam is indifferent between accepting this gamble and sticking with this initial endowment of $10,000 if Liam's utility function is given by U(W) = W. (b) However, if Liam's utility function is given by U(W) = Square Root (W), then Liam strictly prefers to stick with his initial endowment of $10,000 rather than accepting this gamble. (Hint: In answering this question, you should denote utilities using 2 decimal points rather than rounding them up to the nearest whole number. Make sure you show your work.) (c) Draw TWO NEAT graphs with wealth (W) on the x-axis and Utility (U) on the y-axis to depict the utility functions in Part (a) and Part (b).