Question

Daniel’s current wealth is $1000. He has been given a lottery ticket which has a 40% probability that he will win $24 and a 60% probability that he will win $600. Daniel’s utility function is u(w) = √w where w is his wealth. Calculate the least that Daniel would be willing to accept for him to sell the lottery ticket if he is an expected utility maximize.

Answer 1

The outcomes are 1024 at 40% probability and 1600 at 60% probability

Expected outcome =$0.4 \times 24 + 0.6 \times 600 = 9.6 + 360 = 369.6$ (1369.6 as 1000 added)

$Utility = 0.4 \times \sqrt{1024} + 0.6 \times \sqrt{1600} \\ = 0.4 \times 32+0.6 \times 40 \\ = 12.8+24 = 36.8$

Certainity Value $= 36.8^2 = 1354.24$

Price Daniel should at least deserve $= 1354.24-1000 = \$354.24$