Suppose trader i has utility function ui(x) = x.

There are two financial assets; both cost $100. Trader i is going to buy one of these.

They will both pay off after a short time. Asset 1 pays $103 for sure. Asset 2 pays $110 with probability 0.95, and $0 with probability 0.05. Suppose trader j has utility function uj (x) = x 2 .

Will trader i and j buy a same asset? Why?

Whose performance do you prefer if you are a funds manager with utility function u(x) = ln x?