Please help me question on the game theory, thanks

[coldway]

A person has a utility function defined over her wealth given by
u(w)=ln(w). Her initial wealth is $2 and she faces a risky prospect in which she will
lose $1 with probability 0.4 and gain $1 with probability 0.6.
(i) Show that this person is risk averse by demonstrating that her utility function is
concave.
(ii) What is her expected utility of this gamble?
(iii) Find her maximum willingness to pay to avoid taking this risk.

 

[Disconnected]

Hey there, welcome to PF!
I'm not uh-mayzing at game theory, but I'll see what I can rustle up here. What have you tried so far? Do you understand all of the terms?

 

[SteamKing]

This post should be in one of the math forums.

 

[coldway]

This involves the question of marginal utility, ln (w) is concave, meaning that derivatives along the x-axis positive direction is decreasing, which means that the marginal utility of winning is less than the marginal loss of output,so far i just up to here, i still looking for futhermore help and try to solve the question

 

[coldway]

for the part2, is the answer u(w)=ln(0.6*1-0.4*1)=ln0.2, but i am not sure about it

 

[coldway]

is frist part second derivtive??differential