Given a consumer with a utility function, $u(w)$, and a wealth of $w>1000$. Assuming that the consumers relative risk aversion is constant and equal to 1, that is $R_r(w)=1$ for $w>0$, the consumer is facing a lottery that gives him 50% chance to win 1000 and 50% chance to lose 1000.
My question is, how much is the consumer willing to pay to avoid this lottery, and how does it depend on $w$? I can't seem to figure it out, and I really have no idea where to start.
u(w). Make sure that w>1000 is a correct condition. It seems strange. May be, u(w) is defined on w>0 and his/her current wealth is a point in a range w>1000? $\endgroup$