3
$\begingroup$

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.

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ Start here. Than graph your 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? $\endgroup$
    – garej
    May 31, 2015 at 13:21
  • $\begingroup$ $u(w)$ is defined for $w>0$ - his current wealth is $w>1000$ when he is facing the lottery. Sorry I didn't make that clear :) I'll have a look at your link, thanks. $\endgroup$
    – Phillip Bredahl
    May 31, 2015 at 13:23
  • $\begingroup$ You should edit your question, and my comment will be redundant. And do not forget to carefully read site rules =)) $\endgroup$
    – garej
    May 31, 2015 at 13:26

1 Answer 1

Reset to default
2
$\begingroup$

You want the household to be ex-ante indifferent between taking the lottery and paying some $p$ and voiding it.

With van-Neumann-Morgenstein utility, the utility of taking the lottery is given by $$U_L(w) \equiv 0.5 U(w-1000) + 0.5U(w+1000)$$

Now, you're looking for a payment $p(w)$ such that $u(w - p(w)) = U_L(w)$.

Improve this answer
$\endgroup$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.