0
$\begingroup$

I'm trying to figure out what the non-stochastic equivalent payment is for someone who is risk-averse. Suppose we have a lottery that pays out\$100 with probability one half and \$0 with probability one half. If we are using a coefficient of relative risk aversion of 2, then we have a utility function of the form $$u(w) =\frac {w ^ {1-2} -1} {1-2} = -w ^ {-1} +1 $$

This seems very weird to me because utility is negatively correlated with wealth. What am I doing wrong?

(I am specifically asking because I want to understand this paper, which uses a similar utility function on page 18)

$\endgroup$
5
  • $\begingroup$ My two cents (beyond the fact that in the page you linked, the isoelastic utility function you use is introduced in the context of intertemporal decision-making): you pick $R(w) = 2$, but you cannot really impose it, right? This should be because $R(w) = w A(w) =$ etc etc, as written in the wiki entry. $\endgroup$
    – Kolmin
    Sep 1, 2015 at 14:02
  • $\begingroup$ Thanks – I added a link to the paper I am actually trying to understand, which does have hardcoded values for this coefficient (I believe). Let me know if I misunderstanding this as well! $\endgroup$
    – Xodarap
    Sep 1, 2015 at 14:20
  • $\begingroup$ Ok, I took a look. Well, I think what I wrote about imposing the value $R(w) =2$ still stands. To me, you cannot really do it, because that value does depend on $w$ as well, as you can see in the wiki entry. $\endgroup$
    – Kolmin
    Sep 1, 2015 at 15:20
  • $\begingroup$ It seems to me that in the paper cited in table 5 they have a hardcoded value (which they denote $\gamma $) which they plug into equation (10). Are you saying that I am misunderstanding what they did, or that what they did is wrong? $\endgroup$
    – Xodarap
    Sep 1, 2015 at 16:02
  • $\begingroup$ Of course I did not write the paper, but I simply went to the page you pointed out to me and I try to roughly see the context. Hence, I am not saying they did anything wrong. What I am saying is that I think that their $\gamma$ is defined as the $\rho$ in the wiki entry you linked. Hence, it is in function of something. $\endgroup$
    – Kolmin
    Sep 1, 2015 at 18:40

1 Answer 1

1
$\begingroup$

What do you mean with "utility is negatively correlated with wealth"? The utility function $$1- 1/w$$ is increasing in w. See http://www.wolframalpha.com/input/?i=Plot[1-1%2Fx%2C{x%2C0%2C100}]

However, it is not defined at $w=0$. So you need some initial wealth You can calculate $$\frac{1}{2} u(w+0) + \frac{1}{2} u(w+100) = u (w+x)$$ Then, $x$ is the deterministic payment such that the agent is indifferent between the lottery and the safe payment of $x$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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