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)
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 $x$.