Depends how you define “risk averse”. When utility is computed in terms on another parameter, diminishing returns result in what appears like “risk averseness”. For example, suppose that you assign utility 1u to having 1000$, utility 3u to having 4000$ and utility 4u to having 10000$. Then, if you currently have 4000$ and someone offers you to participate in a lottery in which you have a 50% chance of losing 3000$ and a 50% chance of gaining 6000$, you will reject it (in spite of an expected gain of 1500$) since your expected utility for not participating is 3u whereas your expected utility for participating is 2.5u.
Ergo, if you’re risk-averse, you aren’t a rational agent. Is that correct?
Depends how you define “risk averse”. When utility is computed in terms on another parameter, diminishing returns result in what appears like “risk averseness”. For example, suppose that you assign utility 1u to having 1000$, utility 3u to having 4000$ and utility 4u to having 10000$. Then, if you currently have 4000$ and someone offers you to participate in a lottery in which you have a 50% chance of losing 3000$ and a 50% chance of gaining 6000$, you will reject it (in spite of an expected gain of 1500$) since your expected utility for not participating is 3u whereas your expected utility for participating is 2.5u.