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> the poorer a person is the larger a percentage they are willing to risk

Utility function is logaritmic.



Is there any evidence that it is?


Pretty common assumption. [1]

The need for money saturates slowly. Think about winning 1000 dollars (nice dinner pehaps), 10 000 (better car), 100 000 (larger appartment), .... , 10 000 000.

At some point it doesn't matter if its 200 000 000 or 300 000 000.

On the other hand a lotter ticket is 1$. What is the utility of 1$ - a can of coke pehaps. But the perspective of winning $1 000 000 - thats a nice idea to hold for a few days... So many people do despite the slim chances.

[] https://economics.stackexchange.com/questions/23952/is-the-u...

[] https://www.forbes.com/sites/rogerkay/2013/08/05/how-the-mar...


That's evidence for a concave utility function wrt income, not logarithmic per se.

But your first link does cite evidence that _if_ utility is CRRA, we are not far from the case where utility is logarithmic




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