<p>I'm studying how the willingness-to-pay differs for individuals who can 'select' lotteries. Individuals are presented with L1 first and can pay some amount to get lottery L2. Assume these are my lotteries:</p>
<p>L1: 100 with probability 0.5 and 20 with probability 0.5</p>
<p>L2: 120 with probability 0.5 and 20 with probability 0.5</p>
<p>I know that a risk-neutral person would be willing to pay E(L2)-E(L1)=10. Is a risk-averse person is willing to pay more than or less than her risk-neutral counterpart? Is there any measure I can use to predict what a risk-averse person would be willing to pay?</p>

CC BY-SA 4.0
2024-01-11T13:01:32.047Z
What exactly do you mean with "the results become wildly incomparable"?
VARulle
CC BY-SA 4.0
2024-01-12T11:43:32.207Z
When I assumed utility functions U=x and U=√x (risk-neutral and risk-averse individual respectively), I ended up with WTP = 10 for the risk-neutral person and WTP = 0.477 for the risk-averse individual. 

This slightly confuses me because it also holds when I define L2 as 100 with probability 0.5 and 40 with probability 0.5. The WTP for a risk-averse person is still lower than that of a risk-neutral person.
comparing-lotteries-help
CC BY-SA 4.0
2024-01-12T11:56:44.663Z
The other approach I was considering was this. If I assume my risk-averse individual has to pay 10 to get lottery L2 (in the example in the question), she faces the choice between L1 (100 with probability 0.5 and 20 with probability 0.5) and L2' ((120-10) with probability 0.5 and (20-10) with probability 0.5).

In this case, since L2' is a mean-preserving spread of L1, the risk-averse person would prefer L1 to L2' and thus would be willing to pay less than 10 (?). Once, again, not sure if this is the right approach. Just a bit confused about ordering lotteries.
comparing-lotteries-help
CC BY-SA 4.0
2024-01-14T11:10:49.050Z
This looks as if you just calculated the difference $U(L2)-U(L1)$. But this is not the WTP. You have to calculate the certainty equivalents for the two lotteries (the square of their utilities) and then take the difference. This is about $7.13$.
VARulle
CC BY-SA 4.0
2024-01-16T15:38:29.187Z
Ah, this makes sense - thank you!
comparing-lotteries-help
<decision-theory><risk><risk-aversion><stochastic-processes>
Estimating willingness-to-pay for a risk-averse person who can 'select' lotteries
comparing-lotteries-help
# Estimating willingness-to-pay for a risk-averse person who can 'select' lotteries

(Asked by: username_0 on 2024-01-11)

I'm studying how the willingness-to-pay differs for individuals who can 'select' lotteries. Individuals are presented with L1 first and can pay some amount to get lottery L2. Assume these are my lotteries:

L1: 100 with probability 0.5 and 20 with probability 0.5

L2: 120 with probability 0.5 and 20 with probability 0.5

I know that a risk-neutral person would be willing to pay E(L2)-E(L1)=10. Is a risk-averse person is willing to pay more than or less than her risk-neutral counterpart? Is there any measure I can use to predict what a risk-averse person would be willing to pay?

**Tags:** decision-theory, risk, risk-aversion, stochastic-processes

> **Comments:**
> **username_1**: What exactly do you mean with "the results become wildly incomparable"?  
> **username_0**: When I assumed utility functions U=x and U=√x (risk-neutral and risk-averse individual respectively), I ended up with WTP = 10 for the risk-neutral person and WTP = 0.477 for the risk-averse individual.   This slightly confuses me because it also holds when I define L2 as 100 with probability 0.5 and 40 with probability 0.5. The WTP for a risk-averse person is still lower than that of a risk-neutral person.  
> **username_0**: The other approach I was considering was this. If I assume my risk-averse individual has to pay 10 to get lottery L2 (in the example in the question), she faces the choice between L1 (100 with probability 0.5 and 20 with probability 0.5) and L2' ((120-10) with probability 0.5 and (20-10) with probability 0.5).  In this case, since L2' is a mean-preserving spread of L1, the risk-averse person would prefer L1 to L2' and thus would be willing to pay less than 10 (?). Once, again, not sure if this is the right approach. Just a bit confused about ordering lotteries.  
> **username_1**: This looks as if you just calculated the difference $U(L2)-U(L1)$. But this is not the WTP. You have to calculate the certainty equivalents for the two lotteries (the square of their utilities) and then take the difference. This is about $7.13$.  
> **username_0**: Ah, this makes sense - thank you!  

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## 0 answers

