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I'm struggling with this question: There is a lottery which gives you D with p = 0.25 and L with p = 0.75 while initial wealth is w (w > D > L > 0). What is the minimum price the person would sell the lottery ticket for? And what is the maximum price, this person would be willing to pay in order to buy a lottery ticket? Do these two prices differ and why so?

I would say this depends on the risk attitude of this individual. But if it was risk averse, the price it would ask selling the ticket would be equal to the Certainty Equivalent. But I think that this must also be the price it would be willing to pay for the lottery ticket, isn't it?

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I was struggling with this problem too, but I think the key idea is that a person with wealth level w and who also owns a ticket "has more wealth" than a person with wealth level w and doesn't own the ticket. So if their risk aversion is affected by wealth level, then the prices would be different.

So, using a non-rigorous example, imagine that this person has a risk aversion function based on wealth such that when they own the ticket they are "infinitely" risk loving but when they don't own the ticket they are "infinitely" risk averse. They would sell it for 0 and buy it for "infinity".

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