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I am trying to solve this question about preferences and I got into an argument about it. I just want to make sure I am not overlooking something really simple.

What can you tell about the risk tolerance of someone who prefers a lottery C (pays 48,000 with 50% chance and 54,000 with 50%chance) over lottery B2 (pays 50,000 with 100% chance). Explain.

My answer: The information that a person prefers C over B2 by itself is insufficient to determine risk tolerance. This is because lottery C has higher expected payout (51,000) than the fixed payout of B2 (50000), and we are not able to deduce a preference between C and E(C) = 51000, i.e. its own expected payout. Indeed, a risk loving or risk neutral person would choose lottery C over B2. But a risk averse person with a sufficiently "flat"-ish utility curve would also choose C over B2, as shown in the image below (green is the utility curve).

enter image description here

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  • $\begingroup$ "Lotteries are a tax on people who are bad at math." $\endgroup$
    – Scott Rowe
    Commented Mar 17 at 12:19
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    $\begingroup$ Fyi Scott in economics, the term "lottery" is a general phrase that can refer to any situation where outcomes are uncertain, not just the lottery you buy tickets for. The decisions whether or not to buy insurance, speed on the highway, or bring your umbrella to work are all choices between lotteries. $\endgroup$
    – H Rogers
    Commented Mar 19 at 15:15

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Ah, I misunderstood the question initially. It's like this: the question suggests that this person's risk tolerance doesn't necessarily follow diminishing marginal utility. It could be understood that this person is a risk seeker, whose utility curve might decrease more slowly than that of an average person, or it might not decrease at all. For someone with a gambler's mentality, utility doesn't necessarily diminish

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  • $\begingroup$ Hi! Maybe have a look around the site and see the style in which other people are answering? Though it varies, the ideal answer is a bit more thorough, shows what it starts from and supports its statement. $\endgroup$
    – Giskard
    Commented Mar 17 at 9:29
  • $\begingroup$ Also, you can edit/delete your answers if in retrospect you are not satisfied with them. $\endgroup$
    – Giskard
    Commented Mar 17 at 9:30
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Because the marginal utility for individuals is diminishing, and in this model, it diminishes rapidly. Therefore, the utility of the combination of 54,000 * 50% + 48,000 * 50% is less than 50,000.

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    $\begingroup$ I am assuming you meant that the "combination" of the utilities 54000*50% + 48000*50% is less than 50,000. Because if you take utility of the combination , the combination equals 51000. And the utility of 50000 has to be less than utility of 51000. $\endgroup$
    – Indraneel Kasmalkar
    Commented Mar 17 at 4:36
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    $\begingroup$ But even if we make that correction, consider the utility, U(x) = log(x). This is concave, i.e. represents risk averseness. However, then your statement is not true, because 50% x U(54000) + 50% x U(48000) > U(50000) for this specific utility function. $\endgroup$
    – Indraneel Kasmalkar
    Commented Mar 17 at 4:37
  • $\begingroup$ (-1) Where did you get "in this model, it diminishes rapidly" from...? $\endgroup$
    – Giskard
    Commented Mar 17 at 6:39
  • $\begingroup$ @Giskard right, I was thinking that normal humans wouldn't notice the small difference, and probably wouldn't care, even if it was shown to them. The question seems incredibly contrived. The Coke vs Pepsi street test makes more sense. $\endgroup$
    – Scott Rowe
    Commented Mar 17 at 12:33

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