[ShaneP]

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For some reason this isn't making sense to me, so hopefully I can get the right answer here.

Question: What is the expected value of a random toss of a die? (Fair and six-sided.)

This next question I just have no idea how to do it.

Suppose your current wealth, M, is 100 and your utility function is U = M^2. You have a lottery ticket that pays $10 with a probability of 0.25 and $0 with a probability of 0.75. What is the minimum amount for which you would be willing to sell this ticket?

Thanks.

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Both of the answers so far for the second question are wrong...the 3.5 for the dice answer is correct.

One answer came close...your utility function is M^2, so what you want to do is find the point where selling the ticket for a fixed amount is equal to the expected utility from the ticket. I'll show you the easier one, you'll have to do the lottery ticket, figure the expected util, and then some math.

From selling the ticket (for X dollars, say), your wealth after is (100+X), so your utility form selling the ticket is (100+X)^2.

Figure out the expected utility from selling the ticket, and find out where X makes you indifferent between the two options.

Shane