Econ HW - Expected Value
 

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.

Re: Econ HW - Expected Value
 

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

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I would say it's 1/6

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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?

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I'm not sure how the utility function and current wealth plays into this question, but I'd assume the minimum price you'd sell the ticket for is P=0.25(10)+.75*(0)=$2.50.

It's possible since the prize is 10 dollars your utility from the prize is 10^2 or 100. If this is the case, then the minimum price would be Pmin=0.25(100)+.75(0)=25.


disclaimer: these may/may not be correct.

Re: Econ HW - Expected Value
 

isnt the dice answer 3.5?

I also think the minimum price you should sell the ticket for is $2.50.

Re: Econ HW - Expected Value
 

EV= probability*value
1/6*1+1/6*2+1/6*3....+1/6*6

so yes it is 3.5

The second part... hmmm EV of U without selling ticket is 1/4*(110)^2 + 3/4*(100)^2= 3025+7500= 10525= U

so... because U=m^2, m= 102.59...
Sell it for at least $2.59. It probably doesn't make that much sense, but its what I see.

Re: Econ HW - Expected Value
 

[ QUOTE ]
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.

[/ QUOTE ]

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

Re: Econ HW - Expected Value
 

Dice: EV = 1(1/6) + 2(1/6) + 3(1/6) + 4(1/6) + 5(1/6) + 6(1/6) = 3.5

If you sell the ticket for price P, you now have (100 + P) dollars. Your utility is now (100 + P)^2.

If you keep the ticket, 25% of the time you hit for $10 and now have $110. 75% of the time you stay at $100.

Your utility here is: (.25)(110)^2 + (.75)(100)^2

You are willing to sell the ticket if your utility from selling is >= to the expected utility from holding on to the ticket. The least you will sell it for is when the two are exactly the same. So solve:

(100 + P)^2 = (.25)(110)^2 + (.75)(100)^2
10000 + 200P + P*P = 10525
P^2 + 200P - 525 = 0

P = $2.59

This is slightly larger than the solution of $2.50, which makes sense if you think about it.

Re: Econ HW - Expected Value
 

What I don't understand about the dice problem is, why are we weighting the sides of the die? Assume that we only roll the die once, then each side has an equal chance of coming up, one out of 6 or 1/6. Why weight them 1, 2, 3, 4, 5, 6?

Re: Econ HW - Expected Value
 

How much would you pay to play this game with me?:

You pay me some amount of dollars. You roll a 6-sided die. I pay you the number dollars equal to the number that comes up.



You should be willing to pay no more than the expected value of the die. Do you still think this number is 1?

Re: Econ HW - Expected Value
 

Think about it like this: you get the number of dollars as the dice rolls (i.e. a roll of 4= $4).

What is the expected value of one roll (in dollars)?

Re: Econ HW - Expected Value
 

[ QUOTE ]
Think about it like this: you get the number of dollars as the dice rolls (i.e. a roll of 4= $4).

What is the expected value of one roll (in dollars)?

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Ok, that makes sense. Maybe I'm thinking too much in probabilities?

How would this relate to the EV of a flip of a coin? Could you show me that? I know it's .5, but I'd like to see how we do that too.