Two Plus Two Newer Archives  

Go Back   Two Plus Two Newer Archives > Other Topics > Student Life

Reply
 
Thread Tools Display Modes
  #1  
Old 10-22-2007, 03:52 PM
ItalianFX ItalianFX is offline
Senior Member
 
Join Date: Nov 2005
Location: 3 Weeks to Freedom
Posts: 4,808
Default 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.
Reply With Quote
  #2  
Old 10-22-2007, 04:15 PM
relativity_x relativity_x is offline
Senior Member
 
Join Date: Sep 2006
Location: 3 bet min-raising
Posts: 947
Default Re: Econ HW - Expected Value

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

[/ QUOTE ]

I would say it's 1/6

[ QUOTE ]

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?

[/ QUOTE ]

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.
Reply With Quote
  #3  
Old 10-22-2007, 04:22 PM
buttonpusher buttonpusher is offline
Senior Member
 
Join Date: Oct 2007
Location: pushing various buttons
Posts: 169
Default 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.
Reply With Quote
  #4  
Old 10-22-2007, 04:37 PM
jman3232 jman3232 is offline
Senior Member
 
Join Date: Feb 2007
Posts: 113
Default 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.
Reply With Quote
  #5  
Old 10-22-2007, 04:42 PM
ShaneP ShaneP is offline
Member
 
Join Date: Aug 2006
Posts: 80
Default 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
Reply With Quote
  #6  
Old 10-22-2007, 04:48 PM
tabako tabako is offline
Senior Member
 
Join Date: Sep 2006
Location: Madison
Posts: 1,393
Default 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.
Reply With Quote
  #7  
Old 10-22-2007, 05:33 PM
ItalianFX ItalianFX is offline
Senior Member
 
Join Date: Nov 2005
Location: 3 Weeks to Freedom
Posts: 4,808
Default 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?
Reply With Quote
  #8  
Old 10-22-2007, 05:37 PM
tabako tabako is offline
Senior Member
 
Join Date: Sep 2006
Location: Madison
Posts: 1,393
Default 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?
Reply With Quote
  #9  
Old 10-22-2007, 08:24 PM
jman3232 jman3232 is offline
Senior Member
 
Join Date: Feb 2007
Posts: 113
Default 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)?
Reply With Quote
  #10  
Old 10-22-2007, 09:15 PM
ItalianFX ItalianFX is offline
Senior Member
 
Join Date: Nov 2005
Location: 3 Weeks to Freedom
Posts: 4,808
Default 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)?

[/ QUOTE ]

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.
Reply With Quote
Reply

Thread Tools
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off

Forum Jump


All times are GMT -4. The time now is 04:17 PM.


Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2024, vBulletin Solutions Inc.