Stats/Econ help -- Expected Utility Calculation

truxmonster · #1 $Old$ October 4th, 2008, 11:58 PM

Matthew is a contestant on the game show "Behind the Curtain." The host has given him $50. In front of Matthew are three curtains. Behind one curtain is a jar with three dimes. Behind the second curtain is a check for $30. Behind the third curtain is a check for $120. Assuming he is risk neutral and interested only in the cash value of the value, is Matthew willing to trade the $50 for a chance to pick a curtain at random and take whatever prize it conceals? Explain by writing the appropriate expected utility calculation.

mr fantastic · #2 $Old$ October 5th, 2008, 12:24 AM

Quote:

Originally Posted by truxmonster $View Post$

Matthew is a contestant on the game show "Behind the Curtain." The host has given him $50. In front of Matthew are three curtains. Behind one curtain is a jar with three dimes. Behind the second curtain is a check for $30. Behind the third curtain is a check for $120. Assuming he is risk neutral and interested only in the cash value of the value, is Matthew willing to trade the $50 for a chance to pick a curtain at random and take whatever prize it conceals? Explain by writing the appropriate expected utility calculation.

I also posted this in Statistics Help. Sorry for double posting, but I'm hoping to get as many people as possible to answer this quickly.

You will not get help more quickly by double posting. Posting a question once is sufficient for it to be seen by any member competent and willing to help.

Forum rules clearly state:

Quote:

1) Do not create identical threads. Do not double post.

The rule is there to prevent people wasting their time time answering a question that may already have been answered.

Your desire to get a quick reply is not an excuse for breaking this rule.

mr fantastic · #3 $Old$ October 5th, 2008, 12:28 AM

Quote:

Originally Posted by truxmonster $View Post$

Matthew is a contestant on the game show "Behind the Curtain." The host has given him $50. In front of Matthew are three curtains. Behind one curtain is a jar with three dimes. Behind the second curtain is a check for $30. Behind the third curtain is a check for $120. Assuming he is risk neutral and interested only in the cash value of the value, is Matthew willing to trade the $50 for a chance to pick a curtain at random and take whatever prize it conceals? Explain by writing the appropriate expected utility calculation.

Consider the expected value of the prize that can be selected from behind the curtain:

(1/3)(0.3) + (1/3)(30) + (1/3)(120) = ......

Is this greater or less than $50 .....?

truxmonster · #4 $Old$ October 5th, 2008, 05:06 PM

Quote:

Originally Posted by mr fantastic $View Post$

Consider the expected value of the prize that can be selected from behind the curtain:

(1/3)(0.3) + (1/3)(30) + (1/3)(120) = ......

Is this greater or less than $50 .....?

Sorry for double posting!

Since the expected value of the prize is greater than $50, then he is willing to trade the $50 for a chance to pick a curtain at random.. is that correct?

What I had initially done was calculate the loss and gain of each possibility:
(1/3)(-$49.7) + (1/3)(-20) + (1/3)(70) = 1
Would it also be right if I did it like that? I assumed that an answer of 1, as opposed to 0 for neutral and -1 for a loss, would mean a gain.

icemanfan · #5 $Old$ October 5th, 2008, 05:20 PM

Quote:

Originally Posted by truxmonster $View Post$

What I had initially done was calculate the loss and gain of each possibility:
(1/3)(-$49.7) + (1/3)(-20) + (1/3)(70) = 1
Would it also be right if I did it like that?

Yes, with a positive answer indicating an expected gain.