Stats/Econ help -- Expected Utility Calculation

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.

Quote:

---

Originally Posted by truxmonster

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.

Quote:

---

Originally Posted by truxmonster

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 .....?

Quote:

---

Originally Posted by mr fantastic

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.

Quote:

---

Originally Posted by truxmonster

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.