Lost: a decision maker’s risk attitude toward monetary gains or losses...

[hallbra1]

Lost: a decision maker’s risk attitude toward monetary gains or losses...

Good afternoon,

I'm working on some practice sets, and I have hit a roadblock. My professor had a short except from a video entry giving a very basic utility function problem, along with a paragraph devoted to the topic in our textbook. However, he elevated the level of difficulty with several similar practice problems. I can't wrap my head around this. His example was easier as it compared a sure thing ($500) to two other uncertain higher value outcomes. Any guidance would be greatly appreciated.

Sample style problem below:


Suppose that a decision maker’s risk attitude toward monetary gains or losses x given by the utility function U(x) = (10,000 + x)^0.5. Suppose that a decision maker has the choice of buying a lottery ticket for $1, or not. Suppose that the lottery winning is $500,000, and the chance of winning is one in a thousand. True of false: The decision maker should buy the lottery ticket.

 

[JeffM]

Is x the expected value of the gain or loss?

 

[hallbra1]

It just says the "attitude towards gains or losses". There are a handful of similar practice problems, all with the base working. See 2nd example below:

Suppose that a decision maker’s risk attitude toward monetary gains or losses x given by the utility function. Suppose that a decision maker has been given a lottery ticket for free. Suppose that the lottery winning is $500,000, and the chance of winning is one in a thousand. What is the minimum price that the decision maker would be willing to sell the ticket for?

 

[JeffM]

The questions are not phrased with the greatest clarity, but perhaps that has been provided with context in the text or lectures. So I am guessing that this is about expected utility.

\(\displaystyle U(-\ 1) = \sqrt{-\ 1 + 10000} \approx 99.995\ and\)

\(\displaystyle U(-\ 1 + 500000) = \sqrt{509999} \approx 714.142.\)

\(\displaystyle E \left ( U \right ) \approx 99.995 * 0.999 + 714.142 * 0.001 \approx 100.61 > 100.\)

The expected utility of not buying is \(\displaystyle \sqrt{0 + 1000} = 100.\)

So buy the ticket.

Does this look like what was going on in class?

 

[hallbra1]

His example in class was very elementary. However, I did scrubbed the web and read other articles. I actually made it through your first step, finding U(-P). However, I missed the second step and went straight to the last step. I used 500000 instead of the 714. Thank you for helping me fill in the missing link.

Brad

 

[stapel]

It just says the "attitude towards gains or losses". There are a handful of similar practice problems, all with the base working. See 2nd example below:

Suppose that a decision maker’s risk attitude toward monetary gains or losses x given by the utility function. Suppose that a decision maker has been given a lottery ticket for free. Suppose that the lottery winning is $500,000, and the chance of winning is one in a thousand. What is the minimum price that the decision maker would be willing to sell the ticket for?

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