Suppose your utility function is U(I)=I^1/2 a) If your income is $36000, how muc
ID: 1248679 • Letter: S
Question
Suppose your utility function is U(I)=I^1/2a) If your income is $36000, how much utility do you enjoy?
b) Suppose your brother-in-law offers you an investment that would cost you $10000. It has a 50% chance of doubling to $20000 and 50% chance of halving to $5000 in value. What is your expected utility when you invest?
c) Suppose your brother in law would only allow you to invest if you paid him a $1000 finders fee? What is your expected utility when you invest?
d) How big of a finders fee are you willing to pay?
Explanation / Answer
The previous attempt is, indeed, incorrect. A) U=(36000)^(1/2)=189.7367 B) Let's look at the utility derived from each outcome. 50% of the time, you get U=(20000)^(1/2)=141.4214 and 50% of the time, you get U=(5000)^(1/2)=70.71068. This means you're expected utility is EU=.5*141.4214+.5*70.71068=106.066 The utility you derive from keeping the 10000 is U=(10000)^(1/2)=100. So, you should take the bet. C) Now, we calculate the new expected utility by subtracting off the 1000 from each outcome. EU=.5*(20000-1000)^(1/2)+.5*(5000-1000)^(1/2)=100.543. It's cutting it close, but you should still take the bet and pay the fee. D) To find this, we have to see what fee would drive us to an expected utility of 100, since that is our expected utility from not taking the bet. Let F represent the fee that would do that. EU=.5*(20000-F)^(1/2)+.5*(5000-F)^(1/2)=100 From here, it is some simple algebra. The answer is $1093.95. You can do this with a graphing calculator or Excel. I'm not sure how you would do it algebraically because you can't combine the square roots.
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