Let's say that my utility function over wealth is LaTeX:U=\ln\left(W\right) U = ln ⡠( W ) where W is my wealth in dollars.Suppose I currently have $1,000,000 in wealth (oh ye-ah), but myfriend Rob offers me an opportunity to invest in his new start-upcreating autonomous window-washing robots. [Note: the robots partis a kinda-true story. Ask me sometime!] If the start-up issuccessful—and we estimate it has a 10 percent chance ofsuccess—Rob will pay me $2,000,000. If it fails, however, I am paidnothing. He offers me this opportunity at a price of $100,0001.What is the expected value of this opportunity? 2.What is theexpected *utility* of this opportunity? 3.Would I take Rob's offergiven my risk preferences?
