(0) It is a slow day at Bunsen Motors, so since he has his calculator warmed up, Clarence Bunsen (whose preferences toward risk were described in the last problem) decides to study his expected utility function more closely.
(a) Clarence first thinks about really big gambles. What if he bet his entire $10,000 on the toss of a coin, where he loses if heads and wins if tails? Then if the coin came up heads, he would have 0 dollars and if it came up tails, he would have $20,000. His expected utility if he took the bet would be _____ , while his expected utility if he didn’t take the bet would be _____. Therefore he concludes that he would not take such a bet.
(b) Clarence then thinks, “Well, of course, I wouldn’t want to take a chance on losing all of my money on just an ordinary bet. But, what if somebody offered me a really good deal. Suppose I had a chance to bet where if a fair coin came up heads, I lost my $10,000, but if it came up tails, I would win $50,000. Would I take the bet? If I took the bet, my expected utility would be _____. If I didn’t _____ the bet, my expected utility would be _____. Therefore I should take the bet.”