Lucky is tired. Not an uncommon occurrence, granted, but this time for a couple reasons. Last night, he found an equation that he wanted to solve, and set out on a merry little quest to do it. It reminded him of his days in high school and college, when he fancied himself rather OK at math. "This will be a nice, thirty-minute respite," he thought, a welcome step on quantitative ground that can be so reassuring after the bewildering quicksand of pseudo-science subjects so common in MBA programs.
Four or five hours later, closing in on 0330h, after calling in favors from timezones far away, he threw in the towel. Three hours after falling asleep, he woke up and headed back to campus for an early class. He showed the professor the equation, and restrained himself suitably when the prof said, "I think that equation has no closed-form solution." After thinking about it, the prof did admit that he seemed to remember solving it years ago and would search for the appropriate references.
Ok, now you want to try your hand at it? Have at it:
Solve for Y in terms of R:
e^(-y/r) + e^(y/2r) = 2
What is this equation? It has to do with risk tolerance, and the fact that most people's utility functions can be represented with an exponential form: u(x) = 1 - e^(-y/r). If you use this function, ask yourself the maximum value of Y for which you would accept a 50/50 bet to win Y or lose Y/2...
If your eyes glaze over, don't worry; business school (at Insead, at least) requires very little quantitative ability of this kind. However, Lucky enjoys using math to gain, shall we say, competitive advantage, because if you match up quant jocks against poets, odds are that the quant jocks will have better performance. Most important, managing quant jocks is difficult if you can't speak the language.
7:20:40 PM 
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