Mathematics is a crucial tool for economics. In my view, it is good for all economists to try to understand better what is going on in mathematics. So I have decided to host an occasional math column in this blog.
Those of you who have been following this blog closely have seen the very interesting posts based on Gary Cornell’s emails to me. Gary has agreed to be this blog’s math columnist! For now, the math column will always be headed by a title that begins “Gary Cornell on …” or a title that has the word “math” or “mathematics” somewhere in it.
Here is Gary’s post for today:
One thing I noticed when I was watching the whole financial crisis at work which I never saw mentioned in the econ blogs was this. Consider the following model for a financial firm. You work for a firm on wall street worth 50 billion dollars. Your part of the business actually consists of once a year spinning a roulette wheel with 100 numbers marked zero to 99. If 1-99 comes up you get a 1 million dollar bonus and your firm makes 10 million from some third party. If the 0 comes up your firm goes bankrupt wiping out 50 billion dollars in its market cap.
Question: How many spins before there is even a 50% chance of my company blowing up?
The elementary probability calculation needed for the answer in turn leads to the problem that while the expected value is hugely negative, the most likely scenario is that I and all my bosses and their bosses will be long since retired and very rich before my company goes under, so I would have to be a fool not to play.