Hi,
How can the infinite sum of Bernoulli's proposed resolution of the St Petersburg paradox be calculated using Mathematica?
I tried the below formula in Mathematica but it didn't give me a numerical solution. I was expecting 'c', the player's maximum price to take part in the lottery, to be 10.95 dollars.
w = 1000000;
NSolve[Sum[1/2^n*(ln[w + 2^n - c] - ln[w]), {n, 1, Infinity}] == 0, c]
I tried simulating the infinite sum using a spreadsheet and for a player with a wealth of 1,000,000 dollars who has a natural log utility function, I found that he would pay a maximum of 10.95 dollars. This spreadsheet is here.
The formula above
Sum[1/2^n*(ln[w + 2^n - c] - ln[w]), {n, 1, Infinity}]
is the solution proposed by Daniel Bernoulli. The details of the St Petersburg paradox are described here.
Thanks for your help. Apologies if this is a silly question.
Cheers,
Keith