The assumption that the marginal utility of wealth decreases exponentially doesn’t seem justified to me. Why not some other positive-but-decreasing function, such as 1/W (which yield a logarithmic utility function)?
What properties does the utility function need to have for this result to generalize, and are those priorities reasonable to assume?
1/W is totally fine! If that was your utility function you’d reject the bet at low wealth and accept it at high wealth.
The exponentially decreasing thing is just a bound—on the domain where you reject the bet your marginal utility of money will be decreasing faster than C⋅e−0.0013w.
The assumption that the marginal utility of wealth decreases exponentially doesn’t seem justified to me. Why not some other positive-but-decreasing function, such as
1/W(which yield a logarithmic utility function)?What properties does the utility function need to have for this result to generalize, and are those priorities reasonable to assume?
1/W is totally fine! If that was your utility function you’d reject the bet at low wealth and accept it at high wealth.
The exponentially decreasing thing is just a bound—on the domain where you reject the bet your marginal utility of money will be decreasing faster than C⋅e−0.0013w.
Sure, but that does imply that your marginal utility of money decreases that fast outside that domain.