What is the utility of gazillion dollars?

Subjective utility of very large numbers is not bounded but undefined. Let

N = 2 to power 1,000,000,000,000,000,000,000,000.

Some people may say that the utility of having 2N dollars is not smaller than the utility of N dollars. The standard explanation for this position is that if you happen to prefer N dollars rather than 2N dollars then you can give away N dollars. When was it last time that someone donated N dollars to a charity? The utility of N dollars is undefined because we have no experience with sums of money that are close to N. We can ask an individual what his or her feelings about N dollars are but whatever the answer might be, it is a figment of imagination. Since nobody has N dollars, no claims about utility of N dollars can be verified in any scientifically acceptable way, such as observations of individuals making decisions involving N dollars.

The utility function was introduced by Bernoulli as a realistic measure of the utility of a given sum of money (at least more realistic than the nominal value of the money). A bounded utility function could explain the St Petersburg paradox, in which a person is willing to pay only a finite fee for an opportunity to play a game with infinite payoff. The explanation works only if the utility of all sums of money is well defined and bounded. For large sums of money, the utility function is not well defined.