We cannot perform the desired comparison.
Namely, it's not clear that one can sum utilities over multiple individuals in a meaningful way.
Utility is an ordinal measure, meaning it only cares about order.
The reason the utility functions exist is because I can perform a mapping to a utility function for any list of preferences.
Example of the Mapping:
If my preferences are, in order:
- Answer SO questions.
- Go to Movies.
- Play Games.
Then I can map this to the values:
- Answer SO questions. (5 utility points)
- Go to Movies. (3 utility points)
- Play Games. (1 utility point)
But the points themselves are meaningless, and the difference between them and relative magnitudes are also equally meaningless. I could have also assigned them 200/3/-100 and the order and structure would be the same, this means they are ordinal. But because I can perform an ordinal assignment we can easily construct a function for lists like:
- Consume 100 units of widgets.
- Consume 99 units of widgets...
- Consume 0 units of widgets...
Economics is not explicitly committed to the idea that individuals assign utility points in a remotely comparable pattern. Even if this were the case, there is no way to perform this calculation.
As an aside, however, we can look at the decline in consumption that occurs from taxation for wealthy people.