“The general consensus is that utility of money goes as log(income), so giving a fixed percentage is more painful at lower incomes than higher ones”
Seems to me from the math that if it’s literally log then giving a fixed percentage of income has exactly the same effect on utility regardless of income level.
The personal utility cost of giving 10% is approximately constant, but the benefit/cost ratio definitely isn’t, since benefit (the numerator) increases linearly with income. I’ve edited this sentence to make it clearer.
“The general consensus is that utility of money goes as log(income), so giving a fixed percentage is more painful at lower incomes than higher ones”
Seems to me from the math that if it’s literally log then giving a fixed percentage of income has exactly the same effect on utility regardless of income level.
The personal utility cost of giving 10% is approximately constant, but the benefit/cost ratio definitely isn’t, since benefit (the numerator) increases linearly with income. I’ve edited this sentence to make it clearer.
I think you mean benefit increases linearly with income?
Alternatively, perhaps you meant that benefit increases exponentially with cost (since cost is log income)?
Yup, you’re right, thanks