Who values money more- the poor or the rich?

For an individual, a dollar is not always a dollar. I gain far more utility through my first 500 dollars a week than through my second 500 dollars a week income. Even more so is the value of Bill Gate’s “last” 500 dollars diminished, relative to the value of his first 500 dollars.

Naturally this has led to the proposal that redistribution will increase total welfare. The problem is that comparisons between individuals are nowhere near as straightforward as comparisons within individuals. True, Bill Gates values his last dollar less than his first, but maybe he values every single dollar he has more than any poor person values any dollar they have. Maybe Bill Gates is a utility monster!

There are many possible responses, one of my favourite is the argument from equal ignorance based on the equal ignorance theorem by Lerner. Very, very roughly If we have no information about the relative magnitude of different people’s curves over utility, our best bet, under a few assumptions is to treat everyone equally.

One reply to this line of argument is as follows. Insomuch as rich people have more money than other people, and insomuch as people tend to acquire what they desire, all other things being equal, we have prima facie evidence that the rich value money more. Probably not massively more, but a bit more. Another reply is that the rich have had time to become habituated to their luxuries, so removing them would be especially strenuous and hard to bear (poor darlings). Thus we are not equally ignorant in relation to the rich, but rather should expect them to value money more than the poor.

I want to give the opposite argument here- all other things being equal, it may be that a poor person will value their 50,000th dollar more than a rich person will value their 50,000th dollar. My argument for this is that rich people have a number of goods, not directly connected to income, that can partially substitute for income.
The most obvious respect in which this is true, so obvious it almost feels like cheating, is that the rich are more likely to own houses. Let us suppose a genie wishing to redistribute money in a utilitarian optimal way between two people snaps her fingers and gives the poorer man as much as the richer man, taking it from the richer man’s pocket. Because the richer man is more likely to own a house and does not have to pay for rent, it is likely that the poorer man has not yet been made equal to the richer man in terms of real, post-rent income, thus the poorer man may well still have a higher marginal utility of income. While many studies impute home-ownership as a form of income, not all do.

The above is also true for many lesser assets, like appliances, computers and devices.

Moving on to something a little less obvious, physical and mental health. Better health is a substitute for income in any number of ways- and poor health requires us to spend money. The rich are generally healthier- this is both because being rich makes you healthy, and being healthy makes you rich. Thus the “real” income of the rich is higher, and the real marginal utility of the poor is higher, than you would expect if you did not consider the benefits of health.

The rich are also more likely to have social support networks, hold social and cultural capital and be married. All of these can substitute for income in all sorts of ways both surprising and obvious.

All these are reasons we might expect that for any value of x, a poor person will need an xth dollar more than a rich person due to differences in their non-consumption attributes. It may well be that far from the rich valuing equivalent amounts of income more than the poor, the opposite is so. Not only do the poor have less money, they may need the money more.

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