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Poor people don't need to gamble to imagine themselves as rich. It does happen sometimes, but the expected value of lotteries etc. is negative.
What's the evidence that the psychic thrill of gambling is less for the rich? Note that, to substantiate this claim, you can't assume a diminishing marginal utility of wealth.
If it's less urgent, then that means that their preference for saving a marginal unit of money vs. spending it is greater. As I said, in modern utility theory, something only has utility relative to something else; mathematically, utility is defined as an ordinal variable corresponding to a ranking of alternatives.
There's a further issue, of course, of defining a common unit of utility across people. I'm assuming that's somehow not a problem, because otherwise the "diminishing marginal utility" position is REALLY stuffed.
I also forgot another reason why "diminishing marginal utility of money" is a misnomer: it should really be called "diminishing interpersonal marginal utility of money", because the marginal utility can be decreasing for each individual and yet the value of one more unit of wealth can be greater for rich people rather than poor people. Diminishing marginal utility of money for each individaul does not imply that an additional dollar gives greater utility to a poor person than a rich person. In fact, it's logically possible that money can have diminishing marginal utility for each person and yet one still maximises utility by taxing the poor to give to the rich.
For example, consider a society with two people, A and B. We define MUn(a) as the marginal utility of money for the nth unit of money for A and MUn(b) for B mutatis mutandis.
Suppose that MUn(a) = 1^(-n). So the marginal utility of the 100th unit of wealth for A is 1 / 100. The marginal utility of the 10,000th unit is 1 / 10,000. Thus, the marginal utility of money for A is diminishing: it decreases with each unit. In fact, it's monotonically diminishing: the marginal value of the nth unit is less than each previous unit.
Suppose that MUn(a) = 1^(-√n). So the marginal utility of the 100th unit of wealth for A is 1 / 10. The marginal utility of the 10,000th unit is 1 / 100. Again, the marginal utility of money for B is (monotonically) diminishing.
If A has $499 and B has $159,999, then the value of an additional dollar for A is 1 / 500 and the value of an additional dollar for B is 1 / 400. Utility is maximised by B having the additional dollar, even though we are assuming utility is (montonically!) diminishing.
And again, this is all assuming away the problem of interpersonal utility comparisons, because otherwise I don't begin to have a functioning version of your position with which to play. You could say "Obviously, utility doesn't work the way you specify in your example," but then you ARE obliged to explain how you find a common unit of utility for people in the real world, because all I am granting in this example is diminishing marginal utility of money (relative to something else that is common between A and B, e.g. assuming a common valuation of a Big Mac).
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