I answered this question over at Quora. Just about all the other answers were wrong, so I thought I’d set things straight.
No. Value is not a quantity. It cannot be compared across individuals, so we cannot say that $50 is more valuable to person A than to person B.
To understand value, you must understand action. To act is to select one thing and set aside another. Thus, an ability to evaluate one thing over another is a necessary prerequisite to action, one that all mentally functioning humans possess. Valuation is always a comparison between two alternatives. It is a comparison made in the mind of an acting human.
Because the high income person and the low income person are different individuals, their valuations cannot be compared. We could say something like, “the low income person values an hour of his time less than $50, while the high income person values an hour of his time more than $50.” But this does not mean the low income person values $50 more than the high income person does in any absolute sense, because an hour of time is not the same to different individuals.
Some people have said that the answer is yes because marginal utility decreases with quantity. This is a misinterpretation. It is true that people tend to value additional units of a stock of interchangeable consumer goods less with each additional unit. This is because a person will use the first unit of the good to satisfy his highest unmet need, the second unit to satisfy his second highest unmet need, the third unit to satisfy his third highest unmet need, and so on. Thus, marginal utility does decrease with quantity. But it only meaningfully decreases with respect to other goods! If I have five dumplings, I might value an additional dumpling more than a battery, but if I have six or more dumplings I might value the battery more than an additional dumpling.
While I value things less with each additional unit, we can’t take this to mean my valuation of my total wealth must decrease as I grow wealthier. Total wealth comprises everything, leaving nothing to compare it against, so valuation is meaningless.
UPDATE: To clarify, if the question had been, “Would a gift of $50 improve the well-being of a poor person more than it would improve the well-being of a rich person,” then other people’s interpretations would be acceptable. The primary error is in using the word “value” without recognizing that value is a purely ordinal concept that has no interpretation outside the mind of the person doing the evaluating. “He would choose A over B,” is an identical statement to “he values A over B.” But neither of those statements are equivalent to “A would improve his well-being more than B” because sometimes people choose to sacrifice their well-being to achieve other ends. Think of soldiers volunteering for suicide missions.
While I am not a believer in any major government redistribution, I do think it is obvious that a very poor person values 50 dollars more than a very rich person. I am not particularily well off, but if I lost 50 dollars I would stop caring within a few hours. I have encountered people who live on 50 dollars a month and would be devastated by the loss (in the third world). And I wouldn´t do much to earn 10 dollars, but I know people who would be stoked for days if they earned 10 dollars. I don´t think you can numerically compare value; but, it is clear to me from my interactions with other people that some people value money more than others. The extent to which an individual values money is also a function of more than their earning potential. Some wealthy people obsess over small amounts of money and some poor people spend little mental energy over larger amounts.
My point is that value is an ordinal concept. I would certainly agree that a poor person would have a stronger emotional reaction to gaining or losing $50, but emotional reactions are not valuations. They can certainly motivate valuations, but the valuation itself is a comparison of one thing against another. To say that A is more valuable than B is to say that some specific, choosing individual would select A over B if they were given as alternatives. In the question, we have one item, $50, and two choosing individuals, the rich person and the poor person, so we don’t have any basis to talk about value.