The Y axis measures utility (i.e. benefit, satisfaction) and the X axis measures income. The slope of the utility profile is the marginal utility, or the additional satisfaction, gained by one more dollar of income. In this picture it is easy to see that the slope of the total utility line is steeper at $50,000 than $500,000. So if two people had this same utility profile there would be a net gain in the total utility of society if a dollar was taken from the person earning $500,000 and given to the person earning $50,000.
Seems simple right? But of course this is not the whole story. There is no reason to think that all people have the same utility profile when it comes to income. People of similar ability often choose different career paths. Some high ability people choose occupations where they work long hours and receive large incomes. Other people with similar ability choose less stressful occupations with lower incomes. In fact, it is easy to find people of similar ability in the same occupation working for the same employer who choose to exert different amounts of effort on the job. This usually results in different incomes. Think of salesman working for the same employer, bankers working in the same branch, or even professors working for the same university in the same department. Some of these people will work long hours trying to get the next raise or make the next sale, while others prefer to work less and spend more time with their friends or families. Neither choice is correct, but they are different.
In this case, the utility profiles might look something like the diagram below.
In this diagram, person A is the person who really values money. Their marginal utility of another dollar of income is higher at all income levels than person B's. In this diagram, the marginal utility of another dollar for person A is greater at $500,000 than the marginal utility of another dollar for person B is at $50,000. So it is no longer a net utility gain to take a dollar from person A and give it to person B, even though person A is wealthier. If diagram 2 more accurately portrays reality than diagram 1 the utility justification for taking money from the wealthy and giving it to the less wealthy no longer applies.
My personal opinion is that diagram 2 more accurately reflects reality. The empirical observation that people with similar ability and in similar occupations exert different amounts of effort on the job implies that people have different utility profiles over income.
Some people might say that their are other factors going on though and that in reality the profiles of people are in fact quite similar. In this case it is different opportunity costs that lead to the observable differences in work effort, not necessarily differences in marginal utility holding all else constant. So let's assume that people do have the same utility profile over income. Does that mean that all income sources must have the same utility profile? What if earned income has a different utility profile than "free" income?
The argument I am making is that people value a dollar differently depending on where it comes from. If I work harder at my job or work more hours to earn another dollar, the satisfaction I get from that dollar is different than the satisfaction I would get if I found a dollar on the ground.
Nobel Prize winning economist Milton Friedman observed that people act differently when they spend money depending on whose money it is and who they are spending it on. The marginal utility, marginal cost decision that results from spending another dollar is different depending on the source of the income. I think a similar idea is true when it comes to earning income. People take pride in earning their own money; that is they get satisfaction above and beyond the value of the dollar they earn. People on average do not seem to enjoy being given money, whether through charity or by government programs, as much as they enjoy "earning their keep". Most people do not like being labeled a charity case. In this case a person's utility profile would be different based on the source of income and might look like the diagram below.
In diagram 3 earned income, the black profile, has a higher marginal utility at all income levels than what I label "free" income. "Free" income is unearned income that is the result of charity, a government program, a serendipitous event, etc. If this diagram is accurate and every person has similar profiles over earned and "free" income then taking a dollar from someone who earned $50,000 and giving it to someone who already has $50,000 is not a net utility gain since the marginal utility of an earned dollar is greater than the marginal utility of a "free" dollar. This is the case even if the person who is receiving the "free" dollar has has less than $50,000 in income e.g. only $20,000 or $10,000.
I believe that diagrams 2 and 3 accurately reflect reality. That is, people have different utility profiles over income as a whole and different utility profiles over the sources of income.
In real life utility is impossible to measure with 100% accuracy. But even if it could be measured accurately I think we would find that the assumption that wealthy people have a lower marginal utility of another dollar than less wealthy people is incorrect. Taken together diagrams 2 and 3 invalidate the utility justification for taking money from the relatively wealthy and giving it to the less wealthy.