How is the principle of diminishing marginal utility used to justify income redistribution?
In order to understand this, let us first look at what the theory of diminishing marginal utility actually is. This is a theory that says that consumers get less marginal utility from using a good or service as they come to use it more and more. In other words, the more you use of something, the less valuable each use is to you. Let us look at some examples.
If I am extremely hungry and I eat a hamburger, that hamburger is very useful to me since it stops me from feeling so hungry. A second hamburger might be really useful as well since I was very hungry. But no matter how hungry I am, a fourth or fifth hamburger is not going to be as important to me. I have already gotten pretty full by this time and eating that fifth hamburger will not be as useful. Or imagine that I bring my kids to Disneyland. The first few times will be really exciting. But what if I force them to go 20 days in a row? They are likely to get tired of it. In these ways, the more times something is consumed, the less useful it is to the person consuming it.
This can be used to justify redistribution of income. To justify it, we would say that richer people are not benefitting from their money as much as poorer people would benefit from it. If you take $10,000 from a person who made $150,000, they will not miss it that much. By contrast, if you gave that $10,000 to someone who only made $10,000 on their own, it will be extremely valuable to them because it will allow them to consume things they could not have consumed before. Rich people are getting less marginal utility from their money because it is being used (as it were) to buy the fifth hamburger whereas it could be used to buy the first hamburger for a poorer person. Therefore, one can argue, it is just to redistribute income.