What is the utilitarian case for the redistribution of income?

The utilitarian idea of income redistribution is based on an assumption. They call it diminishing marginal utility. This name of course is part of the philosophies name. The point made is that extra dollars to a poor person with more additional utility than the extra dollars do to wealthy people. Thus in its shortest form, the poor person will add spending into the economy while the wealthy population may simply place it in savings or to make an extreme point, spend it abroad on a vacation.

With this in mind, not only are poor people helped, but the larger good is done by increased spending in the economy.