Assuming the average person's utility function is concave with respect to money and given the current income distribution the simplest and highest utility change is to take a fixed amount from high income people and give it to low income people.

When you consider second order consequences, such as the creation and elimination of certain incentives, the effect of currency transfers on utility is not quite so straightforward. Even without those consequences, it is far from obvious that the statement

This follows from simple economics as the people on the lower end of the distribution know best what it is they need.

holds.