Wealth Gap Simplified

Is there a simple way to understand how the wealth gap is created? 

Wealth is now the bad guy in the movie

Considering the latest wave of wealth-redistributionists lurking around every corner of the internet, this is an important question that should be addressed as succinctly as possible. So, let's take a shot at it.
Two people, Person A and Person B, get a job at company X. They make the same income. They both pay for the basics like housing and food.
Besides the basics, Person A prefers to buy things that loose value over time, like a new car. The car is, of course, bought with a loan.
Person B buys only the basics and accumulates any leftover as savings.
Over time, Person A continues to show a better standard of living but creates no wealth.
Meanwhile, Person B takes the accumulated savings and invests them into a machine that makes gizmos. She operates the machine after hours and sells the gizmos during weekends. There is decent demand for the gizmos and the machine is quickly paid for. Soon, a third person is hired to handle the machine and gizmo sales. All along both maintain their job at company X.
Person B continues to accumulate savings from her job plus the proceeds from the sales of the gizmos. These savings are later used to buy more machines, thus increasing the investable cash flows.

Should entrepreneurs be punished?

Fast forward a few cycles and Person A continues to have a good standard of living from his job. Unfortunately he has also failed to accumulate wealth.
In comparison, Person B has invested in income generating machines and has accumulated great wealth thanks to the compounding effect of re-invested earnings.
The wealth gap is now massive, even when both have done their job at company X just as well.
No one acted badly at any moment. The only issue was that Person A did not know about the benefits from compounding savings through investing; but that could easily be solved with a little education.
The understanding that neither has been unfair with the other is what makes America what it is today. Here, our presidents don't discuss taking money from investors to give it to those who only spend. In other countries, on the other hand, people complain when others succeed. Not in America.