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Income Inequality Math

The President made more comments in regards to income inequality during his State of the Union and again during his budget release.

It is not that I don't think income inequality exists, I wonder if it is natural. Is income inequality just a function of math?

For example, you have two families, Family 1 and Family 2. Family 1 has a take-home pay of $100,000 per year and Family 2 has a take home pay of $50,000 per year. Both families have firm budgets and live within their means. Both families invest 5% of their take home in dividend producing securities. Matter of fact, they invest in the exact same stocks at the exact same time.

The stocks have an initial yield of 3% at the time of the investment and between dividend raises and the effects of compounding, the distributions increase by 5% per year.

After ten years, family 1 has an income of $1,887 per year and family 2 has an income of $943 per year.

Is this income inequality? Does family 1 has too much dividend income? Or is it just a function of math. More disposable income that can be saved or invested and have the potential to grow over time?

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