### Tax Rates and Income Distribution

I really want to talk about tax rates, the cost of labor, and its impacts on employment and product costs; but first, I need to talk about a hot-button political topic:  income inequality.

Income inequality, in a political grenade shell, means the rich get more money than poor people.  In the United States, the top 10% earners take 48% of all income; the remaining 90% take 52%.

We’ll call it 50/50.

## Growth

First, let’s look at a graph of the growth of income over time.

Income Projection Per Year

These graphs assume 4.1% economic growth per year, or 22% over 5 years. Growth isn’t constant, and the common estimate—GDP—is all over the place.

As you can see, the working class (blue) gain more and more income each year as wealth and productivity increase.  So what’s wrong with this?  Why do people complain?

Income Distribution over Time

That’s why.

These graphs assume that, for every extra \$10, the rich collectively take \$7.50, and the working class collectively take \$2.50.  The rich are growing their collective income three times as fast as everyone else.

That means the working class isn’t actually getting poorer; it’s just looking up to see the rich climb further and further out of their view, and then look down from on high through their golden monocles while sipping their billion-dollar Champagne.

## Progressive Tax Systems

Progressive tax systems leverage income inequality.  Where a flat-tax system charges a marginal rate equal to the percentage of income required as tax revenue—30% in the United States—a progressive tax system charges above-marginal rates to the high-income earners, while charging below-marginal rates to the lower-income earners.

To illustrate, I’ll use a fictitious progressive tax system.  This system achieves a nominal 30% tax rate by charging the top 10% a higher rate than the working-class (90%).

Marginal tax rates to reach a nominal 30% tax

As shown above, at a 1:1 distribution (2015), the pay-off is 1:1.  The rich, in total, earn the same amount of money as the entire working class; if we take 1% more from the rich, we can take 1% less from the working class.

As you approach 2:1, the rich in total are earning twice the amount of money the entire working class brings in.  If we raise taxes 1% on the rich, we can lower taxes 2% on the working class.  That’s because the rich are taking, say, \$2,000, and the working class are taking \$1,000:  if we take an extra 1% from the rich, that’s \$20; but 1% of the working class’s money is only \$10, so we have to give them 2%.

To put in simple math:

• 30% of \$3,000 = \$900 (total income, 30% flat tax)
• 40% of \$2,000 = \$800 (rich people, 40% tax rate)
• 10% of \$1,000 = \$100 (working class, 10% tax rate)
• \$100 + \$800 = \$900 ( total taxes from progressive tax system)

We can compare this to a 1:1 system where the income is more equal:

• 30% of \$3,000 = \$900
• 40% of \$1,500 = \$600 (rich people, 40% tax rate)
• 20% of \$1,500 = \$300 (working class, 20% tax rate)
• \$300 + \$600 = \$900

There’s a reason I put a graph here.

This all doesn’t guarantee the after-taxes take-home remains even, or even distributed a certain way.  Carrying out the projections on this fictitious system produces the below graph of aggregate take-home income:

Class total take-home after taxes

As we can see, the rich, in total, take home less than the working class.  This actually holds true today when considering the Adjusted Gross Income (AGI), including either just personal income or personal and business income.  The AGI makes up about 80% of the total income; capital gains—taxed at 15%—fills in part of the remainder.

Over the long term, the rich actually catch up as a class to the working class.  They eventually pass the working class despite the reduction in working-class income taxes.  Because of the way my Citizen’s Dividend affects effective taxes, workers under about \$50k in 2013 dollars collect an effective negative income tax, which significantly slows this process.  The above graph would look different under a Citizen’s Dividend:

Class total take-home after taxes using a model of a Citizen’s Dividend

An incredibly wealthy society begets a high income gap, and even having a rich upper-class with this much collective income above the working class is novel.  The Romans had a population of over 100, million and 23,000 equites—a very small aristocracy and a very large population; America had 314 million people in 2014, and 31.4 million of them together collected half the income.  Part of the enormous gap is just that we have more rich folks than ancient empires; the other part is that our rich folks are richer than historical rich folks, hence why we have multi-millionaires running businesses where employees make \$30k.

## Conclusion

Income inequality isn’t a new problem; in the long view, it isn’t even really a problem, so long as the buying power and, by extension, the standard-of-living of all classes increases at a reasonable rate. A progressive tax system which lowers the income tax rate on the working class while not increasing the income tax rate on the high-income earners can steadily decrease the cost of labor, increasing employment and keeping the cost of any standard-of-living low.