A Daily Kos author beat me to the punch by several years (probably due to being older than me) and wrote a beautiful equation. I have made a few tweaks to it, first of all I removed his 20% increase at the end and reduced the maximum rate to 50%. This reduces the maximum rate and increases the number of people who get money from the government, which will be a big boost to the economy since they spend close to 100% of their income.
The only other issue is how the government will be able to afford everything. The one thing with his calculation is that he probably didn't include capital gains as regular income, which I do. I need to do some work on to see what the impact will be of this policy change in the future, but I expect that treating capital gains as regular income, since they make up most of the income of millionaires, will make a tremendous difference to the government budget.
The only other thing is I increased the number of people who would pay a negative income tax. Using Census bureau data from Wikipedia it is then very easy to calculate how much revenue the government will receive from any tax code.
My equation looks like this: (Maximum Rate*Taxable Income/0% Tax threshold-Subtractor)/Square root(Divisor+(Taxable Income/0% Tax threshold)^2. This is basically the same as the equation proposed in the Daily Kos article, but made so the variables are undefined so they are easily changed. The values I used make the equation look like this: (0.50*Taxable Income/Cost of living for your family in your state - 4)/Square Root(50+(Taxable Income/Cost of living for your family in your state)^2.
For this equation this means that the average family making under roughly $142,000 will receive money as opposed to paying taxes, because of how unequal our distribution of wealth is, and everyone above that number will pay taxes. The Actual tax rate's lowest amount with these numbers is -28.28% and it increases forever approaching but never touching and never exceeding 50%. There will be a few deductions for things such as health care and education as well.
For a family in the 98th percentile they will pay around 15% of their income in total Federal income tax. Even while paying for the negative income tax for 86% of all Americans they will still have close to $5 trillion in income to pay for our expenses (I say our because they are public projects). For comparison the Federal government spent $3.5 trillion last year. This will mean we can either increase the amount of transfer payments people receive or pay off the deficit, whatever will be best for the economy.
When it come to income inequality this tax code will make a tremendous difference. The top 2% of wage earners currently make approximately 58.2% of all income is my estimation in the spreadsheet I used to model this, after tax income for them will then be reduced to 39.5% of income, for almost a 20% reduction. This will help make us a much more equal society.
This has a direct impact to poorer regions in the United States. Let's say you live in a county where the median household income is $40,000. The average tax rate in this county will be approximately -9.8%, meaning a stimulus of approximately $4,000 per person in the county. This tax code will help stimulate the economies of rural areas which will help small businesses across the nation by putting money in the hands of customers who will then spend that money in these local stores. If we look at the economy of Spokane County, Washington (for a random example) they have a median household income of $37,308 and a population of 471,428. This means an economic stimulus of $900 million to their economy, or $2000 per person. Every county in America will receive a stimulus since the top 7% who will pay taxes are dispersed across America and spend only a small percent of their income, and every county's median income is below the 0% threshold.
On the extreme side, Owsley county, Kentucky is the third poorest county in the nation with a median household income of $15,000, a per capita income of $10,000 and a population of 4,600 would have an average tax rate of roughly -25% meaning they would receive approximately $2500 per person for a grand total of $1.2 million. This will stimulate local businesses in these regions which are constantly in depression and move them towards a better future. This is what a tax code should do.
We need a more progressive tax structure, and one of the easiest ways to alleviate poverty and create a more equitable distribution of income is to give people money. This is hardly a Marxist idea since it was proposed by Milton Friedman of all people, and is something that we should all agree on to make our nation a better place. When one looks at what countries use taxation, the vast majority have a progressive tax structure, with the majority of countries with flat taxes being former Warsaw Pact nations, which are hardly known for their successful economic policies. If you want to stimulate an economy you have to look at the multiplier effect on the people your policies are going to effect, and this means that you want to tax the poor who spend the highest percent of their income the least (since consumption has the highest available multiplier, and they use almost all their income for consumption) while those who make the largest amount of money use most of their money for investment which has a lower multiplier than consumption. This is a basic fact of modern economics, and essential to conducting good policy. So, a good tax policy will tax the most on places and people which have lowest impact on overall productivity and tax the least on places and people which use almost all of their income for consumption. This is because the added benefit of one more unit of consumption decreases the more I own. Going from having no lunch to one lunch makes me very happy. Getting a second bite to eat might make me more happy if I am still slightly hungry, but there will come a point where I am going to be full, and at that point getting more to eat might actually make me worse off than just not eating more food. This is satiation. Satiation is why people who make more money save more money as a percentage of their total income than people who make less. This is the reason why we want to have a progressive income tax which means government investment doesn't cut too much into consumption but means that public sector investment is mostly displacing private investment as opposed to consumption, though it will always displace some consumption such an effect is minimized.
I have designed the whole code and here is what the effect on income inequality would be like based on US Census Bureau Data on American Income Inequality:
This is a good thing because short-term economic growth comes from consumption, and if we cut that too much we could trigger a current recession. The government expenditure should mostly be focused on long-term investment in normal non-recessionary times anyways, meaning it has minimized its disturbance in the economy. This is why we want a progressive income tax.
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