A Thought Experiment: Progressive Tax
A progressive tax imposes a lower tax rate on lower earners and a higher tax rate on higher earners. I believe a progressive tax code is an important pillar of a healthy society. But as individuals earn more money and thus pay more taxes at a higher rate, they often become less and less convinced of the merits of such a tax structure. I seem to have a lot of high earning professionals visit this blog, so let me attempt a defense of progressive taxation.
Imagine a country with the following characteristics:
- Exactly one hundred people, all living separately.
- Each person is distinctly numbered from 1 to 100.
- Each person makes an income of $1000 times their number. For example, Person #54 makes $54,000 per year.
What system of taxation is best for this population?
Levels of Pain
My definition of “pain” is pretty similar to my definition of “stress” in this context. It’s a measure of how difficult life is at each level on the financial spectrum. The stress you feel depends on how able you are to satisfy your wants and needs.
Level 1: Basic Needs
There’s a level of wealth necessary to meet the basic physical needs of food, water, sleep, clothing, and shelter. Every dollar you make up to this level is super important and any dollar you lose below this level causes maximum pain. To impose a tax on someone who cannot meet their most basic needs is obviously counterproductive, not to mention foolish.
For our thought experiment, let’s set $10,000 as the threshold to satisfy basic needs. Persons #1 (making $1000) through #9 (making $9000) have not met their basic needs, while Person #10 is exactly at the threshold. Money they lose under this $10,000 limit carries a maximum pain of 100 on a 100 point scale. I’ll explain that below, hold on to the idea for a minute.
Level 2: Other Needs
Once your basic needs above are relatively satisfied, some other needs come to the fore. These are centered around your safety and security. Physical safety is important, but so to is emotional and financial security. Your health (which you might argue deserves a spot in Level 1) is another need that gets attention once your most basic needs are met.
Just like above, these things cost money. Perhaps the next $15,000 one earns can be used towards satisfying these other needs. Importantly any dollar lost in this range, from $10,001 to $25,000, also causes financial pain, though not as much pain as losing out on your basic needs from Level 1. Let’s say that money lost in this range carries a pain of 80 on the same 100 point scale.
Level 3: Basic Wants
Needs are complex and varied, wants are even more so. Basic wants can be pursued after the above needs are met. They could include participation in friendships, family, and social groups. A basic want could be saving for a child’s college education – something you think is important but isn’t really mandatory for your existence. Let’s imagine our little colony of 100 people can start pursuing basic wants with income in the range of $25,000 to $50,000.
Person #40, as an example, is able to meet all their Level 1 and Level 2 needs because they make $40,000 per year. They have an additional $15,000 to spend on their wants. They would feel a little pain when they lose money that was used for their basic wants, but it’s not the same level of stress they feel if they’re unable to meet their basic needs. I’ll give them a pain of 50 on our 100 point scale.
Level 4: Other Wants
It becomes difficult to write with specificity, but imagine our thought experiment has a higher level of less important desires that can be met when everything else has been attended to. These could be status or ego purchases. They might also manifest as activities that inspire more self-confidence and freedom. Once your basic needs and wants are met, you might have the freedom to spend many hours a week writing a blog that has yet to make a penny of profit!
In the great stack of money that you make each year the first portion that goes towards meeting your basic needs is most important. Each dollar after that becomes less and less useful – though still important and still painful to lose! I’m setting the stress of losing money from the $50,000 to $100,000 range to a pain of 20 out of 100. They don’t want to lose those dollars, but the impact is not as painful as the losses in Levels 1-3 above.
Total Pain Calculation
Line up every person and assess how much financial pain (stress) they are feeling. Person 100 has the maximum income, so in our experiment they have the least amount of pain. Person 99, in a sense, has lost $1000 compared to Person 100. And they lost that $1000 from their Other Wants in Level 4 above. That loss had a pain of “20”, so Person 99 has a pain of 20. Person 98 lost $2000 compared to the maximum level — they have a pain of 2 x 20 = 40. Likewise, Person 97 has a pain of 3 x 20 = 60.
We can calculate the pain of every person in the experiment in a similar manner, keeping in mind that losing basic needs is more stressful than losing optional wants. Person 1, the most stressed person around, is feeling a pain of 50 x 20 + 25 x 50 + 15 x 80 + 9 x 100 = 4350! I picked the numbers out of thin air and I’m still worried about Person 1.
The advantage of having low (or no) taxes is that those who are willing and able will be more efficient and productive with their labor. Because they keep the fruits of their labor, they have ample incentive to harvest more fruit. That might increase our society’s total wealth, but those who are not willing and able will truly suffer.
So what’s the total stress in our imaginary country when there are no taxes involved? I calculated the Pain Number for each person and added them up.
No Tax System: Total Pain = 145,650
Flat Tax 13%
So what if we assessed a flat tax on all income? This idea has historically been fairly popular in some U.S. Presidential election cycles. The country of Russia currently implements a flat tax of 13% on all earnings. There’s nothing magic about 13%, but I’ll use that for our example.
Our thought citizens in our thought example have a combined income of $5,050,000. A flat tax of 13% on all citizens would bring in $656,500 in revenue for the government. I know there’s cost to that transaction, and I know there’s benefits that get used by everyone (like roads and bridges), but let’s assume for now that no money is lost and the government spends its tax revenue to minimize the pain of its citizenry.
Rationally, the government will distribute the wealth so that all citizens have their Level 1 Basic Needs met. After that, if money still remains the government will distribute it to help meet Level 2 Other Needs. I redistributed the tax revenue to minimize overall pain, and while the highest earners have more stress than they did previously, the lowest earners are dramatically better off.
13% Flat Tax: Total Pain = 121,662
We might try to minimize pain in our society by taking from each person according to their wealth and giving to each person according to their need. The total wealth in our society, adding up each person from 1 to 100, comes out to $5,050,000. So we can divvy that up evenly – each person gets $50,500.
The problem, of course, is that we presume people are generating wealth through their hard work and in order to benefit themselves and their families. Without an individual profit motive, I’m not sure how many side hustles and profitable new ventures we’re going to encounter. Communism does minimize pain, hypothetically, but it’s obviously going to destroy motivation and wealth. If you disagree, drop me an email with examples of sustainable communistic countries throughout history.
If a “No Tax” system maximizes production but concentrates pain, a communistic system minimizes production and diffuses pain.
Communism: Total Pain = 97,500*
*If everyone is happy to work for the common good, no slacking!
In my opinion, a progressive tax is a fair compromise to reduce the pain of the less fortunate while still encouraging the production of the more able.
Let’s look at an example with the following tax brackets:
-100% BRacket: $0 – $5000
In our example, we know that people making under $10,000 are unable to meet their most basic needs. A negative tax rate means that for each dollar made in this range, the government gives you a dollar back! This helps ease the “high pain” area of income and really encourages more production for low wager earners. Matching dollars are the single best investment you can make [see the 401(k) contribution in Plan 7: Stacey], every dollar you earn gets you an extra dollar.
-50% Bracket: $5000 – $15,000
Moving up to the next bracket, the government kicks in 50 cents for every dollar you earn. This corresponds with Level 2 Pain: Other Needs. Low income earners that have their basic needs met are both assisted and incentivized until they have all their needs met. And if you think negative taxation is an absurdity that could never happen, you’re wrong! People living below the poverty line in the United States reap more than they pay into the system. Consider the value of food and housing assistance programs, public education, clean air, food safety, … the list goes on and on.
25% bracket: $15,000 – $55,000
The above incentives have to be paid for, unless we plan on running a government that borrows from the future. So we start taxing individuals who have all their needs met, and have started satisfying their wants instead. I pulled the 25% number out of thin air — but it’s a reasonable approximation for the real world. Sure, it doesn’t feel as good to keep 75 cents out of every additional dollar you make, but it’s still worth it if you’re trying to build that second home on the lakefront.
??? Bracket: $55,000 – $100,000
As I write this, I don’t know yet what the top bracket should be! But it’s easy enough to figure out for our thought experiment. By evaluating each person’s tax refund (or liability) and adding them up, we can figure out what tax rate the top bracket should pay to balance the books. And here’s what I determined:
Top Bracket: 27.8%
We could do a few things with that number. First, the budget of our little country would be exactly balanced with a 27.8% tax rate on the highest income earners. If we exceed that tax rate, for example with 30%, the government runs a surplus. Just like in your household, running a surplus helps you withstand future unexpected emergencies.
Another choice would be to lower taxes on the “middle class”. Instead of a 25% tax rate, perhaps they should just pay 20%?
Or maybe you’d like to increase benefits, by funding universal health care for all?
Finally, you could decide to raise taxes on the rich to help some of the lowest earning workers meet their basic needs. The high income earning Person #100 still retains $87,500 of their original $100,000 salary under this plan, so perhaps there is room for a little more social welfare before we would declare the tax burden to be onerous.
Progressive Tax: Total Pain = 132,528
The progressive tax plan outlined above strikes a balance between the benefits to society of easing the burden on the very poorest members while maintaining a healthy incentive for each person to be industrious and productive in their lives.
I started this article with the intention of proving through cold, hard math that a progressive tax system is best. Upon analysis, I have to conclude that it’s not a provable thing. Rather, there’s a balance to be struck. On the one hand, we want to encourage innovation and reward risk taking. At the same time we should provide a common safety net for those who would otherwise suffer. The balance is found through an appeal to our humanity, not to a spreadsheet of numbers.
It’s up to each of us to reasonably determine borders between wants and needs, and to determine the pain caused by lost or missing wealth across the spectrum. I think a progressive tax system allows for this kind of debate, and ultimately is the best path to a productive and prosperous future for individual and society alike.