How would you change the U.S. tax system?

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Netreker0
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Re: How would you change the U.S. tax system?

Postby Netreker0 » Thu Aug 03, 2017 8:19 am UTC

jewish_scientist wrote:
Netreker0 wrote:As for your other reasons, they are laudable goals that, unfortunately have nothing to do with our current system of tax brackets.

I said that this is where I would start; not where I would end. Doing this is not going to fix the huge mess that is U.S. tax law. However, it is a relatively uncontroversial change that Congress could eventua- :lol: Oh man, give me a second. I can do this. *deep breathing* However, it is a relatively uncontroversial change that Congress could eventually pass given enough political pressure.


Is the purpose to get a token, meaningless change passed so that we can get some bipartisan ball rolling and hopefully let inertia carry us to more meaningful changes? If so, it's an interesting idea.

Otherwise, my original point still stands--even as a "start," your suggestion would provide zero meaningful progress towards achieve that particular goal.

There have been some great ideas in this thread, but most would be quite complicated to implement. I favor simplification...

I understand why you want this, but I think that boat has sailed. A modern industrial economy is so inherently complex that I believe that any effective tax system would be so complex that no single person would understand all of it; and that is o.k.


You're going to have to give some reasoning to support this assertion, beyond merely hand-waving that complex economy must mean complex tax system. At a basic level, a tax system has one primary goal--to fund the government. Below this are a few subordinate, somewhat interconnected goals: fund the government in a way that is sustainable, satisfies some standard of fairness, resists being "gamed," resists corruption and conforms to some legal restraints, and doesn't substantially anger the citizenry. While some changes are necessary as the economy grows complex--a tax code that focuses on "what you grow" and "all your wages" would have to adapt once things like investment income are added to the mix--there is no intrinsic reason that we need have entirely different and mutually incomprehensible tax rules for a farmer organized as an LLC growing and selling crops and a single guy paid a monthly salary at a corporation.

Plants are inherently complex--it's plausible that some plants are too complex for any one person to understand. However, our systems for cultivating and harvesting plants are relatively simple. More importantly, when those systems are adapted from more simple plants to use on more complex ones, they generally didn't have to be made more complex in order to reflect the increasing complexity of the plants. Sometimes, the simple plant has a problem that requires a simple solution, while the complex plant has a problem that requires a complex one. More often, however, the complex plant has the same problem as the simple plant, and requires the same solution, or alternately, the complex plant has a different, complex problem, and the solution is different, but still simple.

Your suggested "too complex for one person to understand" tax system is a bad idea because it is not necessary to achieve some of goals and in fact undermines others. In a roughly democratic nation, people should generally be able to understand their government and their laws. Even when most people don't have the time to understand one aspect of government--like the tax system--then at the very least, it should be possible for a substantial number of specialists, coming from a wide variety of viewpoints, to understand how the system works as a whole and to act as intermediaries. I don't like the idea of a system conceived to be so complex that even one of these specialists can't understand it all. It is too easy for such a system to get away from its creators, and too easy for those charged with implementing that system to disclaim responsibility for what it does.

Your technological examples overlook some important points. A cell phone, with all its hardware and software, probably wouldn't be able to work without being complex. That is a practical constraint. A tax code, on the other hand, can and has effectively funded the government--while achieving many of those subordinate goals--without being too complex for one person to understand. Yes, with more complexity we might achieve marginal gains in these areas, or we might--as you seem to want--be able to achieve other, unrelated goals. However,this complexity comes with a trade off, which is why I would prefer to achieve these goals in other, more practical ways. Plus, when you break down the phone into more elementary components, it becomes not only more practical, but also beneficial for someone to be able to understand the full system. For example, security might be very difficult without having people who have a general idea of how the OS works as a whole.

The other thing about the cell phone--for many of its functions, success or failure is self-evident. You don't have to trust that everyone who made every part did their job, because failure will most likely be self-evident, at which point you can systematically look for the specific person who failed. This is less true with the tax code. If we fail to raise enough money to support government spending, that failure would be self-evident. However, this isn't true for those important subordinate goals. I can't simply say, "I trust those parts of the tax code I don't understand are working towards a fair and equitable tax system, because if they weren't, the results would be obviously unfair and inequitable." Fairness is not only a characteristic of results but also of the system itself--the only way to know if a system is fair is to understand every part well enough to know if that part is fair, and to examine the system as a whole and see if it's fair. Even when the metric of success is largely external to the system, when it comes to the tax code, they're not always easy to measure accurately and objectively, particularly when the code is constantly being changed.

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Re: How would you change the U.S. tax system?

Postby Leovan » Mon Aug 07, 2017 9:21 am UTC

I'm not sure why all those sub-goals should even be accomplished through the tax code. A tax deduction is basically a subsidy, but somebody thought it would be stupid to collect the money in taxes then distribute it again and this would be easier. Except now every single taxpayer has to work their way through deductions that don't apply to them to fill out their taxes. And the US already collects the tax money and then the deductions are just for figuring out how much you get back, so the whole purpose is mixed up.

I'd be with Netreker0, collecting a simple progressive tax where the only two numbers you need are your income and persons in your household. The deductions would then be through subsidies instead. Each household gets 250$ per month per minor. If your income is below x/person you apply for health insurance subsidies. Building a house? Check if there are subsidies for that. If you're a business you can apply for subsidies applicable to your industry and don't have to worry about all the other subsidies. There might be lawyers who specialize in getting you one kind of subsidy. But because this is removed form the tax code they really don't have to know much about how the rest of the subsidies work or anything else about your taxes. It decouples the system with a simple divide-and-conquer.

You could even make welfare etc just another subsidy. Divide the whole thing into "give the government" and "get from the government".

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Re: How would you change the U.S. tax system?

Postby Chen » Mon Aug 07, 2017 11:32 am UTC

Wouldn't that make things MORE complicated for people? They'd have to dig on their own to determine what subsidies are even available. With the continuous addition of tax preparation software its getting far easier to find all the deductions you can get money from anyways. If you have enough deductions that you need to hire an accountant you're probably making more than enough money to do so. The deductions, in principle, are there to incentivise certain behaviors. Certainly it may be worth looking into some to see if they are still good ones to have, but otherwise they seem to be working as desired.

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Re: How would you change the U.S. tax system?

Postby Leovan » Tue Aug 08, 2017 11:27 am UTC

No more complicated than digging on your own to find what deductions are available and you're eligible for. The same software can be used to find your subsidies. In that sense the structural change doesn't necessarily make the process easier. But like in coding, as tempting as spaghetti code is, as soon as you try to do something as complex as a tax code, you simply need to separate the functions as much as possible. Every function should have one purpose and if it takes more than one page to do it you need to break it down. Right now the process is that they take some, and then you figure out how much you really owed minus what they use to encourage behaviors and then you get back some money that they took, or you owe even more money. I'd like to simplify that to they take money from you, then you take money from them.
Every type of income should have a function for how much of it you pay. Monthly for a job, yearly for interest/investments, etc. That's how much you pay and no buts about it, you don't even have to fill out a tax return. Your bank/employer should do that for you. Then when you have a reason to get a subsidy, you ask for it for that specific case. When you give birth they hand you the form for child subsidies, and then you get that for 18 years. With your college acceptance letter comes your college subsidy application. When you buy a house the bank has a stack of home owner subsidy applications. Each at most one page long.
It's easier to understand for everyone, and instead of hiding subsidies as tax deductions (which seem free) you actually have to declare them for the subsidies they are.

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Re: How would you change the U.S. tax system?

Postby Chen » Tue Aug 08, 2017 1:43 pm UTC

If all the same subsidies (deductions) exist, what's the benefit of changing it this way? The government could already do the base filing for you. I mean tax software now downloads most of your information from the government anyways and puts it into the appropriate boxes. So sure this could be expanded so that the government just does it all up front and you either take their word for it or re-check yourself and re-submit. But that doesn't really have anything to do with subsidies or deductions. Basically what are you gaining from the simplification you're proposing?

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Re: How would you change the U.S. tax system?

Postby jewish_scientist » Tue Aug 08, 2017 4:21 pm UTC

Zohar wrote:And the graph for this function looks like this (yes I have some time, why do you ask?). I didn't go all the way to the top bracket because reasons:
Spoiler:
tax.png

Oh, I see the miscommunication now. I was taking about the Income vs Tax Rate function and you were talking about the Income vs Taxes Payed function.

Netreker0, there will still be people with general understanding of the tax code. My point is that while no individual knows everything, a group does. This works because a group can sub-divide the large amount of information into smaller units that each individual can process independently. This method is not revolutionary; virtually every system in our world works on this way.

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Re: How would you change the U.S. tax system?

Postby Zohar » Wed Aug 09, 2017 12:40 pm UTC

jewish_scientist wrote:
Zohar wrote:And the graph for this function looks like this (yes I have some time, why do you ask?). I didn't go all the way to the top bracket because reasons:
Spoiler:
tax.png

Oh, I see the miscommunication now. I was taking about the Income vs Tax Rate function and you were talking about the Income vs Taxes Payed function.

Income vs. tax rate is just as continuous. Your overall tax rate doesn't jump to a different distinct value when you go up a tax bracket.
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Re: How would you change the U.S. tax system?

Postby CorruptUser » Wed Aug 09, 2017 1:20 pm UTC

Zohar wrote:
jewish_scientist wrote:
Zohar wrote:And the graph for this function looks like this (yes I have some time, why do you ask?). I didn't go all the way to the top bracket because reasons:
Spoiler:
tax.png

Oh, I see the miscommunication now. I was taking about the Income vs Tax Rate function and you were talking about the Income vs Taxes Payed function.

Income vs. tax rate is just as continuous. Your overall tax rate doesn't jump to a different distinct value when you go up a tax bracket.

That's not strictly true, when you include all the welfare benefits which suddenly stop after you get a certain income.

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Re: How would you change the U.S. tax system?

Postby Zohar » Wed Aug 09, 2017 1:52 pm UTC

Obviously if we start including exemptions, deductions, benefits, etc., that changes the situation drastically.
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Re: How would you change the U.S. tax system?

Postby jewish_scientist » Thu Aug 10, 2017 4:48 am UTC

Okay, I have no idea what you are talking about. People who make < $9,325 have a tax rate of 10%. People who make between $9,325 and $37,950 have a tax rate of 15%. [Citation] The function goes from 0.1 to 0.15 without ever going to 0.13. How is that continuous?

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Re: How would you change the U.S. tax system?

Postby Soupspoon » Thu Aug 10, 2017 7:00 am UTC

The higher tax is on the excess over the lower tax band(s).

Earn 1¢ over the lower limit and (in potentia, depending on how the immediately uncollectible fraction gets either ignored, rounded up or held up until it accumulates) the higher rate acts upon just that single cent, making the effective total rate slightly more than the lower rate. Earn double the lower rate (without reaching a new higher rate bracket, and - in this simple example - ignoring any previous lower rates including the zero-rated initial allowance) and half the quantity is at one rate, half at the other, for an effective rate of the average of the two, with a smooth transition between the two points. It is entirely possible for 0.1 to pass through 0.13 on the way to 0.15 (which it cannot reach, unless there's a greater value added in above the 0.15 ceiling point to draw the compound average higher still).

Slightly more complicated, but while there are inevitable sudden angle changes and inflection points in sufficient differentials of the compound (and, yes, technically discontinuous) function, it is not actually a leap in taxes, at any point. Except psychologically. Which is where it most matters.


That said, I still think something like $tax=($income-$allowance)*0.01*Logx($income-$allowance) (for some suitable x designed to get 50% from the topmost earner, and I'm sure you could make it a badge of pride to be that and 'ease' all marginally lesser earners!) might work. At least for $allowance+1 incomes.

(That's a top-of-my-head formula, so E&OE.)

An anti-tax top-up formula (to be argued about - vehemently!) could apply to <=$allowance incomes, according to policy about safety-net vs encouragement towards getting into the continuous function.


(I feel lucky that I don't have to work out this shit, though. PAYE, with an uncomplicated income that isn't enough to worry about spending some of it to save slightly more of it by employing a personal accountant, is probably marginally below optimum but not so much that I'd gain by trying to game the system outside of ISAs/etc. And no annual paperwork.)

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Re: How would you change the U.S. tax system?

Postby Zohar » Thu Aug 10, 2017 11:33 am UTC

jewish_scientist wrote:Okay, I have no idea what you are talking about. People who make < $9,325 have a tax rate of 10%. People who make between $9,325 and $37,950 have a tax rate of 15%. [Citation] The function goes from 0.1 to 0.15 without ever going to 0.13. How is that continuous?

If I make 9325, I pay 0.1*9325=932.5. So my actual tax rate is 932.5/9325=0.1=10%
If I make 9400, I pay 0.1*9325 + 0.15*(9400-9325)=943.75. So my tax rate is 943.75/9400=0.1004=10.04%

This is a continuous function. It passes through 0.13 on its way to 0.15 (up to cent resolutions).
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Re: How would you change the U.S. tax system?

Postby jewish_scientist » Thu Aug 10, 2017 12:08 pm UTC

Zohar, that is the function for taxes owed, which is on the far right column of the table. I am talking about the tax rate, which is on the far left column.

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Re: How would you change the U.S. tax system?

Postby Chen » Thu Aug 10, 2017 12:17 pm UTC

jewish_scientist wrote:Zohar, that is the function for taxes owed, which is on the far right column of the table. I am talking about the tax rate, which is on the far left column.


And why is it important for that rate to be continuous? When you take how much you owe in taxes divided by your earnings you get a number which is your effective tax rate. That one IS continuous though its slope varies. The marginal rates as you move through each bracket aren't terribly relevant in and of themselves and it's not clear why they should be continuous.

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Re: How would you change the U.S. tax system?

Postby Zohar » Thu Aug 10, 2017 12:30 pm UTC

jewish_scientist wrote:Zohar, that is the function for taxes owed, which is on the far right column of the table. I am talking about the tax rate, which is on the far left column.

That is just not true. If you make $9,400 a year, your tax rate isn't 15%. Your tax rate is 10.04%. Unless you have a wildly different definition than what's commonly used for it. Quoting from Wikipedia: "In a tax system, the tax rate is the ratio (usually expressed as a percentage) at which a business or person is taxed." The hypothetical person we're talking about isn't taxed 15%*$9,400=$1,410.
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Re: How would you change the U.S. tax system?

Postby Thesh » Thu Aug 10, 2017 1:08 pm UTC

jewish_scientist wrote:Zohar, that is the function for taxes owed, which is on the far right column of the table. I am talking about the tax rate, which is on the far left column.


ftax rate(income) = ftaxes due(income)/income

Both the tax rate function and the taxes due function are continuous, even if taxes due has a piecewise definition.
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Re: How would you change the U.S. tax system?

Postby jewish_scientist » Thu Aug 10, 2017 2:43 pm UTC

Chen, the largest tax bracket for single persons is $418,400+. The typical CEO makes that much in ~2 weeks. The problem is obvious.

Zohar wrote:Quoting from Wikipedia: "In a tax system, the tax rate is the ratio (usually expressed as a percentage) at which a business or person is taxed."

I quoted the Tax Foundation, which has been in operation since 1937 and every member of the senior staff has a college degree, and you countered with Wikipedia.

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CNBC wrote:The standard definition of the marginal tax rate is that it's the amount of tax imposed on every last dollar of income.

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Re: How would you change the U.S. tax system?

Postby speising » Thu Aug 10, 2017 2:47 pm UTC

jewish_scientist wrote:P.S.
CNBC wrote:The standard definition of the marginal tax rate is that it's the amount of tax imposed on every last dollar of income.

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Re: How would you change the U.S. tax system?

Postby Soupspoon » Thu Aug 10, 2017 2:55 pm UTC

jewish_scientist wrote:Chen, the largest tax bracket for single persons is $418,400+. The typical CEO makes that much in ~2 weeks. The problem is obvious.

That marriage is under-rated?

(Ninjaed but) https://en.wikipedia.org/wiki/Tax_rate

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Re: How would you change the U.S. tax system?

Postby Chen » Thu Aug 10, 2017 3:03 pm UTC

jewish_scientist wrote:Chen, the largest tax bracket for single persons is $418,400+. The typical CEO makes that much in ~2 weeks. The problem is obvious.


What does that have to do with continuous or non-continuous functions for tax rates? Adding higher brackets has nothing to do with continuity. You could add a bunch more brackets if you wanted, all at similarly discontinuous rates to deal with the issue of people at the top not paying enough.

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Re: How would you change the U.S. tax system?

Postby Zohar » Thu Aug 10, 2017 3:22 pm UTC

jewish_scientist wrote:I quoted the Tax Foundation, which has been in operation since 1937 and every member of the senior staff has a college degree, and you countered with Wikipedia.

As ninja'd by speising, you quoted the marginal tax rate, a term which you haven't used or mentioned until now. All you (and everyone else) has been talking about is the tax rate. That's what people are talking about. When people ask "How much taxes did Trump pay?" no one cares how much he paid on his last dollar, people care what percentage of his total income he actually paid. The marginal tax rate is important, of course - it lets me figure out how much a raise is actually worth for me, for example. But that's still just a proxy for "overall, how much will I pay". So yes, if you use this term that you haven't bothered mentioned until now and its few implications and usage in real life, then yeah - it's not a continuous function.

And changing it to a continuous function would still be a bad idea, for reasons mentioned about a dozen times here already.
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Re: How would you change the U.S. tax system?

Postby Netreker0 » Thu Aug 10, 2017 4:46 pm UTC

jewish_scientist wrote:I quoted the Tax Foundation, which has been in operation since 1937 and every member of the senior staff has a college degree, and you countered with Wikipedia.


Respectfully, are you trying to have a productive conversation, or are you merely trying to score points? The definition of tax rate, as opposed to marginal tax rate, is well-known. The fact that the citation came from wikipedia would substantially undercut your credibility if it were backing some assertion that were obscure or controversial; however, I don't have any strong objections to using it as a shortcut for something elementary and well-known. At the risk of sounding blunt, it's starting to look as though your main contributions to this thread have taken the form of you asserting that "tax rate" (note you stated tax rate, not marginal tax rate) is not continuous, and needs to be, and almost everyone else at some point explaining to you why tax rate is in fact already continuous (if you neglect deductions and other highly situational discontinuities), and you trying to move the goal post, or challenge the credibility of evidence, or do whatever else is necessary to arrive at some set of circumstances where your original assertion was not incorrect.

So how about we all just agree that your original statement would make sense if you meant to say marginal tax rate, and move on to the more interesting conversation: Why do you think marginal tax rate should also be a continuous function?

I understand why the amount of tax paid and the total tax rate should be continuous. If it were not, it would tend to tend to push the economy towards discrete strata of income. At the most extreme, it means that at certain points, you might lose net income by increasing gross income. For example, if you're paying a set 10% of up to $10,000, up to $1000, but if earning more increases your total tax rate suddenly to 15%, you get the perverse situation where take home $9000 out of $10000 a year, but only $8925 out of $10500.

However, what you have thus far neglected to make the case for is your assertion that there is some benefit to setting a continuous marginal tax rate that outweighs the substantial complexity of actually implementing the system. Remember, a continuous marginal tax rate also means we cannot (exclusively) rely on traditional tax brackets--at the very least, the points where marginal tax rate increases must effectively have tax brackets the size of a differential. (In practice, I suppose they would be the size of a penny.)

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Re: How would you change the U.S. tax system?

Postby jewish_scientist » Thu Aug 10, 2017 5:03 pm UTC

O.k. I forgot the word marginal; but in my defense, I did name the exact column of the chart that I was referring to. Maybe now that the stupid semantics are clear up, I can actually talk about my ideas.

Chen, you could add more brackets, but that is not solving the underlying problem. At one time, a $418,400+ bracket was good enough and there was no need to have debates over how much a theoretical very-rich person should be taxed. Then these theoretical incomes became actually possible and the system had no way to deal with it. Adding new brackets immediately raises some very tough questions, the two biggest being 'Where should the cut offs be?' and 'How much should the marginal tax rate be set to?', but this solution is temporary. Eventually the new brackets will become outdated and the problem will rear its ugly head all over again. It there was a continuous function, then this problem would not even exist. No matter how rich someone became, the system would already have their marginal tax rate ready.

Also, I realized that I may have made a mistake. :oops: Are 'continuous' and 'piecewise' antonyms? If not, what is the antonym of 'piecewise'?

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Re: How would you change the U.S. tax system?

Postby Thesh » Thu Aug 10, 2017 5:14 pm UTC

jewish_scientist wrote:O.k. I forgot the word marginal; but in my defense, I did name the exact column of the chart that I was referring to. Maybe now that the stupid semantics are clear up, I can actually talk about my ideas.

Chen, you could add more brackets, but that is not solving the underlying problem. At one time, a $418,400+ bracket was good enough and there was no need to have debates over how much a theoretical very-rich person should be taxed. Then these theoretical incomes became actually possible and the system had no way to deal with it. Adding new brackets immediately raises some very tough questions, the two biggest being 'Where should the cut offs be?' and 'How much should the marginal tax rate be set to?', but this solution is temporary. Eventually the new brackets will become outdated and the problem will rear its ugly head all over again. It there was a continuous function, then this problem would not even exist.


Huh? No, the reasons to change the brackets are because the distribution of income change. Unless you have a formula for computing tax rate that is undeniably ideal, there will always be debate on what that formula should be and what rate it should increase at what point.

jewish_scientist wrote:No matter how rich someone became, the system would already have their marginal tax rate ready.


I still don't think you understand; unless you have a bracketed tax system "marginal tax rate" is meaningless.

My understanding is you want people to be able to plug in "tax rate = f(income)" and get a single percentage that people can multiply their income by that will change very slightly with slight changes in income, correct? The point is that you can do that with a bracket tax formula - it can easily be converted into a continuous tax rate function. How does applying a different continuous function make it any different?
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Re: How would you change the U.S. tax system?

Postby speising » Thu Aug 10, 2017 5:26 pm UTC

He wants the marginal tax rate to increase constantly, presumeably up to 100%? Or what should the maximum be? Unless it increases without bounds, ie. to above 100% for sufficiently high incomes, you'll always have a flat end.
Just like the current system.
Or, you always have to re scale the function to the highest income across the nation each year.

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Re: How would you change the U.S. tax system?

Postby Pfhorrest » Thu Aug 10, 2017 5:30 pm UTC

(kinda ninja'd)

I wonder if possibly jewish_scientist's intention is to make sure that there's never such a thing as a "top tax bracket"; that each additional dollar is taxed at some (slightly) higher rate than the last, always, no matter how many additional dollars you're talking about.

If so, that still leaves room for political debate about the rate at which marginal tax rate should increase with income, and doesn't require anyone claim that their proposed marginal-tax-rate-function is ideal.

You do need to make sure that the function converges to something less than or equal to 100% marginal tax rate as income goes to infinity, to make sure that you never end up taxing an additional dollar more than a dollar, but beyond that there's lots of room for debate within such a scheme.

Can someone with a clearer head for math answer a question for me about that: would a flat rate minus a fixed credit accomplish that goal in effect? So the effective tax rate = (bx - c)/x for variable income x and some constant rate b (between 0 and 1) and constant credit c (greater than zero). I'm not sure how to back-calculate what marginal tax rates would be from that.
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Re: How would you change the U.S. tax system?

Postby Netreker0 » Thu Aug 10, 2017 6:16 pm UTC

jewish_scientist wrote:O.k. I forgot the word marginal; but in my defense, I did name the exact column of the chart that I was referring to. Maybe now that the stupid semantics are clear up, I can actually talk about my ideas.


I have been repeatedly asking you to talk about your ideas. You were the one who made the decision to repeatedly focus on defending your (perfectly understandable) omission of "marginal." I joined this conversation late, but it was quite obvious from the responses that everyone was behaving as if you meant tax rate, and not marginal tax rate.

It there was a continuous function, then this problem would not even exist. No matter how rich someone became, the system would already have their marginal tax rate ready.


Also, I realized that I may have made a mistake. :oops: Are 'continuous' and 'piecewise' antonyms? If not, what is the antonym of 'piecewise'?


Okay, you are definitely working with the wrong definition of "continuous." Continuous and piecewise aren't strictly antonyms, but generally a piecewise function won't be continuous. A continuous function is one that has no discontinuities (or in real world situations with quantized units such as currency, as close as you can get.) It is a function that produces a graph with a single line.

A piecewise function is one that is defined differently at different intervals. For example, y = x^2 from x = 0 to x = 1, y= x for x > 1 is a piecewise function that is also continuous. Because of the nature of a piecewise function, it is quite often not continuous.

From your last statement, it seems like your definition of "continuous" might have nothing to do with the definition that everyone familiar with math might have. Instead, what you're basically arguing is that at some point, marginal tax rate stops increasing, and this is a bad thing.

It's an interesting idea. In practice, I think it's needlessly complicated and a bit pointless. If you want a marginal tax rate that increases "continuously" "no matter how rich you became," then there are three different ways to do so. 1) You keep increasing the marginal tax rate until 100% and (hopefully) stop increasing it. 2) You keep increasing the marginal tax rate until it asymptotically approaches some percentage below 100%, meaning that at some point, for all practical purposes, you become rich enough to reach the top tax bracket because all addition increases in marginal tax rate will amount to a rounding error. 3) I suppose it's possible to do something weird with a log-scale function of marginal tax rate versus income, and if you have a comprehensive proposal to do so I'd love to hear it, but I fear that at this point the government goal would become subordinate to the mathematics. Thus, any proposed "JC-continuous" tax system would in effect just be a mathematically overcomplicated version of a tax bracket system where it takes a much, much higher income to reach the highest bracket.

Now, what I am guessing you see in your system is that the system--in theory--self-adjusts. We're about to have our first trillionaire, and instead of having to change our tax brackets through legislation every time we hit some milestone, your system automatically adjusts. As I have already explained, this is an illusion. At some point, for all practical purposes, you will reach an effective top tax bracket. More importantly, such a self-sustaining bracket system isn't even a worthwhile goal, because circumstances change. Inflation happens, not always at a predictable rate, and not in an even manner that lends itself to easy indexing. In other words, even using your system, people will start creeping into higher tax brackets even if they're not getting meaningfully more wealthy, and that problem will have to be addressed. You could theoretically build an inflation index into your system, but again, this only works if you can capture inflation in a single number that is accurate for all situations.

In practice, inflation and other circumstances--wars, shifting expectations of what the government should and should not do for us, changes in the nature of the economy--mean that every so often, we're going to have to put human eyes on our tax rates and ask ourselves what rates are necessary and appropriate for the foreseeable future. In practice, this will have to happen often enough that we can manually set increasing tax brackets up to several kiloCubans, and be reasonably sure that by the time we have to adjust tax rates again, we're not going to have many people surpassing the top tax bracket. So what's the point? Why adds layers of needless mathematical complexity for the sake of creating an illusion of permanence?

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Re: How would you change the U.S. tax system?

Postby Thesh » Thu Aug 10, 2017 6:29 pm UTC

Pfhorrest wrote:Can someone with a clearer head for math answer a question for me about that: would a flat rate minus a fixed credit accomplish that goal in effect? So the effective tax rate = (bx - c)/x for variable income x and some constant rate b (between 0 and 1) and constant credit c (greater than zero). I'm not sure how to back-calculate what marginal tax rates would be from that.


Well, if you used a function like arctan and scaled it to the desired rate, both the effective and marginal tax rate would be different for every penny of income, with funny effects on the actual marginal rate due to rounding errors. Doesn't matter what the marginal tax rate really is; no matter what you choose you will be able to group it into brackets and compute marginal rates (up to one per penny) from any continuous function, it's just that a function like arctan gives you a lot more brackets and it will be easier to just directly compute the effective rate.
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Re: How would you change the U.S. tax system?

Postby Chen » Thu Aug 10, 2017 6:34 pm UTC

Pfhorrest wrote:Can someone with a clearer head for math answer a question for me about that: would a flat rate minus a fixed credit accomplish that goal in effect? So the effective tax rate = (bx - c)/x for variable income x and some constant rate b (between 0 and 1) and constant credit c (greater than zero). I'm not sure how to back-calculate what marginal tax rates would be from that.


I think that equation would just give you a two bracket system with 0% rate up until a value of c/b. The c/b would be equivalent to the basic deduction we currently have now in our system.

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Re: How would you change the U.S. tax system?

Postby Pfhorrest » Thu Aug 10, 2017 8:24 pm UTC

Would it be accurate to say that the marginal tax rate function is the first derivative (with respect to income) of the effective tax rate function? (i.e. in order to see how marginal tax rates fall out of a given effective tax rate function, just calculate its first derivative?)
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Re: How would you change the U.S. tax system?

Postby Thesh » Thu Aug 10, 2017 8:35 pm UTC

I believe the marginal tax rate is going to be the first derivative of the function "taxes paid = f(income)" i.e. the rate at which their taxes change with respect to income at their income level.
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Re: How would you change the U.S. tax system?

Postby Chen » Thu Aug 10, 2017 8:50 pm UTC

Pfhorrest wrote:Would it be accurate to say that the marginal tax rate function is the first derivative (with respect to income) of the effective tax rate function? (i.e. in order to see how marginal tax rates fall out of a given effective tax rate function, just calculate its first derivative?)


I don't think that works. The simplest case a flat tax say of 10% would have a marginal rate of 10% as well. The derivative would be zero though, wrt to income.

Taking the derivative with respect to income would leave you with the wrong units too. The function you were differentiating would need to have the same units of income for the derivative wrt income to give you the marginal tax rate (which is dimensionless). I'd imagine it would be the derivative of the amount of tax owed function that would end up letting you determine the marginal rate at a point.

edit: Ninja'd by Thesh

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Re: How would you change the U.S. tax system?

Postby Thesh » Thu Aug 10, 2017 8:52 pm UTC

Also, Zohar posted the graph of taxes paid vs income. It's pretty easy to see from that that the slope is the marginal tax rate.
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Re: How would you change the U.S. tax system?

Postby Pfhorrest » Thu Aug 10, 2017 9:23 pm UTC

Thanks. So the marginal tax rate function of my "flat tax minus fixed credit" scheme, where the taxes paid on income x are bx - c, would be the first derivative of f(x) = bx - c, which if I'm not mistaken is just the constant function f(x) = b, correct? (Which now that I say it sounds appallingly obvious... yes, of course a flat tax has a constant marginal tax rate, duh).

So my proposal does not meet (what I think is) jewish_scientist's criterion, and I'd like to join in asking him why that criterion matters again, so long as effective tax rate increases indefinitely with (but not necessarily proportional to) increased income, which my scheme still does. If richer and richer people still pay a greater and greater portion of their income in taxes, then what is not being accomplished?

An additional question, for anyone. Does the term "progressive taxation" imply only a graduated effective tax rate, or does it require a graduated marginal tax rate to count? E.g. does my proposed scheme (where someone with income x = c/b pays 0% in taxes, and people with higher incomes pay closer and closer to b*100% in taxes as income approaches infinity, but if I'm correct above, marginal tax rate is constant) count as a progressive tax or not?
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Re: How would you change the U.S. tax system?

Postby Thesh » Fri Aug 11, 2017 3:12 am UTC

I'd say the most important measure of progressiveness is its effect on the distribution of income. A flat nominal tax credit + flat income tax rate can arbitrarily reduce inequality - essentially, you set the tax rate and distribute it equally to everyone and at 100% everyone gets completely equal income, while at 50%, everyone takes home at least half the per-capita income and the people at the top make half of what they would at 0%. So, yes, I'd say it has the potential to be very progressive.
Last edited by Thesh on Sat Aug 12, 2017 12:45 am UTC, edited 2 times in total.
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Re: How would you change the U.S. tax system?

Postby jewish_scientist » Fri Aug 11, 2017 10:23 pm UTC

I think there is something else I did not explain properly. In by system there are no brackets at all; the 'marginal tax rate' is the tax rate. That probably contributed to my failure to communicate well earlier.

One thing that I think is a big advantage is that cherry-picking is very difficult to impossible. It you want to increase taxes on the poor, then you have to change the same function that dictates the tax rate for the rich. I am 99% sure that this change would be an increase, but there may be some kind of complicated, mathematical gymnastics that can make sure that the rich's tax rate is unaffected.

I am having some trouble working out what form(s) the actual function could be. I know that it would have to contain 0,0 and have an asymptote at x = c, where c is a number between 0 and 1. I did some messing around on Wolfram Alpha, but could not find an equation that fit this bill. It has been a while since I took calculus.

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Re: How would you change the U.S. tax system?

Postby Pfhorrest » Sat Aug 12, 2017 12:26 am UTC

jewish_scientist wrote:I think there is something else I did not explain properly. In by system there are no brackets at all; the 'marginal tax rate' is the tax rate. That probably contributed to my failure to communicate well earlier.

I'm not clear now if you mean that the marginal tax rate is constant (i.e. every additional dollar everyone makes is taxed at the same rate as every previous dollar anyone made), or just that it varies continuously (i.e. every dollar anyone makes is taxed differently than the previous dollar they made; there's never a discrete threshold where the change happens suddenly after being constant for a while). I think you mean the latter.

I'm also still not sure you understand the difference between marginal and effective tax rates, and whether it's really the marginal one you care about. Is all that's important that someone making X+1 dollar always pays a higher total percent of their income than someone only making X dollars? Or is it important to you that the X+1th dollar itself be taxed at a higher rate than the Xth dollar? You don't have to do the latter to achieve the former; for example, in my earlier proposal, every additional dollar anyone makes is taxed at the same percent as every other dollar, but because everyone also gets the same fixed dollar amount discounted from their taxes owed, only people making literally infinite money actually pay that whole percent, and everyone else pays a lower percent of their total income, down to 0 at some point, and then even possibly negative below that. In that example the marginal tax rate is constant for everyone, but the effective tax rate varies continuously. (And in the current system, the marginal tax rate varies discontinuously, but the effective tax rate still varies continuously).
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Re: How would you change the U.S. tax system?

Postby Thesh » Sat Aug 12, 2017 1:35 am UTC

I think he wants something like "marginal tax rate = 2/pi*arctan(x/k)", where k is the income level in which the marginal tax rate is 50%. This would make the taxes collected the area under the curve.
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Re: How would you change the U.S. tax system?

Postby Zohar » Sat Aug 12, 2017 2:53 pm UTC

Ah yes, so much simpler to calculate than y=ax+b.
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Re: How would you change the U.S. tax system?

Postby Netreker0 » Sat Aug 12, 2017 7:37 pm UTC

jewish_scientist wrote:One thing that I think is a big advantage is that cherry-picking is very difficult to impossible. It you want to increase taxes on the poor, then you have to change the same function that dictates the tax rate for the rich.


Wait, so the reason you want to change the tax calculation regime to math that you can't even do yourself is because you believe that if you complicate the math enough, it'll be harder to selectively tax one group over another? Allow me to propose a simpler solution that will accomplish the same thing: Write it into the law.

Here's the thing about your equation idea: Unless you intend a Constitutional amendment, it will be no more or no less difficult to repeal than a statute that says something to the effect of "Any regulatory or administrative changes to the tax rate cannot violate these constraints. 1) Those making under X% of the median income cannot be taxed at all. 2) The top Y% of earners must contribute to no less than Z% of revenue from income taxes" etc. If the government wants to raise taxes on the poor and leave the rich alone, they'll either hire a mathematician who can do it within the constraints of your proposed math, or they'll repeal the math as part of the legislation that raises tax rates.


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