My goal was only a rough sketch to show the concept rather than exact numbers (as a result it may be “untethered to reality” in some respects). However I made a conceptual mistake of showing the progressive tax as stair-stepped. In reality it is more of a linear approximation to a curved line.

http://i.imgur.com/VpzRt.png

With regards to the continuum think of it this way: one end of the spectrum puts the burden of paying taxes unfairly on the poor (set fee), the other unfairly on the wealthy (100% tax). A “progressive” tax and “flat” tax are compromises between these two extremes. A flat tax has a heavier burden on the poor than the progressive or 100% tax but a lighter burden than a set-fee tax. On the other side, the flat tax has a lighter burden on the rich than the progressive tax or 100% tax but not as light as a set-fee.

As for burden being larger on poor than on rich, well…you’re poor. You should expect life to be harder. And, there’s always an alternative to being poor. (More or less, that is. We can imagine extremes of, say, mentally handicapped quadriplegics, where this wouldn’t be the case, but: as in law, hard cases make bad policy. Treat such exceptions more specifically, not through the vague and diffuse mechanism of tax policy, but rather perhaps through precisely targeted direct subsidies. Although, in general, I’m not convinced private charity is incapable of being up to the task of responding in such cases.)

One other thought on your graph: it’s mathematically accurate, but it’s practically misleading, in a first-impression sense. A cursory glance at your graph might give the impression that progressivity or income caps generate more tax revenue than a flat tax (or set fee). A horizontal axis determined by probability density on incomes would show how much extra revenue tax hikes will actually generate (although even that’s not quite accurate as static scoring ignores responses to such policies, but that’s a much subtler concern), rather than showing some free-floating large number untethered from reality. I know the graph wasn’t intended to mislead, but it still rubs me just a little bit the wrong way because, at an unthinking level, it subtly suggests that higher taxes on higher incomes mean big new revenue.

I wasn’t endorsing option 2 (above) merely pointing out that the “flat” tax is on a continuum of options. I wasn’t saying that the “flat” was the same as a set fee, just “leaning” towards that end of the spectrum.

I was also pointing out that you ignore the fact that the burden of paying a flat taxes is higher for those in poverty than for those above poverty. To make the point clear I would rather that a person in poverty spend their money on feeding their family than on paying taxes. For a wealthier person the choice might be between a nice car and taxes.

What makes the tax code complicated are deductions and credits. You can have
a progressive tax with or without deductions and a flat tax with or without deductions. “Flat” has little to do with it. A half-page table of tax rates
is hardly mind-boggling complexity.

Agreed. But I don’t think the utility part matters. The progressivity of your taxation system is a social choice, not a logical one. I think we need a simple income progressive tax with fewer deductions. Deductions erode the tax base in unpredictable ways and are needlessly complex. Most of the mare stupid. I understand the idea of trying to shape behavior but I don’t think this is the best way to do it. If you are interested in shaping behavior then do it on the consumption side where it’s uniformly applied and is passed with greater consensus than obscure deduction law changes (such as a carbon tax, etc.).

I tend to disagree with most of the people who say higher taxation is an disincentive for people working. It’s not that it isn’t to some degree but it’s overestimated. 100% clearly is a disincentive. But, 60% top bracket for those making over $5 million is not fully unreasonable to me. It’s not because I hate the rich, but it’s because when you’re in a bracket that big you’re earnings tend to increase exponentially. It’s very different to be taxed 60% on $5 million of your $10 million salary than it is to be taxed 60% on your $1,000 raise from your $31,000 salary. I doubt many people say “no, I’m only getting $2 million out of my $5 million, I’m not going to work”. And, if they do we have to decide how bad of thing that would be.

The latter extreme would be disastrous, because it completely removes any monetary incentive for individuals to work once they achieve that certain level of income (or even before, depending on their inherent thriftiness). The evaporation of economic progress as the greatest of incentives to innovate is removed — particularly because it would affect the most successful — would be breathtaking. There are certainly other incentives to work past that threshold, and I’m sure many would still continue to work, but a very large number would not.

Try as I might, I can’t bring myself to empathize with your closing question. If I benefit from rule of law, it should be my duty to pay for it, no matter how little or much I earn or consume. Equal protection of the law must mean something: that if I make a dollar, I be treated the same way as any other person earning a dollar, regardless whether that dollar be my first or my last; that if I spend a dollar on something, I be treated the same way as any other person spending a dollar on the same thing, regardless whether that dollar spent be my first on something or my last.

Obviously rich people would prefer the first, poor people would prefer the second. In the full spectrum “Flat” tax leans towards the first. Current system leans toward the second.

If you were earning less than $10,000 would you prefer that the first ten thousand wasn’t taxed or would you prefer that you paid the same percentage as a millionaire?

How would we measure utility to properly tax it? We have no way to accurately measure individual utility functions across all variables. We can measure utility with respect to single variables, with some inaccuracy, using diff-in-diff techniques, with considerable time delay, but we can’t extrapolate that to all possible variables. However, we can precisely measure income and expenditures. They’re reasonable proxies if you think utility is even worth considering for purposes of taxation, so why shouldn’t we use them?

Finally, accurately taxing utility in some unspecified manner leads to absurdities. Suppose I visit family over Christmas. Each day we sit down to eat a dinner of a fixed set of ingredients in a fixed prepared form. In one situation, we sit and eat without interacting in any manner. In another, we sit and eat while interacting, talking, and generally enjoying each other’s company, while consuming the same ingredients as in the first situation, in the same prepared form. Suppose in the latter situation we derive utility from this interaction, more than we do in the first situation with no interactions. Do you suggest the extra utility in the latter situation deserves to be taxed somehow? The external world is completely indifferent to the two situations; why does society have any claim whatsoever on some fraction of that extra utility? It’s no skin off their noses. In contrast, a consumption tax penalizes you for taking value out of the economy, which by definition has an effect on the world external to a particular individual’s situation and choices. It is a penalty on taking away things the rest of society might have enjoyed. Utility is an entirely personal concept; it is not a zero-sum game, so an increase in utility for one individual does not necessarily result in equivalent decreases elsewhere. What reason is there to penalize gains in it?

What makes the tax code complicated are deductions and credits. You can have
a progressive tax with or without deductions and a flat tax with or without deductions. “Flat” has little to do with it. A half-page table of tax rates
is hardly mind-boggling complexity.

A flat tax is inherently unfair because of a simple fact known to every
economist: The utility of money is not a linear function of the amount of
money you have. Utility would be what you would look at to determine fairness.
Discussions of “flat” taxes that do not address this are totally missing the point.