I didn’t have time to respond, but the IPA brought Arthur Laffer out to Australia a month or two ago. For those interested, over the fold is a relevant extract from Zombie Economics.
Of rather more concern is the evidence that both the Secretary of the Treasury, John Fraser, and his Deputy for Revenue, Rob Heferen are adherents of the Laffer hypothesis or something very close to it. Fraser gave evidence to the Senate endorsing the Reagan tax cuts (based on Laffer’s hypothesis), while Heferen has claimed that something like 50 per cent of the revenue lost through a company tax cut will be returned through dynamic effects.
Although no issues are ever truly resolved in economics, this informal survey published by Ezra Klein is revealing. Klein asked various people about the tax rate at which revenue would be maximized. His respondents fell into three groups: left/liberal economists, who mostly gave answers around 70 per cent, rightwing pundits with zero credibility who gave answers around 20 per cent, and serious right/centre-right economists, who declined to give a direct answer to the question.
This suggests to me that the debate over the Laffer hypothesis has been won fairly conclusively by the left, and that those on the right would prefer to frame the question in the more defensible (though still, in my opinion, incorrect) claim that we face a long-run trade-off between equality and growth.
Everyone knows the story of how Laffer drew a graph on a napkin, illustrating the point that tax rates of 100 per cent would result in a cessation of economic activity and therefore yield zero revenue. Since a tax rate of zero will also yield zero revenue, there must exist some rate of taxation that yields a maximum level of revenue. Increases in tax beyond that point will harm economic activity so much that they reduce revenue.
Wanniski christened this graph the ‘Laffer curve’, but as Laffer himself was happy to concede, there was nothing original about it. It can be traced back to the 14th century Arabic writer Ibn Khaldun. Laffer credited his own version to the nemesis of supply-side economics, John Maynard Keynes. And while few economists had made much of the point, that was mainly because it seemed too obvious to bother spelling out.
What was novel in Laffer’s presentation was what might be called the ‘Laffer hypothesis’, namely that the United States in the early 1980s was on the descending part of the curve, where higher tax rates produced less revenue.
Unfortunately, as the old saying has it, Laffer’s analysis contained a mixture of correctness and originality. The Laffer curve was correct but unoriginal. The Laffer hypothesis was original but incorrect.
For the Laffer hypothesis to be supported, tax cuts would have to increase revenue more rapidly than would be expected as a result of inflation and normal income growth. In fact, as Richard Kogan of the Center on Budget and Policy Priorities reported, income tax receipts grew noticeably more slowly than usual in the 1980s, after the large cuts in individual and corporate income tax rates in 1981.
To the extent that there was an economic response to the Reagan tax cuts, and to those of George W. Bush twenty years later, it seems largely to have been a Keynesian demand-side response, to be expected when governments provide households with additional net income in the context of a depressed economy
John Quiggin 
A couple of points.
1. It’s not difficult to come up with the idea contained in the Laffer curve. Anyone who uses “reasoning to extremes” can come up with this idea. It’s obvious that zero tax will be raised at 0% tax rate . It’s also obvious that there is no reason to work or invest at 100% tax rate. I came up with this idea independently many years ago before I ever heard of Laffer in any context or Ibn Khaldun in that particular context. It’s no great claim. The idea in itself is trivially obvious.
2. Must there not be many Laffer curves? The Laffer curve for a minimum wage worker will look different from the Laffer curve for a multi-millionaire investor. If I work 40 hours a week for a minimum wage and a 90% tax rate is invoked then I will leave off work. I could not even afford food, accommodation and fares to keep body and soul together and get to work. If I ” earn” $100 million a year profit after expenses from shares then it is still worth me engaging in this even in the face of an inescapable 90% tax rate. I can still live very handsomely on $10 million a year after-tax income. Again this point is trivially obvious.
Thus the notion that a single, simple Laffer curve can be any kind of tax regime model for the entire economy is absurd.
@Ikonoclast
No you won’t. Not if there is no alternative way to get a dollar.
I’m thinking of “the hungry mile”, food stamps and poverty wages doing triple jobs in the US…etc. (not that they pay 90% tax, just making the point that when you are desperate you will work for next to nothing if that is how the system is set up – that’s why civilized societies invented the minimum wage and welfare).
@Ikonoclast
“Thus the notion that a single, simple Laffer curve can be any kind of tax regime model for the entire economy is absurd.”
And thus you have removed the fig leave and discovered why people like John Fraser talk only about top marginal tax rate!
Very timely post, JQ.
According to a smh article of today, referenced below, Mr John Fraser promotes cutting the top marginal tax rate in Australia because, he asserts, to do otherwise would make Australia ‘uncompetitive’ and stifle ‘growth’. He refers to Singapore, Hong Kong, the UK, Canada and NZ for comparative top marginal tax rates (putting ‘insurance’, ie other social services taxes in the UK in brackets without stating rates).
http://www.smh.com.au/business/federal-budget/federal-budget-2015-cut-income-tax-says-treasury-secretary-john-fraser-20150515-gh2zcs.html
Having read so much about the ‘competitive threat’ coming from Singapore’s taxation system, I had a look at their tax rate changes for 2015 and found they reduced the consumption tax a little bit and increased the income tax a little bit. (They seem to have independent thinkers in their government.)
Even though all EU data is published also in English, the T Secretary ignores all except the UK (and her former Colonies). Why?
The Howard government reduced income taxes, starting from the wrong end (top; the bottom had to wait until the tax threshold was lifted by the Rudd-Gillard government). Now the T Secretary promotes a repetition of this error. I say it is an error because it contributed to asset price inflation; there is only so much locally produced food the top income earners can eat, even allowing for Veblen-type conspicuous consumption, and, no matter how many times a bathroom in a local house is renovated due the top marginal tax rate being reduced, it doesn’t follow that national income will increase (because some other bath rooms remain un-renovated due to lack of spending power of their owners, etc etc). The idea that lower top marginal tax rates generates entrepreneurs, as Fraser asserts, isn’t watertight either because entrepreneurs don’t tend to start off earning an income that attracts the top marginal tax rate. The top marginal tax rate is relevant for managers of existing companies (not to be confused with entrepreneurs in the original sense) and a few professionals. In this regard, I do recall the increased ‘income tax competitiveness’ (lowering the top marginal tax rate) during the Howard era attracted international managers whose creativity consisted of creating difficulties for customers of Telstra, the corporation itself (loss of customers), job losses for engineers and other technical people, and, later on, for the Howard government. Obviously, the ‘income tax competitiveness’ did not prevent the GFC. In the meantime, the London School of Economics has created a research team, including the French economist T. Piketty, to work on a global wealth tax. This, I take, is a ‘competitive threat’ to the T. Secretary’s mental model.
Thanks for linking to the February 2015 article in which John Fraser says he has no opinion on whether or not the Rudd-Gillard government’s response to the GFC was appropriate, he lived through the GFC while managing some specified UBS asset portfolio, he found the time period personally taxing, and he believes this event was unpresedented in world history.
We all lived through the GFC! The only aspect of the GFC which I can see as having been unpresedented in world history is that a repetition of the Great Depression was prevented in the countries he seems to consider to constitute ‘the world’ (and elsewhere) due to private money, generated by the proverbial Wall Street bankers (including UBS), having been laundered via central banks and emergency measures by governments such that it is now public debt (more or less, using a big brush but not quite as big has his, IMHO). It seems the government is happy having a T. Secretary who has no opinion on what happened during the time of his absence from the Treasury, managing asset portfolios for UBS. It is amazing how many ex-bankers, after having their bacon saved by tax payers, are now being paid by tax payers directly.
The Laffer curve and what you call the Laffer hypothesis is of no interest to anybody who is of interest, IMHO, because the question: What tax (rate or rates?) produces the maximum revenue may have been of interest to some Arab ruler in the 14th century but, surely, we have moved on since then.
According to the Ezra Klein categories, I would belong to the “right/centre right” category for the simple reason that any prediction about the effect of a ‘tax cut’ (or ‘hike’, to use news speak) on government revenue depends on the conditions prevailing at the time, in a particular economy which is embedded in the ‘global economy’, including but not confined to the steepness of a progressive income tax scale, if any and whose taxes are cut and in which order.
In today’s smh article Fraser also talks about tax creep. This issue can be better dealt with by replacing the very course income scale in Australia with a finer income tax scale. In any case, the T Secretary’s focus on the top marginal tax rate may make sense to his financial position but it does not make sense in terms of the actual economic issues in Australia and elsewhere.
Rightly or wrongly, I’ve reached the conclusion that the Laffer curve and everything that goes with it is either of interest to lazy thinkers (leaners) or it is a fig leave for non-satiated personal wealth maximisers (leaners). Ikonoclast nailed the technical shortcomings pretty well. Lets send the Laffer curve back to the 14th century.
I can only say that my personal knowledge of Rob Heferen is that he is not stupid, and has always preferred hard evidence to ideological assumptions. He’s a technocrat through and through.
He’s also far from the only tax expert who thinks company taxes can have a pretty high deadweight allocative loss, and unlike personal income tax could easily be quite regressive in their final incidence. It depends on industry structure, and the consequent relation between various elasticities, who they get passed on to – customers, workers or shareholders. There’s good reason to believe that in a small open economy rather little of it ends up on shareholders.
The best arguments for company tax is as a withholding tax to avoid big avoidance opportunities in other taxes, especially the personal income tax. Eg – absent company tax I reckon an awful lot of employer-employee arrangements would quickly become contracting ones with personal companies.
By that theory, we here in Canada should be dining of caviar and nightingale tongues. We have had 10 years (or maybe a bit more now) of fairly steady reductions in corporate taxes. A hint, we are not that wealthy.
We did get to the point that Mark Carney, Governor of the Bank of Canada at the time, was publicly complaining of corporations sitting on cash surpluses and not investing.
Of course, our idiot, and probably criminal, government kept doing the same thing. Well they made lots of other economic mistakes too but that is another matter.
Ask Mr. Heferen to drop over and see for himself how successful his approach is likely to be.
The argument that 100 percent tax rate yields zero economic active is fundamentally flawed. Such an action is simply a phase of economic activity present in all pure socialist and communist economies.
The statement requires a set of conditions to be even slightly true such as perhaps: “given maximum greed and maximum brutality” 100 percent tax rate yields zero economic activity.
In order to fully understand Libertarianism one must introduce “empathy” as a variable scale into the economic algorithm. Greed and brutality are consequential forces of declining empathy, which itself is integrally connected to “cognitions”.
I don’t know how one would quantify empathy but I suspect that the scale might be describe as a graduated range between Vlad the Impaler at one end and Mahat Maghandi at the other. The Tea Party and Barak Obama would represent scale points in between. How would you lay out the scale and who would you include to make a uniform grading of applied empathy. Then the real question becomes how to use this understanding to make a functioning and fair economy.
@Megan
My example was theoretically “pure”. It assumed no welfare and no crime (to name two other possibilities).
A person cannot actually work for nothing or even for too little. There is a cost called the reproductive cost of labour. To be able to produce physical or mental labour one must be fed and rested before the start of each working day. If a person’s wages will not pay for adequate food for nourishment to reconstitute the body and mind after labour and a better resting spot than “under the bridge” then labour is a negative sum activity. That is to say I might use x calories above basal metabolism to work 8 hrs. If my wages will only pay for 1/2 of x calories then the labour is a negative sum activity. I would be better off (live a little longer) doing nothing.
Note, the concept of the reproductive cost of labour goes further than the above to include the costs of feeding, housing, raising and educating the next generation of workers.
We’re already running a natural experiment in cutting company tax, because multinationals are using international transfers to reduce their tax to very low levels.
So what happens? Type “ikea cash holdings” or “apple cash holdings” or “microsoft cash holdings” into Google.
If untaxed, a lot of companies hoard cash. I don’t believe this is what low-tax proponents expect.
I’m reminded of the rhetoric around personal tax cuts during the Howard years. They kept saying that if they cut my personal rate of income tax, I’d work harder and make more money. Actually, I worked less and made the same amount of money. It was the only rational response. I expect it’s the same for a lot of businesses.
@Ernestine Gross
Excellent comments. I agree on every point.
“This issue (bracket creep) can be better dealt with by replacing the very course income scale in Australia with a finer income tax scale.”
A single formula could be used to derive tax owed in relation to income. Nothing would be more finely gradated than a continuous formula. I assume the formula would incorporate the tax free threshold and then a function to increase the percentage of tax paid on income above the threshold and do so in a smoothly and shallowly gradated exponential fashion.
@Ikonoclast
“Bracket creep” or fiscal drag actually has very little to do with tax brackets and would still occur even if we had very fine tax scales or a continuous formula. It is purely an artifact of a progressive tax system where tax paid is a direct function of nominal wages. As nominal wages increase (whether due to real wage growth or inflation) then tax paid (and average tax rate) increases. This is only avoided if the function is directly indexed, most easily through indexation of the brackets.
Also people often misunderstand tax brackets. Moving to a higher tax bracket only affects the rate of tax paid for that portion of income that is in the higher tax bracket, so the tax paid and average rate of tax moves smoothly. Thus we already have a continuous formula for tax, that does increase in a “smoothly and shallowly gradated” function. The only discontinuity is in the first derivative of the tax function; the slopes change as wages increase.
@BilB
Re: empathy. Before quantification one needs to translate the idea into a mathematical object (well, this is what math economists do).
Are you familiar with work on interdependent preferences? Postlewaie’s paper, referenced below, from the late 1990s is a good one to start off with. By the around 2005 there were several interesting papers in Econometrica which deal with evolving traditions among sets of people.
Click to access Postlewaite_%28EER_98%29.pdf
This is a bit off topic so I won’t expand.
One point that should be made about Laffer’s Hypothesis is that it is not
falsifiable. The theorem that Laffer relies on (Rolles Theorem, IIRC) merely
says that there is at least one inflection point in the range, there can be an
arbitrarily large number. So the curve could be like a camel’s back and if
revenue is falling at point a, it may be rising again at point a+e, where e is
small.
But then, when have economists worried about falsifiability?
I don’t think a diagram on a napkin can be regarded as relying on Rolle’s theorem. There’s no reason to think that the rate-revenue curve would have multiple maxima, and plenty of reasons to think otherwise.
In any case, Laffer’s hypothesis may be stated in a form that’s about as falsifiable as any claim involving a counterfactual, namely that the tax cuts proposed by Reagan would produce more revenue than the existing tax schedule. All serious economists who have examined the question have concluded that this claim was false.
So the US had top personal income tax rates over 90%, back in the 60’s. It was a horrendous time, wasn’t it? Vast unemployment, slow growth, poor social cohesion. Thank God they saw sense!
Peter,
The tax function is a step function over the income range from 0 up to that which attracts the top marginal tax bracket. It is not a smooth (twice differentiable) function everywhere (“… the slopes change …”, as you note). The question arises whether the change of the change in slopes is the same for the entire range of the income distribution. The answer is NO. The easiest way to demonstrate this is to note that the rate of change of the tax rate (sometime called ‘average tax rate’, defined as tax payable/taxable income) is a decreasing function of income for incomes above that which attracts the top marginal tax bracket (the tax rate approaches the top marginal tax rate asymptotically as income increases; for ‘top income earners’ the difference between marginal tax rate and average tax rate becomes increasingly irrelevant as their income increases). Would you call such a tax function ‘progressive’ irrespective of the range of the income distribution above the top marginal tax rate? Further, would your argument regarding the unique solution of the ‘fiscal drag’ via indexation of the tax brackets be valid in general, that is, irrespective of changes in the distribution of income?
@Peter
Isn’t it actually an artifact of not indexing the brackets?
Any proper analysis of tax cuts will go beyond “tax revenue” and look at total welfare or some suitable proxy. Underlying the Laffer effect is the fact that higher taxes make the private sector less productive. At 100% the private sector becomes completely unproductive. This represents a large loss of human welfare and makes people more dependent on the state sector. Although at 100% tax as Laffer points out the state sector can no longer offer us much either because the tax base is gone. The other consideration is the diminishing returns that occur when you shovel money at government departments. Beyond a certain point they fail to use the extra money efficiently. They start inventing initiatives that are unworthy.
I should have read Ernestine’s reply before replying myself. Of course, indexing a crudely stepped set of tax brackets is not enough in itself to create a genuinely progressive tax system. A continuous function delivering an ever higher tax percentage rate to ever higher income earners would be the answer I think. Then that continuous function could be indexed.
However, I will pose again a question I have posed elsewhere. The current economic system operates to continuously concentrate wealth and generate inequality. Piketty is the latest economist to demonstrate this very conclusively. The current system has an in-built bias which we might call systematic and/or systemic. Progressive taxation for redistribution seeks to (very partially) correct the effects of this inbuilt bias after the fact; after the income and wealth bias has operated.
To permit the inbuilt bias to operate and then seek to steer against the bias after the fact seems inefficient to me. It would be better to re-engineer the economic system to not be so excessively biased in the first place.
I often use the car driving analogy. If your steering is badly biased you can continuously fight it with effort at the steering wheel. Or you can get your steering realigned so the bias is corrected and the car steers true without effort. Instead of a heavy redistributive effort after the fact, after the bias in the system has started to create such large inequities, we need to re-engineer the economic system to remove the bias towards excessive accumulation of income and wealth by a minority. The highly unequal ownership of capital is at the base of the problem. In turn, the social-political-economic construction of ownership itself is the problem.
I had no idea it was that high- wow! I see in 1944 it was 94%
Imagine trying to get that through the house these days 🙂
@Troy Prideaux
Of course the need, or even the practical workability (and it did work!) of having tax rates so high begs the question of how distribution of income got so unequal in the first place. Such a situation illustrates a condition of enormous income bias which needs correction by enormous progressive taxes. Would it not be better to re-engineer the economy such that the enormous bias in income distribution did not occur in the first place?
The enormous income bias comes mostly from an enormous ownership bias. Some few people own a lot of capital and many people own little capital. It is worth asking how this comes about. Piketty is a good place to look. Historically, once the system was up and running as it were, it mostly came about from existing ownership and inheritance. Having lots of preexisting capital is the best indicator for accumulating even more capital both in absolute and relative terms.
There was a period in history (about 1919 to 1969) where this became somewhat less the case and Piketty uncovers the reasons why. However, Piketty also demonstrates we have entered a new (but actually historically more common) phase where once again owning and inheriting a lot of capital becomes easily the best predictor for accumulating even more capital.
It is worth asking what exactly ownership is and how it is conferred? It is command, control and disposal of capital and the income it generates. It conferred by arbitrary law. The law could be “many-otherwise” as both laws for high taxes and laws for conferring ownership in other ways (worker cooperative ownership) can be seen to have existed in history.
The question of efficiency and effectiveness arises. The current system of capital ownership, which naturally tends, or rather systematically tends by inherent system processes, to ever greater concentrations of individual wealth is nevertheless held to;
(a) generate more wealth overall; and
(b) lead, notwithstanding inequality, to more wealth for the poor anyway.
These claims need to be tested. I assume they have been tested by some economists. Those who know about such testing of empirical outcomes can perhaps enlighten us about the results.
Underneath the tolerance and indeed outright advocacy of highly unequal ownership is the assumption (in a nutshell) that people working for themselves collectively and conjointly are more lazy and inefficient than either;
(a) people working for one taskmaster (a rich, powerful employer); or
(b) people working solely for themselves (self-employed, business of one).
Again, these claims need to be tested. Again, I would interested if people who know of studies which investigate such assumptions have been conducted.
Note: It is quite clear that the state capitalism of Soviet Russia did not meet the criteria of people working collectively and conjointly and making their own production and distribution decisions democratically. Rather the setting of targets (and remuneration) by autocratic capitalist employers was replaced by the setting of targets (and remuneration) by an absolutist state as sole autocratic, monopoly employer making all production and distribution decisions.
TerjeP,
This
“Underlying the Laffer effect is the fact that higher taxes make the private sector less productive”
is an assumption, and so anything but a “fact”.
Your point is entirely circumstantial. It depends fully on what the taxes do for the public. The higher the pay scale the less that taxes can provide for those citizens, but then those people become less productive the higher the pay level, with or without taxation. If services provided through taxation exceed that which can be achieved through direct private supply then the taxation path is more efficient where those services are relevant to the community’s needs.
BilB – do you dispute the notion that the private sector will cease to produce if they are taxed at a rate of 100%? Or is your point merely that it isn’t a smooth ride between 0% and 100%?
@TerjeP
Nobody sensible is proposing a tax rate of 100% on anyone. The other point is that high taxes or even tax increases are not necessarily proposed for everyone. It would be quite possible for example to reduce taxes for the lower income-earning 80% of the population and increase taxes for the higher income-earning 20% of the population. This could be done in a revenue neutral manner. The economic evidence is that this would increase total activity in the economy over current settings. One might even think you would be in favour of tax cuts for 80% of the population.
You can’t say that Heferen is a Laffer adherent. Laffer said that cutting tax rates gets you more revenue. Heferen said that cutting tax rates gets you less revenue, but not as much less as the immediate effect. In itself, this is mainstream economics, because cutting tax rates is almost always going to stimulate some more of the thing you are taxing. (Cut taxes on carbon emissions, get more carbon emissions). If you want to you can argue about his 50% number, but that’s not Laffer-ism
@TerjeP
“do you dispute the notion that the private sector will cease to produce if they are taxed at a rate of 100%? Or is your point merely that it isn’t a smooth ride between 0% and 100%?”
Terje, your question is too vague. If it is of assistance to you, one concept of ‘perfect competition’ is characterised by “zero profits” (in equilibrium). Zero profits does not entail ‘no production’. In this world of ‘competition’, any positive profit which would be taxed at 100% would still not entail no production. (References: older econ textbooks)
EG – no it is not of assistance to me. Anybody that has spent any time in the real world knows that we don’t have “perfect competition” and that the world of commerce is not characterised by “zero profits”. If it was then I suspect we would quickly have zero investment but given it’s a hypothetical I’m not too worried about that unfortunate prospect.
For what it’s worth in a world of perfect people everything would be awsome. I hope this is of assistance to you.
I agree with cutting taxes for the bottom 80% of people. It’s a no brainer in my book. The tax free threshold should be increased to at least $40000.
I don’t see any virtue in raising the tax rate for the top 20%. But they should be free to pay more tax than they have to if they feel so inclined.
@TerjeP
You forgot your original question (which I considered to be too vague) to which I replied by means of trying to elicit what it is on which the 100% tax rate is supposed to be applied.
Now you tell me there exist people who do not exist or people who lived some time in the past and now know that ‘perfect competition’ does not exist. But if these dead people would be alive now then at least some of them could tell you there is a large part of the ‘private sector’ who do ‘produce’ at zero profits. Indeed the most private part of the ‘private sector’, the family, produces a lot at zero profit for own consumption.
I still don’t know what it is to which the 100% tax rate is supposedly applied. I give up.
<blockquoteIndeed the most private part of the ‘private sector’, the family, produces a lot at zero profit for own consumption.
When I cooked dinner for the family this evening it was not for zero profit.
Terje,
I intentionally did not cover the 100% end of the argument as you suddenly introduced the notion of a “private sector” something which is not a feature of the Laffer Curve definition, even though it might be assumed. Can there be a private sector when the re is 100% taxation? On the surface of it there appears to be a contradiction.
Where there is a working economy and 100% taxation there would have to be taxation and subsequent redistribution. It would largely depend on how that redistribution occurred.
The fact is that very large private corporations, where all invoicing and cash flow (100% taxation) is managed through a head office, work in this exact manner. Large businesses have departments that process product without any funds changing hands locally at all. Materials are ordered, received, processed, packaged and dispatched without any funds changing hands locally, or within that state, and in the most extreme within that country.
My business actually operated a function in entirely that manner. We warehoused, processed, and dispatched product for a NZ business. The invoicing was done from NZ and all proceeds were directed straight to NZ. We performed our part of the operation enthusiastically for our post distributed share of the turnover.
So, no, your argument does not hold up at all, neither does the Laffer hypothesis. As I said above the outcomes of taxation are entirely governed by the specific circumstances.
@TerjeP
As so often, you get it half-right while totally missing the point.
You may like the idea of living in Galt’s Gulch, but I prefer to live in a society. Societies cost money to run, so they need to collect taxes. Where better than from the wealthy, who have benefited the most from living in a society?
Has a 100% marginal income tax rate ever been seriously proposed in the world? Like for example anyone earning over (a really big number) say $10M p/a in $today’s will be taxed at 100% for every dollar earned over that threshold in an attempt to cap income levels for the very rich? I realise it’s probably not practically possible, but was curious to hear if it’s even been seriously considered.
@Troy Prideaux
I considered it after I wrote the post @16. The clue is the term ‘bracket’. The convention is that [ ] denotes a closed set and ( ) denotes an open set. The so-called progressive tax system in Australia (and probably in most countries) looks like this: [ ], [ ], [ ], [ . Ah, there is a bracket missing! What if we write [ ], [ ], [ ], [ ], and [ )? No cap on income is specified. But whatever is in the last bracket is taxed at 100%. I suspect a lot of people would like to have many more tax brackets than what we have now (approximating a continuous function).