Slighty unfortunate that Hari makes exactly the same mistake about The Laffer Curve that Jonathan Chait does.

Trying to explain this idea to an eager Cheney, "Laffer pulled out a cocktail napkin and drew a parabola-shaped curve on it," writes the liberal

New Republicjournalist Jonathan Chait. "The premise of the curve was simple. If the government sets a tax rate of zero, it will receive no revenue. And if the government sets a tax rate of 100 per cent, the government will also receive zero tax revenue, since nobody will have any reason to earn any income. Between these two, Laffer\’s curve drew an arc. The arc suggested that at higher levels of taxation, reducing the tax rate would produce more revenue for the government."

No, there\’s a reason it\’s called the Laffer Curve rather than the Laffer Arc. The point is that there is a level of taxation (and we must be very careful to point out that this will vary for different taxes too) which maximises revenue collection. Go to the right of that point and raising the rate will reduce collections. If you\’re already to the left then reducing the rate will indeed reduce collections.

The point is that if you\’re to the right then reducing the rate will increase collections….and vice versa, if you\’re to the left then increasing the rate will.

We also need to be careful to distinguish between the short and long term. Let\’s have a completely made up example, shall we? OK, we have a taxation system which, via its deadweight costs (which is what we\’re really talking about with the Laffer Curve, the lifting of them, and there isn\’t a single economist alive who would try to insist that taxes don\’t have deadweight costs) leads to a growth rate of 2% pa. We fiddle around with such taxes until we\’ve engineered a growth rate of 4% (well, I did say this was completely made up, didn\’t I?). In the process, we\’ve reduced tax collections by some amount. And we find that we\’ve reduced collections in year two, and three, and four….does that mean we\’ve reduced collections for all time then?

Clearly, no, because the difference between a growth rate of 2% and 4% compound quickly (for one meaning of "quickly") starts to get noticed. For example, a 2% growth rate means the economy doubles in size in 35 years or so. A 4% one means it doubles in 17.5 years or so.

So if we had a 4% growth rate, and taxation levels of only 75% of those in the 2% growth rate scenario, you would see that at some point in the future total tax collections in the higher growth scenario would in fact be higher than in the high tax scenario.

OK. So The Laffer Curve is not buncombe then. The statement that always lowering taxation rates will always increase revenue is indeed buncumbe though: as is the statement that they never will.

The question is, where are we on the curve and further, what timescale are we talking about?

I\’ll also add my usual whine here about the phrase "supply side". It has come to mean, in the annals of American liberalism, exactly this about marginal taxation rates. But that\’s not the way it started out, not the way I continue to understand/use it. It\’s about reform of the supply side. Privatising BT, breaking up AT&T, these are also supply side reforms. Education vouchers would be supply side reform, GP fundholding was a supply side reform. It\’s about what it says on the tin: reforming the supply side of the economy.

From 1947 to 1973, the US economy grew by 4 per cent a year – while the richest Americans paid a 91 per cent top rate of tax.

Err, Johann? A little research perhaps before you write about things where you have no knowledge base?

President John F. Kennedy proposed a series of tax rate reductions in 1963 that resulted in legislation the following year that dropped the top rate from 91 percent in 1963 to 70 percent by 1965. The Kennedy tax cuts helped to trigger the longest economic expansion in the history of the United States. Between 1961 and 1968, the inflation-adjusted economy expanded by more than 42 percent. On a yearly basis, economic growth averaged more than 5 percent.

That\’s just sloppy.

So from 1947 to 1963, the top rate of tax was 91 percent… and the economy grew by 4 percent every year, right?

Tim adds: Indeed it did. Something that has been known to happen at the end of a war, a boom.

Also worth noting that the top rate came in at $200,000 a year (in 1945 money). In fact, it’s said that when FDR brought in that top rate only one person actually paid it. John D. Rockefeller.

http://www.taxfoundation.org/taxdata/show/151.html

Who should we care about maximising the amount the state can extort?

I’m not sure that the Laffer curve would be similar for different societies and, if the curve has different sociological variations, one has to wonder if it has any predictive value. Gemany, for example, initiated the greatest tax rise in the history of the country after that last election and now is seeing record tax revenue. One wonders if the result would have been the same if the same tax rise had happened in the US or GB.

‘No, there’s a reason it’s called the Laffer Curve rather than the Laffer Arc. ‘

You have lost me-are you saying that Hari is wrong because he used the word ‘arc’ instead of ‘curve’?

What do you think he means by ‘arc’ if not a ‘curve’?

I assumed that by “arc” he meant a finite, monotonic curve, each end of which lies on the horizontal axis. Which would seem to be suitable.

I think what Tim meant is that an arc is merely a shape whereas a curve is a term that has mathematical signifcance, in this case as an inverted parabola with marginal tax rate as the dependent variable and total tax revenue as the dependent variable. The mathematical significance of this is what proves the point of the Laffer curve.

What I do not understand is why so many politicians and journalists on the left get so annoyed with the Laffer curve. My prof for mathematical economics was fairly left-wing (he was one of the relatively few economists who signed on the minimum wage raise petition in the US), but he told my class that no economist argues with the basic premise of the Laffer curve itself (and that economists knew of this phenomenon well before Laffer), that there is a point where marginal rates are too high and people will work less or work off the books and tax revenues will therefore decrease and vice versa. The debate among economists is how often will the economic growth stimulated by the tax cuts lead in the long run to an increase in tax revenue due to economic expansion, even if the marginal rate is to left of the peak of the Laffer curve.

Sorry, it should say independent variable in the third line

The Laffer Curve arises from a fundamental theorem of calculus, which states that if there exists a

continuousfunctionf(x)that maps some abscissaxonto some ordinatef, then for any pair ofx(aandb, say) such thata<bthere exists somec,a<c<bsuch that the slope offatci.e.f'(c)is the same as the average gradient betweenfataandb, which is to sayf'(c)=f(b) – f(a)/b-aIf we fix the end points at zero, corresponding to the maxim that tax revenue is zero at both the 0% and 100% rates, then the theorem states that there is an extrememum (where the slope of the revenue is zero) in the interval. There is thus some revenue-maximising tax rate between zero and one hundred percent. Laffer’s question was to ask which side of the maximum, extant tax rates were situated.

There’s nothing magical about the Laffer curve. It is a fundamental statement of mathematics allied to some very uncontroversial economic theory. The complications arise in actually drawing the damn thing, and situating an economy at a given point on the curve. Empirical evidence indicates that most post-industrial economies live in a region where the first differential of the curve is negative i.e. reducing taxes increasing revenues. But this is merely empirical. And from a mathematical standpoint, the contuinity of the revenue/tax curve is assumed, rather than proven.

OK, if all those italics work it will be a miracle.

Bloody hell, they did. Tim, get a frickin’ preview button, toot sweet.

Nice aplication of the ‘rule of 70’ there!

Possibly ignorant question (engineer not economist) but;

Why does the curve have to be continuous? Wouldn’t a discontinuous curve explain some situations easier?

I liked this line about Gilder:

“He applied the same evidence-free approach to his economic writing.”

Words like pots, kettle, black immediately spring to mind…

Actually there is also the question of working harder. I am not convince that it follows all the benefits from the Laffer curve come from future economic growth. A reasonable amount would probably come from people working longer and that would be more or less immediate. If you have a choice about working overtime or an extra shift, or even taking an extra job, whether you are paying 90 percent or 19 percent tax probably has a big effect. Europeans take much longer holidays than Americans or East Asians do. They are likely to be trading the extra money they could be earning for extra time with their families – after all the government does not take 50 percent of their holidays. So in a high tax society, more leisure time always makes sense. Reduce the tax, and so increase the incentive to work longer, then the economy grows and the tax revenue take may actually increase. That shouldn’t take four years either.

While reasonable people might accept the existence and general shape of the LC (a bump with a single maximum – a parabola is more than a little idealized), the complication is that some politicians think their policies can change the LC’s shape and so move the maximum arbitrarily close to 100% taxation, or 0% taxation, dependent on inclination. For example, imposing a death penalty for any form of tax evasion might move the maximum take closer to 100%.

Steve, the continuity requirement stems from the underlying mathematics. The Laffer curve invokes Rolle’s Theorem, which is a special case of the Mean Value Theorem. Both assume that the curve is continuous and differentiable in the interval. Since a slope is not well-defined at a discontinuity,

you cannot apply either of these theorems to a discontinuous curve.

SMFS: indeed a great deal of the variability in working hours between Europe and the US can be explained in terms of the substitutability of leisure for labour.

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Bugger me, I said “monotonic” when I meant “unimodal”.