Double Tax Rates, Quadruple the Economic Harm
At last Wednesday’s hearing on tax reform, three witnesses–Rosanne Altshuler, Larry Lindsey, and I–invoked a famous rule of thumb about taxes. We each told the Senate Budget Committee that high tax rates are disproportionately harmful for the economy and that:
If you double tax rates, you quadruple the resulting economic harm.
If a 10% tax rate on some activity does a certain amount of economic damage, for example, then it’s a reasonable guess that doubling the tax rate to 20% would multiply that damage by a factor of four.
It was nice to hear such agreement among the panelists, but judging by the senators’ reaction, this idea is not intuitive. So let me try to explain with a simple example.
Suppose there are five people who might buy a pizza. The first person values a pizza at $14.50, the second at $13.50, the third at $12.50, the fourth at $11.50, and the fifth at $10.50.
If pizzas cost $10, all five people will buy one. The first person gets a net benefit of $4.50, since the pizza was worth $14.50 to her, but she paid only $10. The second person gets a benefit of $3.50, and so on. Add it all up, and the benefit of the pizza market is $12.50 (= $4.50 + $3.50 + $2.50 + $1.50 + $0.50).
Now suppose that the government levies a 10% tax on pizzas; that lifts the price to $11. Now only the four consumers who place the highest value on pizzas will buy them; Mr. $10.50 won’t buy. The four remaining consumers now benefit by $3.50 + $2.50 + $1.50 + $0.50 = $8.00 from buying pizza. The government collects $4.00 in revenue, so the total economic benefit of the pizza market is $12.00, $0.50 less than before. That 50-cent loss falls on the hungry guy who no longer buys a pizza. The $1 loss for each of the four buyers isn’t lost to the economy; instead, it transfers to the government.
Now suppose, instead, that the tax is 20%; pizzas now cost $12 each, and only three consumers will buy. Their total benefit is $4.50 (= $2.50 + $1.50 + $0.50). The government collects $6.00 in revenue, so the total economic benefit is $10.50. That’s $2.00 less than without a tax.
So there you have it. When you double the tax from 10% to 20%, you quadruple the economic harm from $0.50 to $2.00.
Why does this happen? Because doubling the tax doubles the number of consumers who drop out (from 1 to 2) and doubles the average economic value of the pizza sales that never happen (from $0.50 to $1.00). Two times two is four, so the overall effect is to quadruple the economic harm.
Put another way, the value of the second lost pizza ($1.50) is three times larger than the value of the first one ($0.50). So the economic harm of the 20% tax is four times the harm of the 10% tax.
This is a big deal when you design a tax system for the entire economy. To avoid needless economic harm, you should aim for low tax rates and the broadest possible tax base. If you need to raise $6.00 from our mythical food economy, for example, it would be far better to levy a 5% tax on pizzas, tacos, and hamburgers, than a 20% tax on pizzas alone.
I hope that whets your appetite for base-broadening tax reform.
P.S. Did I cook the pizza example to get the increase to be exactly a factor of four? Of course. In the real world, the actual multiple will vary. If the fifth person valued the pizza at only $10.25, for example, the loss from the 10% tax would have been $0.25, and the loss from the 20% tax would have been seven times larger at $1.75. Conversely, if the fourth person valued the pizza at only $11.00, the loss from the 20% tax would have been $1.50, only three times larger than the $0.50 loss from the 10% tax. The double/quadruple rule of thumb assumes an even spread of consumers and their values — a reasonable starting assumption until you have more information.
Great post and an interesting perspective
Donald, you don’t seem to understand that the whole theory behind PSQD graphs is based on substitution. Economies do not consist of the single “pizza” good.
Which renders this whole illustrative example incoherent.
Micro is necessary but not sufficient to explain macro.
Taxvox Blog Archive Double Tax Rates Quadruple The Economic Harm…
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Good to see you’ve got the economics covered. Now, does anyone around here have a good grounding in philosophy, psychology, sociology, pedagogy, politics, history, law, theology, computer programming, architecture, and nutrition as well? Anyone thought of upgrading from homo economicus to homo evolutionus? Might make you think more kindly about my brand of normative economics, the tax structure of which I summed up in the following way:
JF: “progressive personal-exemption spacial and temporal taxes, levied in the coin of the realm, on the consumption (including the consumption of good money known as income) of unsustainable, unhealthy, or antisocial types or amounts of physical or mental goods or services, in order to guarantee the positive right to self-improvement worldwide through United Nations equalization payments, or, in laymen’s terms, from each according to his feast of wealth, to each according to his famine of health.”
(from: Joseph Furtenbacher on Huffington Post)
I must admit, I’m sort of curious as to what any of you people could say to me to justify your incomes (mine has averaged ~$(Cdn)10,000/yr for the last seventeen years). The economy (not to mention the environment) was in the toilet the last time I checked, and it occurs to me that all of you put together have no real ideas on how to go about creating large numbers of sustainable, living-wage jobs, something I could do in my sleep if only everyone wasn’t so busy blowing their own horns at the top of their lungs. But perhaps things are different When It’s Sleepy Time Down South…
Oh well. Any thoughts on implementing a prebated carbon tax? About taxes on meat, sugar, salt, fat, television, etc. (you know – the kinds of things that have led to the lifestyle diseases responsible for the majority of your health care costs…)? Maybe an end to agribusiness tax breaks? In order to subsidize the production of things like organic fruits and vegetables, composting toilets, rooftop community gardens, bikes, books, sporting equipment, etc.?
Ever think about the price of Texas Tea in China, or the cost of TARPs, er, tarps, in Haiti?
Oh, and just so everyone knows it’s safe to reply, I’ll be the first to stick my head in the Polymathic Lions’ Den.
See? Nothing to be afraid o- *CHOMP*
Gee, if you are going to make statements like
“the least destructive tax system is the one that minimizes tax rates and maximizes the scope of what is taxed. If you disagree, take it up with Paul Krugman.”
Can you at least cite some studies, and define exactly what is meant by the subjective term “destructive” and how it is measured. I mean, even the author admitted that the example cooked the books and I find it pretty difficult to accept a very serious hypothesis like this based solely on a manufactured anecdote.
And, while Prof. Krugman has very impressive credentials, I think I will do my own economic analysis, you know, read the literature, weigh the different sides and draw my own conclusions. I think that is what is called the scientific method.
I don’t have the time to teach microeconomics here, but if you google “deadweight loss” you can read up on it. That’s how the economic damage is measured. By all means, do your own analysis before questioning those who already have done so or demanding that they spoon feed you proof in simplified terms. Donald Marron’s attempt at a simplified explanation apparently did not convince you, and I don’t know if it can be made any simpler. Maybe Wikipedia can help you understand it: That’s the first place I go when I want to learn about an unfamiliar concept.
You guys are way over-thinking this. A 20% rate on a narrower base is 4 times as harmful to the economy as a 10% tax on a broader base that raises exactly the same revenue. That’s not a conjecture; that’s a fact.
Sid, your objections address non-revenue-neutral rate changes. That’s not what the author was discussing. The author’s point is simple: For any given amount of revenue, the least destructive tax system is the one that minimizes tax rates and maximizes the scope of what is taxed. If you disagree, take it up with Paul Krugman.
This seemed like the most biased posting I have seen on this blog in a while and it didn’t even seem to make a valid point.
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Unless they repeal the laws of double entry bookeeping and financial equilibrium, the example is invalid because it does not address the impact of a change in a second variable needed to keep a system in balance. It is only a good example to illustrate price elasticity of demand and consumer surplus.
The basic equation of government economic activity is
G = T + dD
where G is government spending
T is Tax Revenue
dD is the change in Government debt
You cannot change just one variable, at least not in this universe.
In a revenue neutral program of “base broadening/lower rates”, T does not change,but the composition and burden of T changes. Unless you can know the impact of that composition and burden change, it is impossible to know whether the policy is good or bad for whatever economic goal has been adopted as the object of the policy change. Of course, ignoring this equation is in the political interests of all. Those who advocate increasing G never seem to get around to addressing the right side of the equation, and those who want to decrease T never state how G will be cut (we know they don’t want more debt because they say so). Such arguments lack intellectural integrity.
We are also dealing with perjorative terms here. “Broadening the base” sounds good, as does eliminating tax preferences (preferences by their very nature are undemocratic, unfair and bad) but policy should be based on objective, not subjective analysis. Changing the name of the Estate Tax to the Death Tax does not change anything about it and its economic impact, but it does alter perception and political positions, which is the purpose of changing the name.
The example applies to a consumption tax with no reduction in other taxes and no increase in income to compensate. Do both of those and the economic impact is zero, as you point out in suggesting a more broad based tax reform.
Would a tax increase on the wealthy have similar impact? It might – however if that impact reduces the concentration of savings and wealth rather than expenditure, it might not necessarily be a bad thing.
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If you look only at taxes and tax rates, then of course any tax increase does economic harm. If however you complete the picture and look at both sides of the coin, taxes and spending the conclusions get a lot murkier.
Let’s say that taxes are increased on Pizza’s and the proceeds are used to help pay for infra-structure needed to build a billion dollar football stadium for an ego-maniac Texas football team owner. (Yes, the owner could pay all the costs but if he can get a couple hundred million from the taxpayers, why not?). This facility generates few jobs, and what jobs it does generate are low skilled, low paying. The facility sits idle for more than 340 days a year, and in short does very little to aid the economy. Is there a lot of economic harm? You betcha!
Now let’s suppose the proceeds were invested in education. This resulted in a more productive workforce, with higher productivity and greater earnings. Some of this money is spend on buying even more pizza’s then would otherwise occur. Is there economic harm? No. The multiplier effect produces a higher level of national income than would otherwise take place.
(Did I cook these examples, yes, that’s what I do when I do not have data and analysis to support the positions).
Now a couple of questions about broadening the base:
1. About 47% of American pay no income tax at all. How many will have to pay taxes under the “base broadening” and how much economic harm is done by that?
2. In a revenue neutral “base broadening” with lower rates, how much of the tax burden is shifted from high income individuals to middle and lower income families?
3. If a high tax rate is so detrimental to economic growth, how does one explain much higher tax rates in the rest of the world, many of which of doing as good or better than the U. S.?
How about an actual proposal. One that details exactly how the tax system would be changed, the impact on effective tax rates for various income/social unit groups and one that details the negative impact that removing preferences from the Code would have on various sectors. That, I think, might whet the appetite, or it might expose the fact that any such proposal will have serious negative effects which may or may not offset any beneficial effects.
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