# Bad Arithmetic and Blatant Political Lies

I've been trying to say away from the whole political thing lately. Any time that I open my mouth to say anything about politicians, I get a bunch of assholes trying to jump down my throat for being "biased". But sometimes, things just get too damned ridiculous, and I can't possibly let it go without comment.

In the interests of disclosure: I despise Mitt Romney. Despite that, I think he's gotten a very unfairly hard time about a lot of things. Let's face it, the guys a rich investor. But that's been taken by the media, and turned in to the story through which everything is viewed, whether it makes sense or not.

For example, there's the whole \$10,000 bet nonsense. I don't think that that made a damned bit of sense. It was portrayed as "here's a guy so rich that he can afford to lose \$10,000". But... well, let's look at it from a mathematical perspective.

You can assess the cost of a bet by looking at it from probability. Take the cost of losing, and multiply it by the probability of losing. That's the expected cost of the bet. So, in the case of that debate moment, what was the expected cost of the bet? \$0. If you know that you're betting about a fact, and you know the fact, then you know the outcome of the bet. It's a standard rhetorical trick. How many of us have said "Bet you a million dollars"? It doesn't matter what dollar figure you attach to it - because you know the fact, and you know that the cost of the bet, to you, is 0.

But... Well, Mitt is a rich asshole.

As you must have heard, Mitt released his income tax return for last year, and an estimate for this year. Because his money is pretty much all investment income, he paid a bit under 15% in taxes. This is, quite naturally, really annoying to many people. Those of us who actually have jobs and get paid salaries don't get away with a tax rate that low. (And people who are paid salary rather than investment profits have to pay the alternative minimum tax, which means that they're not able to deduct charity the way that Mitt is.)

So, in an interview, Mitt was asked about the fairness of a guy who made over twenty million dollars a year paying such a low rate. And Mitt, asshole that he is, tried to cover up the insanity of the current system, by saying:

Well, actually, I released two years of taxes and I think the average is almost 15 percent. And then also, on top of that, I gave another more 15 percent to charity. When you add it together with all of the taxes and the charity, particularly in the last year, I think it reaches almost 40 percent that I gave back to the community.

I don't care about whether the reasoning there is good or not. Personally, I think it's ridiculous to say "yeah, I didn't pay taxes, but I gave a lot of money to my church, so it's OK." But forget that part. Just look at the freaking arithmetic!

He pays less than 15% in taxes.

He pays 15% in charity (mostly donations to his church).

What's less than 15 + 15?

It sure as hell isn't "almost 40 percent". It's not quite 30 percent. This isn't something debatable. It's simple, elementary school arithmetic. It's just fucking insane that he thinks he can just get away with saying that. But he did - they let him say that, and didn't challenge it at all. He says "less than 15 + 15 = almost 40", and the interviewer never even batted an eye.

And then, he moved on to something which is a bit more debatable:

One of the reasons why we have a lower tax rate on capital gains is because capital gains are also being taxed at the corporate level. So as businesses earn profits, that’s taxed at 35 percent, then as they distribute those profits as dividends, that’s taxed at 15 percent more. So, all total, the tax rate is really closer to 45 or 50 percent.

Now, like I said, you can argue about that. Personally, I don't think it's a particularly good argument. The way that I see it, corporations are a tradeoff. A business doesn't need to be a corporation. You become a corporation, because transforming the business into a quasi-independent legal entity gives you some big advantages. A corporation owns its own assets. You, as an individual who owns part of a corporation, aren't responsible for the debts of the corporation. You, as an individual who owns part of a corporation, aren't legally liable for the actions (such as libel) of the corporation. The corporation is an independent entity, which owns its own assets, which is responsible for its debts and actions. In exchange for taking on the legal status on an independent entity, that legal entity becomes responsible for paying taxes on its income. You give it that independent legal status in order to protect yourself; and in exchange, that independent legal status entails an obligation for that independent entity to pay its own taxes.

But hey, let's leave that argument aside for the moment. Who pays the cost of the corporate taxes? Is it the owners of the business? Is it the people who work for the business? Is it someone else?

When they talk about their own ridiculously low tax rates, people like Mitt argue that they're paying those taxes, and they want to add those taxes to the total effective tax that they pay.

But when they want to argue about why we should lower corporate tax rates, they pull out a totally different argument, which they call the "flypaper theory". The flypaper theory argues that the burden of corporate taxes falls on the employees of the company - because if the company didn't have to pay those taxes, that money would be going to the employees as salary - that is, the taxes are part of the overall expenses paid by the company. A company's effective profits are (revenue - expenses). Expenses, in turn, are taxes+labor+materials+.... The company makes a profit of \$P to satisfy its shareholders. So if you took away corporate taxes, the company could continue to make \$P while paying its employees more. Therefore, the cost of the corporate taxes comes out of the salaries of the corporations employees.

You can make several different arguments - that the full burden of taxes fall on to the owners, or that the full burden of taxes falls on the employees, or that the full burden of taxes falls on the customers (because prices are raised to cover them). Each of those is something that you could reasonably argue. But what the conservative movement in America likes to do is to claim all of those: that the full burden of corporate taxes falls on the employees, and the full burden of corporate taxes falls on the customers, and the full burden of corporate taxes falls on the shareholders.

That's just dishonest. If the full burden falls on one, then none of the burden falls on anyone else. The reality is, the burden of taxes is shared between all three. If there were no corporate taxes, companies probably would be able to pay their employees more - but there's really no way that they'd take all of the money they pay in taxes, and push that into salary. And they'd probably be able to lower prices - but they probably wouldn't lower prices enough to make up the entire difference. And they'd probably pay more in dividends/stock buybacks to pay the shareholders.

But you don't get to count the same tax money three times.

• BugDoc says:

I am also not at all a fan of Mitt Romney. I do think the media and other candidates have inflated his tax return info into a giant red herring. We can all voice our opinion about how we think the 1% SHOULD be taxed, but if Mitt paid in the past the amount of tax he was legally required to pay, how can we hold that against him? Should we expect him to pay extra tax just as a protest? We can certainly ask him to better justify his position on future changes in the tax code, but just as President Obama said in the SOTU, the President and lots of members of Congress pay a lower percentage tax than many of us. I don't think we can hold that against Mitt (as much as I'd like to). However, we can hold his poor arithmetic against him and the rest of the media for being clueless about that.

• Besomyka says:

The problem with Mitt and his taxes isn't that he paid only 15% -- that is what was legally required of him, and if his tax attorney had him pay more then that attorney needs to find another line of work.

The problem is that Mitt thinks that only paying 15% is okay. That somehow profits taken from an investment should be taxes lower than profit earned through work.

Income from investments should be taxes at the same rate as other income, along the progressive scale. If he lived on investment profit, but only took in 20k a year, maybe it's be taxed at a very low rate, but anything over 250k, or 1000k should be taxes at the highest bracket. What is it right now, 31%. Democrats want to let it go back to 34%? Some where around there.

The problem is that a CEO paid 20 million for his work pays more than Mitt's 20 million for doing close to nothing at all.

• becca says:

Thank you!
Changing what you count like that is crazymaking (whoever does it). Like you can probably say 'Mitt has more than 40% of his income going to communities' but only if you count federal income and charity and other taxes... and if you do that, you have to drop the 52% rhetoric.

• Manuel Moe G says:

I wouldn't mind an investor qualifying for a 15% effective tax rate, if that investor could document the creation of a certain number of American jobs of at least a living wage and full benefits. Heck, if enough good jobs were created, 15% might be too high.

The really-existing-conservatives/today's-Republicans want you to forget:

(1) It makes sense to tax wealth from the very people in possession of the wealth - taxing Mitt Romney is the corollary of "you can't get blood from a stone".

(2) Tax code should enforce social goals, and social justice is just another social goal.

(3) We are "enjoying" historically low taxation on the wealthiest. Richard Nixon would be considered a radical Socialist in today's political terminology. Quit the belly-aching - higher taxation on the wealthiest can be easily sustained.

(1) (2) (3) are not just good sense, they also give America's system of capitalism + democracy the best chance to flourish for generations to come. The really-existing-conservatives/today's-Republicans are Conservative in name only.

• Deen says:

The problem is that Mitt thinks that only paying 15% is okay. That somehow profits taken from an investment should be taxes lower than profit earned through work.

It's even worse than that: he actually think he's paying too much taxes, as his own tax proposal would lower his taxes even further.

• [...] bet a million dollars you do [...]

• John Miller says:

A bit of history on the 15% investment tax rate. Aside from very rich people like Gov. Romney the other group who earns income primary through investment are retirees. Of course Grandma's retirement fund in total is worth less then the profits on Romney's portfolio, but investment income is not subject to a progressive tax rate; just a flat 15%.

Now, think back to the early 80's when inflation was running just below 10%. Imagine you held a (fictional) asset that earned no profit, but did track inflation. In one year you would have shown an increase in paper (taxable) value of 10% due to inflation, but you would not have any more buying power. Never the less you would have to pay taxes on that 10% paper gain. Under Pres. Reagan, the Capitol Gains Tax was lowered so to take into account the value loss due to inflation, and thus protect retirement accounts from huge tax bills

But it was don in a sloppy way so that now, when inflation is running less then half a percent a year, the "inflation protected tax rate" still applies. A fair solution would be to allow a deduction for value loss due to inflation, but this would require tax lawyers to understand integrals. It would also create the potential for a huge positive feedback loop in the government in an era of high inflation.

• I think it's good that attention is being drawn the the 15% capital gains rate. Obviously, we are at the point of thinking about how to raise taxes.

Aside from that, Romney isn't just benefiting from low taxes, which is fine, he's working to defend them and lower them further, which is not fine. Having his tax returns in the paper is good because is highlights who wins and loses given the way current tax rates are set.

• eric says:

So as businesses earn profits, that’s taxed at 35 percent, then as they distribute those profits as dividends, that’s taxed at 15 percent more

Terrible argument for two reasons. That 35% is the statutory tax rate. It has about as much to do with the real corporate tax rate as the income stautory rates have to do with income real rates. IOW, it ignores deductions, loopholes, etc...

Secondly, he's implying businesses are being penalized in a way regular people are not. But we regular folk are in the exact same situation. When I earn income, I pay taxes on it. If I turn around and buy stuff with it, the vendor pays tax on the money I give them. If I give my money away away, except for some one-time gift exceptions, the person I give it to has to declare it as income. When I receive money from someone, they got taxed on it before I got taxed on it.

So, bullflop because the rate they quote is deceptive. And bullflop because they imply investors are unusually double taxed when it is standard procedure to re-tax with most change-of-hands. 35/15 is still a lot less than 35/35, so what right do you have to complain?

• Harald Korneliussen says:

One of the things I have come to appreciate from learning the basics of corporate bookkeeping, is how hard it can be to count the right things - and only count them once.

But that doesn't excuse people who vary what they choose to count to suit themselves.

Accountancy an underappreciated field, which is really terribly important in the big picture. Not just for economy, but for the environment and all sorts of planning.

• Jon Shea says:

I oppose all tax on investment income (capital gains) because, in a world with an income tax the capital gains tax results in savings being taxed at a higher rate than income, which distorts the incentive to save. This is true even if the capitals gains tax is 1%. As an example, consider two people in a world with a 40% income tax and a 20% capital gains tax. In this world there is Mark, who does not save anything, and his almost identical twin Kram, who saves everything.

Mark makes \$100. He pays 40% in income tax, leaving him with \$60. If there were no taxes he would have \$100, so his final tax rate is 40%.

Kram makes \$100. He pays 40% in income tax, leaving him with \$60. He invests his \$60 until it doubles in value to \$120. He now pays a 20% capital gains tax of \$12, leaving him with \$108. If there had been no taxes he would have \$200, so his final tax rate is 46%.

In this world, savings is clearly taxed at a higher rate than consumption! We could have achieved the same effect on Kram by simply taxing his income at 46% and not taxing capital-gains at all, which would have the advantage of not discouraging people from saving.

• stigant says:

Isn't the incentive to save the fact that Kram now has \$108 as opposed to Mark who, for the same amount of work - the effort/risk of investment has only \$60?

• Jon Shea says:

Kram saved and invested because he hoped to realize a return, sure. I was attempting to demonstrate that capital gains tax causes saving to be taxed at a higher rate than income tax.

In my example world, the income tax is 40% and the capital gains tax rate is nominally “only” 20%. Many people would say that capital gains is taxed at a lower rate than income. But those people are clearly wrong. Kram, who saved, lost 46% of his consumption to taxes, while Mark, who did not save, lost only 40% of his consumption. If capital gains was taxed at a “lower” rate than income, can it be that the person who saves gives up a greater percentage of their consumption than does the person who does not save?

• The thing is that if I pay taxes on my income, then on whatever I do with that income, I will always pay a higher overall rate of tax than just the individual tax components. That's just the nature of compounding rates.

In much the same way, sales tax at 5% is not lower than income tax at 40% - I can do exactly the same arithmetic you do for capital gains, and demonstrate that a 5% sales tax results in an overall tax rate greater than the income tax rate on its own.

You can argue that there are times when this double-taxation effect is unfair; one way to then deal with it is to permit offsetting paid income tax against capital gains tax liability, thus not penalising savers who save from their earnings, while still penalising those who do not work when they could live off their savings instead.

In this world, imagine an income tax at 40%, and capital gains at 50%. Both Mark and Kram earn \$100, and receive \$60 after tax. Kram then invests it all (while Mark doesn't), and doubles his money, for a capital gain of \$60. He pays 50% tax on that (\$30), leaving him with \$90 to Mark's \$60 - so he's still better off than Mark.

Now, if we add the rule is that you can offset your paid income tax against your capital gains tax liability, he gets to reclaim some tax. He's paid \$40 in income tax, and \$30 in capital gains - he has paid more income tax than capital gains, so he gets \$30 back, leaving him with \$120 - and hey presto, he's only paid 40% tax overall. In this world, each earned \$100 allows him to avoid tax on \$80 of capital gains - and the higher his capital gains are likely to be, the more earned income he will strive to obtain, in order to minimise his tax bill.

Remember that in your world (0% CGT), someone who happens to have \$10,000,000 - not necessarily from their own hard work - can choose to not pay tax, just live off the interest. This encourages the creation of a corps of people who do not contribute beyond capital previously acquired; in particular, they do not strive to work for earned income. Whether this is a problem or a good thing is a matter for debate.

• Al says:

But where did that 10 million come from in the first place? He's already paid taxes on it, whether it was wage/salary or investment returns. It's not like he's earning 10 million dollars a year; he already earned it earlier, and was taxed on it then.

Of course, people avoiding taxes by living off of interest is one of the reasons I propose mainly taxing consumption rather than income.

• A Guy says:

I know it's a little late, but for anyone who's reading this in the future (like I am 12 days later), that's some REALLY bad math on Mr. Shea's part. In his example, Kram's income is actually \$160 for the time period (\$100 made initially + \$60 made on investments) and his taxes paid come out to \$52 (\$40 paid on the initial \$100 + \$12 paid on the Cap Gains), which leaves Kram with an actual tax rate of 32.5% - lower than his brother, Mark's 40%.

This example also glosses over a very important detail. If Mark spent all of his remaining \$60 (because apparently Mark must be a lot poorer than his brother Kram if Mark can't save any of his money and Kram can save all of his), if he lives in a state with a 5% sales tax, for example, then Mark's total taxes paid would be \$43 on \$100 of income (\$40 on 40% of the \$100 earned + \$3 on 5% of the \$60 spent), so Mark is actually taxed at a 43% rate.

So that's a 32.5% tax rate to rich brother Kram vs. a 43% tax rate to poor brother Mark. So, why aren't we taxing capital gains like regular income, again?

• Jon Shea says:

Where does your “32.5%” analysis go wrong? After all, the government has only \$52 from Kram. If it had taken 46% of his \$200 (like I claim), then it would have \$92, right? Well, your analysis neglects the time value of the money that Kram paid in income tax. If the government were as smart as Kram, then it could have invested the \$40 he paid them and likewise doubled it to \$80. Add to that the \$12 the government takes from Kram’s investment and we get \$92, exactly the 46% of \$200 that I state Kram gave up in my analysis.

Your accounting charges the time value of money against Kram (he has to pay taxes on it), but doesn’t credit the time value of money to the government (they got it and could have invested it). That’s not fair accounting. Maybe the government wasted or otherwise squandered Kram’s income tax payment, but you can’t hold that against Kram.

• Doug says:

First off there's a very specific reason investment income is taxed at a lower rate than wage income. To explain this you must understand that the central purpose of good tax revenue is to distort the economy as little as possible while raising as much money as possible. (The notable exception to this is when policy makers are intentionally trying to change people's behavior, usually because of externalities, e.g. a tax on pollution or a tax on hard liquor).

For example a 30% tax on orange dress shirts is very bad tax policy. Most people will switch to red or yellow dress shirts instead because of the lower cost. The government will end up raising very little revenue. And a lot of people will be less happy, because they preferred an orange shirt but are now wearing a red or yellow shirt. In economist talk this is called "deadweight loss."

In contrast a very good tax is a property tax on the unimproved value of land. In fact this is the closest to a "perfect" tax that one could come up with. Since the supply of land is basically fixed, no matter what the tax rate is it will not distort how much land is used. Sure many people will be worse off with very high land taxes. But the way they will be worse off is only in the form of tax revenue which will go to someone else and presumably make them better off. Once again "Good Economics" would say that this tax basically has zero deadweight loss.

Now let's talk investment versus wage taxes. Let's say the government needs to raise revenue and it can choose to do it through either new taxes on investment or wages. Consider the deadweight loss of wage taxes. It occurs in the form where someone will choose to substitute leisure for work, who otherwise would have worked more had the tax rate been lower. For example consider a doctor who's 55 with substantial savings and makes \$500k a year. His breakeven point for choosing to work another year versus retiring is a take home of \$350k a year. So if the tax rate is greater than 30% he will choose to stop working and retire, whereas otherwise he would have worked another year. Deadweight loss.

Now consider how deadweight loss occurs with investment income. If I take home \$100k a year in disposable income I can choose to do two things with it. One I can consume it immediately, buy a sports car, make a renovation on my home, take a grand vacation, etc. Or I can choose to consume it in the future, i.e. save and invest it. All things being equal I prefer to consume in the present versus delaying gratification. However the preference is not infinite. There's some expected rate of return, such that the incentive of being able to consume more in the future is higher than the disincentive of delaying gratification.

If I'm 30 and the stock market has an expected return of 8% a year then investing \$1000 today will yield \$14,800 at age 65, before investment taxes. If investment taxes (capital gains and dividend) are 15% then it yields \$12,700 after taxes at age 65. If investment taxes are raised to 35% (current top marginal rate), then investing today only yields \$9,960 at 65. If my break-even point to invest or consume is \$11,000 at age 65 then raising capital gains would create deadweight loss in this instance.

So a "bad economist" will choose tax policy based on what seems fair. A good economist picks tax policy based on what raises the most revenue relative to deadweight loss. In this instance the empirical evidence is nearly overwhelming. Wage taxes create far less deadweight loss than investment taxes at anything close to current rates. Therefore a good economist would recommend higher wage (income) taxes and lower investment taxes.

• Stephen says:

Your analysis doesn't seem consistent. Yes, a person retires and stops working so that is a deadweight loss, less is being produced.

I don't understand the deadweight loss on the investment. If you spend X now, somebody will do X amount of work now for your money. If you invest X now somebody will do X amount of work now with your investment and promise to pay you Y at some future date. In both cases, X amount of work is being done now. So the question is is there currently too much or too little investment, and our current recession seems to be driven by a lack of demand (spending). You have made, what appears to me to be a powerful argument for raising the capitol gains tax at this point.

• Keshav Srinivasan says:

Mark, off topic but I found an extreme example of Bad Math that you might be interested in talking about. Mediaite has an article that says Jan Brewer's book sales has gone up 1.35 *million* percent (no, that's not a typo):
http://www.mediaite.com/online/jan-brewers-book-up-over-150000-on-amazon-com-in-last-24-hours/
It bases this on Amazon's list of Movers and Shakers here:
http://www.amazon.com/gp/movers-and-shakers/books/
Amazon is portraying these numbers in an unimaginably misleading way. It's listing the books whose sales rank has increased, and it displays the improvement in the rank as a percentage, so if a book has gone from 6th to 1st on the bestseller list it says the book has 500% increase!
Jan Brewer (governor of Arizona) may or may not be a good writer, but the way Mediaite is portraying it it's as if her sales have experienced a multi-million-fold increase.

• trrll says:

I'm unconvinced that the "deadweight" loss from people choosing to retire is all that great. I could probably afford to retire right now. That I haven't done so has nothing at all to do with my tax; I'm just not ready to retire. I expect that that is true of a lot of people who are receiving substantial income in the form of capital gains. Certainly, if you look at the statistics, the country has had booming productivity with much higher capital gains rates, so the numbers don't seem to support the argument that a somewhat higher rate is a big drag on the economy.

• Physician Scientist says:

As an AMT payer, mortgage interest and charity contributions are the two things you CAN deduct with the AMT.

• Doug says:

@trrli

Productivity gains have very little to do with the elasticity of investment income. One primary reason investment income is so elastic is because its the timing of its realization can easily be deferred.

Investment gains are only taxed on the year that they are realized. E.g. if you're Warren Buffer and you bought some Coke stock and it went up 15% and you made \$3 billion you don't pay a single dime in taxes until you actually sell the stock and realize your gains.

In contrast wage income cannot very easily be timed at all. It's not like you can choose to not work for the next three years and then work quadruple the year after that because you forsee lower tax rates four years from now.

If there was some credible way to raise investment income tax rates for the next 100 years this would be less of a problem. But assume Obama gets what he wants and taxes on investment income go up. Most wealthy investors are not fools, and know that at some point in the future it is likely Republicans will get into power and lower capital gains tax. They can easily defer realizing their capital gains taxes until this day.

All they have to do is sell their losing, not their winning positions, when they need cash. In addition their are dozens of derivatives products that Wall Street sells to hedge out your exposure or monetize your gains that don't trigger capital gains realizations.

The fact is raising capital gains tax rates will hardly raise any revenue. Paradoxically it may even lower it. In contrast raising ordinary income taxes is a much more effective revenue source. An even simpler way to raise revenue, one which would actually reduce deadweight loss, is to simplify the tax code by eliminating "tax expenditures." Cutting the mortgage interest, property tax, state income tax income tax deduction, the corporate healthcare insurance tax deduction, many forms of accelerated depreciation, many tax breaks for "renewable energy investment", LIFO inventory tax accounting, student loan interest deductions, social security and veteran benefits deductions and even charity tax deductions would raise a significant amount of revenue without causing a single penny of deadweight loss.

In fact these changes would reverse deadweight loss caused by the distortion of economic activity imposed by the tax code. The total estimated cost of tax expenditures is estimated to be over \$900 billion. This is far more than a raise in capital gains tax could ever produce.

• Steve Ruble says:

Doug, I don't think I quite understand your last example:

If I'm 30 and the stock market has an expected return of 8% a year then investing \$1000 today will yield \$14,800 at age 65, before investment taxes. If investment taxes (capital gains and dividend) are 15% then it yields \$12,700 after taxes at age 65. If investment taxes are raised to 35% (current top marginal rate), then investing today only yields \$9,960 at 65. If my break-even point to invest or consume is \$11,000 at age 65 then raising capital gains would create deadweight loss in this instance.

Let's see if I understand how the deadweight loss works here. It seems a little strange when we're talking about investments and discounting and so on rather than present day supply/demand, so I want to make sure I've got it.

So, someone is willing to - in a sense - buy \$1,000 from me today for the price of [\$14,800 in 35 years]. I'm willing to sell my \$1,000 for as little as [\$11,000 in 35 years], so this sounds like a great deal for me. However, if the capital gains tax is high enough (35%) that I will only receive [\$9,960 in 35 years] for my \$1,000 dollars today, then I won't sell it to the guy offering me [\$14,800 in 35 years], I'll just spend it today, on something which is worth, to me, [\$11,000 in 35 years] (my break-even). The economy has therefore lost a value equivalent to [\$3,800 in 35 years], and the government has lost the [\$2,100 in 35 years] worth of taxes they would have collected if they had stuck with a 15% capital gains tax. Am I right so far? Is [\$3,800 in 35 years] the thing you're calling deadweight loss here?

It seems likely that when I spend the \$1,000 today, some fraction of that money will be collected by the government in sales taxes or income taxes. If the government gets 15% of that, and then invests it the same way I could have, they end up with [\$2,217 in 35 years], so it looks like it's not necessarily the case that the government realizes a loss by having a higher capital gains tax. I do see how there's a loss to the economy (assuming I'm understanding this correctly) but I feel like there's some issue with that idea that I don't quite understand. I'll need to sleep on it, I guess.

• Al says:

I apologize for potential arithmetic errors in this post, you should be able to calculate the areas for yourself.

I don't think that's the part that's referred to as deadweight loss. Generally, DWL does not refer to lost tax revenue, but a reduction in total surplus (consumer surplus+producer surplus). Calculating it in this instance is complicated because the good being bought is (money, but more at a later time period). It can be done, but getting reasonable numbers requires more risk/reward and patience analysis than is reasonable here.

It's also important to note that surplus is an abstract quantity denoting utility, not a monetary quantity. The two can be related, but that's beyond the scope of this discussion. For now, we only really require typical supply and demand curves.

The wiki article Shadonis linked has some examples, but let's work out a full example. We'll use this graph for reference: http://en.wikipedia.org/wiki/File:TaxWithTax.svg

Say the good in question is pizza. In a perfectly competitive market with a few assumptions, the price comes to rest at the equilibrium price, p_e, and equilibrium quantity q_e. This is the intersection of the supply and demand curves, as you can see. Demand slopes down and supply slopes up, so we pick some very simple example functions: demand is given by p=10-10q, supply by p=10q. Then these intersect at (5, .5) (yes, p is the y-axis and q is the x-axis. Don't worry about it), so 1 pizza costs p_e=50 cents, and the market will supply 5 pizzas.

Now, due to the way these curves are constructed, the area between the demand curve and the line p=p_e is consumer surplus, and the area between that line and the supply curve is producer surplus. You can think of it this way: some people are willing to pay more than 50 cents for a pizza. These people fall to the left of q_e on the demand curve, so that if the prices rises, they will still buy pizza. Since they are willing to pay more than p_e, they gain surplus equal to the savings=price willing to pay (the reservation price, where they are indifferent to pizza or the money)-p_e.
Similarly, some producers will supply pizza at less than p_e, represented by the lower left part of the supply curve. So they gain surplus equal to p_e-reservation price.

The total producer and consumer surpluses is given by summing all these individual surpluses, so if our graph is on a large enough scale, PS+CS= the integral of (demand minus supply)dq from 0 to q_e. With linear functions, this is just a triangle with height q_e=10 and base=p_e=.5, so total surplus TS=10/4

Now, let's say we impose a tax of 25 cents on pizza (it doesn't matter where in the process we do so; I will explain more further below). Then the price of a pizza is 75 cents, so some people who bought pizza before no longer do so, and similarly for some suppliers. Therefore, consumer surplus is only the triangle between demand and tax revenue, and producer surplus between that between tax revenue and supply. In our case, each of these is a right triangle: CS=PS=2.5*.25*.5=5/16. Since TS=10/16, total surplus has decreased by 15/8.

It is called Deadweight Loss because no one gets it. It's just burning resources. The government doesn't get it, consumers don't, producers don't. In general it is the result of changes in behavior that result from taxes or subsidies, and it is one of economists' worst nightmares. The only way to reduce DWL is to tax goods with low elasticities (ie people don't change their consumption or production of it much when the price changes).

One last comment before I end this already-too-long post. As I said, the tax incidence is not controllable (in the long run). Whether government taxes the producers, the consumers, or a mix, in the long run equilibrium will adjust (based on elasticities) and the actual tax incidence will be purely a result of market forces.

As a quick qualitative demonstration, imagine if the government taxes the profits of car companies. In the short run, the government collects some revenue from them, because it's hard to reduce output quickly. But in the long run, since car-making is less profitable, fewer people get into the business, factories may be closed or have their output reduced, etc. This drives up the price of cars, since demand is unaffected, and so the government is really now getting some its revenue from consumers.

One last thing:
" I doubt anyone is going to defer capital gains for a decade or two while they wait for the tax code to change because they *might* shave 5% off their capital gains. At face value that's just ridiculous."

You may think so, but you're completely wrong. The data indicate that most heavy investors have a "patience ratio" (I forget the exact term, but it is usually denoted by beta) close to 90%, which means that they value future gains by at about 99% of its current value (adjusting for inflation, risk, expected market returns, etc.)

"I don't claim to know what the optimal value of capital gains is for raising the most revenue. I doubt you know that number either. However, 15% is quite low by historical standards, and is definitely not fair given that it allows the wealthiest to pay taxes at the same rates as the poorest."

Decide on what you want your taxes to do before keep commenting, please. If you want to raise amounts of revenue, that's different from raising revenue efficiently, and both are different from "fairness" (which is not, in economics, even a remotely agreed-upon term).

If these historical standards are as arbitrary as you said in your post, why are we comparing the current rate to them? Of course, more importantly is the fact that, as I said above, (at least, I believe capital gains taxes work this way), is that the actual tax incidence is entirely dependent on market forces (in particular, elasticities). If producers are more willing to produce than consumers are willing to consume, as makes sense if producers have so much more money in this case, then the actual tax incidence is probably much more heavily on the production side (I doubt I have the tools to compare the incidence among shareholders, owners, and employees, and I'm certainly not doing it now).

• Brendan says:

@Doug It is difficult take take what you say seriously.

1. The 15% number was chosen relatively recently. Capital gains was much higher in the past, and was the result of a political compromise and not any kind of deep thinking. Taxes are largely reflective of who has bargaining power in congress. After the fact justifications of something arbitrary in highly intellectualized terms seem silly to me.

Here's a graph of capital gains taxes over time:
http://krugman.blogs.nytimes.com/2012/01/18/the-history-of-capital-gains-taxes/

2. I doubt anyone is going to defer capital gains for a decade or two while they wait for the tax code to change because they *might* shave 5% off their capital gains. At face value that's just ridiculous.

3. Overall your tone suggests that you "know what you are talking about." You keep talking about evidence without giving references, and suggesting you "know" that raising capital gains won't raise revenue. Claiming certainty of a future event without providing evidence, especially when that event seems unlikely at face value, makes it difficult to take what you say seriously.

I don't claim to know what the optimal value of capital gains is for raising the most revenue. I doubt you know that number either. However, 15% is quite low by historical standards, and is definitely not fair given that it allows the wealthiest to pay taxes at the same rates as the poorest.

• _Arthur says:

Wouldn't the monies Mitt gives to various charities be a big factor in his low rate ?
Such donations are tax-deductible, right ?

• Dave W. says:

To be fair to Romney, he files as a Massachusetts taxpayer. Massachusetts has a flat state income tax rate of 5.3% (http://www.tax-rates.org/Massachusetts/income-tax), with few exemptions. So your elementary arithmetic should probably take this into account, which would push his federal+state+charity to around 35%. With a really generous view of rounding, you could consider that "almost 40%."

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