## Wednesday, June 11, 2008

### Taxes 101: Tax Rates, Tax Base and Tax Revenue

Especially in an election year, we hear a lot of talk about "raising taxes," "lowering taxes," "tax hikes for the rich," "tax cuts for the middle class," etc. etc. and as a result of an epiphany earlier today while driving to the university, I think I finally figured out why there is so much confusion about taxes. As a result of imprecise language, we interchange the terms "raising (lowering) taxes" and "raising (lowering) tax rates," assuming that increases (decreases) in tax revenues are always associated with increases (decreases) in tax rates. Let me digress to clarify the confusion.

1. Standard economic theory tells us that Price (P) X Quantity (Q) = Total Revenue (TR). Now, notice that all three variables (P, Q and TR) have different names, so that there would be absolutely no way to confuse, mix or interchange the three completely different variables!

2. We also know that if P changes, Q changes in the opposite direction, according to the Law of Demand, and further, TR changes, but in an uncertain direction. If demand is elastic (inelastic), quantity will change by a greater (smaller) percentage amount than the percent change in price, and TR will change in the opposite (same) direction of the price change. If P goes up, TR may either go down or up, depending on the elasticity (price sensitivity) of demand.

Back to tax rates and tax revenues.

We also know that THE TAX RATE x THE TAX BASE = TAX REVENUE, and here is the source of the confusion: each of the three key terms have the word "tax" in them, which results in the common, but often incorrect, assumption that changes in "tax rates" lead to changes in "tax revenues" in the SAME DIRECTION. We also frequently forget, or ignore, the inevitable fact that changes in the tax rate will cause the tax base to change, IN THE OPPOSITE DIRECTION!

For example, underlying the common phrase "tax cuts for the rich" is the incorrect assumption that reductions in tax rates necessarily leads to a reduction in tax revenue. Reason? We incorrectly interchange the terms "tax rate cuts" and "tax revenue cuts" because both terms have the word "tax." In reality, tax rate reductions usually lead to an increase in tax revenues, because the tax base increases in response to lower tax rates!

Most people have a much greater understanding that significant changes in prices might either raise or lower sales revenue, and would readily accept the suggestion that if McDonald's offers a \$1 menu, its sales revenues might actually increase! But those same people don't always understand that reducing tax rates might actually increase tax revenues!

Bottom Line: When it comes to basic economic theory and the Law of Demand, economists have a much greater chance of getting the public to understand the effects of price changes, and the dynamic interaction among P, Q and TR, largely because the three key variables all have different and distinct names.

When it comes to basic tax theory, the general public, media and even politicians gets confused about the dynamic interaction among Tax Rates, Tax Base and Tax Revenues, because the three variables sound too much alike! Oh, and politicians always seem to ignore the reality that the Tax Base ALWAYS CHANGES when tax rates change, in the OPPOSITE DIRECTION (the "Law of Demand" applied to taxes). That is, they use static tax analysis (incorrectly assuming the tax base is unaffected by tax rate changes), instead of dynamic analysis (correctly assuming that the tax base changes in response to tax rate changes).

At 6/11/2008 6:16 PM,  Biebs said...

Excellent post! Well stated and (should be) easy to understand logic.

I will pass this post on to all of my peers who still don't get it.

At 6/11/2008 6:46 PM,  Ironman said...

Speaking of tax bases, tax rates and tax revenues, did you know you can put all these things together and design your own brand new U.S. income tax with this tool?

Have fun!...

At 6/11/2008 7:01 PM,  bobble said...

i understand, and agree that tax cuts can generate more revenue.

but why is it that our tax cutters (reagan and bush43) don't understand that 'more revenue' is not the same as 'infinite revenue'?

national debt

At 6/11/2008 7:57 PM,  OBloodyHell said...

> and even politicians gets confused

"gets"?

Mark, I believe you missed one of the key things about this. It's the politicians who are confusing things, not getting confused.

> but why is it that our tax cutters (reagan and bush43) don't understand that 'more revenue' is not the same as 'infinite revenue'?

bobbie. This is THE GOVERNMENT we are talking about. THey don't cut spending -- ever -- unless the people ram it down their throats, usually via direct passage of instructions at the ballot box (see Proposition 13).

It's not Reagan. It's not Bush (either one) -- it's Congress+PotUS. It's pork barrel -- or did you think the continued existence of "Wool and Mohair Price Supports", starting in 1955 was a Reagan initiative? (In 1993, Congress "abolished" the wool and mohair subsidies as a result of bad publicity about them. They were quietly reinstated, in a somewhat different form, in subsequent farm bills. -- BILLS, you note. "Congress". Here.)

After the end of the Cold War (ca. 1990-1992), it was clear that we did not need the same degree of military we had maintained during the Cold War -- we could cut back substantially on the 700 billion (Yes, "b") we spent each year on the military. And we did.

Does this mean that the Fed spent less money?

Does The Pope defecate in the woods?

The *Clinton* administration took virtually EVERY PENNY of cutback on the military and shifted it to various "social programs". At the beginning of the Clinton Admin, the federal budget for non-social-security "assistance" programs was ca. 300 billion (Yes, "b") Before the end of the Clinton Admin, the military's expenditures were ca. 300B a year, and the various social programs stood at 800B a year. every single dime of the so-called "peace dividend" was "reinvested" in still more (but "different") government -- none of it was returned to the taxpayers.

And I've got news for you. Look closely -- very closely -- at the numbers. Clinton NEVER had any "surplus". The only thing the Clintons did was lower the rate of increase, which is a massively different thing. They were only charging 500 on the credit card each year rather than 700. They were never, EVER paying any of the credit card debt off.

And, as far as what Bush has done for the economy, note this CD Entry. That's a lot more significant than you grasp. A lot of economists have been concerned with the growth of the "M1" money supply for a long while, believing that it was too much too fast. I'd argue either side of that (probably moderately ineptly, not being an economist) but it's probably a very good thing it's been curbed for the last 3+ years.

And no, Clinton increased it -- rapidly -- it all through his admin.

bobbie:
I'm pretty sure you don't have any clue about what the M1 supply is or means. You should probably go read the Wiki entry. It's a basic, critical part of understanding how economies fluctuate. Also read up on Fractional Reserve Banking (Note, those are wiki entries -- I suggest them for neophyte readability, more than deep accuracy. Anyone finds anything doubtful or debatable in them, by all means, call attention to it!)

Understanding those two key concepts is an important step to understanding the complexity of the economy, which is one of the most complex systems humans are currently trying to develop their understanding of (and having only limited success, as I'd suspect Mark would agree).

In summary -- the notion that Reagan OR Bush (either one) were enormously worse than their prececessors or successors is based on swallowing the media hype wholesale.

============

As far as that graph goes. I'll point out a commenter's observations, not exculpatory but very applicable nonetheless:
The first bias is that the President does NOT control the economy, Congress does. For most of those presidents​, above, there was an "opposite" congress. In fact, it was the Republican​s that lowered spending, not the Democrats​.
--(snip)--
T​here's more bias there (ie, economic plans under one President didn't take effect until the next President)​.
.

Someone else pointed out the relevance of 911 on an economy already sliding into recession. And follow that with the grasp that Reagan was handed one of the worst economies in US history (yes, the Depression was much worse) and handed over to Bush I (and subsequently) Clinton one of the strongest (there was a downturn at the end of the Bush I admin but that was a brief cyclical matter, not a matter of bad policies, and the roaring 90s was the result).

At 6/11/2008 8:05 PM,  OBloodyHell said...

BTW the best thing the PotUS could do would be to veto the hell out of bills with pork in them, using Grover Cleveland's argument about pensions --

Cleveland vetoed the expenditure. In his veto message, he espoused a theory of limited government: "I can find no warrant for such an appropriation in the Constitution; and I do not believe that the power and duty of the General Government ought to be extended to the relief of individual suffering which is in no manner properly related to the public service or benefit. A prevalent tendency to disregard the limited mission of this power and duty should, I think, be steadily resisted, to the end that the lesson should be constantly enforced that, though the people support the Government, the Government should not support the people."

We need more politicians with THAT attitude, rather than the endless nanny-staters of today -- in both parties. The PotUS isn't enough -- it has to be done at all levels and all branches -- State, County, and Federal, Legal, Judicial, and Executive. And I confess, I have no idea how to make that happen short of outright revolution.

At 6/11/2008 8:28 PM,  Anonymous said...

But those same people don't always understand that reducing tax rates might actually increase tax revenues!

The qualifier is might. Those people perfectly understand that there is no credible evidence that reducing tax rates raises tax revenues.

"An economist claiming tax cuts pay for themselves is like a snake oil salesman who is trying to sell a miracle cure." - Greg Mankiw, Principles of Macroeconomics, 1998

“It is very rare and very few economists believe that you can cut taxes and you will get the same amount of revenues.” - Alan Greenspan, Testimony before House Budget Committee on September 8, 2004

“I don’t think that, as a general rule, that tax cuts pay for themselves.” - Ben Bernanke, Testimony before Joint Economic Committee on April 27, 2006.

Static scoring or dynamic scoring be damned.

At 6/12/2008 5:58 AM,  Anonymous said...

Tax Rate X Tax Base = Tax revenue...hmm too bad you didnt describe HOW lowering the rate increases the base.
It is a linear relationship: increase the rate/lower the base the revenue is the same, except from the right people. The problem has been closing the loopholes in the stupid tax code to force those who profit to pay.
The other part that you entirely dismiss is spending by the Govt...the very people who are being enriched by the Government get to pay less or nothing.

Ridiculous, vacuous post. Can we expect anything less from a NEOECONOMIST?

At 6/12/2008 7:29 AM,  Anonymous said...

Anon. 5:58,

"hmm too bad you didnt describe HOW lowering the rate increases the base."

Economic growth

Instead of sending dollars to Washington, the money stimulates economic activity. Companies and individuals will invest, create jobs, open businesses, develop new inventions and buy goods with money that would have gone in taxes.

Investment in emerging technology or opening a business involves risk in the hope of a return on investment. High tax rates discourage investment by lowering the potential for a positive return.

Another distortionary effect is the effect of high marginal tax rates. There is very little incentive to earn the next dollar if one is in a high marginal tax bracket. The most productive individuals also have an incentive to relocate to a tax friendly jurisdiction like Ireland, Hong Kong, or one of the many Eastern European countries that offer flat taxes.

An example of distortionary taxation is the US estate tax:
Any Canadian citizen who purchases property in the US can have their entire estate subjected to the US death tax (not just the U.S. assets but all the assets). The result of such punitive taxation policy is to discourage foreign direct investment in the U.S.

While a social safety net, rule of law, education, infrastructure and self-defense are essential government functions, there are multitudinous examples of profiligacy in government spending. Government does not produce the wealth of a nation but parasitizes the productive capacity of its citizens.

At 6/12/2008 7:48 AM,  E. Harokopos said...

"In reality, tax rate reductions usually lead to an increase in tax revenues because the tax base increases in response to lower tax rates!"

Not when recession is around the corner and oil is hovering at around \$140.

That is nto to say that the whole idea of federal taxes makes sense. They should be abolished in favor of a consumption and pollution tax.

Then, you can maximize the tax base, according to your rational and thus maximize TR in an appropriate way.

At 6/12/2008 8:13 AM,  Anonymous said...

anon 7:29 Economic growth

Phooey. The 2006 Treasury "dynamic scoring" Report (Table 3) on extending the 2001 and 2003 tax cuts beyond the sunset date to 2016 indicates that the long run growth rate would increase 0.7% (that's total growth not annual growth) over trend line if government outlays were cut and that the long run growth rate would decline 0.9% if the cuts were deficit financed.

Hasn't the Laugher (sic) Curve been discredited enough already?

At 6/12/2008 10:18 AM,  Robert said...

This has long been a gripe of mine. Even people I like and respect often talk about "tax cuts paying for themselves". They only pay for themselves if the rate if above the maxima on the Laffer curve. Tax rates should be set to maximize revenues in the LONG TERM. Those that don't believe in the Laffer curve MUST admit that a 100 percent rate would bring in the most revenue. Laugher curve indeed.

At 6/12/2008 10:23 AM,  Robert said...

Probably should throw this back in the mix...

http://online.wsj.com/article/SB121124460502305693.html?mod=todays_us_opinion

Clearly when rates are over 20 percent people avoid taxation.

At 6/13/2008 1:17 AM,  OBloodyHell said...

> The qualifier is might. Those people perfectly understand that there is no credible evidence that reducing tax rates raises tax revenues.

What planet have you been on that you aren't aware of "evidence" to support this?

In case you didn't know it, despite the Bush tax cuts, Fed revenue went UP, and, as a result, cut the amount of the initially expected spending deficit.

I'm not going to bother to cite sources, because if you had any intention of looking at them, you would have already seen them, this information has been readily available and has been demonstrated time and again in different places, not just the USA.

At 6/14/2008 10:08 AM,  megnichols said...

Either that or you have simply made these up since no sane economist or statistician can claim these as evidences.