developing a supply side/public choice synthesis

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Developing A Supply-Side/

Public-Choice Synthesis

Supply-Side Fundamentals for Tax Reform

Presented at The Heritage FoundationOctober 17, 2000

By

Lawrence A. Hunter



CHART 1

Original Laffer Curve

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100%

0%

Revenues

T a x R a t e

A

B

C

D

E



Chart 1: Art Laffer observed that there are two rates

at which the government gets no stuff for its taxing

efforts ± Zero and 100 percent. He connected the

dots in between and the Laffer Curve was created.

Two fundamental considerations where taxes are

concerned:yWhat Stuff is taxed ± i.e., what¶s the tax base;

yHow much of the Stuff does the government

confiscate ± i.e., what¶ the tax rate;

The more Stuff is taxed, the less Stuff you get; and

The less Stuff is taxed, the more of it you get.



CHART 2

0%

0% 100%

Tax ate

O u t p u t

B

Ym

A

Y+

r mr

+r -

C

Y-



Chart 2: I don¶t know why Art put the independent variable²the tax rate²along

the y axis, so I always reorient the curve so the tax rate is along the x axis where it

belongs.

Laffer¶s observation was not new, indeed it is derivative of a fundamental

concept of economics²diminishing returns. In fact, the concept was wellunderstood by America¶s Founding Fathers: Hamilton in Federalist # 22:

³It is a signal advantage of taxes on articles of consumption [what today are

called tariffs and sales and excise taxes] that they contain in their own nature a

security against excess. They prescribe their own limit, which cannot be

exceeded without defeating the end proposed--that is, an extension of the

revenue. When applied to this object, the saying is as just as it is witty that, µin

political arithmetic, two and two do not always make four.¶ If duties are too high,

they lessen the consumption; the collection is eluded; and the product to the

treasury is not so great as when they are confined within proper and moderate

bounds. This forms a complete barrier against any material oppression of the

citizens by taxes of this class [i.e., indirect taxes], and is itself a natural limitationof the power of imposing them.´

This analysis implies that if we decide to enact some version of a flat income tax

or a consumed income tax or a cash-flow tax collected like an income tax, which

are less sensitive to the tax rate, some ³constitutional´ rule would be more

important than if we opted for a national sales tax, which ³contains in its own

nature a security against excess.´



Laffer Curve is a fine heuristic, especially when the top tax rate is 70

percent as it was back in 1980. But, it doesn¶t suffice to inform

comprehensive tax reform. Moreover, the Media and demand-siders

parodied the Laffer Curve to ridicule Reaganonomics. George Bush theElder called it Voodoo Economics and George W. has yet to say ³we¶re all

supply siders now.´

Supply-side economists played into their opponents¶ hands by making a

fundamental mistake early on. Jude Wanniski, a former editorial writer at

the WSJ was supply-side economics¶ chief propagandist and in a famousarticle in 1978 in the Public Interest he made an heroic assumption:

³Revenues and Production are maximized at point E,´ he contended. ³It

is the task of the statesman to determine the location of point E, and

follow its variations as closely as possible.´

The reason Jude made this mistake is that he did not analyze the morefundamental, underlying relationship between production/output and taxes.

As we will see in just a moment, the Laffer Curve is a derivative of this

relationship and completely determined by it. The relationship I am talking

about is the relationship between the tax base and the tax rate, not between

revenues and the tax rate.



CHART 3

Rahn Curve

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1

0% 100%

Tax Rate

I n d e x o f O u t p u t

Output

T1

YMAX

Output is maximized at Ymax with a tax rate of T1



Chart 3: I call this the Rahn Curve because when I first met Richard Rahn back at the

US Chamber of Commerce, he was always emphasizing that it was output that we

were seeking to maximize, not revenues, and he drew a version of this curve to make

the point. Over the past 15 years or so there has been considerable research on thisrelationship, some by Richard. Richard always focused on spending rather than the

tax rate, but under a balanced budget constraint, they reduce to the same thing.

I have drawn an arbitrary Rahn Curve²notice there are no specific tax rates²and

the truth is, there exists an entire family of Rahn Curves depending upon

circumstances and the tax base.

Remember, Alexander Hamilton¶s words. He was making the point about taxes onconsumption because he wanted to justify the constitutional provision

(apportionment) limiting the federal government¶s ability to levy ³direct´ taxes, i.e.,

income and property taxes, over and above the natural constraint of the Laffer Curve.

In terms of a supply-side analysis, Hamilton would argue that where consumption

taxes are concerned, the Laffer Curve is narrow and skewed to the left, i.e., quite

sensitive to the rate at which consumption is taxed.Whereas in the case of income taxes, it is more symmetric or even skewed to the

right and quite wide, i.e., not so sensitive to the tax rate, which makes them require

³constitutional´ constraints to keep them within reason.

We will return to the implications of this insight in a moment, because this is one of

the most important considerations to think about regarding tax reform circa 2000. But

first, I want to show how the Laffer Curve is really derivative of the Rahn Curve.



EXAMPLE 1Output Maximized @ 13% Tax Rate Tax

Revenues Maximized @ 26% Tax Rate

0

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Tax Rate


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60%

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100%

R e v e n u e A s P e r c e n t O u t p u t

Output Revenues

Maximizing Revenues Reduces Economic Output by 27%

CHART 4



Chart 4 (Example 1). For any given Rahn Curve, the Laffer

Curve can be derived by multiplying every possible tax rate

times the amount of output determined by the Rahn Curve at that

rate. If you plot that curve, it will look like the red curve in

Example 1.

In this instance, I have drawn the Rahn Curve so that output is

maximized at a 13 percent tax rate, resulting in a revenue-

maximizing rate of 26 percent. (I assume that each marginal taxdollar below the output-maximizing tax rate is spent efficiently

by the government, i.e., so as to yield the largest increase in

output. We will see why that is a reasonable assumption in a

minute and when inefficient ³pork-barrel´ spending is likely to

arise in a democracy.)Example 1 also illustrates why Jude was wrong in his

conjecture that the revenue-maximizing tax rate is the point at

which production is maximized. Here maximizing revenues at a

tax rate of 26 percent reduces output by some 27 percent.



EXAMPLE 2Output Maximized @ 18% Tax Rate

Revenue Maximized @ 39 % Tax Rate

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Tax Rate

I n d e x o f P o t e n t i a l

O u t p u t

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110%

R e v e n u e A s P e r c e n

t O u t p u t

Output Revenues

Output-Maximizing Tax Rate Equals 18%

Revenue-Maximizing Tax Rate Equals 39%

Pure Rent Seeking

between Tax Rates of

18% and 39%

Up to 25% Lost Economic Output Due to Excessive Tax Rates

CHART 5



Chart 5 (Example 2). But, of course, depending upon the preferences of the

electorate and the nature of the tax base, the Rahn Curve might look quite different

than Example 1. In Example 2, for example, output is maximized at an 18 percent tax

rate, which yields a revenue-maximizing tax rate of 39 percent.

Notice how maximizing revenues at 39 percent in this example results in a 25

percent reduction in output.

Why is all of this important? Look at the range of tax rates between the output-

maximizing rate and the revenue-maximizing rate. In this range, all of the productive

and efficient ways government can spend tax revenue have been exhausted.

Beyond the tax rate that maximizes output, taxes can be raised but because the use

of the revenue cannot be put to the general welfare, only to the benefit of specialinterests, politicians must play ³pork-barrel´ politics, i.e., increase taxes on a minority

of the population to bestow government goodies on a small majority or a coalition of

minorities. It is here that supply-side economics meets public choice economics.

The range between these two maximizing tax rates creates a range for pure

rent seeking by politicians. Even though economic output is reduced by 25

percent in this example by raising tax rates from 18 percent to 39 percent, the

additional revenues that flow into the treasury in this range can be used to buy

votes.

This is the very essence of concentrated benefits (derived from government

spending financed by the revenues raised in this range) and diffuse costs (the lost

output that people do not directly observe that results in an overall lower standard of

living. And, the reduced standard of living is greater than the benefits concentrated

on favored constituencies.



CHART 6

Demand For Taxable Output

0%

100%

Taxable Output

T a x R a t e

Tax RevenueExcess

Burden

T1



Chart 6. Larry Lindsey illustrated why this is the case with the concept of the ³excess

burden of taxation.´ Larry Lindsey explained the relationship depicted in the Rahn

Curve in a conventional micro-economic analysis in which he focused on the ³excess

burden´ of taxation. The excess burden of a tax is the loss in the taxpayer¶s well-being

above and beyond the taxes he pays; there is no offsetting gain to the government from

the loss in taxpayer well being resulting from having to pay the taxes.

Along the x axis is pre-tax income. The diagonal line determines for any given tax

rate along the y axis, how much pre-tax income an individual will demand. At no tax,

the individual will demand, i.e., work to earn, Y1 income, and the government will

receive no tax revenue.It the government institutes a tax at a tax rate of T1 the individual¶s demand for pretax

income will fall to Y2, and the government will raise (T1 x Y1) in tax revenue (the rate

times the base), which is illustrated by the rectangle. But notice, the little triangle

represents a loss in income that is neither picked up in tax revenue by the government

nor in after-tax income by the individual.

Larry also used this framework to argue that Jude was wrong in his assertion that therevenue-maximizing rate maximizes production. But Larry did not draw out the

implications of his observations on excess burden nor did he seem to comprehend the

nature of the Rahn Curve. In fact, he contented himself with showing that the marginal

excess burden of raising an additional dollar of revenue approaches infinity as the tax

rate gets close to the revenue-maximizing rate. I¶ll return to this at the end of my

presentation.



CHART 7

EXAMPLE 3Output Maximized @ 33 Percent Tax Rate

Tax Revenues Maximized @ 60 Percent

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0%

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100%

R e v e n u e A s P e r c e n t O

u t p u t

Output Revenues



Chart 7. Finally, in Example 3, output is maximized at a 33

percent tax rate, with a revenue-maximizing rate of 60 percent.

What might account for such a relationship? Jude makes the point

that when a nation is at war, it may be quite willing to maximize

output at a very high tax rate. Korea after WWII comes to mind

as to why the public tolerated the top tax rate remaining at 70

percent. And, we also should not over look the fact that the

American welfare state based on rent seeking began to take holdin the 1950s.



CHART 8

Derived Laffer CurveOutput Maximized @ 33% Tax Rate

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10.0%

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50.0%

60.0%

70.0%

80.0%

90.0%

100.0%

0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0%

Revenues As Percent Output

T a x R a t e

E = Revenue Maximizing Rate of 60%



Chart 8. I have just thrown this chart in to illustrate that thederived Laffer Curve looks like one would expect.

Now, before going any further, I want to discuss an important

fact that has been overlooked by supply-side economists. Infact, I would state it as a basic theorem of political economy

that can go a long way to integrating supply side economics

and public choice economics.

i Theorem: Under reasonable circumstances, the revenue-maximizing tax rate always exceeds the output-maximizing tax rate.



CHART 9

Revenue-Maximizing Tax Rate

Exceeds Output-Maximizing Tax Rate

Even With Output Extremely Sensitive To Tax Rate

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Tax Rate


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R e v e n u e A s P e r c e n t O u t p u t

Output Revenues



Chart 9. The proposition to disprove is Jude¶s

Conjecture (he stated it as a theorem) that production is

maximized at the revenue-maximizing tax rate. I won¶t

go into the details of the proof of this proposition but

inspecting a couple of graphs gives you the insight youneed. In this example, it is obvious how even with a

very steep output curve with a very low output-

maximizing tax rate²10 percent²the revenue-

maximizing rate is still higher²17 percent in this case.



CHART 10

Revenue-Maximizing Tax Rate Exceeds

Output-Maximizing Tax Rate Even With Output-Maximizing Rate Skewed Unrealistically to Right

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Tax Rate

I n d e x o f O u t p

u t

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t O u t p u t

Output Revenues



Chart 10. At the other extreme, even with the output

curve skewed far to the right and an extraordinarily high

output-maximizing tax rate (about 91 percent), the

revenue-maximizing rate is still higher (93 percent).

The following slides present the formal proof of the

theorem and the implications that flow from it.



CHART 11



CHART 12



In order for the revenue-maximizing tax rate to equal the output-

maximizing rate, Y+ must lie beneath and to the left of the graph, r +.

In Diagram 2, the thick red line graphing the power function Y+

= isthe envelope that establishes the boundary on the family of all possible

output curves satisfying the condition required for the Conjecture to be

true.

The thin red [horizontal] solid line below this envelope is the graph of the revenue [Laffer] curve generated by it, which means that the red line

traces out the boundary on the family of all possible revenue [Laffer]

curves that satisfy the condition making the Conjecture true. Notice

from the depiction of the Laffer Curve boundary that the output curve

synonymous with the boundary condition does not itself satisfy the

Condition of the Conjecture since in the case of the boundary, R + = R m,

r +, which violates (1).



Diagram 2 establishes the relationship between output and revenue that

is required for the output-maximizing and the revenue-maximizing tax

rates to be the same. The Condition an output function must satisfy to

meet the terms of the Conjecture demands that output be hyper-sensitiveto changes in the tax rate near the output-maximizing rate. This is

verified by the fact that a power function with an exponent of -1 has a

infinitely negative first derivative at its asymptote (r m in this case), which

means output falls dramatically for small increases in the tax rate above

the output-maximizing rate.

The thick blue dashed line in Diagram 2 represents one arbitrary output

function that satisfies the conditions of the Conjecture, and it¶s

associated Laffer Curve is depicted by the thin blue gray line below it.

Notice that the revenue-maximizing tax rate lies on a cusp of the Laffer

Curve.

The practical implications of this result are enormous.



Lemma: If mi

Y Y thenm ji ji r r r r r e

, and

i j r r H , where ³i j

r r H ´

means jr dominates

ir through a unanimous coalition, i.e., a unanimous coalition will

always be willing to increase the tax rate to from

ir to

jr in order to enjoy the additional

output.

Proof : By assumption 0 <

ji r r < 1.0

Hence

iii

Y Y ¡

and ¢

j j j Y Y r

Subtracting i jii j j Y Y Y ¥ Y ¥

which is to say the increase in tax revenues is less than the increase in output generated

by raising the tax rate from

ir to

jr . Consequently, raising the tax rate under this

circumstance generates surplus new output over and above what is required tocompensate all taxpayers for the additional tax liability they incur when the tax rate is

raised. Which is another way of saying that raising the tax rate from

ir to

jr is a

Pareto-superior move to which everyone would consent.

The revenue-maximizing rate is necessarily greater than the output-maximizing rateunless output is so sensitive to the tax rate that output falls off so precipitously when thetax rate moves slightly above the output-maximizing tax rate. In other words, unless therevenue increase generated by an increase in the tax rate is overcome by a decline inoutput resulting from the higher tax burden, it will always be possible to increase

revenues at the expense of output.



CHART 13Static versus Dynamic Output/Revenue Model

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Tax Rate


t O u t p u t

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t O u t p u t

Output Static Output Static Revenue Revenues

18.2% Tax Rate

Reduction from

55% to 45%

18.2% Static Revenue Loss

9.5% Dynamic Revenue Loss



Chart 13. We now can examine Dynamic v. Static revenue estimating. In this chart, the

green dashed horizontal line across the top represents the Rahn Curve under the basic

assumption of static revenue estimating, namely that output remains unaffected by a change

in the tax rate. The pink diagonal line represents the degenerate case of the Laffer Curve

under this assumption. Revenue is determined by multiplying the tax rate, whatever it may

be, times the constant output. Notice, revenues are zero at a zero tax rate and 100 percent of output at a 100 percent tax rate.

Superimposed on the static Rahn Curve is a dynamic Rahn Curve²the turquoise dashed

curve²and its derivative Laffer Curve²the solid red line.

Notice what happens in each case if the tax rate is reduced 18.2 percent, from 55 percent to

45 percent. Under static revenue methodology assumption²that output is unaffected by tax

rates²revenue falls proportionately by 18.2 percent. In dynamic case, I have intentionallychosen an instance where the tax rate reduction takes place on the up side of the Laffer

Curve. Therefore, revenues do in fact decline when the tax rate is reduced, but notice that

because output also is declining with a rising tax rate, though not as fast as revenues, the

revenue loss from the tax rate reduction is roughly half that estimated under the static

assumption.

Indeed, I would argue that what happened after the 1986 tax reform was that we altered the

tax based in an inefficient manner²raising capital gains tax rates and lengtheningdepreciation schedules²and lowered the rate sufficiently that given the new tax base it was

below the revenue-maximizing rate but still considerably above the output-maximizing rate.

The 1986 reform effort left the tax rate in the rent-seeking range and points out the dangers

of trading off lower rates in exchange for damaging the base. It sets us up for a perfect ³bait

and switch´ routine, which is exactly what happened under George Bush the Elder and Bill

Clinton. We got stuck with the ill-defined tax base and the rates were raised back toward therevenue-maximizing point.



CHART 14

Demand For Taxable Output

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100%

0% 100%

Taxable Output

T a x R a t e

Tax Revenue

Burden

DeficiencyTax

Revenue

T1



Chart 14. I have adapted Larry¶s graphic demonstration to apply

to a dynamic Rahn Curve to illustrate that below the output-

maximizing point, it is possible to get a consensus on taxincreases and why once the tax rate exceeds the output-

maximizing point, rent seeking sets in with a vengeance. In

micro-economic terms, this depiction of the Rahn Curve

represents a backward sloping demand curve.

Larry had focused on the Excess Burden of a Tax. But there is

also a symmetric concept on the up-side of the Rahn Curve in

which there is an absolute loss to taxpayers over and above the

revenue lost to government when the tax rate is set below the

output-maximizing rate. I¶ve called it the ³Burden Deficiency.´



CHART 15

Eff t f T R t r B r D f y Excess B r en

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100%

0% 100%

T xable Out ut and Revenues

T a x R

a t e

Output R v ues

T2

T1

A

B

C

J

M¦ N

§

T3

T4

Bur den Def ciency @ Tax Rate T ̈

= (L + M + N + O)

Bur den Def iciency @ Tax Rate T© = (M + N + O)

Excess Bur den @ Tax Rate T

= (P + O)

Excess Bur den @ Tax Rate T4 = (P + O + C + B + N)

O

TRev -M

TOutput -M

O1 O2 O4 O3



Chart 15. This chart combines the concept of excess burden and

burden deficiency in the same graphic, complete with a Laffer

Curve.

developing a supply side/public choice synthesis

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