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Comment on Preferred Tax Type:
Reply to Tabarrok

Jeffrey M. Herbener*

appreciate the opportunity to respond to the criticisms made

by Alexander Tabarrok of my preferred-tax-type article since

it provides a forum to clarify and elaborate on what is wrong
with this neoclassical “theorem,” as he calls it.

Before addressing the critique, I would like to make two historical
clarifications. J. R. Hicks did not originate indifference curves as my
critic claims (p. 107n). That “honor” goes to Francis Edgeworth, who
gave a complete mathematical description of this technique in his
Mathematical Psychics, published in 1881." Vilfredo Pareto’s exten-
sive development and use of indifference- -curve analysis also predates
the work of Hicks in this area.’ Hicks even gives credit to these two
authors at various places in hisValue and Capital’

Second, I expended considerable effort at the beginning of the
original article to establish the fact that I am an unabashed Misesian
economist, and thus my major complaint against the neoclassical
economists approach to the preferred-tax-type question is their fail-
ure to correctly employ the axiomatic-deductive method. Tabarrok
seems to imply that my point about the government’s inability to
conduct the postulated experiment concerning equal tax revenues
concerns the empirical problem of the testability of an hypothesis.
But I wholeheartedly agree with him when he states, “For a theory
to be correct it need not be experimentally testable. But it must have
true premises and sound reasoning” (p. 109). The major argument of

*Jeffrey M. Herbener is assistant professor of economics at Washington and
Jefferson College.

1See F. Y. Edgeworth, Mathematical Psychics (New York: Augustus M. Kelly
Publishers, 1967 [1881]), pp. 35-36.

See V. Pareto, Manual of Political Economy (New York: Augustus M. Kelley
Publishers, 1971 [1909]), pp. 118f.

3See J. R. Hicks, Value and Capital, 2nd ed. (Oxford: Oxford University Press, 1946
[1939]), pp. 13 and 41f.
The Review of Austrian Economics, Vol. 5, No. 2 (1991): 111-116
ISSN 0889-3047

111


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112 The Review of Austrian Economics, Vol. 5, No. 2

my original article was precisely that the neoclassical theory had
false premises and unsound reasoning and was therefore false. The
problem of conducting the experiment that I referred to was the
mental experiment necessary to the praxeological method.*

Tabarrok makes two criticisms of my original article: indifference
curves are not required to prove the “theorem” and the proof does not
depend on a specific sequence. By dropping indifference curves,
Tabarrok has dramatically changed the conditions of the analysis and
thus, his criticisms do not affect my original results, derived assum-
ing a well-behaved set of indifference curves. This is not much
consolation, however, if his assertion is true that indifference curves
are not necessary for the proof. Let me demonstrate the difficulty of
proving the “theorem” without them, or at least some additional
restrictions on preferences beyond Tabarrok’s “more is preferred to
less” assumption.’

Consider figure 1, a reproduction of Tabarrok’s figure 1. The
individual begins by choosing point A with no taxation. Now the
government imposes an excise tax on good X, at some fixed rate per
unit (they do not fix the amount of the tax revenue, the individuals
choice determines his tax payment), causing the budget constraint to
rotate inward to MoXE. The individual chooses point B with an
amount of tax extracted of MoM 1. Now he is offered another opportu-
nity; pay the same amount of tax and choose any combination along
M1X1. Given the expanded range of choice, he can assuredly find a
preferable point, say C. But note carefully, he prefers C to B because,
by assumption, it is his most preferred point on his entire income tax
budget line. From a tax-payment standpoint, when he compares C to
a point along MoXE, say D, he prefers it because it involves a lower
tax payment. It has nothing to do with comparing equal tax revenues
extracted in two different forms. By construction, his choice is be-
tween a fixed income tax payment and a fixed excise tax rate. With
the latter, point B is the only point on MoXE that extracts the same
amount of tax, MoM, as the income tax. With the excise tax option,

4Ludwig von Mises calls such mental experiments imaginary constructions, Mises,
Human Action , 3rd rev. ed. (New Haven: Yale University Press, 1966 [1949]), pp. 31-32,
64-69, and 236-237.

There are two praxeological laws of utility: the law of diminishing marginal utility
and the law of increasing total utility. The first states that with units of a given size
the marginal utility of each unit declines as the stock of the good increases. The second
states that the marginal utility of a larger-sized unit exceeds the marginal utility of a
smaller-sized unit. Both laws derive from the same source, viz., the purposefulness of
human action, and thus in praxeological analysis one cannot “assume” the latter
without “assuming” the former. See Murray N. Rothbard, Man, Economy, and State
(Los Angeles: Nash, 1962), pp. 17-28 and 270.


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Herbener: Comment on Preferred Tax Type: A Reply 113

M

Figure 1.

the individual must stay at point B, in order to pay the same tax, while
the income tax option he can select from various combinations of M
and X. The individual’s choice of the income tax is not based on his
preference concerning tax types but on the fact that the analysis
allows him no effective choice with the excise tax option.

Let me make this point from a different angle. What if his most
preferred point on M1X) was point E? With indifference curves this
would be impossible but without them, or some added restriction
beyond more is preferred to less, this can not be ruled out.’ Then what
he would prefer to do is move to some point on MgB to the left of point
B. He may prefer point B to any other point on MoXE, but he prefers,
say, point F, to point E because it involves a lower tax payment. The

®1t is insufficient to respond to this choice by arguing that it violates the law of
demand. Indifference curves are the underpinnings of the neoclassical conception of
the law of demand and the latter cannot be assumed to exist without them, in the
neoclassical paradigm, without restrictions on preferences beyond more is preferred to
less (see note 5). Also, the law of demand can only be derived ceteris paribus. Point B
is selected under different underlying conditions than point E and thus, cannot be ruled
out by the assumption that more is preferred to less. If this still seems untenable then
consider the alternative sequence of tax offerings. Say an income tax is offered first and
the individual selects point E, establishing it as his most preferred point on M1X;. Now
he is given the excise tax option at a rate resulting in MoXg along which he prefers
point B. The same situation is created.


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114 oo The Review of Austrian Economics, Vol. 5, No. 2

analysis only allows the comparison of a fixed excise tax rate with a
fixed income tax payment.’ Equalizing tax payments forces the indi-
vidual to consider only one combination of M and X with the excise
tax against many such combinations with the income tax.

. Only one way exists to make the two tax types render the same
tax payment (while not eliminating the individual’s choice under the
excise tax): allow the individual to freely select the excise tax rate.
(The original excise tax rate is arbitrary and no specific rate is
necessary to extract a given sum of tax revenue; it depends on the
individual's choice.) Otherwise, one is comparing a fixed excise tax
rate with a fixed income tax payment, which, as I stated. in the
original article, is not the postulated question. If the individual picks
the excise tax rate, without indifference curves to bind him, he will
pick the rate so that the excise tax budget line will go through point
C, allowing him to continue to consume his most preferred combina-
tion on M1X1. (With indifferénce curves this is impossible since they
cannot intersect). Such a rate is the only one that allows the question
of comparing the two tax types to be answered. And the answer is: He
will be, dare I say it, indifferent between the two tax types.’ This
result stems from posing the correct question: The government will
take MoM in income from you regardless of the collection method;
which do you prefer? Without indifference curves to obscure the
analysis, this question can finally be meaningfully asked, but the
result is to reveal the two tax types as a lump-sum. tax’ from the
individual's perspective collected in two different ways (we are ignor-
ing the other diverse effects of the two taxes). As I mentioned in the
original article, the individual cares much more about how much he
is forced to pay than in what manner the tax is collected. SO

Tabarrok’s quip about an excise tax on toothpicks not being a
source of tax revenue equivalent to.an income tax is erroneous (p. 109).
As long as the individual continues to purchase at least one toothpick
the government could indeed raise an equal amount of tax revenue
by applying a very y high excise tax rate. And why should it matter to

"Unless the government forces the individual to buy the amount of X at point B. I
made this point in the original article; see Herbener, “Austrian Methodology: The
Preferred Tax Type,” Review of Austrian "Economics 2 (1988): 106. It is this additional
coercion that makes the excise tax option less preferable.

8See Herbener, “Austrian Methodology,” p- 106.

" ®His indifference in this situation is an artificial construct of the analysis; not a
conceivable demonstrated preference. Only his action, i.e., his choice, can reveal which
he actually prefers. The point in this analysis is that nothing definitive can be said
about this choice, e.g., he must prefer one to the other.

19See Herbener, “Austrian Methodology,” p. 105.

EN TE


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Herbener: Comment on Preferred Tax Type: A Reply 115

the individual if the government forces him to pay $5000 in income
tax by sending a check payable to the IRS or $5000 in excise tax by
sending a check to Tom’s Toothpick Outlet which Tom sends on to the
IRS? This is the only plausible meaning of the phrase “equal tax
© revenue,” i.e., the only way in which the government can conduct the
postulated (mental) experiment.

But this result is not what an individual unbound from indiffer-
ence curves will accept under the sequence of excise tax then income
‘tax options. Without indifference curves, the individual would do the
following (remember, he prefers point A to all others): Offered the
excise tax option at the fixed rate, he would choose point My, i.e., he
. would consume no X (zero tax payment); then, offered an income tax
of the same amount, he would move back to point A, paying nothing
in taxes. This result does not require shifting preference rankings.
His rankings would be: (1) point A with no tax, (2) point Mo with the
threat of excise tax, (3) point C forced to pay the tax of MoM, (4) point
B forced to pay the tax of MoM1 and forced to buy the amount of X at
point B. Indifference curves prevent this subjective maneuvering,
making it appear that the analysis is answering the posited question.

For further clarification, let us explore the alternative sequence.
Without indifference curves and forced to pay the income tax of MoM1,
the individual selects point C, which, by construction, must be his
most preferred combination on M1X1. Now he is offered the excise tax
option that renders the same tax payment, but not a given excise tax
rate, and asked to choose. Because point C is his most preferred
combination, he will continue to choose point C, not some point to the
left of C as Tabarrok contends, asking for an excise tax rate such that
the budget line runs from point Mo through point C. (Otherwise the
analysis is comparing a fixed income tax payment with a fixed excise
tax rate.) Again he is indifferent between the two tax types. This
result is impossible with indifference curves since the indifference
curve tangent to the excise-tax budget line at point C would intersect
the one tangent to the income-tax budget line at point C. The use of
indifference curves obscures the analysis, making it appear to answer
the question that it cannot even meaningfully ask. Tabarrok notwith-
standing, the “theorem” cannot be proved without indifference curves
or at least some restrictions on preferences beyond “more is preferred
to less.”

Tabarrok’s second criticism, that the proof of the theorem need
not follow a specific sequence (if indifference curves are removed),
depends upon how one poses the question to be answered. If the
government offers what the original question appears to ask, both tax
types simultaneously, then the choice is: You must pay MoM regard-


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116 The Review of Austrian Economics, Vol. 5, No. 2

less but you can select to pay either by income tax or by an excise tax
on X, and the individual will not prefer one tax type to the other. If
the government offers the excise tax first (at a fixed rate, for how else
can it offer this option?), the individual (not bound by indifference
curves) will substitute away from X to avoid the tax payment, then
given the income tax alternative (with a zero tax payment), the
individual will choose the income tax option and consume at the
original point. If the government offers the income tax first (at a fixed
amount, for how else can it offer this option?) the individual will
adjust accordingly, then given the excise tax option (allowing the
individual to choose the rate else the analysis is comparing a fixed
excise tax rate with a fixed income tax amount), the individual will
not prefer one type to the other. Sequence still matters, only now,
without indifference curves, the solution is different.

Finally, Tabarrok failed to mention the most obvious result of the
analysis (with or without indifference curves): The individual prefers
not to be taxed. By extension, an individual will prefer a tax offering
that provides ceteris paribus, more chances to avoid so as to lower his
tax payment. In the real world, where the government cannot enforce
equal tax payments for different tax types, an excise tax on one good
tends to be more easily avoided and thus preferred to an income tax,
ceteris paribus. However, in the real world governments rarely allow
citizens to make such choices. Instead they impose broad-based taxes
for the very purpose of extracting greater tax revenues and search for
theories they can use to pacify the long-suffering taxpayer.