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The Pareto Rule and Welfare Economics

Jeffrey M. Herbener

It is [my] contention . . . that the wake for all welfare economics is premature,
and that welfare economics can be reconstructed with the aid of the concept of
demonstrated preference. This reconstruction, however, will have no resemblance
to either of the “old” or “new” edifices that preceded it. In fact . . . our proposed
resurrection of the patient may be considered by many as more unfortunate than

. 1
his demise.

hen Murray N. Rothbard published his seminal article, “Toward a
Reconstruction of Utility and Welfare Economics,” these were
bold words indeed, considering the disarray into which welfare
economics had fallen by 1956.2 The Old Welfare economics had
crashed to the ground decades before when Lionel Robbins, building on the
subjective-value foundation laid by Ludwig von Mises, demonstrated that its
underpinning—interpersonal utility comparisons—was an impossibility.’ Being
subjective, utility has no cardinal index and, thus, no common cardinal units
could possibly exist for the purpose of comparing the utility of different indi-
viduals. Since individual ordinal rankings of utility cannot be compared, the
argument advanced by Pigouvian welfare theorists, that redistribution of wealth

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

"Murray N. Rothbard, “Toward a Reconstruction of Utility and Welfare Economics,” in Mary
Sennholz, ed., On Freedom and Free Enterprise: Essays in Honor of Ludwig von Mises (Princeton, N.].: D.
Van Nostrand, 1956), p. 249.

The importance of this article as a contribution to the Austrian literature can be scen in the
assessment of Israel M. Kirzner, who said, “[I] can personally attest to the excitement engendered by
the lucid manner in which this paper deployed Austrian insights to illuminate fundamental theoretical
issues (concerning which contemporary economics was floundering), and by the characteristic
erudition which Rothbard poured into that single essay.” See Kirzner, “Welfare Economics: A Modern
Austrian Perspective,” in Man, Economy, and Liberty: Essays in Honor of Murray N. Rothbard, Walter Block and
Llewellyn H. Rockwell, eds. (Auburn, Ala.: Ludwig von Mises Institute, 1988), p. 77.

3 For the original contribution of Ludwig von Miscs on the ordinal nature of utility, see Miscs, Theory
of Money and Credit (Indianapolis: Liberty Classics, [1912] 1980), pp. S1ff. For the blow delivered by
Lionel Robbins to Old Welfare economics, see Robbins, An Essay on the Nature and Significance of Economic
Science, 3rd ed. (New York: New York University Press, [1932] 1984), pp. 137-41.

Review of Austrian Economics 10, no. 1 (1997): 79-106
ISSN:0889-3047

79


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80 Review of Austrian Economics 10, No. 1 (1997)

from the rich to the poor would increase social welfare because of diminishing
marginal utility of money, fails. To the chagrin of advocates of Old Welfare
redistributionist policies, economists conceded that the subjective nature of
utility renders cardinal measurement, a necessary requisite of interpersonal
utility comparisons, impossible.’ Moreover, they admitted that advocates of such
policies were not value-free economists but ethicists advancing their own, usually
egalitarian, ethical biases.’

Paul Samuelson, a major architect of New Welfare economics, characterized
the egalitarian desire typical of Old Welfare economists to equalize income as “a
fetish or shibboleth, albeit a useful one, in that the means becomes the end, and
the letter of the law takes precedence over the spirit.” According to him, egalitari-
anism fails because “it is easy to show that the rule of equality of income . . . applied
to individuals of different tastes . . . is actually inconsistent with any determinate,
definite [social welfare] function”; a statement more revealing of the importance he
placed on his social-welfare construct than of the genuine deficiencies of egalitari-
anism.’ He also rejected Old Welfare economics for making the “essentially unnec-
essary assumption” that the social welfare function to be maximized was “the
sum of the cardinal utilities experienced by each individual .”’

Yet, Samuelson’s cavalier attitude toward the demise of cardinal utility and
consequent acceptance of ordinal utility did not result in a simple and quick

“In addition to cardinal units for each individual's utility, interpersonal utility comparisons
require a common cardinal unit in which the utility units of different individuals could be expressed.
Those familiar with Ludwig von Mises’s argument that socialism is impossible because of the
inability of central planners to make economic calculations will recognize a parallel between that
argument and the impossibility of interpersonal utility comparisons. The impossibility of economic
calculation in socialism rests on the absence of a common, cardinal unit in which different types
of factors of production can be reckoned. See Mises, Human Action: A Treatise on Economics, 3rd rev.
ed. (Chicago: Henry Regnery, [1949] 1966), pp. 206-9.

*Pigouvian Welfare Theory is developed in Arthur C. Pigou, The Economics of Welfare (London:
Macmillan, 1920). For a discussion of the necessity of having ethical judgments taken from disciplines
outside economic theory as the foundation of Old Welfare economics, see Lionel Robbins, “Interper-
sonal Comparisons of Utility: A Comment,” Economic Journal 48 (December 1938): 635-41.

paul Samuelson, Foundations of Economic Analysis (Cambridge, Mass.: Harvard University Press,
1947), p. 225. He added analytic rigor to this line of argument in idem, “Social Indifference
Curves,” Quarterly Journal of Economics 70, no. 1 (February 1956): 8—14. He had less sympathy with
“the bourgeois penchant for laissez-faire,” which he claimed was “the only case on record where
a substantial number of individuals have made idols of partial derivatives, i.e., imputed marginal
productivities.” That Samuelson rejected “the belief that the individual should rightfully receive
his imputed productivities,” because “[it] is not consistent with a [social welfare] function
having properties” which he deems important reflects more on his own ethical biases than on a
genuine ethical assessment of laissez faire. See, Samuelson, Foundations, p. 225. Oscar Lange, a New
Welfare economist sympathetic to the egalitarian leanings of the Old Welfare school, demonstrated
that the Pigouvian analysis can be recast in the New Welfare framework. See idem, “The
Foundations of Welfare Economics,” Econometrica 10 (1942): 221-23.

7 Samuelson, Foundations, p. 226.


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Herbener: The Pareto Rule and Welfare Economics 81

solution to the problem of explaining the relationship between ordinal utility and
the cardinal magnitudes in the social welfare function to be maximized. New
Welfare economists struggled in vain for several decades to show how ordinal
ranks relate to cardinal numbers and were useful for welfare analysis. One by one,
they began to admit defeat and surrendered to the impossibility of interpersonal
utility comparisons of ordinally-ranked utility.

Had they not been wedded to their mathematical formulations, perhaps they
could have accepted the solution given by Mises. From his development of the
concept of ordinal marginal utility in 1912 Mises went on to explain how ordinal
utility can be the basis for socially-meaningful cardinal comparisons of value.
Money is a common denominator in which ordinal preferences can be expressed,
by exchanges of private property for and against money, resulting in cardinal num-
bers, namely, money prices, which are in the same units, namely dollars, for all goods
and factors traded on the market. The price for the existing stock of each consumer
good reflects, but is not and cannot be equal to, the subjective value of its marginal
unit, i.e., the unit with the least subjective value. The price for each factor is imputed
to it by entrepreneurial demands to rent the factor, according to the objective value
of the amount of the consumer good the factor produces at the margin, i.e., its
marginal value product. This price will also reflect the subjective opportunity
cost factor owners place on the marginal unit of the factor, including renting the
factor into other production processes.’

As Mises showed, by transforming the ordinal preference ranks of different
individuals, which are impossible to compare, into a quantity of common, cardinal
units, the monetary, private property, market system provides the basis for economic
calculation. Entrepreneurs use money prices to make calculations of profit and loss,
and in so doing compare, in objective value, different factors of production against
each other and one set of factors against others in producing each consumer good
and each factor or set of factors in producing different consumer goods. That money
prices, only possible in a monetary, private property, market system, provide acommon
cardinal unit in which different factors can be compared in social value is an essential
part of Mises’s economic calculation argument. '° Moreover, entrepreneurial calcula-
tions of profit allow for cardinal comparisons of the social value of the consumer good
produced (the total revenue generated by consumer purchases) with the social value
of factors used (the total cost generated by entrepreneurial purchases). Any time an

80n ordinal marginal utility, see Mises, Theory of Money and Credit, pp. 59—61. His discussion
of the relationship between ordinal utility and cardinal value is in Economic Calculation in the Socialist
Commonwealth (Auburn, Ala.: Ludwig von Mises Institute, [1920] 1990), pp. 11-13, 23, and
48-49,

%0n the pricing process, see Mises, Human Action, pp. 327-50.

"1bid., pp. 206-9.


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82 Review of Austrian Economics 10, No. | (1997)

entrepreneur earns profit, social wealth increases; any time he suffers a loss,
social wealth decreases. It is within this general economic framework that
Professor Rothbard developed Austrian welfare economics.’

By showing that the voluntary exchanges of private property using money
transform ordinal ranks into cardinal numbers reflective of those ranks, Mises
solved the theoretical problem that welfare theorists, both Old and New, would
attempt, within their neoclassical framework, to solve in vain."

Old Welfare theorists, such as Alfred Marshall, approached this problem in
a superficially similar, but entirely unsatisfactory, manner. His consumer-surplus
approach implicitly assumes that the marginal utility of a good equals a sum of
money." Thus, cardinal utility enters by the back door, the common cardinal unit
for utility being a dollar. Writing of a consumer purchase, Marshall says, “the
economic measure of . . . the satisfaction which he gets from its purchase” is “the
excess of the price which he would be willing to pay rather than go without the thing,
over that which he actually does pay.” Defining producer surplus in an analogous
way (the excess of the price he receives over that which he would be willing to
accept rather than forego the sale) allows one to add the money sums of con-
sumer and producer surpluses, treating the aggregate, total surplus, as a measure
of total utility. The total utility from the production and exchange of different
goods can then be compared and policy directed toward the maximization of
total surplus.

In addition to assuming cardinal utility this analysis makes the illegitimate
assumption that the marginal utility of a dollar to everyone is the same since each
dollar added into total surplus counts as one. It would seem, however, that if
these objectionable features could be expunged, the analysis could be saved.’

Such a purification provides the theoretical justification for cost-benefit analy-
sis. There is no need to assume anything about cardinal utility, proponents of this

"The connection between Misesian general economics and Rothbardian welfare economics
will be explored below.

“This is an excellent illustration of the inferiority of a mathematical method vis-a-vis a verbal
method in economic reasoning. Mathematics is inherently incapable of solving this basic economic
problem which is easily handled using literary means. On mathematics and pricing, see Mises,
Human Action, pp. 350-57, 701-3, 710-15.

!*Marshall’s discussion of consumer surplus is in Principles of Economics (New York: Macmillan,
[1890] 1948), pp. 92-101, 124-37, and 831-32.

"*Ibid., p. 124. Emphasis added.

Bir Hicks attempted to expunge cardinal utility from the surplus approach in a manner
consistent with the New Welfare economics. See Hicks, “The Rehabilitation of Consumers’
Surplus,” Review of Economic Studies 8, no. 2 (1941): 108-16; idem, “Consumers’ Surplus and Index
Numbers,” Review of Economic Studies 9, no. 2 (1942): 126~37; idem, “The Four Consumers’
Surpluses,” Review of Economic Studies 11, no. 1 (1943): 31-41; idem, and “The Generalized Theory
of Consumers’ Surplus,” Review of Economic Studies 13, no. 2 (1945-46): 68-74.


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Herbener: The Pareto Rule and Welfare Economics 83

approach argue, if government officials can use the market in the same way that
entrepreneurs do—as the basis for calculation of profit. When contemplating a
government intervention, they can use existing market prices to project antici-
pated benefits and costs in sums of money. If the project renders net benefits
then intervene, if not, social wealth would be greater without the intervention.

Cost-benefit analysis does not fail as a social-welfare technique for lack of a
method for assessing the subject value of individuals in cardinal terms. It circum-
vents that problem by relying on the same market procedure that entrepreneurs do.
Its fundamental error is in equating the appraisal that can be performed only by
entrepreneurs in economic calculation with the superficially similar “paper” calcu-
lations made by government officials. Genuine appraisal of social values requires
entrepreneurs to put their own wealth at risk in the process of production and
exchange. Without this, there is no connection between existing market prices and
the expectations of future prices upon which profit and loss will hinge. Government
officials can only “play” market and, thus, cannot make genuine appraisals.'®

Mises made this point in rebutting economists, in particular those following the
approach of Enrico Barone, Oscar Lange, and Abba Lerner, who used the neoclas-
sical apparatus of general equilibrium in attempted refutations of his economic
calculation argument against socialism.'” Barone and Lerner are cited as im portant
forerunners of the New Welfare economics by its major architects, Abram
Bergson and Paul Samuelson. Bergson’s seminal article is dedicated to presenting
“the value judgments required for the derivation of the conditions of maximum

On this point, see Mises, Human Action, pp. 705-10. Moreover, both bureaucratic
cost-benefit calculations and entrepreneurial appraisals require formulating expectations of
the future. Bureaucratic expectations are categorically different than entreprencurial ones
because government officials do not place their own wealth at risk on the accuracy of their
forecasts. And for those government projects for which there will be no future market,
bureaucrats have less basis than entrepreneurs for formulating any type of expectations. On
the differences between bureaucratic and entrepreneurial management, see Ludwig von
Mises, Bureaucracy (Cedar Falls, lowa.: Center for Futures Education, [1944] 1983).

What came to be called the Lange—Lerner rule states that central planners can
maximize social welfare by solving the perfectly-competitive, general-equilibrium equations
to obtain “shadow” prices of all inputs and outputs, then make this list of prices known to
the relevant consumers and producers, and finally instruct them to behave as if they were
maximizing utility and profit in a perfectly-competitive economy. Enrico Barone, “The
Ministry of Production in the Collectivist State,” in Collectivist Economic Planning, F.A. Hayek,
ed. (Clifton, N.].: Augustus M. Kelley, [1935] 1975), pp. 245-90; this article was first published
in Italian in 1908. Oscar Lange, “Mr. Lerner’s Note on Socialist Economics,” Review of Economic
Studies 4 (October 1936): 143—44; and idem, “The Foundations of Welfare Economics,” Economet-
rica (1942): 215-28. Abba Lerner, “Economic Theory and Socialist Economy,” Review of Economic
Studies 2 (October 1934): 51-61; and idem, “Theory and Practice in Socialist Economies,” Review
of Economic Studies 6, no. 1 (1938): 71-75. In refuting this approach, Mises specifically identifies
Barone as failing to “penetrate to the core of the problem,” Human Action, p. 701.


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84 Review of Austrian Economics 10, No. | (1997)

economic welfare which have been advanced in the studies of . . . Pareto and Barone,
and Mr. Lerner.”'® Samuelson calls Barone’s article on optimizing social welfare
“masterly,” claiming that “it is a tribute to this work that a third of a century after it
was written there is no better statement of the problem in the English language.” Of
Lerner, Samuelson says, “[He] developed the Paretian conditions which show that
the marginal equivalences realized by perfect competition lead to an optimum of
production and exchange.”"’ Since the New Welfare economics emerged from the
debate about economic calculation, it is not surprising to find Mises’s arguments
demonstrating the impossibility of economic calculation in socialism useful also
* in rebutting the New Welfare economics; nor is it surprising to find proponents
of the New Welfare economics dedicated to demonstrating that the free market
fails to maximize social welfare.”

It was left to Rothbard to reconstruct welfare economics upon Mises’s
foundation or, rather, within Misesian general economic theory. The crucial
concept in that reconstruction is demonstrated preference, that, as he says, “a
man’s preferences . . . are deducible from what he has chosen in action.””’ That
demonstrated preference is the operative concept in value-free, welfare econom-
ics is implied by the subjective nature of value. Because the value a person places
on alternative ends is an intensive mental state, another person can say nothing
about it unless it is revealed in action.’ Moreover, modern price theories,
both Austrian and neoclassical, presuppose demonstrated preference. In both

18 Abram (Burk) Bergson, “A Reformulation of Certain Aspects of Welfare Economics,”
Quartetly Journal of Economics 70, no. 2 (February 1938): 310.

Samuelson, Foundations, pp. 214-17.

at is surprising is Samuelson’s befuddlement that “Barone satisfies himself with deriving
optimal production conditions” without bothering to extend his analysis to consumption condi-
tions. He claims that this “oversight resulted from his wish to avoid the use of indifference curves
and utility.” Samuelson, Foundations, p. 217, emphasis in original. The absence of consumption
optima, however, is no oversight at all for managing a collectivist regime of production. As Mises
argued, socialism solves the problem of determining what consumer goods to produce by having
the central planners use their own preferences. Mises, “Economic Calculation,” pp. 23-24. Since
Barone developed his framework of welfare theory to explain how to manage production in a
collectivist state, it is not at all surprising that consumption optima were absent from his set of
optimum conditions.
21 Rothbard, “Toward a Reconstruction,” p. 225. On the early development of the concept of
demonstrated preference by Mises, see Theory of Money and Credit, p- 60; and idem, Human Action, pp. 94-96.
To remain value-free economists, i.c., to abstain from injecting into economic theory ethical
propositions, adherents of cardinal utility among the Old and New Welfare economists had to agree
with the ordinalists that actions are necessary to demonstrate utility, e.g., consumer surplus is a
monetary calculation of utility using a demand curve, which is the result of the actions of buyers
in the market. Those cardinal-utility advocates who did not develop value-free theories were not
bound by the demonstrated-preference principle, e.g., the Pigouvian prescription, driven by
egalitarian ethical notions, of increasing social welfare by equalizing monetary incomes is founded
on the undemonstrable principle that each person has a capacity for utility satisfaction identical to
that of every other person.


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Herbener: The Pareto Rule and Welfare Economics 85

theories, price is determined by the actions of buying and selling that are
prompted by subjective evaluations. The imaginary constructs of consumer
surplus (from Old Welfare economics) and general equilibrium (from New
Welfare economics) are built from the assumption of demonstrated preference.
Thus, when adherents of Old or New Welfare economics discuss improving or
maximizing social welfare, they are not referring to more general concepts of
social “well-being.” To be value-free, this is a necessary restriction on welfare
economics. It is no defect of Austrian Welfare economics that it fails to encompass
a broader concept of social “well-being.” Value-free economic theory cannot do
sO.

Acceptance of the subjective nature of value required economists to
reject cardinal utility in favor of ordinal utility. The inability to make cardinal
comparisons of the gain in utility to some with the loss in utility to others from
a social interaction, in turn, forced them to “reintroduce Pareto’s Unanimity
Rule into economics, and establish it as the iron gate where welfare economics
must test its credentials,” as Rothbard puts it.”* To increase social welfare, according
to the Rule, a social interaction must benefit at least one person while harming
no one. If so, the post-interaction state is called Pareto Superior to the pre-interac-
tion state. Pareto Optimality exists when all Pareto-Superior changes have been
exhausted.’® Forced to accept the Pareto Rule and demonstrated preference, it
would seem that economists could make pronouncements about the social
welfare of voluntary exchanges, which necessarily demonstrably benefit each
participant while doing no demonstrable harm to non-participants, but not
involuntary exchanges (such as government intervention), which necessarily
benefit some and harm others. Only a social system of unanimous consent
can generate the greatest benefit for society; the free market is the “eco-
nomic” component of such a social system.’

Non-socialist advocates of the New Welfare economics, far from being
predisposed to provide a welfare justification for the free market, were anxious

20n this limitation of welfare theory, see David Gordon, “Toward a Deconstruction of Utility
and Welfare Economics,” Review of Austrian Economics 6, no. 2 (1993): 103—4. Gordon makes this
point in response to a criticism of Professor Rothbard’s welfare theory made by Roy Cordato, who
argues that, “demonstrated preference . . . does not allow for any consideration of harm that is not
demonstrated,” which rules out “the welfare effects of envy, trauma, etc.” Thus, voluntary
exchanges “may have negative psychic effects on others,” which negates the claim that such activity
renders an “unambiguous increase in ‘social utility.” Cordato, Welfare Economics and Externalities in
an Open Ended Universe (Boston: Kluwer Academic Publishers, 1992), pp. 42-43.

24Rothbard, “Toward a Reconstruction,” p. 244.

BVilfredo Pareto, Manual of Political Economy (New York: Augustus M. Kelley, [1927] 1971).

26Given the strictures of value-free economics, consent can only be inferred from voluntar-
ily-undertaken actions by which preferences are demonstrated.


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86 Review of Austrian Economics 10, No. 1 (1997)

to demonstrate the welfare superiority of interventionism.”’ Thus, they set
themselves to circumventing this stricture of the Pareto Rule. Two approaches
~ were attempted: trivialize the Rule by subsuming it into a general equilibrium
framework and transcend the Rule with the compensation principle. The first
attempt led to the development of the social welfare function and the concept of
market failure, the second to the concept of potential compensation and political
rules for defining consent.

Bergson pioneered the social welfare function approach.” This technique
trivializes the Pareto Rule by making it the criterion of attaining the set of optimal
conditions for maximizing the social welfare function. The social welfare func-
tion approach uses the Pareto Optimality interpretation of the Pareto Rule,
demonstrating that the Rule merely describes the static, end-state condition
necessary, but not sufficient, for maximum welfare. As such it provides no barrier
at all to advocacy of government intervention to increase social welfare by
redistributing income and correcting for market failure.

There are three optimum conditions derived using the Pareto Rule in this
way.” The Exchange Optimum requires every individual to consume so that the
Marginal Rate of Substitution (MRS) for each pair of goods, which is equal to the
ratio of the goods’ marginal utilities, be equal. If violated, then goods can be
exchanged between individuals moving atleast one to a higher indifference curve
without moving anyone else to a lower indifference curve. The Factor Use
Optimum requires each good to be produced so that the Marginal Rate of
Technical Substitution (MRTS) for each pair of factors, which is equal to the ratio
of the factors’ marginal products, be equal. If not, factors could be rearranged
to produce more of at least one good without reducing the production of any
other good. The Production Optimum requires each good to be produced so that
the Marginal Rate of Transformation (MRT) between each pair of goods be equal
to the corresponding MRS. If unequal, production of the high-cost good could
be reduced and that of the low-cost good increased; thereby moving at least one
person to a higher indifference curve without moving any other to a lower
indifference curve.

"The socialist proponents of the technique used by New Welfare economists were anxious to
show by mathematical proof that central planning could operate a division of labor as efficiently as
the market by solving the system of perfectly-competitive, general-equilibrium equations. For
Mises’s criticism of their attempts, see Human Action, pp. 701-3.

28 Bergson, “A Reformulation of Certain Aspects of Welfare Economics”: 310-34.

Bergson’s list of optimum conditions differs from the one presented here. For our purposes,
the differences between this list, as developed and synthesized by later authors, and Bergson’s is
inconsequential. For a presentation of how the perfectly-competitive market achieves the optimum
conditions, see Francis Bator, “The Simple Analytics of Welfare Maximization,” American Economic
Review 47, no. 1 (March 1957): 22-59.


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Herbener: The Pareto Rule and Welfare Economics 87

Achieving the Production Optimum ensures production along society’s Pro-
duction Possibilities Frontier (PPF), where any increase in production of one
good necessarily reduces the production of another good. There are an infinite
number of production combinations along the PPE. For each point on the PPE,
the goods produced can be divided among individuals in an infinite variety of ways,
each of which is Pareto optimal, i.e., no one can increase his utility without reducing
the utility of someone else. Only one such consumption combination, however, has
a MRS in consumption equal to the MRT in production. Thus, each of the infinite
number of Pareto optimal production combinations along the PPF renders one
Pareto optimal consumption combination. A Utility Possibility Frontier (UPF) can
then be constructed showing the utility each individual acquires from each Pareto
optimal consumption combination: along the UPF, any change in production or
consumption that increases one person’s utility must decrease another person’s
utility. To select the social-welfare maximum combination, a social welfare function
having all the properties of an individual's utility function, e.g., smooth, continuous,
convex indifference curves, is constructed. The socially-optimal point on the UPF
is the one corresponding to the highest social-welfare indifference curve.

It would seem that a social welfare function, so constructed, must of necessity
compare the utility of one person with that of another, which is precisely what the
stricture laid down by the impossibility of interpersonal comparisons of utility
prohibits. If so, the efforts of New Welfare economists to provide a complete,
value-free, social welfare theory were in vain. Its proponents struggled mightily to
avoid this conclusion. Samuelson made the most notable attempt by formulating a
version of New Welfare economics based on his own interpretation of ordinal utility
in which he followed Bergson.” But the lack of a cardinal index for utility by which
interpersonal utility comparisons could be made, which he treats in a cavalier
fashion in criticizing the Old Welfare economics, brought up short his attempts.

Samuelson postulates a social welfare function dependent upon the welfare
each individual obtains from the amounts of all goods and services he receives.
He then asserts that such a social welfare function is “only ordinally determin-
able” but can be subject to all mathematical operations (e.g., aggregation of
individual utilities and differentiation) by assigning arbitrary cardinal numbers
to each ordinal rank.’

30Samuelson calls Bergson “the first who understands the contributions of all previous
contributors, and . . . the first to develop explicitly the notion of an ordinal social welfare function
in terms of which all the various schools of thought can be interpreted” and claims that “there is
only one all-inclusive welfare economics, which reaches its most complete formulation in the
writings of Bergson.” Samuelson, Foundations, pp. 219 and 249. Emphasis added.

Ibid., pp. 228-29.


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88 Review of Austrian Economics 10, No. 1 (1997)

The construction of Samuelson’s social welfare function is illegitimate. To
be an ordinal function consisting of ordinal utility ranks of individuals, the social
welfare function must make interpersonal comparisons of utility in every case
where one person's utility rank increases while another’s decreases. Its existence
presupposes interpersonal comparisons of utility. This problem is not circum-
vented by asserting that the social welfare function has a reduced form that
depends only on the amount of each good going to each individual. Then the
social welfare function must either compare the utility of different individuals
for different distributions of income or it must ignore the utility of individuals
and impose upon them the preferences of a dictator.’

Moreover, Samuelson’s construction of the social welfare function on the -
analogy of the standard treatment of individual utility as an indifference map fails
on the crucial point. He is in error when he claims that the problem of interper-
sonal utility comparisons can be circumvented by a social welfare function that.
“need only be ordinally defined” and then having done so assign to each social
indifference curve an arbitrary cardinal number.*’ The possibility of circumvent-
ing the problem of interpersonal utility comparisons in the construction of an
individual’s utility map by building with ordinal ranks alone and then assigning
cardinal numbers to each indifference curve exists only because the items being
subjectively evaluated by the individual are goods (the dimensions of the graph
are the amounts of the different goods). The individual must be able to compare
his own utility for different combinations of goods. But the social welfare
function must be able to compare the utility of different individuals (the dimen-
sions of the graph are the utilities of different individuals) in order to construct
the social indifference curves. To construct social indifference curves, one must
presuppose cardinal utility and infinitesimal units of cardinal utility.

Additionally, whether individual or social, indifference curves either imply
cardinal utility or forbid utility functions. Drawing a set of indifference curves
with cardinal numbers assigned to them is mathematically equivalent to having a
differentiable utility function. But any function that can be differentiated must
be defined cardinally. One cannot differentiate a function of ordinal rankings.
Thus, drawing a set of indifference curves without assigning cardinal numbers to
them forbids a corresponding utility function. It is precisely the absence of such
cardinal numbers that gives indifference curve analysis the appearance of being
consistent with ordinal utility. That Samuelson knows this point full well is
revealed by his attempt to claim the efficacy of arbitrary assignment of cardinal

2 The latter possibility is examined in Samuelson, “Social Indifference Curves”: 14-18.
33 Samuelson, Foundations, p. 221.


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Herbener: The Pareto Rule and Welfare Economics 89

numbers instead of stating that cardinal numbers are simply not necessary for
his theory. It does no good to claim to replace cardinal marginal utility with
ordinal marginal rates of substitution if the analytic devise to do so, i.e., the utility
function, mathematically implies the equivalence of the marginal rate of substi-
tution of one good for another with the ratio of their marginal utilities. Yet, this
is precisely what any utility function, individual or social, does. In the hands of
its practitioners, indifference curve analysis is not a means of expunging cardinal
utility from economic theory; it is a way of disguising its use.

The comment of Joseph Schumpeter on the measurability of utility, that
“there is in fact no compelling necessity of insisting upon measurability so long
as we are interested only in a maximum problem: there are means of telling
whether or not we are on the top of a hill without measuring the elevation of the
place where we stand,” illustrates the fundamental misunderstanding of the
problem posed to the social welfare function by ordinal utility. ** If utility is
ordinal, there is no hill; to construct the hill one must assume cardinal utility and
a social welfare function that is continuous and differentiable. What would a
“hill” of ordinal ranks look like? The reason the assertion works for a real hill is
that it is continuous and differentiable; therefore it is possible to assign cardinal
numbers, which one could plausibly maintain are arbitrary since there is no
absolute unit of altitude, to the various elevations on the hill. While one could
construct a “stair-step” from ordinal ranks of an individual from which one
could plausibly find a maximum position, i.e., a highest rank, to do so for a social
welfare function presupposes interpersonal utility comparisons.

Samuelson clearly understood that an ordinal social welfare function was
useless within his mathematical framework since without cardinal numbers it
could not be maximized in the standard calculus manner. Furthermore, he
implied that his method of specifying arbitrary cardinal numbers to the social-
welfare indifference curves both avoids assuming cardinal utility and renders a
useful social welfare function. This claim, however, is patently false. Any set of
indifference curves, either for individuals or society, with cardinal numbers
arbitrarily assigned to them, implies cardinal utility. As they emanate from the
origin of the diagram, the numbers must increase in magnitude to reflect the fact
the curves farther from the origin are preferred to those closer to it because, by
assumption, more goods are preferred to less. But the very assignment of cardinal
numbers means that the differences in ordinal rank between combinations of goods
are cardinally measurable. For example, if an individual’s indifference curve with
2 units of X and 3 units of Y is assigned the number 12 and his indifference curve

Joseph Schumpeter, History of Economic Analysis (New York: Oxford University Press, 1954), p. 1062.


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90 Review of Austrian Economics 10, No. I (1997)

with 2 units of X and 4 units of Y has the number 15, the difference in rank is 3.
The extra utility of having the fourth unit of Y is 3, i.e., its marginal utility is
cardinal.

Thus, despite his thinly-veiled hostility toward “Robbins’s dicta concerning
the inadmissibility of welfare economics,” his solution is a mathematically-
dressed up version of the one posed by Robbins himself. *’ Although Robbins
denied that cardinal numbers are thereby implied, he did assert that one can
assess the differences in ordinal rankings, a condition which is “accepted doc-
trine” as a requisite for measurement of the preference rank. As Rothbard makes
clear, the preference rank can only be revealed in action; “only pure rankings are
revealed by acts of choice” while “differences in rank are not so revealed and are
therefore . . . irrelevant to economics.”

Furthermore, if differences in rank cannot be demonstrated in action,
neither can “indifference.” Instead, both indifference and intensity of prefer-
ence are psychological concepts and, thus, using them in utility analysis is
impermissible.’ While this argument is widely accepted for “differences in
rank,” it is widely rejected for indifference. Yet, if preference can only be
demonstrated in action, economic theory can say nothing about either differ-
ences in rank or indifference.’

Finally, to construct indifference curves one must presuppose infinitesimal
units: for individual indifference curves, units of the goods; for social indiffer-
ence curves, units of the utility of individuals. Yet, human action cannot be
predicated upon infinitesimal differences. Such differences are imperceptible so
a person could not establish a preference between the imperceptibly-different
options; thus, he could not demonstrate a preference by action on the basis of
the imperceptible difference.” Demonstrated preference precludes the exist-
ence of smooth, continuous utility functions and the use of calculus in utility and
welfare economics.

It was not these criticisms, made by Rothbard, that convinced New Welfare
economists to surrender their attempts, but the demonstration by Kenneth
Arrow that, given reasonable preconditions, it is impossible to construct a

355amuelson, Foundations, P: 249. Contra Samuelson, Robbins did not think that the impos-

sibility of interpersonal comparisons of ordinal utility ranks prohibited welfare economics. He
argued that it prohibited the Old Welfare economics based on the assumption of cardinal utility.
This es the major theme offered in Robbins, “Interpersonal Comparisons of Utility.”

36Robbins’s discussion is in Robbins, “Robertson on Utility and Scope,” Economica (May 1953): 104.
Professor Rothbard’s comment is in idem, “Toward a Reconstruction,” p. 235.

371t makes utility and welfare theory branches of psychology instead of strictly praxeological
disci lines.

On indifference, see Rothbard, “Toward a Reconstruction,” pp. 236-38.

bid.


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Herbener: The Pareto Rule and Welfare Economics 91

consistent social welfare function.’ This demonstration destroyed the previous
work of Tibor Scitovszky in constructing social indifference curves by proving
that they intersect, i.e., they have intransitive preferences.” In his response,
Samuelson failed to grasp the destructive power of Arrow’s theorem. Samuelson
used the analogy of family welfare to explain how the social welfare function
evaluates the utility of different individuals in a consistent way.'? Assuming that
society consists of at least two members, each one has utility dependent on the
consumption of his own set of goods which is independent of the consumption
of other members. The “ethical worth” of each person’s consumption is ac-
counted for by a social welfare function that constrains society to act “as if it were
maximizing their [sic] welfare function.” The constraint is the distribution of
social income across all members which must be distributed by “lump-sum
transfers . . . that ensure ending up with equal social marginal utilities.”

While these conditions do result in a consistent social welfare function, they
still fail to circumvent Arrow’s theorem. Arrow did not contend that it was
impossible to construct a consistent social welfare function, but that if it was
consistent it would violate at least one of his “reasonable” preconditions, as
Samuelson’s function did. Samuelson’s exercise was in vain.** Social welfare
theory of the New Welfare economics, therefore, lay in ruin by the mid-1 950s."

The market-failure approach has had a much longer and more pernicious life.
It takes note of the fact that actual market systems never achieve perfectly-competi-
tive, general equilibrium; and thus, they are never Pareto Optimal, let alone at the
bliss point of social-welfare maximization. Thus, various types and degrees of
government intervention can be justified as movements toward Pareto Optimality,
i.e., increases in social welfare.

*Okenneth Arrow, Social Choice and Individual Values, 2nd ed. (New York: John Wiley and Sons,
[1951] 1963).

“Tibor Scitovszky, “A Note on Welfare Propositions in Economics,” Review of Economic Studies
9 (1941): 77-88.

*25amuelson’s thinly-veiled contempt for Arrow’s work is illustrated in his comment about
how “conventional theory” can be saved on the analogy of “family consensus.” He says, “Perhaps
Arrow will produce a proof that such a consensus is impossible.” Samuelson, “Social Indifference
Curves”: 9.

“Ibid. 10 and 13. The condition of “equal social marginal utilities” cannot be met by a social
welfare function of ordinal ranks; only if cardinal numbers are attached to the social indifference
curves is such a condition definable, let alone achievable. But assigning cardinal numbers implies
cardinal utility whose marginal social values can be made equal. Ordinal ranks cannot make the
“social (ordinal) utility of every person’s last dollar equal,” as Samuelson claims. Ibid.: 15.

*4Arrow, Social Choice, pp. 96-103.

>On the concession of defeat, see Abram Bergson, “On the Concept of Social Welfare,” Quarterly
Journal of Economics (May 1954): 249; and Paul Samuelson, “Welfare Economics: Comment,” in A Survey
of Contemporary Economics, B.E. Haley, ed., vol. 2 (Homewood, 1ll.: Irwin, 1952), p. 37.


===== PAGE 14 =====

92 Review of Austrian Economics 10, No. 1 (1997)

Given certain preconditions, a perfectly-competitive market system can be
shown to achieve a point on the Utility Possibilities Frontier, i.e., it satisfies all
three Pareto Optimality conditions. If consumers maximize utility, they will
purchase each pair of goods so that its MRS is equal to its corresponding ratio of
prices. Under perfect competition, prices for all goods, and therefore price
ratios for all pairs of goods, are the same for all consumers. By equating his MRS
to the common price ratio, each consumer (unwittingly) equates his MRS to that
of every other consumer, satisfying the Pareto Optimal condition for consumption.
If producers maximize profit, they will hire factors so that the MRTS between any
two equals the corresponding price ratio between them. Perfect competition en-
sures that all producers face the same prices for all factors; thus, their maximizing
behavior leads to the satisfaction of the Pareto Optimal condition for factor use. The
Pareto Optimal production condition requires the MRT for each good to equal
its MRS. Since, for each pair of goods the MRT is identical to the ratio of its
marginal costs, perfect competition satisfies this condition because profit maxi-
mization occurs only when the price of each good equals its marginal cost.

Within this framework, the theory of market failure proceeds from the obser-
vation that real world market systems neither satisfy the preconditions for nor
. exhibit the outcomes of perfect competition. Consumers and producers pursue
non-economic goals instead of maximizing utility and profit. Prices diverge from
marginal costs because of “monopoly” elements. Real markets do not always equate
the prices paid by different consumers for the same good. Costs born by private
producers may not include all those born by society at large because of externalities. *®

This approach turns the Pareto Rule on its head; instead of being a barrier to
intervention, it guarantees high levels of government activity. Real world markets
cannot be perfectly competitive; a perfectly-competitive situation assumes condi-
tions that cannot be achieved in the real world.*’” Demand curves in the real world
always slope downward to the right, ensuring, within the neoclassical framework,
that prices will always exceed their corresponding marginal costs. Thus, government
can be kept busy intervening with anti-trust laws to make actual markets more like
perfectly-competitive ones, regulation to force actual firms to act like perfectly-com-
petitive ones, and taxes and subsidies to equate actual private costs to social costs.

*60n the theory of market failure, see Francis Bator, “The Anatomy of Market Failure,”
Quarterly Journal of Economics 72 (1958): 351-79.

Not the least of these assumptions is perfect information. After listing the standard set of
assumptions, F. A. Hayek comments on the meaning of perfect information. “I shall here,” he says,
“not go into the familiar paradox of the paralyzing effect really perfect knowledge and foresight
would have on all action.” See Hayek, “The Meaning of Competition,” in Individualism and Economic
Order (Chicago: University of Chicago Press, 1948), p. 95.


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Herbener: The Pareto Rule and Welfare Economics 93

These problems of market failure are chimeras—illusions created by the
artificial construct of perfectly-competitive, general equilibrium. *® They pose no
difficulty for Rothbard’s welfare theory because it is not constructed within such
a framework. As he puts it, “the theorem of maximum social utility applies not
to any type of ‘perfect’ or ‘pure’ competition, or even to ‘competition’ as against
‘monopoly.’ It applies simply to any voluntary exchange.”" Moreover, general
equilibrium is inconsistent with the principle of demonstrated preference upon
which both the New Welfare and Austrian Welfare economics are built. Prefer-
ence can only be demonstrated in actions taken by participants in actual ex-
changes given actual situations. Pareto Optimality or Efficiency as developed
within the general-equilibrium framework fails to describe actual situations or
allow for actual exchanges; in fact, action itself is inconsistent with general
equilibrium. New Welfare economics utterly fails to provide a useful criterion of
even the necessary condition of social welfare maximization.

Moreover, the use of a general-equilibrium method to define Pareto Optimality
makes this technique unable to provide a framework for price determination, but the
conditions of Pareto Optimality are defined in terms of perfectly-competitive,
general-equilibrium prices. Demand and supply-cur ves are actions based upon, and
demonstrations of, people’s ordinal preferences, given the existing conditions under
which the actions are taken. Since the conditions of actions in general equilibrium
cannot exist in the real world, the prices of general equilibrium cannot exist either.
Yet, the definition of efficiency, e.g., price must equal marginal cost (or the condi-
tions of Pareto Optimality, e.g., price ratios must equal marginal cost ratios) are
defined by these prices, i.e., in terms of the conditions of general equilibrium.

The existence of general equilibrium prices is inconsistent with the principle
of demonstrated preference upon which any theory of price determination rests. It
is impossible for a person to be in a situation of acting as described by general
equilibrium; therefore, he cannot demonstrate a preference under such conditions,
since preferences can only be demonstrated in actual situations and postulated about
in conceptually-possible situations. Even if one accepts the existence of such prices,
the market failures developed in this framework are fictitious since they compare
two general-equilibrium states, both impossible to attain in the real world. When
asserting market failure, New Welfare economists are not comparing an ideal-

BEA. Hayek says, “It is difficult to defend economists against the charge that for some 40 to
50 years they have been discussing competition on assumptions that, if they were true of the real
world, would make it wholly uninteresting and useless.” See Hayek, “Competition as a Discovery
Procedure,” in New Studies in Philosophy, Politics, Economics and the History of Ideas (Chicago: University
of Chicago Press, 1978), p. 179. Emphasis in original.

Rothbard, “Toward a Reconstruction,” p. 255.


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94 Review of Austrian Economics 10, No. 1 (1997)

ized, perfectly-competitive, general-equilibrium market system with an actual
market system, they are comparing an idealized, perfectly-competitive, general-
equilibrium market system with an idealized, imperfectly-competitive, general-
equilibrium market system. That the latter is inferior to the former is wholly
irrelevant to any actual market system and, thus, to genuine welfare theory.

In contrast, Austrian price theory has as its goal the explanation of actual
market prices. It demonstrates that the actual price of the existing stock of each
good is determined solely by the subjective value placed on it. Each individual
acts in accordance with his preferences: buying to add to his stock, selling to
diminish his stock, or holding to retain his stock. The price that exists at any
moment in time results from these actions. These actual prices are unrelated to
those of general equilibrium; but being real prices determined by real actions,
they are based on demonstrated preferences and, thus, are relevant for welfare
theory. This is the foundation of Mises’s demonstration of profit and loss as the
correct objective test of social-wealth changes discussed above. Moreover, the
voluntary exchanges by which actual prices are determined in real markets
involve a set of Pareto-Superior moves as each participant demonstrates his
preference by his action. Since nothing can be or need be said about the end-state
of these interactions, Pareto Optimality, as an end-state condition, is irrelevant
to Austrian welfare theory.

Rothbard recognized that by rejecting the neoclassical penchant for analyz-
ing the real world solely with the imaginary construct of general equilibrium, one
must dispense with the use of the Pareto-Optimal version of the Pareto Rule as
well, since it is a “static,” end-state principle. To reconstruct welfare eco-
nomics, it must be made consistent with Austrian general economic theories
of real markets. Doing so requires using the Pareto-Superior version of the
Pareto Rule, which is a “dynamic,” step-by-step principle. As he says, “Since we
cannot discover people’s utilities over time . . . the free market at any time will
maximize social utility . . . . Thus, in Period 1 the free market will maximize social
utility. Then, suppose some producers voluntarily form a cartel in an industry.
This cartel makes its exchanges in Period 2. Social utility is again maximized, for
again no one’s exchanges are being altered by coercion.”*’

Proponents of the New Welfare economics attempted a superficially similar but
fundamentally flawed approach to integrating the Pareto-Superior criterion into the
general-equilibrium framework. The Kaldor-Hicks compensation principle at-
tempts to circumvent the static, end-state character of the Bergson—Samuelson
framework by employing a Pareto-Superior version of the Pareto Rule to judge

*O1bid., p. 255.


===== PAGE 17 =====

Herbener: The Pareto Rule and Welfare Economics 95

movements toward the satisfaction of the optimal conditions. Yet it debases the
Rule in a more damaging way than Bergson and Samuelson did by formulating it
in potential terms, i.e., a change is Pareto Superior if those who gain benefit
enough so that they could compensate those who lose in such a way that no one
is worse off.

Nicholas Kaldor demonstrates the ability of the compensation principle to
transcend the stricture of the Pareto Rule using the example of repeal of the corn
laws in nineteenth-century England. Because this policy would increase the real
income of society, though reducing that of landlords, the economist has made his
case for it, he claims, “since in all such cases it is possible to make everybody better
off than before, or at any rate to make some people better off without making
anybody worse off.”*! As Rothbard points out, this argument suffers from a grave
defect.” By transcending the Pareto Rule (some can be worse off after a change
and yet the change increases social welfare), it contradicts the very foundation
of all welfare theory: social welfare must be based on the welfare of individuals
that make up society, which can only be demonstrated in action. Unless the
compensation is actually made, it is impossible to tell from the fact that real
income has risen whether or not the reduction in utility of those who lose can be
more than offset by monetary compensation. Thus, potential compensation does
not eliminate interpersonal utility comparisons; it merely camouflages them in
money terms. The Pareto Rule cannot be transcended with a social-welfare
calculation that strictly adheres to individual, ordinal utility.

Moreover, the compensation principle, being an extension of the
Bergson—Samuelson approach, suffers from the defects of general equilibrium.
It is impossible to pronounce on the economic consequences, including welfare,
of changing from one actual social state to another with the apparatus of general
equilibrium, since neither state can be compared to general equilibrium. One
cannot tell which actual social state is closer to general equilibrium. One must
first develop an economic theory of actual markets that can establish criteria for
comparing actual social states; only then is it possible to build a useful welfare
theory.” One must first develop an economic theory of actual markets; from it,

Nicholas Kaldor, “Welfare Propositions of Economics and Interpersonal Comparisons of
Utility,” Economic Journal 49, no. 195 (1939): 550. Emphasis original.

2Rothbard, “Toward a Reconstruction,” pp. 246—47.

$350me neoclassical economists recognized this defect of the general equilibrium approach in
their development of the theory of second best. They demonstrated that if a market system is
not in general equilibrium, then one cannot discern the correct government policy toward a
market failure in any one market using the general equilibrium framework. The seminal article on
the theory of second best is Kelvin Lancaster and Richard Lipsey, “The General Theory of Second
Best,” Review of Economic Studies 24 (1956): 11-32.


===== PAGE 18 =====

96 Review of Austrian Economics 10, No. 1 (1997)

a theory of the determination of actual prices can be built, and criteria for
comparing the social welfare of actual social states can be developed.

Finally, the Kaldor—Hicks argument fails as a value-free justification for
government intervention, even if one accepts the dubious concept of potential
compensation, since it misconstrues the nature of free-market exchange and
government intervention and, by so doing, establishes the status quo as the
appropriate benchmark for judging social change.* In fact, Kaldor invented the
compensation principle in response to an error of Robbins, who said, “the
statement that social wealth was increased [by free trade] itself involved an
arbitrary element—that the proposition should run, if equal capacity for satis-
faction on the part of the economic subjects be assumed, then social wealth can
be said to be increased. Objective analysis of the effects of the repeal of duties
only showed that consumers gained and landlords lost. That such an arbitrary
element was involved was plain.”**

The error in this assertion is defining consumer gain and landlord loss in
terms of the previous state of affairs, i.e., the status quo, which is no longer a
social alternative. Each time the duty was levied on exporters of grain, they had
their utility demonstrably reduced. Given this state of affairs, they entered into
contracts to purchase grain, demonstrably benefiting themselves and the farmers
who sold to them. They, and other retailers, entered into contracts with consum-
ers, demonstrably benefiting all participants. Landlords, and other factor own-
ers, entered into mutually-beneficial rental contracts with farmers. In each of
these contracts, the prices agreed to by both parties were mutually beneficial.
When the duty was no longer levied on exporters, then the demonstrable harm
no longer existed. This new state of affairs led to new contracts among the various
groups at new prices, lower for grain and land. Acceptance of these new con-
tracts, however, demonstrated the preferences of all parties; they all gain. Only
from a fundamental misconception of the nature of voluntary exchange or
demonstrated preference could one conclude that landlords lose when they agree
to the terms of the new contract. Each party to a voluntary exchange demon-
strates that he prefers its terms to whatever alternative actually exists at that
point in time. On demonstrated-preference grounds, one cannot tell if the
landlords lose in comparing the terms of the new contract with those of the old

%0n the compensation principle as a defense of the status quo, see Murray N. Rothbard, The
Ethics of Liberty (Atlantic Highlands, N.J.: Humanities Press, 1982), pp. 203-5.

>>Robbins, “Interpersonal Comparisons of Utility”: 638. Quoted in Kaldor, “Welfare Propo-
sitions”: 549-50. Kaldor rightly criticizes Robbins, saying, “It can be demonstrated. . . that in the
classical argument for free trade no such arbitrary element is involved at all.” Ibid.: 550. It is not
on the basis of the compensation principle, however, that such an argument can be sustained; but
on the principle of mutual benefit in voluntary exchange, as Professor Rothbard demonstrates.


===== PAGE 19 =====

Herbener: The Pareto Rule and Welfare Economics 97

contract, because no one in the market is now offering the old terms. The old
higher price is not a social option and, thus, landlords cannot demonstrate a
preference for it once the new terms are offered. The genuine alternatives are
only those being offered given the new social situation, the old (status quo)
situation is now irrelevant. Comparisons of the ordinal rank an individual places
on an alternative at one point in time with the ordinal rank he places on a
different alternative at a different point in time are impossible. Since an individ-
ual cannot demonstrate a preference between them, such judgments involve
illegitimate inter-temporal comparisons of utility.

The logic of Kaldor’s compensation-principle solution to Robbins’s error
was worked out fully by J.R. Hicks.” After replicating the Pareto-Optimality
conditions of the New Welfare economics, discussed above in somewhat differ-
ent form, he applies the analysis “as a means of criticizing or testing the efficiency
of production by private enterprise,” by asserting that, “under private enterprise,
any ordinary change in economic policy involves a change in the price-system,
and any change in prices benefits those on one side of the market, and damages
those on the other. Thus no simple economic reform can be a permitted reor-
ganization in our sense, because it always inflicts a loss of some sort upon some
people.” In other words, Hicks asserts that market activity itself, and not just the
removal of government intervention, creates losses for some participants when-
ever such activity has effects on prices, i.e., as long as the economy is not in a
general equilibrium. ’® While this would seem to prevent welfare analysis of
almost all market activity, Hicks claims that “this does not prevent us from
applying our [social welfare] criteria to the case of private enterprise, because we
can always suppose that special measures are taken through the public revenue
to compensate those people who are damaged.”

By transcending the Pareto Rule and following the compensation principle
to its logical end, Hicks winds up in absurdity. Voluntary exchange, instead of

*6As Professor Rothbard puts it, “It is not possible . . . for an observer scientifically to compare
the social utilities of results on the free market from one period of time to the next.” Rothbard,
“Toward a Reconstruction,” p. 255.

*TI.R. Hicks, “The Foundations of Welfare Economics,” Economic Journal 49, no. 196 (De-
cember 1939): 696-712.

5%To illustrate conditions under which the free market would not maximize social welfare
(specifically, imperfect competition), Hicks uses the example of a firm closing down. He says, “The loss
involved in its cessation is measured by the compensation which would have to be given to consumers
to make up for their loss of the opportunity to consume the missing product, plus the compensa-
tion which would have to be given to producers to make up for the excess of their earnings in
this use over what they could earn in other uses.” Ibid.: 709-10. Clearly, this “economic reform”
involves no government intervention, but is a purely private affair of voluntary “reorganization” of
factor usage.

Ibid. 706.


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98 Review of Austrian Economics 10, No. 1 (1997)

being mutually beneficial, “inflicts a loss of some sort upon some people.” Yet,
social-welfare judgments of “private enterprise” are still possible because “we can
suppose” that losers in exchange are compensated “through the public revenue.”
But what kind of private-enterprise system is it that requires, for a demonstration
of welfare enhancement, an all-encompassing government program of income
distribution? If Hicks means that the compensation is only potential, and must
not actually take place, then why is it necessary to suppose “special measures are
taken” to compensate losers? And if he means that the compensation is only
potential but the gain to winners exceeds the loss to losers because enough
additional income is generated by the change to compensate all losers so that
everyone is better off, then he is confusing income with utility and making
assertions about preferences apart from people’s actions.

Instead of correcting the deficiencies of the New Welfare economics, the
compensation principle adds to them. Every actual market activity, not identical
to the status quo, is a priori suspect on welfare grounds, since one can identify
“losers” according to the compensation-principle. Thus, a vast new field is
available for government intervention, especially in the form of income distri-
bution. Ignoring these new possibilities, Hicks examines the situations of market
failure within his framework, finding them to be the same as those of the social
welfare function approach. He then concludes in the same way that economists
of the social welfare function variety do: economic theory can delineate the
conditions for Pareto Optimality, what Hicks calls efficiency, but not interper-
sonal utility comparisons, what Hicks calls distributive justice.

For both the social welfare function and the compensation approaches, if
income distribution could be specified by economic theory, then they would
have a complete welfare theory. In fact, the social welfare function technique
could do this ex ante. The social welfare function is necessary to decide among
points on the Utility Possibilities Frontier because the framework does not
specify an initial income distribution among individuals. If it did start with such
a specification, or specified initial factor ownership among individuals, then
market exchange would lead to a single point on the UPF, which by construction
would maximize social welfare.

Since Austrian Welfare economics is based on Pareto Superiority (a step-by-
step analysis), not Pareto Optimality (an end-state analysis), the importance of a
starting point is all the more manifest. The solution provided by Professor
Rothbard rests on two value-free propositions: demonstrated preference and
self-ownership. That each individual owns, i.e., controls the use of his mind and

Orbid.: 712.


===== PAGE 21 =====

Herbener: The Pareto Rule and Welfare Economics 99

body is self-evidently true.®’ As Mises showed, the entire corpus of economic
theory is axiomatic-deductive: the logical implications of the primordial fact that
individuals engage in human action.” Yet, action itself, being done only by
individuals, presupposes self-ownership. One can no more refute the proposi-
tion that individuals are self-owners than the proposition that individuals act,
since any attempt presupposes the proposition in either case.

Moreover, the fact of self-ownership is not accepted by just Austrian economists
but is a presupposition of the neoclassical school as well. Both schools build price
theory from the foundation of individuals who buy and sell in accordance with their
own subjective evaluations. In fact, the central problem of welfare economics—in-
terpersonal utility comparisons—disappears as soon as the presupposition of self-
ownership is dropped. Without individuals, each making their own evaluations and
decisions and actions based upon them, welfare theory could directly postulate a
“collective welfare” separate from the individuals that make up society. This fallacy
is one even New Welfare economists refused to embrace. Instead, they failed to
accept the logical implication of the presupposition of methodological individualism
for welfare economics while accepting its implications for price theory.

For welfare economics, the implication is that self-ownership is the proper
starting point of analysis. New Welfare economists are led into a contradiction,
perhaps by their desire to employ general equilibrium (and thus, mathematical
techniques) when they accept self-ownership in price theory, i.e., allowing
individual utility and buying and selling to determine prices, and then deny its
implications in claiming that income distribution is indeterminate within the
nexus of these market exchanges. They recognize the necessity of private owner-
ship of property as a prerequisite of voluntary exchange and market prices, but fail
to recognize either that self-ownership of labor is also a prerequisite of these
phenomena or the logical connections between self-ownership of labor and
individual ownership of other property.

Professor Rothbard avoids these contradictions by accepting self-ownership
as the appropriate starting point of welfare economics and then proceeding
step-by-step according to the Pareto-Superior version of the Pareto Rule.®’ Each

IWe are not here dealing with the right of self-ownership but with the fact of sclf-ownership.
While moral ownership cannot be established merely by the fact of ownership, economic ownership
can. For a natural-law argument for the right to self-ownership, see Murray N. Rothbard, for a New
Liberty, rev. ed. (New York: Macmillan, [1973] 1978), pp. 26-37; and idem, Ethics of Liberty, pp. 29-34.
For an axiomatic argument for the right to self-ownership, see Hans-Hermann Hoppe, The Economics
and Ethics of Private Property (Boston: Kluwer Academic, 1993), pp. 195-201.

625ee Ludwig von Mises, The Ultimate Foundation of Economic Science, 2nd ed. (Kansas City:
Sheed Andrews and McMeel, [1962] 1978), pp. 1-9.

30n this process, see Hans-Hermann Hoppe, “Book Review of Man, Economy, and Liberty,”
Review of Austrian Economics 4 (1990): 257-58.


===== PAGE 22 =====

100 Review of Austrian Economics 10, No. 1 (1997)

person owns his labor. When anyone employs his labor in an act of acquisition
over some item previously unowned, he owns, i.e., controls in action the use of,
the item. His action demonstrates a gain in utility, while the failure of others to
acquire the item demonstrates their preference not to acquire it. Thus, each such
act of acquisition is Pareto Superior. When the owners of means acquired in this
way make a voluntary exchange, such an act is Pareto Superior—demonstrably
benefiting the participants while doing no demonstrable harm to non-partici-
pants. The totality of these acts of acquisition and voluntary exchange, whether
of factors or consumer goods, constitute the free market; since each of them is
Pareto Superior, the free market creates the greatest satisfaction of individuals’
preferences at every point in time.**

This conclusion about the free market can be further clarified by examining
charges recently made against Professor Rothbard’s welfare economics. Roy Cordato
claims that one “fundamental problem” with it is that it “ignores the fact that
preferences are expressed sequentially through time, as part of a general set of
goal-oriented activities. The actor in Rothbard’s framework is operating in a static
world where actions are undertaken in isolation from one another.”®® But the
conclusion about the free market’s welfare properties is not “static” in this sense; to
the contrary, itis genuinely “dynamic.” It properly accounts for social welfare at each
successive point in time when a social interaction takes place. Thereby, it properly
accounts for any possible changes in circumstances during a sequence of actions that
influence a person’s “goal-oriented activities,” including his own preferences and
the preferences of others. For private actions, involving no demonstrable prefer-
ences of non-participants, which may be part of the sequence of actions a person
undertakes to achieve a goal, welfare theory, per se, does not apply.

To clarify this point, consider the following illustration. Suppose a man
agrees to a one-year contract in which he trades a particular labor skill for some
particular compensation, and furthermore, that he does so as part of a sequence
of actions which he expects to culminate in the acquisition of a capital gain, for
which he has a preference, from trading shares of stock of a particular company.
He benefits, as does his employer, at the time he makes the labor contract. At
that point in time, the free market has created the greatest satisfaction of
individuals’ preferences, given the actual situation they find themselves in at that
time.*® Having accepted the contract, his situation of acting is changed, including

Hoppe, The Economics and Ethics of Private Property, pp. 232-33.
Cordato, Welfare Economics, p. 44.
at these circumstances of action at any point in time depend on past action is clear; but

this fact does not result in an infinite regress or indeterminacy since the starting point of the free
market is self-ownership.


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Herbener: The Pareto Rule and Welfare Economics 101

perhaps his own preferences; thus, some actions he might contemplate taking
will now have a different opportunity cost to him. Over time he accumulates
sufficient savings from his wages to buy shares of the firm's stock. We know,
by the principle of demonstrated preference, that both he and the seller
benefit at the time of the exchange. At that point in time, the free market has
created the greatest satisfaction of individuals’ preferences, given the actual
situation they find themselves in at that time. But suppose after his purchase of
the stock its price falls, so that he regrets having bought it. Or suppose that
he comes to regret having agreed to his labor contract before it expires. These
circumstances do not represent a failure of the free market to create the greatest
satisfaction of individual preferences. To the contrary, if he continues to possess
the stock, instead of selling it to someone in the market, he demonstrates his
preference for retaining ownership compared to the actual social opportunities now
available to him; if he fulfills the duration of his contract, he demonstrates his
preference for the terms of the contract compared to the actual social opportuni-
ties now available to him. If he sells the stock and suffers a capital loss he
demonstrates his preference for the money received at the time of the sale, or if
he resigns his job, he demonstrates his preference for his perceived alternative.
In each case, participating in the free market increases his utility. The (as-
sumed) subjective loss he experiences from the capital loss, when viewing the
sequence of events in its totality, is not caused by his participation in the free
market, but by his lack of entrepreneurial insight into the future state of affairs
before he started the series of actions. It is properly assigned to the period in the
sequence of his actions when he was acting privately, by retaining ownership of
the stock as its share price fell, and not to those moments when he participated
in the free market. That such losses occur in no measure diminishes the conclu-
sion that the free market renders the greatest satisfaction of individual prefer-
ences compared to any other institutional arrangement for social in teractions.”

The entrepreneurial success or failure of each individual's actions when
viewed in sequence is parallel to the success or failure of the specialized entre-
preneur in the market. After formulating his expectations of the future profit-
ability of various courses of action, he contracts with factor owners to rent their
factor services, and thereby, incurs monetary costs. In each of these contracts,
both he and each factor owner gain. Since he owns the goods produced by
combining the factors, he earns the monetary profit or suffers the monetary loss

7 Cordato’s charge, that “Rothbard’s conclusions [about the welfare properties of the free
market] would only hold in an error-free world of perfect knowledge, where expectations
necessarily coincide with results,” is entirely unfounded. Cordato, Welfare Economics, p. 43. This
charge is more suitably made against the New Welfare economics.


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102 Review of Austrian Economics 10, No. 1 (1997)

when they are sold. In each of the sales, both he and each consumer gain. If these
sales generate revenues in excess of his costs, he earns profit; if his revenues
fail to cover his costs, he suffers loss. His profit or loss is independent of the
fact that he acquires, without exception, subjective benefit in each of his
voluntary exchanges. The extent of profit or loss is determined by his en-
trepreneurial insight, that is, how accurately he anticipated the outcome of the
sequence of actions. The welfare enhancing character of the free market is not
impugned by entrepreneurial losses, whether they are monetary or subjective.
Far from having an “emphasis on static, unconnected action,” Professor
Rothbard’s welfare economics correctly delineates between actions (including
social interactions) which demonstrably increase the utility of each participant
at the time they are undertaken given the actual situation in which they are taken,
and entrepreneurial insights about the future consequences of the actions. The
former can never reduce utility; the latter are the source of either profit or loss
from the sequence of actions over time.®® This delineation also defuses another
of Cordato’s criticisms: that “by focusing strictly on demonstrated preferences
and ex ante evaluations, he rules out all consideration of costs and therefore the
possibility of utility loss.”® But acceptance of the principle of demonstrated
preference logically requires restrictions on statements about utility to those
referring to points in time when action is taken. To make an ex post statement
about utility requires an impermissible inter-temporal utility comparison.
Moreover, far from ignoring costs, Professor Rothbard’s welfare economics
correctly accounts for opportunity costs. Opportunity cost exists only for each
action and only at the time the action is taken; it is the subjective value of the
most-valuable alternative to the action actually undertaken. Cordato’s claim, that
“by definition, costs cannot be demonstrated,” is irrelevant for welfare theory;
what is demonstrated in action is that the subjective value of the action taken

**Ibid., p- 44. Professor Rothbard’s discussion of entrepreneurship is in Man, Economy, and
State (Auburn, Ala.: Ludwig von Mises Institute, [1962] 1994), pp. 5-6, 55-56, and 46369.
5% Cordato, Welfare Economics, p. 43.

"Cordato himself criticizes the New Welfare economics for requiring both interpersonal and
inter-temporal utility comparisons to implement Pareto Optimality. Cordato, Welfare Economics, pp.
6-7. Also, discussing his own concept of demonstrated preference, he says, “preferences that are
revealed at one point in time cannot be assumed to remain constant over time.” Ibid., p- 59.
While it is impossible to say anything on demonstrated preference grounds about the ex post,
subjective profit or loss of a sequence of actions, it is possible to calculate the monetary profit
or loss of the specialized entrepreneur ex post, as shown above. Even in the case where a
specialized entrepreneur earns profit (loss) from a sequence of actions, however, it is not
possible to say that his ex post utility is greater (less) than that ex ante. Cordato makes this error in
his example of an individual who expends resources in a free market pursuing a goal, yet fails to
reach it, when he concludes, “clearly he would have experienced a loss in utility.” Ibid., p. 43. Such
a statement presupposes the ability to make inter-temporal utility comparisons.


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Herbener: The Pareto Rule and Welfare Economics 103

exceeds the subjective value of the best alternative.”' Neither the subjective
benefit nor the subjective cost of an action is demonstrated when an action is
taken; preference is demonstrated, and demonstrated preference is a sufficient
foundation for welfare economics.

Value-free welfare economics must be based on the principle of demon-
strated preference, acceptance of which precludes inter-temporal utility com-
parisons, since an individual cannot demonstrate a preference in action between
two different situations at two different points in time. Welfare economics can
say nothing about ex post utility; instead, it must be content to describe utility ex
ante or at the time of action when the individual actually demonstrates a prefer-
ence between two relevant alternatives. As Professor Rothbard has correctly
pointed out, however, general economic theory shows a greater tendency for
correspondence between ex ante anticipations of gains from a sequence of actions
and ex post realization of such gains in a free market vis-a-vis an interventionist
system.” Specialized entrepreneurs on the market appeal to the test of profit and
loss to determine whether or not they have arranged production to best satisfy
consumer preferences while consumers themselves appeal to trial and error to
determine which of the various consumer goods best satisfies their ends. By
distorting economic calculation and interfering with consumer choice, interven-
tionism retards this tendency to match ex ante and ex post utility.

Instead of being a weakness of Professor Rothbard’s welfare theory, the fact
that “by definition, though, people always expect to benefit, relative to the
alternatives, from every action that is undertaken,” as Cordato claims, is true,
and therefore, a great strength of it. Cordato misconstrues how Austrian Welfare
economics judges social interactions, namely, with the Pareto-Superior version of the
Pareto Rule, when he concludes that, “this is true under any institutional arrange-
ment,” including “action taken at the point of a gun.”” The relevant question for
social welfare in such a situation is whether or not this interaction itself increases
the utility of at least one person without decreasing that of another at the time it
occurs. Since the victim of violence would not have voluntarily undertaken the
interaction in the absence of aggression, one can infer that such an involuntary
social interaction, unlike a voluntary one, forces him to accept a less-preferable
alternative. It is by this inference, and not his action under duress (i.e., after the
aggression has begun), that the Pareto-Inferior nature of involuntary interactions is

"!Ibid.: 43. On this criticism of Cordato, see Gordon, “Toward a Deconstruction,” p. 105.

Murray Rothbard, Power and Market (Kansas City: Sheed Andrews and McMccl, 1970), pp.
18-20. David Gordon also makes this point in “Toward a Deconstruction,” p. 105.

3 Cordato, Welfare Economics, p. 43.


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104 Review of Austrian Economics 10, No. 1 (1997)

seen.’ There is no inconsistency between the Pareto-Inferior nature of involuntary
interactions at the moment aggression begins and the achievement by the victim of
his highest preference by adjusting his actions during the time under duress.

Professor Rothbard’s welfare economics is constructed from Misesian gen-
eral economics. It is the only welfare economics that is completely consistent
with the principles deduced from the axiom of action. Each person owns his
labor, i.e., his mind and body. Employing his labor, man acts by evaluating the
possible ends he can attempt to attain by the combination of means he owns. The
scarcity of means requires him to choose from among the possible ends; to be
purposeful his choice must be according to his evaluations. When he acts, one
can infer that he has established a preference between the course of action taken
and the course of action not taken; he chooses to do what he prefers more and
sets aside what he prefers less. From the axiom of action, one can deduce only
an ordinal ranking of preference; quantitative comparisons of subjective value
are impossible for lack of a cardinal index and a common unit of subjective value.
Only his concrete action can demonstrate his preferences.

Welfare economics examines the consequences of social interactions in
terms of the demonstrated preferences or utility of individuals. Social interactions
can be either voluntary or involuntary; the former is done without, and the latter
with, the use or threat of invasive violence. The subjective nature of value implies
the impossibility of comparing either the utility of different individuals from a
social interaction or the utility of any individual at different points in time. The
impossibility of interpersonal comparisons of utility restricts welfare economics
to conclusions about interactions that benefit some without harming any one.
Such an interaction is called Pareto Superior. The impossibility of inter-temporal
comparisons of utility restricts welfare economics to conclusions about interac-
tions at the time they occur. Any voluntary interaction demonstrably benefits each
participant at the time it occurs, while doing no demonstrable harm to any
non-participant. An interaction that benefits at least one person while doing no
harm to anyone else increases social utility, i.e., either improves or leaves un-
changed the preference rank obtained by every individual. Any involuntary inter-
action demonstrably benefits some participants at the time it occurs, while de-
monstrably harming others. An interaction that harms at least one person is called
Pareto Inferior, and cannot increase social utility.

"Consider the analogy of government taxing a person’s income. At the time the tax is paid,
under duress, the person is made worse off than otherwise. After the tax is paid, he will adjust his
action to the new circumstances, including this aggression, in the way he finds most preferable.
That he does so is no refutation of the Pareto-Inferior nature of the interaction between the
tax-man and himself.


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Herbener: The Pareto Rule and Welfare Economics 105

Every social interaction presupposes ownership of the means used by each
participant and every demonstration of preference, upon which rests the welfare
criterion of changes in social utility, and presupposes self-ownership of labor.
Welfare economics is incomplete without an analysis of the acquisition of the
items traded in voluntary exchanges, and is inconsistent if such an analysis
contradicts the principle of self-ownership of labor.

Welfare economics begins with each person owning his labor. With his labor,
he acquires unowned items existing in nature. Each such act of acquisition
demonstrably benefits the person engaged in the act at the time it occurs, while
demonstrably harming no one. Their abstention from acquisition or transforma-
tion of the item demonstrates the preferences of non-participants for devoting
their means to other ends. Each such act of acquisition is Pareto Superior. Once
the item is owned by the first-user, others no longer have the option of being its
first-user; thus, their preferences at that point in time have no bearing on the
Pareto-Superior nature of the acquisition by the first-user. For a person to obtain
ownership of the item from the first-user in a Pareto-Superior interaction, the
person must induce the owner to either voluntarily exchange it or voluntarily give
it away.

With his labor and homesteaded means, each action a person takes benefits
him at the time of the action. This is true for private actions, such as reading a
book in one’s home, and for social interactions, such as contracting to sell one’s
labor or to buy consumer goods. Non-participants in these actions demonstrate
their preferences for allowing these actions and interactions by devoting their
means to other actions and interactions. Each private action and voluntary social

“interaction is Pareto Superior. Once the actions or interactions take place,
non-participants no longer have the alternative of acting toward them in a
participatory way. Whatever actions non-participants take after the action or
interaction of others are irrelevant to the Pareto-Superior nature of the action
or interaction. In fact, non-participants must now establish a preference for the
new alternatives actually available to them. When they act upon these new
preferences in light of the new circumstances, they benefit.

The same principle applies to each person's preferences inter-temporally.
When someone buys a consumer good, he benefits at that time. If after the
purchase, he reevaluates the good, placing it lower on his preference rank, then
he will act according to his new preferences. His new action will again benefit
him. As economists, we cannot compare his utility inter-temporally, since he
cannot demonstrate a preference between these two states of affairs. It is not the
new action or interaction that reduces his utility; rather, it is his failure to
correctly anticipate future conditions, including his own preferences, i.e., it is


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106 Review of Austrian Economics 10, No. 1 (1997)

his failure as an entrepreneur. This assessment of the sequence of actions of the
individual is the analogue to the assessment of the sequence of interactions
directed by the specialized entrepreneurs in social production and exchange.

The free market consists of all acts of acquisition and interactions that are
voluntary, and is brought about by a legal system that defends these property titles
and contracts. The free market consists entirely of Pareto-Superior movements.
Thus, it achieves the highest degree of utility possible for each person, given the
conditions of action and interaction, including the different preferences of
different people. It is in this sense that the free market can be said to maximize
social utility; it is not the utility that is social but the actions—the free market
gives the greatest possible utility to every individual in their interactions.”

Interventionism consists of the mixture of voluntary and involuntary acts of
acquisition and interactions. Each involuntary act of acquisition or interaction
is Pareto Inferior. Thus, interventionism fails to achieve a degree of all individual
utility as great as that of the free market.

Professor Rothbard correctly concludes that the free market achieves the
greatest social utility possible of any economic system. His achievement is no less
than a rigorous proof of the long-standing conviction among economists that the
free market, without qualification, maximizes social welfare.

This is analogous to the distinction Professor Rothbard makes when discussing the differ-
ence between individual utility and total utility, as the aggregation of the marginal utilities of units
of a stock, and the marginal utility of different-sized units. Total utility is an illegitimate, cardinal
concept which must be rejected. As he points out, what is marginal, in cardinal terms, is the unit
of the stock, not the utility obtained by its possession. See Rothbard, “Toward a Reconstruction,”
PP- 234-35. Perhaps this definition of social welfare will satisfy those who have asked explicitly
for one. See, Gary North, “Why Rothbard Will Never Win the Nobel Prize,” in Man, Economy, and
Liberty, Block and Rockwell, eds., p. 105.