La matematica nella storia dell�economia. Primo Workshop, Torino 16-17 ottobre 2003

History of Neoclassical Consumer Theory:

A Neo-Kantian Epistemological Perspective

Ivan Moscati*

ABSTRACT This paper deals with the history of neoclassical consumer theory from 1871 to 1971, and with the Neo-Kantian knowledge theory of the Marburg School, a philosophical movement whose main exponents were H. Cohen, P. Natorp and E. Cassirer. The strictly historical investigation focuses on two aspects somehow neglected in the previous literature: the acceptance in con-sumer theory of a general utility function in place of the original additive function, and the comparison between the behavioral and the utilitarian formulation of the theory. In restating these two aspects, I propose to show the usefulness of the Marburg School�s epistemology in understanding the history of consumer theory and, more generally, the principles that rule the process of knowing of neoclassical economics. I also suggest that the Marburg theory of knowl-edge provides a philosophical foundation to the cognitive logic of neoclassical economics.

Keywords: Consumer Theory, Utility Theory, Revealed Preference Theory, Neo-Kantianism, The Marburg School Epistemology

JEL Codes: B13, B21, B4, D11

* Bocconi University, Milan, Department of Economics, and University of Florence, Ph.D.

in History of Economic Thought. E-mail: ivan.moscati@uni-bocconi.it

I am most grateful to R. Arena, P. Battigalli, N. Bellanca, L. Bruni, M. Dardi, N. De Vec-chi, R. Faucci, A. Gay, N. Giocoli, G. Lunghini, F. Marzano, P. Mongin, A. Montesano, S. Zamagni, C. Zappia for their comments on earlier drafts. All errors remain mine.

1

Neoclassical consumer theory emerged, developed and reached its current standard

form over the course of a century, from the time it first appeared in the works of Menger

and Jevons in 1871 up to the 1971 volume Preferences, Utility, and Demand edited by

Chipman et al., which fine-tuned it in many points. Although, up to now, there has been

no detailed overview of the century-long development of consumer theory, many of its

phases have been examined by numerous authors1. Some of them also try to draw cer-

tain epistemological conclusions about the criteria that seem to characterize the devel-

opment of consumer (or demand) theory2. The history of this fundamental part of mi-

croeconomic neoclassical analysis and the logic that appears to guide its development

are also the subject of this paper.

Even I shall examine the history of consumption theory, focusing on two central as-

pects that have been somewhat neglected in the previous literature: the acceptance of a

general utility function in place of the original additive utility function, and the com-

parison between the behavioral and the utilitarian formulation of the theory3. This his-

torical inquiry concludes that more realistic elements (such as general utility compared

with additive utility) are introduced into consumption theory only if they do not weaken

the systematic order of the conceptual representation of the phenomenon (consumption)

already achieved. If the inclusion of elements that correspond better to common-sense

evidence, empirical data or experimental verifications jeopardizes the determinateness

and the systematic unity of the theory, they are simply put aside. This does not mean

that the search for realism is irrelevant in neoclassical theorizing about consumption,

but just that the pursuit of conceptual integrity is stronger than that of realism. One can

say that neoclassical economics tries to maximize the realism of the theory under the

constraint of preserving its systematic view.

In this paper I argue that such a hierarchy between systematic character and realism

is not an idiosyncrasy of neoclassical consumer theory or of neoclassical economics in

general, but is rooted in a broader character of scientific understanding.

1 See Schultz 1935, Stigler 1950, Schumpeter 1954, Houthakker 1961, Hurwicz 1971, Samuelson

1974, Wong 1978, Blaug 1992 [1980], Dooley 1983, Mirowski 1989, Frambach 1993, Wade Hands�Mirowski 1998, Hurwicz 1998, Mirowski�Wade Hands 1998, Weber 1999a, Weber 1999b, Mongin 2000, Bruni 2002, Mirowski 2002, Chipman�Lenfant 2002, Montesano 2003.

2 See in particular Stigler 1950: 392-396 and Mongin 2000: 1145-1149. 3 Throughout the paper, �utilitarianism� is meant to be related to individual choice theory, not to the

social choice and ethical doctrine of Bentham, Mill or Sidwick.

2

In setting out this thesis I rely on the epistemology of the Marburg School, a Neo-

Kantian philosophical movement whose main exponents were H. Cohen (1842-1918),

P. Natorp (1854-1924), and E. Cassirer (1874-1945). In the literature on economic

methodology, this epistemological perspective is virtually unexplored, even if it seems

more powerful than others in grasping how neoclassical economics actually works4. In

particular, the Marburg Neo-Kantianism makes it possible to explain the reasons why

heterodox criticisms have had little effect on neoclassical theory. It also allows us to ex-

plain the formalist style of the neoclassical theory and proposes a philosophical founda-

tion for the neoclassical method of successive approximations.

The aim of this paper is therefore threefold. First, I reconstruct the history of neo-

classical consumer theory, trying to demonstrate that the Marburg School�s epistemo-

logical perspective is useful in understanding its development. Second, I try to show

how the Marburg epistemology makes it possible to grasp the principles that rule the

process of knowing of neoclassical economics and does so better than other epistemo-

logical theories. Third, I suggest that the Marburg theory of knowledge not only allows

us to comprehend the actual cognitive logic of neoclassical economics but also gives it a

philosophical foundation.

1. AN OVERVIEW OF THE EPISTEMOLOGY OF THE MARBURG SCHOOL

The Marburg School was part of the larger philosophical movement called Neo-

Kantianism that, under the motto �Back to Kant!�, emerged in German philosophy in

the 1870s. Maintaining Kant�s critical method as the reference point, Neo-Kantianism

was opposed to both speculative idealism and positivism. During the late 19th and early

20th century, the movement reached a dominant position in German philosophy, which

it maintained until the 1920s when other philosophical trends (including phenomenol-

ogy and logical positivism) put it on the fringe of the philosophical arena5.

4 The term �Neo-Kantian� is sometimes associated with Mises� claim of deducing economic propo-

sitions from some synthetic, a priori statements regarding the nature of human action (cf. Mises 1949, Parsons 1990 and 1997). However, I do not use the term in the sense of Mises� praxeology: I refer to Neo-Kantianism for a theory of knowledge, not for a theory of action, and hence for an epistemological theory and not, in the end, for an economic one. Moreover, as will be shown, the a priori principles to which Marburg Neo-Kantianism appeals are the regulative principles of under-standing, whereas Mises attempts to employ the category of action as the constitutive principle of the economic domain. Regarding the flaws of such an attempt see Barrotta 1996.

5 For a general introduction to the Neo-Kantian movement see Ferrari 1997 and Ollig 1998.

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Of the different trends included in Neo-Kantianism, the Marburg School is character-

ized by its logicist development of Kant�s theory of knowledge along the rationalist

Plato-Descartes-Leibniz line, and because it elaborates its epistemological view in con-

nection with a thorough analysis of contemporary science. The main epistemological

tenets of the Marburg School can be outlined as follows:

1) Reality is never given in and of itself, but is always mind-correlative. Things are

always given within some kind of �sense� of them: perception, common sense, scientific

knowledge, practical use, moral commitment, aesthetic experience etc. Of all these

forms of experience of things, scientific knowledge, however, holds a position of

prominence in the sense that ultimately something is �real� exactly as science takes it to

be.

2) Because things are given within the knowledge of them, the a priori forms of un-

derstanding determine the things as given. Philosophy must therefore investigate the

principles and laws of understanding instead of the principles and the laws of things. In

line with the basic ideas of Kant, for the Marburg School, philosophy also becomes a

�critique of reason�.

3) Since the a priori principles of understanding guide the development of scientific

knowledge, the Marburg School sees in the actual history of science an a posteriori

manifestation of these guiding principles. What Cohen calls �the fact of science� there-

fore becomes the starting point for the renewed Neo-Kantian critique of reason: �We

objectify [�] reason in science. Critique of reason is a critique of knowledge or of sci-

ence� (Cohen [1984] 1883: 6, my translation).

4) What are the principles that also regulate the process of scientific knowledge? Ac-

cording to the Marburg Neo-Kantianism, scientific understanding basically endeavors to

put in order a domain of phenomena in a systematic unity, i.e. attempts to connect the

diverse experiences in an ordered and stable system of dependencies. Scientific thought

aims to substitute the hazy given of perception with exact notions, it seeks to replace the

imprecise and uncertain relationships between pre-scientific things with concept con-

nections that contain as much exactness and rational evidence as possible, it tries to

supplant variable and indecisive dependencies with constant and necessary ones. What

is �real and objective� in a properly scientific sense is gained by this synthesizing and

systematizing activity of understanding.

5) The goal of scientific knowledge is therefore not to attain a perfect copy of what is

presented in the kinds of experiences (perception, common sense, etc.) that precede sci-

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entific knowledge. In its fundamental tendency to design a systematic unity of the

given, theoretical thought can lose the characteristics of things as they are immediately

offered in perception or common sense. This possible loss of immediacy and concrete-

ness does not mean that the knowledge becomes unscientific or false. This sort of opin-

ion misunderstands the essence of scientific understanding and thus makes it impossible

to account for the actual shape of science.

6) In particular, scientific concepts need not correspond to objects of perception or

common sense nor need they be accurate imitations of �something of the real world� nor

abstractions maintaining the essential features of the �real world�. However, correspon-

dence to common sense is not the right criterion to evaluate scientific concepts since

they are products of thought through which understanding reconstructs experience as a

system of dependencies thus making it intelligible.

7) It is worth noting that the Marburg scientific fictionalism is not to be confused

with instrumentalist fictionalism. Both epistemological views acknowledge that, in the

first instance, scientific theories do not aim to be exact copies of �reality�. Although in-

strumentalism regards a theory as a useful tool for practical ends (typically for predic-

tion), Marburg Neo-Kantianism regards it as primarily useful for theoretical ends, that

is, in order to make experience intelligible.

8) It is also noteworthy that the Marburg epistemological view does not prescribe

what the �right� theory for a particular field of phenomena should be. As a matter of

fact, the intellectual pursuit of a systematic synthesis of a given domain is just a formal

one, which actually and historically produces scientific systems with different contents.

Therefore, two divergent theories of a certain phenomenal domain could coexist, if they

are both able to connect the diverse elements of the domain in an evenly ordered and de-

termined system of entailment relations. On the contrary, if the system of dependencies

set forth by one theory is more complete and exact than the one set forth by another,

scientific understanding will reject the latter and accept the former6.

6 The idea that there can be a multiplicity of theories for giving the manifold phenomena a synthetic

unity links Marburg to the conventionalism of Poincaré (1902) and especially of Duhem (1906). In fact, the Marburg School shares with Duhem�s conventionalism the concept of scientific theories as systematic wholes, whose parts cannot separately be subject to empirical verification, and the subsequent idea that a theory can be evaluated just with reference to another theory and not with reference to the observational data in themselves.

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9) According to the Marburg School and particularly Cassirer, the relations among

the elements of a scientific system could be expressed in the most appropriate way

through mathematical relations, and in particular, as mathematical functions. This is due

to the fact that mathematics is regarded as a science of relations rather than as a science

of quantity: �The object of mathematics [�] is not the compounding of magnitudes, but

the connection and reciprocal determination of relations� (Cassirer 1953 [1910]: 257).

Thus, the more the dependencies between the components of the theoretical system be-

come exact, the more they can be expressed as mathematical functions. One could

therefore say that science intrinsically tends to mathematize its theories.

In the following Sections, I attempt to show how these epistemological tenets of the

Marburg School allow us to understand the historical development of neoclassical con-

sumer theory and, more generally, to account for the epistemic (i.e. knowledge-relative)

logic of neoclassical economics. This does not mean that the economists that played a

part in developing consumer theory were somehow inspired by Marburg epistemology:

to my knowledge, none of them refer to it anywhere, nor do Cohen, Natorp, Cassirer re-

fer to economic science in their writings. Therefore, I am not claiming that the Marburg

School�s epistemology is the common �muse-philosophy� of neoclassical economists,

which has been concealed up to now. Neoclassical economists, moreover, have pro-

fessed and profess different methodological views. Despite these differences, consumer

theory seems to have specific and stable principles that regulate its development. These

regulative principles, and not the possible, hidden roots of the methodological views of

neoclassical economists are the subject matter of the paper. The point I would like to

make is that the Marburg theory of knowledge explains such principles well. The fol-

lowing reconstruction of consumer theory is therefore not an investigation of hidden in-

tellectual backgrounds, but rather a case for the general validity of Marburg School�s

theory of knowledge.

2. ADDITIVE UTILITY AND GENERAL UTILITY

Neoclassical consumer theory originates in the marginalist value theories of Menger

(1871), Jevons (1871) and Walras (1874), and becomes an autonomous body of doctrine

with Marshall�s Principles (1890). As is well known, according to the marginalists the

economic value of a commodity depends on the evaluation that the subjects give its

marginal unities. Such marginal evaluation is called �final degree of utility� by Jevons,

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�Grenznutzen� by the Austrian School, �rareté� by Walras and then simply �marginal

utility�. Even though Jevons acknowledges that utility is not measurable, he first writes

down total utility as a cardinal function ( )xu of the quantity of the good, and marginal

utility as the function ( )xφ obtained by differentiating the former. In addition, Jevons as-

sumes that marginal utility ( )xφ is a positive, decreasing and additive function. This last

feature presupposes that total and marginal utility of any one good are independent of

the quantities consumed of all others goods7. Under these assumption on ( )xφ and for

the two commodities/two agents case, Jevons obtains his famous �equations of ex-

change�, which state that, in order to maximize trader utility under the budget con-

straints, and with no trades at disequilibrium exchange ratios, it must hold that

( )( )

( )( )yx

pp

yx

y

x

2

2

1

1φφ

φφ

==

where ( )ijφ is the marginal utility of the commodity i for the trader j, and yx pp is the

equilibrium exchange ratio between the commodities (Jevons 1871: 95 ff.).

Under the same assumptions as Jevons, in the Élements Walras systematizes the sub-

jective value theory in a coherent and general price theory and first fixes the exact rela-

tionship between the marginal utility of a good and its demand (Walras 1874: 77 ff.). In

his Mathematical Psychics, Edgeworth stresses the need to introduce into the theory a

generalized (i.e. non additive) utility function, which would make it possible to under-

stand the apparent phenomenon of the utility interdependence of goods (Edgeworth

1881: 20, 104). In order to analyze the exchange when utilities are interdependent,

Edgeworth constructs the indifference lines (or curves) which are to become an essential

conceptual tool for the subsequent whole consumption theory.

However, the introduction of a general utility function represents a tricky theoretical

problem. In fact, the assumptions of additive, at the margin positive, and decreasing

utility, make it possible to univocally determinate the relationships between the demand

for goods, their prices, and consumer income, and to ensure that the second order condi-

tions for the constrained maximization of utility are certainly satisfied. As regards the

first issue, if the utilities of the goods are independent, the demand for a good definitely

decreases (increases) as its price rises (falls) (i.e. 0<∂∂ ii px ). In other words, with addi-

7 In mathematical terms, Jevons assumes that ( ) ( ) ( )nnn xuxuxxu ++= ...,..., 111 and thus that

( )iii xxu φ=∂∂ , with ( ) 0>ii xφ and 0<ii dxdφ . Additivity implies that 02 =≡∂∂∂ jiji dxdxxu φ .

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tive utility the so-called �law of demand� holds, and demand curves are always down-

ward sloping. With a general utility function this is no longer univocally true: demand

for a good might also increase as its price rises (the Giffen case). However, in order to

completely understand under what mathematical and economic conditions such a phe-

nomenon can occur, we have to wait until the 1930s. The analytical expression of

ii px ∂∂ in the general utility case was already made by Pareto as early as 1893 (Pareto

1892-93, V: 306). However, it is only with the decomposition of ii px ∂∂ in terms of in-

come and substitution effect in Slutsky�s 1915 article (re-discovered in the Thirties) and

in Hicks-Allen�s 1934 paper, that the economic meaning of an upward sloping demand

curve becomes clear from a theoretical standpoint8.

Second, if the utilities of the goods are independent (and marginal utilities are usu-

ally positive and decreasing), it can be shown that demand for a good definitely in-

creases (decreases) as consumer income I rises (falls). In mathematical terms 0>∂∂ Ixi ,

which means that all goods are normal. With a general utility function, this statement is

no longer true. Even in this case, we need to wait for Slutsky and Hicks-Allen to have a

precise expression and an exact economic understanding of the ratio Ixi ∂∂ 9.

As regards the utility maximization, the assumptions of additive, at the margin posi-

tive, and decreasing utility, ensure that the second order conditions for the constrained

maximization problem of the agent�s utility are satisfied. Therefore, if all commodities

are purchased, first order conditions are sufficient for a maximum. In geometrical terms,

Jevons� assumptions imply that the agent�s indifference curves are strictly convex, so

that tangency conditions are sufficient to discover the optimal combination of commodi-

ties. With a general utility function, this is no longer true. Even with decreasing mar-

ginal utilities, plausible substitution relationships between commodities could cause in-

difference curves to be concave, so that a point that satisfies the tangency conditions can

also be of minimum, not maximum, utility (in the literature of the period such points are

called �unstable equilibria�). Moreover, if the indifference curves are convex in some

tracts and concave in others, there can be not one, but a multiplicity of tangency points,

8 On the relationship between Pareto�s expression and those of Slutsky and Hicks�Allen, see

Schultz 1935: 433-447, Dooley 1983 and Weber 1999b. 9 In Pareto, the analytical expression of Ixi ∂∂ is not present. In Pareto�s general theory of ex-

change, in accordance with Walras� approach, income is not regarded as a distinct exogenous vari-able, but is endogenously given as the value of the agent�s endowment at market prices. More on this in Weber 1999b.

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some of maximum and others of minimum utility. Edgeworth aims to introduce a gen-

eral utility function, but without losing the convexity of indifference curves. Therefore,

the introduction of a general utility function raises two problems: that of providing the

analytical condition for convexity (i.e. the second order condition for the constrained

maximization problem), and that of justifying why such condition should hold. Edge-

worth (1881: 34 ff., 108 ff.) provides the condition at issue for the two-commodities

case, and claims that it is, by and large, satisfied, nonetheless with an utterly deceptive

argument.

In conclusion, although Edgeworth draws attention to the unrealistic nature of the

additive utility assumption, he is unable to solve the problems raised by the adoption of

general utility. In this state of affairs, the introduction of a general utility function in the

theory would have caused the loss of the determinateness of the dependencies between

demand, prices, and income obtained by Jevons and Walras. With a general utility func-

tion, the demand curve can be downward or upward sloping (as well as horizontal) and

indifference curves can be convex or concave, but if one is unable to understand and to

exactly determine under which theoretical circumstances each case occurs, introducing

general utility just means introducing unpredictability and indetermination into the pic-

ture. In this situation, according to the epistemological theory of the Marburg School,

economics is expected to hold to the systematic theory based on the unrealistic additive

utility assumption. This is what, in fact, happens.

3. BETWEEN EDGEWORTH AND PARETO

Marshall basically rejects Edgeworth�s suggestion of a general utility function and

never utilizes indifference lines, which are the typical analytical tool that makes it pos-

sible to take into account the interdependence of commodity utilities. In all the editions

of the Principles (1890-1920), Marshall�s consumption theory relies on the additive

utility assumption in a crucial, even though subtle, way. Without this assumption �the

one universal rule to which the demand curve conforms [i.e.] that it is inclined nega-

tively throughout the whole of its length� (Marshall 1961: 99, note) breaks down. How-

ever, this means that Marshall�s whole partial equilibrium analysis, which is based on

the intersection of a downward sloping demand curve and of an upward sloping supply

curve, totters. As regards the admission of the interdependence of utilities, Marshall�s

attitude is therefore rather inconsistent. Although in the first edition of the Principles

(1890), he explicitly deals with rival commodities, in the second edition (1891) he tries

9

to defend the additive utility assumption against Edgeworth (Marshall 1961: 845). Sub-

sequently, in the third edition (1895), he openly admits that �we cannot say that the total

utility of [two commodities which contribute to the same purpose] is equal to the sum of

the total utilities of each separately�, and afterwards introduces the Giffen goods case,

which can be explained only if the additive utility assumption is removed, but luckily

such a case is �rare� (Marshall 1961: 131 f.). These are all surface adjustments which do

not modify the analytical groundwork of Marshall�s demand theory which continues to

be implicitly based on an additive utility function until the final 1920 edition of the

Principles10.

Apart from the question of additive utility, Marshall is to be remembered because he

introduces a way of dealing with the consumption theory, different from that of Jevons,

Walras and Edgeworth. First, Marshall considers purchasing by an isolated agent rather

than the exchange among many agents. Second, the consumer prices are fixed by the

market and are not the result of the exchange process. Third, the household does not

have an endowment of commodities to trade but a money endowment with which to

purchase the commodities. In this way, Marshall limits consumption analysis to the cur-

rent boundaries and separates exchange theory from consumption theory.

In the 1890s, in addition to admitting the unrealistic nature of the additive utility as-

sumption, another serious limitation of the classical utilitarian theory is highlighted, that

is, the absence of a measure of utility, even if barely theoretical. It is not at all clear

what the values that the function ( )xu associates to the commodity quantities x mean,

how these values could be measured, and, foremost, what the unit of measure of utility

is. In his Mathematical Investigation, Irving Fisher tries to find an empirical measure of

utility based on the economic choices of agents. Nevertheless, Fisher�s attempt also col-

lides against utility non-additivity: he himself recognizes that his method of measure-

ment works only if commodity utilities are independent (Fisher 1926 [1892]: 64-67).

Gustav Cassel also attempts to overcome the problems related to utility by adopting an

alternative demand theory independent from the utility notion, but obtains no satisfac-

tory results (Cassel 1899: 413 ff.).

Therefore, at the end of the 19th century the unrealistic nature of the classical � addi-

tive, cardinal � utility is quite clear. Classical utility is unrealistic in at least three ways:

10 Regarding the methodological reason of why Marshall rejected Edgeworth�s suggestion of a gen-

eral utility function, see Dardi 1991: 96-101.

10

i) as an assumption in itself, since utilities of commodities appear to be interdependent;

ii) for its empirical implications which conflict with Giffen and inferior goods; iii) in the

sense that it does not correspond to anything actually measurable. However, despite the

recognized unrealistic character of classical utility, neoclassical economists hold to it.

The succeeding editions of Walras� Élements (1889-1900) follow the first on this criti-

cal point. As already mentioned, not even Marshall changes the groundwork of his the-

ory in the subsequent editions of the Principles. In their works, Wicksteed (1888),

Wicksell (1893), Barone (1894) and, although in a non mathematically explicit form,

Pantaleoni (1889 and 1898), Wieser (1889), and Clark (1899) maintain the cardinal ad-

ditive utility assumption. In his first cardinalist phase, Pareto builds up a general utility

analysis more than any other without applying his own results. In the five-part article,

Considerazioni, he recognizes the soundness of Edgeworth�s generalization, states the

exchange analysis in general terms, but then develops it within the additive framework.

He subsequently resumes the general utility analysis. He first provides the exact expres-

sion of ii px ∂∂ in the general utility case, but then continues by using the additive utility

which he declares �approximately true� (Pareto 1892-93, V: 306-307). Similarly, in the

Cours, Pareto develops the entire analysis with additive utility functions and discusses

the general case only in a footnote (Pareto: 1896-97: 332-334)11.

4. THE METHOD OF SUCCESSIVE APPROXIMATIONS

The Marburg explanation for this state of affairs is that neoclassical economists hold

themselves to the unrealistic classical utility since it allows them to construct a coherent

and determinate theory of demand. In this case, the commitment to realism conflicts

with the commitment to conceptual intergrity, and the latter prevails. This does not

mean that grasping the observed phenomena ceases to be the task of neoclassical eco-

nomic inquiry. The point is that this understanding must be a theoretical one, that is, the

phenomena at issue (e.g. those related to the demand of commodities) have to be under-

stood in a structured system of clear entailment relations. If capturing empirical evi-

dence requires the introduction of assumptions that, however, make the theory indeter-

minate, then they are temporarily put aside. The method of successive approximations

basically consists in this effort of �approximating� as much as possible the available

11 As regards the use of the additive utility assumption among leading neoclassical economist at the

end of the 19th century and at the beginning of the 20th, see Stigler 1950: 326-327.

11

evidence by means of successive theories based on progressively more plausible as-

sumptions which must not, however, blur the theoretical system. Neoclassical econo-

mists � at least from Menger�s defense of theoretical economics against Schmoller�s

historical school in the Methodenstreit � have repeatedly upheld such a method in re-

sponse to the criticisms of the lack of realism and empirical inconsistency often raised

by the different heterodox schools.

What I assert is that the Marburg theory of knowledge suggests a transcendental (i.e.

relative to the laws of thought) foundation for the method of successive approximations

and, accordingly, a vindication of neoclassical economists� methodological common

sense. As a matter of fact, it explains the introduction and the maintaining of unrealistic

hypotheses, and it recognizes that even those hypotheses, whose implications conflict

with observational evidence, are not rejected until an alternative competitive theoretical

system is proposed. More decisively, the Marburg epistemology legitimizes the neo-

classical condition that in the approximation sequence the model must remain determi-

nate by tracing it back to the regulative principles of scientific understanding.

5. PARETO THE BEHAVIORIST, PARETO THE UTILITARIAN

The second stage of neoclassical consumer theory began in 1900, with the publication

of Pareto�s Sunto (1900), and ended in the middle of the 20th century, with Samuelson�s

last momentous contributions to revealed preference theory. This phase is characterized

by the opposition of two approaches in consumption analysis: the behaviorist and the

utilitarian-ordinalist one. The behaviorist approach, in line with Fisher�s suggestion, in-

tends to overcome every hint of internal and unobservable utility, by referring back to

the effective, observable consumer choice behavior. The utilitarian-ordinalist one in-

stead, continues to base consumer theory on the utility concept and on the utility func-

tion, which, however, are regarded as having just an ordinal, not a cardinal meaning.

Pareto�s work, rich as well as ambiguous, represents the starting point of both ap-

proaches.

As is well known, after having embraced the classical utility theory, between 1898

and 1900 Pareto changes his perspective and considers it possible to construct a demand

theory just by analyzing consumer acts of choice, thus making the reference to utility

superfluous. Nonetheless, as observed by many authors from the 1930s on, Paretian

12

demand theory actually implies many implicit references to utility, not only to ordinal

but also to cardinal utility12.

In particular, utilitarian elements are evident in the way Pareto states the features of

indifference curves. Edgeworth�s indifference curve is indeed the analytical tool that Pa-

reto brings into play in order to obtain the equations of pure economics from the �pure

and naked� fact of choice (Pareto 1900: 217). For Edgeworth the bundles on the same

indifference line are those that give the same utility to the subject, whereas for Pareto

they are simply those the subject is unable to choose from, and in this sense, is

�indifferent�. However, in order to reconstruct a complete demand theory, Pareto re-

quires that the indifference curves resulting from choices be convex, since this ensures

(as seen above) that the first order conditions are sufficient to determine the optimal

combination of commodities. Like Edgeworth, Pareto therefore faces the problem of

justifying convexity but he should solve it just by referring to the characteristics of the

acts of choice. Pareto instead refers surreptitiously to psychological-utilitarian motives

and bases convexity implicitly in the assumptions of decreasing marginal utility of

goods and in disregarding their interdependence relations. He also assumes that the in-

difference curves are decreasing. This feature is also justified on the basis of psycho-

logical motives, namely tracing back the downward slope to the hedonistic principle of

non-satiation (cf. Pareto 1906: 258-259)13.

Moreover, it is noteworthy that decreasing marginal utility is not only a utilitarian

concept but a cardinal one, since this property is not invariant to an arbitrary, strictly in-

creasing transformation of the utility function14. Similarly, Pareto�s notions of comple-

ments and substitutes in terms of second-order cross-partial derivatives of the utility

function, are cardinal. His idea that subjects can order not only bundles but also prefer-

ence differences among bundles is also cardinal15.

12 For the 1930s see e.g. Hicks�Allen 1934: 52 ff. For a defense of Pareto�s utilitarian ambiguities

from a methodological standpoint see Bruni-Guala 2001. 13 On these issues see Ranchetti 1998. 14 In fact, even if 022 <≡∂∂ xxuxu , the second-order derivative of ( ))(xuf ,

( ) xxxxxx uufuffxxuf ′′+′=≡∂∂ 22 )( , could be positive if xxuuf ′′ is large �enough�. 15 According to Pareto�s notion of complements and substitute, two goods are complementary if

0>xyu , and substitute if 0<xyu . Hicks and Allen (1934: 59-60) highlight that the sign of

yxxyxy uufuff ′′+′= can be different from that of xyu . Regarding Pareto�s idea that subjects can or-

der preference differences, see Pareto 1906: 252-253. Lange 1934 shows that this is tantamount to assuming cardinal measurability of utility.

13

Pareto�s utilitarian ambiguities are therefore not only of the ordinal sort but also of a

cardinal nature and exist not solely in the interpretations of the notions but also in the

theoretical analysis of demand. As a result, such ambiguities make Pareto�s behavioral

project of reconstructing demand theory on the basis of the �naked fact� of choice,

flawed.

6. THE ROLE OF THOUGHT EXPERIMENTS

Realist critics of Pareto�s theory also draw attention to the fact that the experiment

through which Pareto expects to determine the indifference lines is a fictitious one (see

e.g. Mayer 1994 [1932]). Pareto, in fact, imagines putting a subject � a sort of Buridan�s

donkey � between two bundles x1 and x2, then changing the composition of x2 up to the

point where the subject is no longer able to choose between x1 and x2, thus determining

that x2 belongs to the same indifference line as x1. This experiment is to be repeated in-

finitely many times in order to discover all the bundles indifferent to x1, and then re-

peated all over again to determine the entire indifference map of the subject. However,

in this case it is not a matter of factual experiments: there is actually no subject, no bun-

dle, and Pareto�s test is just a thought experiment16. From the empiricist standpoint, Pa-

reto�s behavioral project of reconstructing demand theory on the basis of the observable

fact of choice is to be regarded not only as flawed, but simply as groundless.

However, from a theoretical standpoint, the problem is not that Pareto�s experiment

is just a mental one, but that it is somehow inconsistent. First of all, Pareto takes for

granted that the subject�s indecisiveness in the face of two alternatives is tantamount to

indifference, although this interpretation is legitimate only under what is today termed a

completeness assumption. Subsequently, in determining the indifference map, Pareto

presumes that if bundle x1 is chosen against bundle x2, every other x1-indifferent bundle

will be chosen against every other x2-indifferent bundle. However this inference is valid

only under the currently termed transitivity assumption. Lastly, as already seen, indif-

ference curves can be assumed as downward sloping only under the hypothesis of non-

satiation, and convex under other specific postulates, such as preference for variety.

How is the development of neoclassical consumer theory affected by these two kinds

of criticisms of Pareto�s choice analysis � the realist one and the theoretical one? As

16 The first actual empirical attempt to determine the indifference curves is that of Thurstone 1931.

14

will be shown, the subsequent contributions of Slutsky, Hicks-Allen, Hicks, and Sa-

muelson all aim to improve the new Paretian conceptual framework by overcoming its

logical inconsistencies and not its lack of realism. Even in this case, the line of de-

velopment of neoclassical economics is skillfully rationalized by the Marburg School�s

epistemological tenets. Cassirer particularly recognizes the importance of thought ex-

periments as fundamental tools through which understanding reconstructs and repre-

sents to itself the phenomena under consideration (cf. Cassirer 1911: 328 ff.). The fact

that thought experiments just occur �in the laboratory of the mind� is certainly not a

problem for Marburg�s epistemological view, nor for neoclassical economics. Instead

problems arise if a conceptual representation proves to be inconsistent or incomplete

(e.g. as a consequence of the discovery of a paradox) since this makes it difficult for the

understanding to acquire an integral logical picture of the phenomenon. Removing these

inconsistencies therefore becomes an urgent task for scientific research and the same

sense of urgency seems to explain the efforts of neoclassical economists to correct the

inconsistencies of Pareto�s new and promising conceptual framework.

7. HICKS, ALLEN AND THE MARGINAL RATE OF SUBSTITUTION

In 1934, Hicks and Allen publish a famous paper which aims to work out a theory of

consumption choices along a Paretian line but �free of the inconsistencies detected in

Pareto� (Hicks�Allen 1934: 55). Even though a widespread interpretation puts the

Hicks�Allen paper at the origin of utilitarian ordinalism, it belongs to the behaviorist

camp: in fact, they start by admitting the cardinal immeasurability of utility and note

that �if total utility is not quantitatively definable, neither is marginal utility� (Hicks�

Allen 1934: 55)17. In the place of total and marginal utility, Hicks and Allen do not put

ordinal utility but the marginal rate of substitution (MRS). The MRS, defined as the

amount of good 2 which substitutes a marginal unit of good 1 for the individual, is a

quantitatively definable entity which can be empirically observed, and whose notion is

independent from the notion of utility. Starting from the MRS, Hicks and Allen CAN 1)

determine the relationships between the demand for goods, their price, and the con-

sumer income in elasticity terms; 2) decompose the effect of a price change on demand,

17 The first derivative of a strictly monotonic transformation of )(xu , xx uff ′= , only keeps the sign

of xu , not its magnitude. More importantly, the second-order derivative, xxxxxx uufuff ′′+′= , does not even keep the sign of xxu .

15

in what Hicks will later call income and substitution effect; 3) provide a new definition

of complements and substitutes which replaces the Edgeworth-Pareto cardinal notion

relying on utility second-order cross-partial derivatives.

The problem with the Hicks-Allen construction is that all their results rely on two

crucial assumptions: first, that the MRS is negative (which means decreasing indiffer-

ence curves) and second, that the MRS is decreasing (which means convex indifference

curves). The assumptions in hand are the same critical ones, which Pareto found diffi-

cult to justify. As regards the first item, Hicks and Allen postulate the MRS negativity

without any particular explanation. This statement can however seem natural only on

the basis of an unspoken endorsement of the hedonistic non-satiation principle. As re-

gards the decreasing MRS assumption, Hicks and Allen only assert that it is not falsified

by experience, without putting forward any positive justification for it. Therefore, as

Samuelson (1938a: 61-62) will promptly underline, the convexity hypothesis once more

seems to ultimately rely on psychological-utilitarian considerations.

In the end, this second attempt (after that of Pareto) to overcome every reference to

utility does not succeed. The Hicks-Allen restatement of consumer theory in terms of

MRS fails to become the standard neoclassical one for two reasons. From a methodo-

logical standpoint, the fact of overcoming the utility notion is to a great extent just illu-

sory since the crucial assumptions of the MRS rely on postulations that are utilitarian in

nature. In spite of this, the Hicks-Allen paper presents the most advanced results on the

relationships between price, income and demand from a theoretical viewpoint. How-

ever, with the rediscovery of Slutsky�s article and with the publication of Value and

Capital by Hicks in 1939, it becomes clear that the same results, obtained on the basis

of the MRS, can be obtained through ordinal utilities in a much simpler way. Therefore

there are no methodological or theoretical reasons to adopt the Hick-Allen approach

which is hence abandoned.

8. SLUTSKY, THE FINDER REDISCOVERED

In 1915 Slutsky published his article on consumer theory in Italian. It remained basi-

cally ignored until Dominedò (1933) in Italy and later in international journals Schultz

(1935) and Allen (1936) call attention to it18. In his article, Slutsky provides the follow-

18 For a detailed analysis of the rediscovery of Slutsky�s article see Chipman�Lenfant 2002.

16

ing results for any number of goods and for a general utility function (cf. Slutsky 1915:

4-19):

1) The second order condition for the constrained maximization of utility. As already

seen, such a condition coincides with that of convexity of indifference curves, which

however, slutsky does not bring into play.

2) The exact mathematical expressions of Ixi ∂∂ , ji px ∂∂ and ii px ∂∂ .

3) By introducing the notion of �compensating variation�19, Slutsky decomposes the

effect of a price change on the demand for goods in the part due to the substitution ef-

fect and in the one due to the income effect thereby obtaining what will be called �The

Slutsky Equation�:

Ixx

px

px i

ij

i

j

i∂∂

−∂∂

=∂∂ *

��

, which in the particular case ij = becomes Ixx

px

px i

ii

i

i

i∂∂

−∂∂

=∂∂ *

��

where ji px ∂∂ �� is the compensated variation of the demand for i when the price j varies

(the cross-price substitution effect), ii px ∂∂ �� is the compensated variation of the demand

for i when the price of i itself changes (the direct substitution effect, or simply substitu-

tion effect), and *ix is the quantity of good i contained in the initial consumption bundle.

Slutsky notes that ji px ∂∂ �� and ii px ∂∂ �� are, at least ideally, empirically observable quan-

tities.

4) Slutsky demonstrates that, if the second order condition is satisfied, the substitution

effect is always non-positive, i.e. 0�� ≤∂∂ ii px . That means that for the compensated de-

mand, the �law of demand� holds.

5) Slutsky draws attention to the fact that the cross-price substitution effect is symmet-

ric, i.e. ijji pxpx ∂∂=∂∂ ���� . If we call �substitution matrix� the matrix of the terms

ji px ∂∂ �� , this means that the substitution matrix of the demand function is symmetric.

6) Even if Slutsky does not demonstrate, if the second order condition holds, the

substitution matrix is negative semi-definite20.

19 Slutsky� compensating variation is a change in consumer income accompanying a change in prices

which makes the consumer�s initial consumption bundle just affordable at the new prices. 20 This result was proved first by Samuelson 1938a: 69.

17

7) Slutsky demonstrates that, although the substitution effect is always non-positive,

the income effect Ixx i

i ∂∂

− * can be either negative or positive and the Giffen case is due to

a positive income effect which is greater in absolute value than the substitution effect.

8) Lastly, Slutsky demonstrates that with additive utility functions and under the as-

sumption of decreasing marginal utility: i) the second order condition is certainly satis-

fied (i.e. indifference curves are convex), ii) the income effect is always negative, iii)

when the price of a good rises its demand falls and vice versa, i.e. there are no Giffen

goods and the law of demand holds.

Slutsky draws the analytical expressions of Ixi ∂∂ , ji px ∂∂ and ji px ∂∂ �� starting from

the derivatives ( ) ixxu 22 ∂∂ and ( ) ji xxxu ∂∂∂2 of a cardinal utility function. The values of

Ixi ∂∂ , ji px ∂∂ and ji px ∂∂ �� are, however, empirically observable so that it becomes

theoretically possible to go back from them to the values of ( ) ixxu 22 ∂∂ and

( ) ji xxxu ∂∂∂2 , which would thus cease to be merely psychological. This is the initial

purpose of Slutsky�s article. However, in the final part of the paper, Slutsky himself

shows that unfortunately, such a going-back is not possible. Devoid of this piece of the

initial project, Slutsky�s contribution remains cardinal in nature: i) he is apparently un-

aware that second-order and cross-partial derivatives of utility make sense only within a

cardinal view of utility; ii) there is no attempt to verify whether the results obtained in

terms of such utility derivatives are, in any case, independent from increasing transfor-

mations of ( )xu ; iii) he finally maintains the cardinal notions of complementarity and

substitutability in terms of the sign of ( ) ji xxxu ∂∂∂2 (see Slutsky 1915: 23-25)21.

However, in quite a providential way, Slutsky�s results are independent from cardinal

measurability assumptions on utility and can be entirely obtained within an ordinalist

framework, as Allen stresses in his 1936 paper devoted to Slutsky�s results. In fact, if

the function )(xu employed by Slutsky is replaced with an arbitrary ( ))(xuf with 0>′f ,

all the derivatives of f cancel out, so that the second order condition, the expression of

Ixi ∂∂ , ii px ∂∂ , ji px ∂∂ and all the other results obtained by Slutsky do not change (Al-

len: 1936: 191-192). This opens the way to the ordinalist restatement of Slutsky�s find-

21 As regards this issue, I claim that the interpretation of Slutsky�s contribution as ordinalist in na-

ture, e.g. by Samuelson 1974: 1282 or by Chipman�Lenfant 2002: 562-563 ff., is inexact.

18

ings and to the formulation of the standard ordinalist neoclassical consumer theory

which will be worked out by Hicks.

9. HICKS THE ORDERER

Although for a while, Allen (1938: 344 ff.) continues to maintain consumer choice

analysis in terms of MRS as a primary concept, Hicks already in 1937 sets forth con-

sumer theory in terms of ordinal utility (Hicks 1937) and fine-tunes his formulation in

Value and Capital (1939). In this work, the MRS ceases to be the basic element of the

model and is regarded as the opposite of the ratio between the partial derivatives of the

ordinal utility function. In any case, the required features for the MRS are the same as in

the paper written together with Allen: the MRS has to be negative and decreasing.

Negativity is still upheld on the basis of the hedonistic principle of nonsatiation which

makes marginal utilities positive22. The case for the decreasing MRS is more complex

than in the article written with Allen but remains basically the same: the assumption of a

decreasing MRS (i.e. of indifference curve convexity) is required for the determinate-

ness of the theory and does not seem to be disproven by experience (Hicks 1939: 13 ff.).

In the end, Hicks contributes to re-presenting Slutsky�s results in a systematic and

mathematically clear way and demonstrating, more thoroughly than Allen and Schultz,

how these findings are invariant to strictly increasing transformations of a general utility

function.

10. GENERAL UTILITY AS THE RULE

The epilogue of this part of the story concurs perfectly with the Marburg epistemologi-

cal view. From the mid-1930s, the use of a general utility function in consumption the-

ory ceases to be a knotty problem for neoclassical utilitarian theory. On the contrary,

general utility becomes the standard whereas additive utility becomes a special case. In

fact, the works of Hicks, Allen, Schultz and especially Slutsky show that the introduc-

tion of general utility � whose realism was acknowledged by Edgeworth 55 years earlier

� does not imply introducing unpredictability into the theoretical picture. In fact, it be-

comes clear that not only with additive utility but also with general utility is it possible

22 If 0>iu , then the ( ) 0MRS <−= ji uu . Note that the sign of ( ) ii ufxxuf ′=∂∂ )( is the same of

iu since 0>′f .

19

to determine exactly the conditions for the maximization of consumer utility and the in-

terrelations between demand, prices, and income, as well as to set univocally the

substitution and complementary relations between goods23.

The establishment of the Slutsky-Hicks theory as the new orthodox one is not hin-

dered by the fact that it is difficult to apply it empirically, as some scholars of the Uni-

versity of Chicago pointed out. Schultz (1935, 1938) tries to test the empirical implica-

tions of Slutsky�s analysis by comparing them with the data from the statistical demand

curves of some commodities. Although Schultz�s findings do not refute Slutsky�s re-

sults, they certainly do not corroborate them24. Other Chicago scholars, such as Stigler

(1939) and Wallis and Friedman (1942), subsequently point out the difficulty of recon-

ciling the demand curves of the ordinal Slutsky-Hicks theory with the statistical demand

curves. In particular, Wallis and Friedman question the possibility of empirically deriv-

ing the indifference function, either through psychophysical experiments, like that of

Thurstone (1931) or through a statistical estimation. This makes the Slutsky-Hicks

framework useless for empirical evaluations and for predicting the effect of changes in

economic conditions on the consumption of various goods (Wallis�Friedman 1942: 177

ff.).

However, once again this kind of empirical criticisms has no effect. As a matter of

fact, neoclassical consumer theory does not take it into account and instead develops in

two different directions with divergent aims but a similar approach. On the one hand,

Samuelson strives to obtain analytical results comparable to those of Slutsky-Hicks, but

on the basis of a set of postulates different from the utilitarian ones. On the other hand,

first Wold and then Debreu, maintain the reference to utility but seek to rigorously

ground the ordinal utility function and its features starting from an axiomatic theory of

consumer preference.

23 According to the new definition, which is also the current one, two goods are substitutes if their

compensated cross-price effect is positive, and are complements if their compensated cross-price effect is negative; see Schultz 1935: 459, Schultz 1938: 620-628, Hicks 1939: 311.

24 More on the problems related to Schultz�s findings in Wade Hands�Mirowski 1998. Wade Hands and Mirowski propose an alternative history of the American neoclassical demand theory of the Thirties centered on Schultz�s statistical findings and on Hotelling�s different model of demand (Hotelling 1932, 1935). Although Wade Hands�Mirowski�s reconstruction is full of new and in-teresting information, in my opinion, it is untenable, as Hurwicz 1998 convincingly points out.

20

11. SAMUELSON AND THE BEHAVIORIST-ORDINALIST EQUIVALENCE

In an often quoted passage of his 1938 note on consumer theory, Samuelson (1938a: 71)

says that he seeks to �develop the theory of consumer behaviour freed from any vestig-

ial traces of the utility concept�. This does not mean that Samuelson wants to preclude

the introduction of the utility notion or to contradict the results obtained by using related

constructs (as shown by his work of the late 1930s on welfare economics with Bergson),

but merely that he thinks that consumer behavior analysis �can be carried on more di-

rectly [�] from a different set of postulates� (Samuelson 1938a: 62)25. According to

Samuelson, the purpose of consumer theory is to place some restrictions on the features

of the empirical demand functions ( )Ipfx ,= , that is, at least on the ideally observable

values of Ixi ∂∂ , ji px ∂∂ , ji px ∂∂ �� . He claims that such restrictions can be obtained start-

ing from a simple coherence assumption on consumer behavior which will be later

termed the Weak Axiom of Revealed Preference. As is well known, the Weak Axiom

states that if at the price vector 1p a bundle 1x is chosen when another bundle 2x is also

affordable (and in this sense 1x is �revealed to be preferred� to 2x ), then there can be no

budget set containing both bundles for which 2x is chosen and 1x is not.

What are the implications of the Weak Axiom for consumer demand? Samuelson

(1938a, 1947, 1953) proves that, if consumer purchasing choices fulfil the Weak Ax-

iom:

1) The sum of price changes multiplied by the changes in compensated demands

proves to be non-positive: 0�1

≤∆∆∑=

n

iii xp . If the consumer demand function ( )Ipfx ,= is

differentiable, for infinitesimal price changes this inequality becomes 0�1

≤∑=

n

iii xddp , so

that the substitution matrix of the demand function is negative semi-definite, as in the

utility maximization problem.

2) In particular, when only the price k changes, the last expression reduces to

0� ≤kk xddp . This means that the substitution effect is always non-positive (negative if

0� ≠kxd ) as in correspondence of a bundle of maximum utility, and that for the compen-

sated demand the �law of demand� holds.

25 Mongin 2000: 1135-1139 convincingly demonstrates that, already in 1938 and not only later,

Samuelson was not interested in eliminating utility from microeconomic theory.

21

3) The Weak Axiom has no implications on the sign of the income effect. This is per-

fectly consistent with the utilitarian analysis which contemplates goods both with nega-

tive income effect (normal goods) and with positive income effect (inferior goods).

4) The Weak Axiom has neither implications on the way gross demand for a good

changes when its price changes, i.e. on the sign of ii px ∂∂ . This is again quite in agree-

ment with the utilitarian analysis: when the price of a commodity rises the consumer

can either purchase less (ordinary good) or more (Giffen good).

5) Moreover, the Weak Axiom implies that any good whose demand increases when

the income rises, shrinks in demand when its price rises, which corresponds to Slutsky�s

utilitarian demonstration that Giffen goods are a subset of inferior goods.

6) Lastly, the Weak Axiom implies that the demand functions are homogeneous of or-

der zero, i.e. a change in prices and income in the same proportion leaves all demanded

quantities unchanged. This restriction upon the demand functions is also embodied in

the solutions of the utility maximization problem.

The only restriction on demand functions that derives from the utility maximization

problem but that is not involved in the Weak Axiom, is the symmetry of the cross-price

substitution effects, i.e. the symmetry of the substitution matrix. The importance of this

property of demand functions lies in its being a necessary condition (with also the nega-

tive semi-definiteness of the substitution matrix) to go back from a demand function

( )Ipfx ,= to an ordinal utility function ( )xu which generates the demand function itself,

in the sense that the constrained maximization of ( )xu brings the consumer to the con-

sumption choices expressed by ( )Ipfx ,= . The problem of defining exactly under which

necessary and sufficient conditions a generating utility function for a given demand

function exists, is the so-called �integrability problem�, which was first studied by An-

tonelli (1886) and which has been conclusively solved in some of the works collected in

Chipman�Hurwicz�Richter�Sonnenschein (1971)26.

It is beyond the scope of this paper to give a detailed account of the integrability

problem. Suffice it to say that in 1950 Houthakker shows that a stronger axiom on con-

sumer behavior, together with appropriate continuity assumptions on the demand func-

tion (Lipschitz continuity) is sufficient for the integrability of the demand function.

Houthakker�s Strong Axiom is an iteration of Samuelson�s Weak Axiom, which rules

26 A reconstruction of the history of the integrability problem can be found in Hurwicz 1971.

22

out the possibility of cyclical consumer choices: in a chain of commodity bundles, each

of which is shown to be preferred to its successor in the sense of the Weak Axiom, the

last element cannot be shown to be preferred to the first.

On the basis of Houthakker�s contribution, Samuelson re-examines the problem of

integrability and demonstrates that the symmetry and negative semidefiniteness of Slut-

sky�s substitution matrix are not only necessary but also sufficient conditions for the in-

tegrability of Lipschitz continuous demand functions (Samuelson 1950: 376-385)27.

Hence, the Strong Axiom on consumer choices implies the symmetry and negative

semidefiniteness of the substitution matrix, which are in turn sufficient for the existence

of an ordinal utility function, whose constrained maximization generates those con-

sumption choices. On the other hand, the constrained maximization of an ordinal utility

function leads to consumption choices which satisfy the Strong Axiom. Therefore, it

turns out that the Slutsky-Hicks framework and the Samuelson-Houthakker one lead to

identical restrictions on demand functions. This realizes Samuelson�s program of carry-

ing out consumption theory from a non-utilitarian set of postulates, and at the same time

makes the opposition between the ordinalist and the behaviorist approach vanish.

12. THE UTILITY FRAMEWORK AS THE STANDARD ONE

Despite these equivalence results, Samuelson�s restatement of consumption analysis

does not replace the ordinal utility apparatus as the standard framework of neoclassical

demand theory. What are the reasons for this outcome?

From a methodological standpoint, it is important to point out that Samuelson�s re-

vealed preference theory is not more empirically based than the utilitarian one. As in

Pareto�s case, the compelling power of the Weak Axiom does not stem from a factual

experiment on real consumer behavior but from a thought experiment on an imaginary

consumer confronted with fictional prices. In principle, the Weak Axiom can be tested

through individual experiments or on the basis of statistical demand functions. As re-

gards the first suggestion, we must bear in mind that the Weak Axiom, by its very na-

ture, concerns hypothetical alternative choices, not actual successive choices. This

makes it difficult to verify or disprove it through experimental sequences of choices. On

the second point, it must be remembered that since consumer theory axioms place re-

27 Samuelson�s demonstration will be perfected by Hurwicz-Uzawa 1971.

23

strictions on individual demand, and only under specific auxiliary assumptions on ag-

gregate demand, it is difficult to test the Weak Axiom starting from the statistical de-

mand functions. Therefore, as regards the actual testability of the basic postulates, there

is no genuine advantage of Samuelson�s framework over Slutsky-Hicks� one, even if

one embraces the epistemological canons of positivism or of operationalism.

From the standpoint of the Marburg theory of knowledge, there is instead a crucial

advantage of the latter approach over the former: the preference/indifference apparatus

makes it possible to analyze some issues that, within the Samuelson scheme, are not di-

rectly workable and which require, instead, the recovery of the preference/indifference

device. As shown above, if the consumption choices of the individual, expressed by his

demand function, satisfy the Strong Axiom, there exists an ordinal utility function

which generates those choices and which can be determined by integrating the demand

function itself. Therefore, even the results of consumer theory that cannot be deduced

by directly using the Strong Axiom can be obtained indirectly through the integration

procedure. In particular, such a device is necessary for the welfare analysis of economic

changes: without the preference/indifference apparatus, for example, it is impossible to

evaluate the impact on the consumer�s welfare of a prices change, due e.g. to the intro-

duction of a tax28. Thus the preference-based approach proves to be more powerful for

the theoretical understanding of some valuable issues of consumer demand and this can

therefore explain its dominance over the behaviorist approach.

Lastly, preferences and utility functions are basic analytical tools in other fundamen-

tal areas of neoclassical microeconomics which start to intensely develop at the end of

the 1930s: welfare economics, general equilibrium theory, social choice analysis and the

theory of choice under uncertainty. Therefore, it appears that employing the ordinal util-

ity framework makes it possible to connect demand theory to these other areas in a sys-

tematic analytical picture of the microeconomic field. For the Marburg knowledge the-

ory, this is another important advantage of the Slutsky-Hicks theory over the Samuelson

one which rationalizes the prevalence of the former.

28 Passing from consumer theory to exchange theory or to general equilibrium theory, the prefer-

ence/indifference apparatus is required to evaluate the efficiency of an allocation. On this issue cf. Montesano 1996.

24

13. DEBREU AND THE AXIOMATIC FOUNDATION OF SLUTSKY-HICKS� THEORY

From the 1940s on, utilitarian consumer theory strives to find a sounder and more rigor-

ous basis for its fundamental analytical tools, preferences and ordinal utility functions.

In this connection, the pioneer attempt was made by Frisch (1926), but it is Wold who,

in 1943-44, gives the first axiomatic treatment of the utilitarian theory of demand. In

particular, Wold states axiomatically the general properties of the preference/indiffer-

ence relations that allow us to represent �every indifference map [�] as the level map

of a continuous, non decreasing function� (Wold 1943-44, II: 223). Furthermore Wold

proposes a method to construct such a function which is ordinal in nature. Unfortu-

nately, Wold�s treatment is not completely rigorous and correct. In 1951 Arrow intro-

duces in economics the handling of preferences as binary relations whose properties are

stated axiomatically. Preference is conceived as a formal relation R between two generic

alternatives (not just commodity bundles), in which they stand when one alternative is

preferred to the other (Arrow 1951: 11 ff.). However, the subject matter of Arrow�s

book is not to investigate the problems related to the representation of a preference or-

dering by a numerical function. In 1954, the so-called �paradox of lexicographic prefer-

ences� introduced by Georgescu-Roegen (1954) makes it apparent that it is not always

possible to define a real valued order-preserving function on a set of alternatives or-

dered by the preferences of some agent. In the same year, Debreu specifies assumptions

under which the representation of a preference ordering, by means of a real-valued con-

tinuous function, is possible and demonstrates the consequential representation theorem

(Debreu 1954). In his classic monograph, Theory of Value (1959), Debreu carries out

the axiomatic analysis of economic equilibrium, determining when it is possible to de-

rive the specific utility function required by the Slutsky-Hicks theory.

Debreu (1959: 52 ff.) defines in mathematical terms the features of both the con-

sumption set Xi and the binary relation �preference�. In particular, he deals with the

weak preference relation (x can be either strictly preferred or indifferent to y), which is

labeled with the symbol ≿. Debreu demonstrates that if: 1. Xi is connected, 2. ≿ is com-

plete, 3. ≿ is reflexive, 4. ≿ is transitive; 5. ≿ is continuous (in an appropriate technical

sense), then it is possible to construct a function that associates to each indifference

class induced by ≿ a real number, in such a way that, if a class is preferred to another,

the number of the first is greater than the number of the second. This function is called a

utility function and can be chosen to be continuous. Moreover, if it is assumed that: 6.

25

Xi is closed, 7. ≿ is convex, and the hypothesis 1. is reinforced becoming: 1'. Xi is con-

vex (convexity implies connectedness), every utility function that represents the given

preferences is also quasi-concave29.

Yet, a continuous quasi-concave utility function is exactly the ordinal utility function

that the Slutsky-Hicks consumer theory needs, since such a function ensures that the

second order conditions for the constrained maximization of utility are satisfied, i.e. that

the indifference curves are convex. In this way, it is possible to recover all the results

already obtained by ordinal utility theory, but now starting from a basis fully specified

in axiomatic terms. Debreu therefore provides the Slutsky-Hicks theory with a sound

axiomatic foundation and brings neoclassical consumer theory to its current standard

form.

14. FORMALISM AS NEOCLASSICAL METHODOLOGICAL AWARWNESS

The axiomatic method mainly aims to pursue the logical rigor of the theory and not its

realism. In an oft-quoted passage of the Theory of Value, Debreu peremptorily states

that: �Allegiance to rigor dictates the axiomatic form of the analysis� (Debreu 1959: x).

In another text, Debreu observes that the aim of the axiomatization of a certain part of

economic theory is the �full specification of the assumptions under which any one of its

conclusions is asserted�, and that �the complete specification of assumptions, the exact

statement of conclusions, and the rigor of the deductions of an axiomatized study pro-

vide a secure foundation on which the construction of economic theory can proceed�

(Debreu 1983 [1977]: 5-6).

Within the formalist attitude of the axiomatic method, the time-honored question of

overcoming every hint of psychological conjectures (nonsatiation principle, decreasing

marginal utility or preference for variety) in the statement of some basic assumptions of

consumer theory (downward slope and convexity of indifference curves) fades away.

From the formalist standpoint, such assumptions do not, in fact, aim to grasp something

real, whether psychological or not, but have a primarily logical-systematic function:

they in fact ensure the determinateness and the connectedness of the entire theoretical

construction. Therefore, the interpretation e.g. of the convexity of the indifference

29 Quasi-concave is a function ( )xu for which ( ) ( ) ( ){ }213 ,min xuxuxu ≥ for each ( ) 213 1 xxx λλ −+= ,

with [ ]1 ,0∈λ . Quasi-concavity is an ordinal feature, i.e. a feature which is invariant to a mono-tonic transformation of ( )xu .

26

curves in the psychological terms of preference for variety cannot put the theory at risk.

On the contrary, if such interpretations make some axiom appear more plausible, they

are even welcome. However, if an axiom seems indisputably false, the task is to either

remove it (�to relax the assumptions�) without letting the edifice of the theory collapse,

or to replace the entire theoretical construction with another one which ought to be

comparably complete, determined and exact.

However, as I have tried to show, this formalist allegiance to conceptual rigor, and

the priority it has over both the pursuit of a descriptive accuracy of the assumptions and

the search for factual relevance of the empirical implications, are the same that have tac-

itly guided the development of neoclassical consumer theory from its very beginnings.

Instead it is sometimes claimed that after the Second World War there was a �formalist

revolution� in neoclassical economics which involved a change in the very aims of the

theory30. The driving element of this revolution would have been a much greater use of

mathematics which was to have important methodological consequences: economic

theory became more and more directed at achieving internal consistency to the detri-

ment of factual relevance, the empirical element became distorted or vanished alto-

gether in economic model-building, and a permissive attitude to unreal assumptions

pervaded economic theorizing. In short, with the formalist revolution realism was sacri-

ficed to tractability. However, from the historical reconstruction I propose, no formalist

revolution took place since the sacrifice of realism on behalf of tractability has been the

rule from the origin of neoclassical theory. On the contrary, it seems that, according to

the formalist methodological statements expressed by Debreu, neoclassical economics

becomes aware of those which already were its internal epistemic laws.

In line with a Lakatosian methodology it might be suggested that �allegiance to

rigor� is to be included in a set of �hard core propositions� which could characterize the

neoclassical research program from its very beginnings. However, in line with the Mar-

burg theory of knowledge, I argue that �allegiance to rigor� is not a hard core proposi-

tion among a possible set of propositions included in a research program among many

others. Rather, the pursuit of rigor depends on a more fundamental tendency of the un-

derstanding to achieve a systematic picture of the given. It is for this reason, that �alle-

giance to rigor� is helpful in explaining not only the internal development of consumer

30 See Ward 1972, Hutchison 2000.

27

neoclassical theory, but also why the neoclassical research program (i.e. the research

program that endorsed such an allegiance from its beginnings), displaced and super-

seded the others, and became the prevailing one.

15. MARBURG AND THE OTHER TRENDS IN ECONOMIC METHODOLOGY

After having tried to illustrate the explanatory power of the Marburg epistemology, I

conclude by trying to roughly determine its position in relation to some of the other

principal trends in economic methodology. First of all, the starting point of the Marburg

Neo-Kantianism is �the fact of science� which means that the Marburg epistemology

aims to understand economics as it is, without trying to dispense recipes for economic

inquiry, without attempting to decide whether economics meets some alleged �right�

methodological rule, without dealing with demarcation issues (�Is economics really a

science?�) of a Popperian nature. The Marburg epistemology aims to be a positive phi-

losophical theory of scientific knowledge, not a normative doctrine. In the recent litera-

ture, the epistemological position that is closest to the Marburg one is that of Rappaport.

Referring to a suggestion made by Gibbard and Varian (1978), Rappaport calls attention

to the fact that much economic theorizing is based on the construction of models and

their use in various cognitive activities. He claims that economists put forward models

for the purpose of resolving conceptual and normative problems. In doing so, they �do

not put forward these models as true descriptions of reality� (Rappaport 1998: 138). Al-

though Rappaport�s study on the nature, uses, and types of models is certainly useful, in

my opinion, it fails to investigate why these models, even if �false�, can play the funda-

mental role in economic knowledge that Rappaport himself highlights, and which for

the Marburg School is related to the tendency of the understanding to an exact recon-

struction of experience.

As pointed out in Section 1, with regard to the non descriptive nature of scientific

theories, there is some affinity between the Marburg cognitive fictionalism and instru-

mentalist fictionalism which in economics is usually associated with the methodological

positions of Friedman and Machlup. Friedman�s position is the more distant from the

Marburg one since he quite univocally stresses the idea that scientific theories are tools

used to make predictions, and sometimes claims that �in general, the more significant

[is] the theory, the more unrealistic [are its] assumption� (Friedman 1953: 14). This the-

sis upon the irrealism of the assumptions is alien to the Marburg School, which just af-

firms that assumptions can be unrealistic. Machlup is less distant from Marburg Neo-

28

Kantianism since he does not even mention the irrealism of assumption thesis and

points out that theories not only serve as an instrument to predict but also �as an instru-

ment of explanation� of phenomena (Machlup 1955: 12).

With respect to the methodological trends that try to understand economic science

and explain its historical developments on the basis of extra-scientific factors � dis-

course analysis, as in the rhetorical approach; social factors, as in the sociology of scien-

tific knowledge (SSK); self-interest, cost-benefit calculation, marketplace of ideas etc.

as in the economics of scientific knowledge (ESK) � the Marburg epistemology is in

flagrant contrast31. Obviously (economic) science is a human activity, and as such, is in-

fluenced by the following factors: communication skills and persuasion strategies, quest

for wealth and status, customs and fashions, good or bad functioning of selection

mechanisms and institutions, ability to raise funds or create network relationships,

youthful creativity or attachment to old ideas, opportunities and chance. However, if

one considers at least 20-30-year time spans, the success or the abandonment of a re-

search program appear to depend foremost on theoretical factors, which characterize

that particular human activity which is scientific knowledge. I did not discuss here the

general question of whether the internal rather than the external factors are, in the end,

the crucial ones in determining what goes on in (economic) science. I simply contend to

have shown that an �old-fashioned, internal and ultra-Whiggish� reconstruction, like the

Neo-Kantian-inspired one presented here, can still be a sufficiently powerful resource to

account for the history and the logic of neoclassical theory without resorting to extrinsic

explanations.

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