Alexander Mahr, Geht die Theorie der Indifferenzkurven von haltbaren Voraussetzungen aus? Eine Entgegnung (1956)

Alexander Mahr’s journal rejoinder defends Hans Mayer’s criticism of indifference-curve theory against Bäsmann and restates his own further objection. Its central claim is that mathematical precision cannot compensate for assumptions incompatible with consumers’ needs and conduct. Mahr organizes the reply around the empirical standing of Pareto’s indifference curves, the limitations of substitution between consumption goods, and the consequences for Hicks’s marginal rate of substitution. The dispute concerns not principally whether utility can be measured, but whether the relations represented by the theory adequately describe economic behaviour.

Mahr begins by arguing that Bäsmann has missed the substance of the objections he claims to refute. Bäsmann relies on Mayer’s shorter discussion of subjective value rather than his more extensive criticism of functional price theories. Against Mayer’s description of Pareto’s experiment as fictitious, Bäsmann invokes modern scientific conceptions of experimentation and observation. Mahr responds that this does not establish that Pareto actually performed an experiment. The issue is the evidential basis of the construction, not its compatibility with a methodological vocabulary.

The next exchange concerns continuous curves and the assumption of infinitely divisible goods. Bäsmann’s example of fractional automobile consumption per head does not, for Mahr, answer an objection about individual consumption. An aggregate average can be statistically meaningful without representing a quantity available to an individual consumer. Drawing on Mayer, Mahr stresses that the same aggregate demand can produce different prices according to its distribution among persons. Economic explanation must therefore connect individual needs, possessions, and valuations with social outcomes; statistical averages cannot simply replace those individual relations.

The decisive objection concerns unrestricted substitutability. Mahr reproduces Mayer’s argument that different goods satisfy qualitatively different needs. Increasing wine cannot indefinitely compensate for diminishing bread, any more than additional salt can make good an arbitrarily large reduction in food. These examples challenge the generality of the substitution principle rather than denying every possibility of substitution. Mahr accuses Bäsmann of passing over this objection and turning instead to utility measurement:

Ob der Nutzen oder der Index des Nutzens oder sonstige davon abgeleitete Grössen messbar sind oder nicht, ist sicherlich interessant im Rahmen einer Untersuchung über die Messbarkeit oder Rechenbarkeit der subjektiven Werte, wie sie Mayer in der zweiten der vorhin zitierten Abhandlungen tatsächlich vorgenommen hat, ist aber völlig unerheblich für die Beurteilung der Frage, ob die Theorie der Indifferenzkurven irgendeiner empirischen Verifikation fähig ist.

English translation: Whether utility, the index of utility, or other quantities derived from it are measurable or not is certainly interesting within an investigation into the measurability or calculability of subjective values, such as Mayer actually undertook in the second of the previously cited studies, but is entirely irrelevant to assessing whether the theory of indifference curves is capable of any empirical verification.

This distinction determines the burden of proof. Bäsmann would have to show that increasing one of any two consumption goods could preserve utility despite an arbitrarily severe reduction in the other. Mahr regards that claim as untenable. He also resists Bäsmann’s suggestion that preference orderings refer primarily to the empirical data being explained and only incidentally to human beings: for Mahr, a demand theory cannot evade objections concerning the conduct its assumptions purport to represent.

His methodological position is not a wholesale rejection of mathematics. He explicitly acknowledges valuable mathematical results elsewhere in economics, while questioning their application to needs and subjective valuations:

Es genügt nicht, wenn moderne Wirtschaftstheoretiker sich die Naturwissenschaften bloss in ihrem Streben nach möglichst weitgehender Quantifizierung und nach mathematischer Formulierung der Beziehungen zwischen den in Betracht kommenden Grössen zum Muster nehmen.

English translation: It is not enough for modern economic theorists to take the natural sciences as their model merely in their pursuit of the greatest possible quantification and of mathematical formulation of the relationships between the quantities under consideration.

The accompanying demand is for impartial observation and exact representation of facts, particularly economically relevant psychological processes and typical behaviour. Formal exactness must remain answerable to descriptive accuracy.

Mahr then introduces the objection he considers to go beyond Mayer’s: the assumption of indefinitely many equally valuable consumption combinations. His alternative begins from a uniquely favourable quantity ratio in a concrete situation:

Natürlich gibt es zahllose Möglichkeiten in der Kombination von Verbrauchsgütern, und diese offenkundige Tatsache war der Ausgangspunkt für die Konstruktion der Indifferenzlinien. Aber diese Kombinationen sind in Wahrheit alles andere als indifferent.

English translation: Of course there are countless possibilities for combining consumption goods, and this obvious fact was the starting point for constructing indifference curves. But these combinations are in fact anything but indifferent.

Insufficient income often prevents the consumer from realizing the preferred ratio and forces a less advantageous combination. Rising income can consequently improve the ratio until the individual reaches an “ideal” combination. Mahr distinguishes the existence of numerous possible bundles from their alleged equivalence, although this brief rejoinder sketches rather than fully demonstrates his alternative. He refers readers to his earlier treatment, including its use of budget lines and its delimitation of situations in which quantity-ratio analysis yields theoretically relevant results.

The conclusion extends the criticism to Hicks. Because Hicks defines the marginal rate of substitution through the slope of an indifference curve and uses it to replace marginal utility, Mahr holds that it inherits the objections directed against Pareto’s system. He nevertheless leaves a narrower application open:

Die Frage, ob man nicht doch den Begriff der Grenzrate der Substitution in einem wesentlich geänderten Sinne und mit stark eingeschränktem Geltungsbereich für die ökonomische Theorie mit Vorteil verwenden könnte, geht über den Rahmen dieser Entgegnung hinaus.

English translation: The question of whether the concept of the marginal rate of substitution might nevertheless be used advantageously in economic theory, in a substantially altered sense and with a sharply restricted scope of application, goes beyond the scope of this rejoinder.

The article’s significance lies in this insistence on scope: substitution must be established for concrete needs and goods, not generalized solely through a formal construction.