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miércoles, 13 de agosto de 2014

Discrete marginalism, despite being non-mathematical, is superior to neoclassical marginalism.



by Mateusz Machaj

One often wonders whether differences in economic schools of thought are big enough to justify strict theoretical segregations. One such case is “marginal economics.” Most textbooks point to the triumvirate of Walras, Jevons, and Menger, who independently discovered the notion of marginal utility and its relevance to the pricing process. Quite often these brilliant thinkers are homogenized as more or less indistinguishable figures who paved the way for modern microeconomic theory.

The usual simplification of the history of economic thought will tell us that the big three introduced concepts of marginalism and marginal utility into economic science (the exact name “marginal utility” came from Friedrich von Wieser). In general, marginalism was introduced to combat the belief of classical economists that prices have not much to do with individual utility and consumer satisfaction (since many useful things have low prices, as the so-called paradox of value demonstrated). The biggest contribution of the marginal revolutionaries was to invite the concept of utility back into newly-rebuilt consumer theory. Consequently, economics became a much more universal science than it had been.

It cannot be denied that Walras, Jevons, and Menger all played major roles in the advancement of modern consumer theory. Marginal units and marginal utility well-explained how prices are shaped in accordance with subjective preferences and consumer choice. Yet it would be a mistake to say there were no major differences between them. Well-established economist William Jaffé published a famous article about “dehomogenization” of those thinkers. His main point was that Menger differed significantly from Walras and Jevons in presenting marginal theory with Menger’s usage of a non-mathematical apparatus. Various other authors describing the development of marginal theory also referred to this difference. Unfortunately, many of them focused on this aspect as if it somehow illustrated a deficiency of Menger’s thought in that he did not mathematized his theory. Famous Chicago economist George Stigler criticized Menger and argued that it was his main “weakness,” because he could not arrive at the concept of “maximizing want satisfaction.” In other words, Stigler claims Menger's theory is inferior because he did not write equations and present his conclusions in the form of a mathematical apparatus.

Mathematical marginalism can indeed appear to be more rigorous. But just because it looks more complicated does not mean it is a better description of the valuation process. Menger’s so-called weakness is actually his strength, because it adds a more fruitful dimension to marginal theory, which was completely absent in the mathematical approaches of Jevons and Walras. Even though all three economists are seen as referring to “marginal units,” in Menger, this concept means something other than what it does in Jevons and Walras. In the case of Jevons and Walras, marginal units are infinitely small, continuous, and in consequence almost irrelevant. It becomes a part of a broader utility function which can be “maximized” as Stigler wishes with the use of various derivatives.

In the case of Menger, “marginal” units are something else. They are finite and discrete, not continuous, and therefore it is not part of some broader already-existing utility function which can be maximized with the use of derivatives (since only continuous functions can have derivatives).

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