## Posts Tagged ‘**Geometry**’

## The wrong SHOE

A few weeks ago, one contributor to the SHOE (Societies for the History of Economics) list asked a seemingly simple question: “Why did Marshall reverse the axes?”. In economics, indeed, supply and demand curves for a given commodity are usually drawn with prices on the vertical axis and quantities on the horizontal one. It may seem quite puzzling to undergraduate students who cannot understand why they do so, whereas prices are generally considered the independent variable and thus, according to standard practices in graphical representation at least, should be drawn on the abscissa. As another contributor quickly pointed out, the more common answer to this question is given in Mark Blaug and Peter John Lloyd’s *Famous Figures and Diagrams in Economics*: Marshall used to draw his demand and supply schedules this way because he considered price to be the dependent variable. As most early 20th century English-speaking economists got their economics from Marshall’s *Principles*, they followed this tradition, even though they rather took prices as the independent variable.

The answer, as Roger Backhouse cleverly notes, is not completely satisfying from a historical point of view, even though it may hold as a methodological explanation. A historical understanding of why Marshall reversed the axes should explore the way he and his contemporary fellow economists considered the place of geometry in mathematics, the way markets operated and more generally how they regarded the status of economics as a field. Though there might not be simple and direct answers to all these questions, one can find useful elements in the existing literature on Marshall, such as Peter Groenewegen‘s or Simon Cook‘s books.

Other contributors to the SHOE list do not seem more satisfied with Blaug and Lloyd’s answer than Roger but their reasons are diametrically opposed. One scholar, for instance, complains that common explanations refer to “tradition” or “precedent” and think there should be a more “penetrating” answer. But what is history about if it is not about the construction and persistence of “traditions”? What is a historical explanation if it does not deal with “precedent”? Instead, most SHOE list members who contributed to the topic pursued, message after message, a non-historical line of inquiry. For them, there should be an ontological explanation to Marshall’s reversing of the axes: in other words, the answer should lie in the ‘very nature’ of supply and demand itself and of the mathematical equations that underlie their graphical representation. This is of course wrong from a historical point of view but it is also misleading because it offers a poor view of how visual representations operate. Sociologist of science Bruno Latour has argued, for instance, that two-dimensional representations are useful because they are both *immutable* and *recombinable*. We can manipulate them, superimpose them, even though they have different origins and scales. We can even merge them with geometry and use tools upon them – though we cannot measure the sun, we can measure a picture of the sun. The consequence of this is that we cannot reduce graphs to mathematical equations. Supply and demand graphs are not only visual representations of preexisting mathematical equations, they are artifacts that can be used subsequently to produce or spread economic knowledge. This is what economists do when they construct Edgeworth boxes or multiple quadrant diagrams – who complains about “axes reversing” in that case?

Furthermore, in the particular case of Marshall and his contemporaries, the idea that graphical analysis is separate from mathematics is obvious. As Judy Klein correctly pointed out:

According to Marshall, the method of diagrams should be seen as separate from the method of mathematical analysis. By the 1870s, graphs were not substitutes of equations or tables pegged, with apology at the end of a work for the mathematically illiterate; they were tools for exploring and describing phenomena that could not easily be captured by algebra, calculus or words.*

Therefore, it is an anachronism to want to explain Marshall’s use of supply and demand graphs by referring to the equations of supply and demand functions which we are used to think of as premises of these visual representations but which in fact were not viewed as such by Marshall and the likes at that time.

It is quite puzzling – and even saddening – to observe that people who deem themselves ‘historians’ of economics and as such contribute to a ‘history’ of economics list systematically choose to bypass the historian’s toolbox in their discussions.

* Klein, Judy L. (1995) The method of diagrams and the black arts of inductive economics. In Rima Ingrid (ed.) *Measurement, Quantification and Economic Analysis*. London, UK : Routledge, p. 113.