The Fisher – Becker Curio
from Edward Fullbrook
Yesterday evening Merijn Knibbe put up this comment on Lars Syll’s post Utility maximization — explaining everything and nothing.
One of the features of the utility model is that it ´explains´ the downward sloping demand curve, a cornerstone of economics. Which means that neoclassical demand theory seems a pretty coherent building with sound foundations.
It does not explain the downward sloping demand curve. It is only consistent with this curve. And in 1962 Gary Becker showed, in an article called ´Irrational behavior and economic theory´, that many models can ´explain´ a downward sloping demand curve when money is limited, including the throw of a dice. Ockhams razorblade requires us to use the simplest model… http://mcadams.posc.mu.edu/econ/Becker,%2520Irrational%2520Behavior.pdf
Becker himself seems not to have grasped the implications of his article, which shredded neoclassical demand theory. Accepting that demand curves very often slope downwards does not mean that one has to accept utility theory.
My paper (http://www.paecon.net/Fullbrook/IntersubjectiveTheoryofValue.pdf) “An Intersubjective Theory of Value”, in Intersubjectivity in Economics: Agents and Structures, editor Edward Fullbrook. London and New York: Routledge, 2002, pp. 273-299, includes a subsection on the theoretical anomaly noted by Gary Becker in his 1962 paper. But that anomaly had been noted with somewhat greater depth and sophistication by Irving Fisher in 1920. Neither economist, however, was capable of understanding the profound significance of the anomaly, because to do so requires a bit of abstract algebra, which, unfortunately, is not part of the economist’s standard tool kit. Below is the relevant section form my 2002 paper. The first part of that paper includes a gentle introduction to the mathematical ideas missing from Fisher’s book and Becker’s paper.
13 b. The Fisher – Becker Curio
Gary Becker [1962, 1971] showed that from the existence of budget constraints alone it follows that a market demand curve must slope downward, whether consumer behavior is rational or not. By beginning his analysis at the level of the market, rather than at the level of the individual, Becker shows that there exists a macro budgetary effect which entails “the basic demand relations”. [Becker, 1971, p. 11] In other words, scarcity of funds is a condition for negative sloping market demand curves, and rational consumer behavior is not a necessary condition. In fact, Becker showed that the whole of the subjective side of demand theory is otiose when it comes to the deduction of the general inverse relation between price and quantity demanded at the market level.
Becker’s result needed an explanation which would integrate it into a larger theoretical edifice, but none was forthcoming. Without this theoretical grounding, Becker’s “scarcity principle” remained an anomaly and, therefore, survives today only as a curious and obscure footnote to economics, with students continuing to be taught that the downward slope of the market demand curve is due to intrasubjective factors.
But Gary Becker was not the first to point out the budget effect, that is, “the effect of a change in prices on the distribution of opportunities.” [Becker, 1962, p. 6]. With a different emphasis and at a higher level of aggregation, Irving Fisher noticed and expounded on the same macro dimension of relative prices forty years earlier. In The Purchasing Power of Money, Fisher writes:
“if one commodity rises in price (without any change in the quantity of it or of other things bought and sold, and without any change in the volume of circulating medium or in the velocity of circulation), then other commodities must fall in price. The increased money expended for this commodity will be taken from other purchases.” [1920, p. 178]
Note that here Fisher is not considering the absolute level of prices, which he assumes constant, but rather relative prices and how at the macro level there exists an interdependency between them. Fisher realized, in a way that Becker did not, that his discovery posed a major paradox for economics. [1920. p. 180] Furthermore, because Fisher carries the analysis to a higher level of aggregation, he comes much closer than does Becker to discovering the boolean structure of exchange-value. His nearness to this elementary truth becomes apparent when two terms of his foregoing passage are translated into the terminology of the present paper. Substituting “exchange-value per unit” for Fisher’s “price” and “measured exchange-value” for his “money expended” yields the followings statement:
If one commodity rises in exchange-value per unit (without any change in the quantity of it or of other things bought and sold, and without any change in the volume of circulating medium or in the velocity of circulation), then other commodities must fall in exchange-value per unit. The increased measured exchange-value for this commodity will be taken from [the exchange-value of] other purchases.
Thus translated, Fisher’s passage captures “the part of the whole” relation which, as for probability, is one dimension of exchange-value. It captures also the fact that, despite all the concrete individuality that goes into exchange-value’s making, the exchange-value of every unit of every commodity is irreducibly and fundamentally a SOCIAL relation that extends as far as does the economy in which the exchange of the unit takes place.
What Fisher could not do was explain how the micro and macro levels of “causation” were linked. His insight, like Mendel’s discoveries concerning heredity, lacked a contemporaneous means of explanation. Abstract algebra was little known, and without this set of tools the boolean structure which links exchange-value’s two levels of “causation” could not be identified.4