I have for several days wanted to return to writing about Paris in response to the thunderous demand [well, actually one comment and two emails, but I have very acute hearing]. However, before I do, let me say just a word about mathematics and economics, which has been the subject of several very interesting lengthy comments.
I think it is a mistake to ask whether economists should use mathematics. That is like asking whether an electrician should use a Philips screwdriver. The obvious reply is, For what? The really interesting foundational questions in economics can never be answered by introducing more sophisticated mathematical techniques, fun though they are. Before all else, one must decide what questions economics should be trying to answer.
The watershed transformation in economic theory is usually identified as the so-called Triple Revolution, or Marginalist Revolution, of the 1870’s, which is to say the work done independently and more or less simultaneously by Jevons in England, Walras in France, and Menger in Austria. This complete transformation in academic economics was characterized by the introduction of the Differential Calculus, which made it possible to prove all manner of nifty theorems about consumer choice and price determination in a capitalist market.
It is easy and natural to suppose that the marginalist revolution was all about using more sophisticated mathematics, but that is, in my opinion, a complete mistake. What actually happened in the 1870’s is that economists by and large stopped asking one set of questions and started asking a different set of questions.
There are two possible explanations for the decision of academic economists to change the questions they asked. The first is that the new mathematical tools were so powerful, so flashy, such sheer fun that any really smart person interested in economics would naturally gravitate to them. The second is that the old questions were rather uncomfortable, inasmuch as the answers clearly indicated that there was something seriously rotten about the state of things in nineteenth century capitalist Europe.
What were the old questions that economists asked before the 1870’s, and what were the new questions they started to ask afterward? There were two questions that the old economists asked. They were asked by Adam Smith, they were asked by David Ricardo, and they were asked by Karl Marx. They were also asked by all the lesser lights who, together with the leading lights, defined the field known as Political Economy. The first question was: How is the annual output of a nation divided among the three great classes of society, the Landowners, the Entrepreneurs, and the Workers? The second question was: What are the conditions of economic growth, and what are the obstacles to growth? The answers changed over time, of course, and in the work of Marx were profoundly complicated by the introduction of the notions of mystification, false consciousness, and ideological rationalization, but the questions remained the same.
The new economists asked completely different questions, and when they even tried to answer the old questions, their answers, tricked out in fancy math, were transparently ideological rationalizations. The best summary statement of the new questions can be found in a classic 1932 work by Lord Lionel Robbins, An Essay on the Nature and Significance of Economic Science [notice the term “science.”] “Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses.”
Compare this question with the first question of the classical Political Economists. The classical question presupposes that society is divided economically into classes and thus virtually compels us to recognize that the interests of the classes are antagonistic to one another, inasmuch as what is appropriated each year by one class is thereby unavailable to be appropriated by the other classes. The new question of “Economic Science” presents the subject as a purely technical study of alternative inputs into production, the goal being to maximize efficiency.
For a variety of historical reasons, it appeared for quite some time that the old Political Economy was just a gentlemanly reflection on the human condition while the new Economics was SCIENCE complete with differential equations and such like. But in the 1960’s. ‘70’s, and ‘80’s a number of clued up lefty mathematical economists recast the old story in nice, shiny equations, so that it became clear what the real difference between the two traditions was.
There is nothing wrong with mathematics in economics. As I said, what matters is For What?