Foundations of Economic Analysis

"Samuelson is rightly called the father of modern mathematical economics and this book is its foundations. It was Samuelson’s doctoral dissertation that was turned into a monograph. Samuelson was a student of Edwin Bidwell Wilson, who, when Samuelson met him, was a polymath at the School of Public Health at Harvard, but had previously been a very successful mathematician and engineer. Wilson himself had been a student of J Willard Gibbs, probably the first great American mathematical physicist. He developed much of the modern theory of thermodynamics and was one of the first Americans able to genuinely compete with the greatest European scientists in the nineteenth century. So Samuelson had this direct academic lineage back to Gibbs and what is striking about this book is the extent to which this new economic science that Samuelson was introducing was so strongly in the Gibbsian tradition – it was doing economics the way that Gibbs did thermodynamics and statistical physics. Get the weekly Five Books newsletter The basic idea here is that one can relate certain postulates about how individual atoms – or in Samuelson’s case individual investors and consumers – behave with higher level statistical treatments and even general macroscopic observables. The idea is that one can treat a box of gas in terms of things like its temperature, pressure and volume and derive formulas relating them to one another while ignoring the details of what each individual particle is doing. That one can develop a whole theory of gases, heat and of engines, using those kinds of macroscopic variables was part of Gibbs’ big contribution. These are the ideas that you’ll find in Samuelson’s book – that we can use mathematics in the same way to develop statistical accounts of individual level phenomenon and also develop macroscopic, large scale treatments of things like inflation, GDP and economy wide variables. He saw very clearly that you could treat economies as a whole mathematically and that there was a statistical relationship between economy wide variables and the behaviours of people who make up an economy. What makes it relevant today is that basically it’s where everything in mathematical economics comes from. What’s striking from the point of view of science and markets is that we tend to think that sometime in the 1980s and 1990s, physicists started coming to Wall Street and the City of London introducing new ideas that changed economics and finance. Samuelson’s book makes clear how important statistical physics was at the very beginning of mathematical economics."