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Sunday, June 15, 2003

All I Learnt about the World I Learnt from a Phase Diagram

Professor David Begg (formerly of Birkbeck, now principal of Imperial College Business School) once told us that in the 1970s phase diagrams were the rage in economics. While studying for my macroeconomics final two weeks ago it was hard to see why. You spend a while deriving a differential equation that tells you how to achieve the steady state (the long-run rate of economic growth, say, or the trend rate of inflation) and then you draw a phase diagram that tells you how you get there. The rest of the analysis is to show what happens when some externally-determined ("exogenous") variable changes, and how or whether you get back to the steady state in the long run.

So far, so good, those of you who are still reading might say. My point is that most of this analysis takes place through the diagram, not through the calculus. This is good, to a point; it does make the subject matter more interesting, I think. It is also a bit of a rejoinder to those who complain about too much formalism in neoclassical economics--the diagram does help you to understand what is going on, and how change works through the economy.

At the same time, though. it is a bit odd. I can't imagine anyone standing in front of a meeting of experts and saying "if we do this, it should take us on a smooth path to the steady state". (I could be wrong about this--after all, the term "equilibrium" does come up pretty often in stability analysis.) This matters more especially if, with the given data we have, we often don't know where the steady state actually is, though a lot of policy, it would seem, is driven to trying to get to this nirvana, or somtimes to escape from it (for example, the natural rate of unemployment).

I guess this post is about meaning. Two years ago, when I first learnt calculus (yes, i was that bad) My wonderul quantitative techniques lecturer, Tony Humm, explained why economists use calculus. It was wonderful--it all became clear. I understand and like differential equations and their resulting phase diagrams, but I can't help but feel something is missing.