Paul Krugman warns against “caricaturing” Keynesian economics, and in particular the General Theory (GT), Keynes’s best known work. One caricature heard from time to time is that the book is not mathematically tractable. The caricature also claims that no one has succeeded in fitting such a contradictory and confusing bunch of arguments into a clear, mathematically coherent model. Okay, in the spirit of a concession to these macro skeptics, what follows is a schematic caricature of sorts that seems okay to me as a broad summary of the first 18 chapters or so of the book, from a classic book by Pasinetti. So for those who insist that (1) they need a preview in a very concise form or (2) that they will never have time for the lengthy and complicated GT, below is the aforementioned schema. It is only meant to show that one can in fact simplify this oft-misinterpreted work quite a bit using mathematical symbols and keep the gist of the first part of the story.
where the variables are defined as follows:
L = liquidity preference (psychological factors affecting long-term interest rates, especially expected future rate changes)
M-overbar = policy-determined money supply
I = nominal interest rate
E = expected profitability of investment projects, given economic conditions
C = consumption
I = investment
Y = total output
All arrows (→) show directions of causality, so that A→B means that knowing A allows us to determine B.
Finally, f(), ψ(), and φ() signify functions endowed with properties that allow one to use math to analyze the model.
(I have altered some of Pasinetti’s notation slightly.)
As Pasinetti points out, this causal schema is different from Krugman’s favored IS-LM model, and it does leave out much that is important, including changes in the numéraire (chapter 19) and long-run dynamics, which the formal argument left up in the air. In a footnote, Pasinetti says that the model is only a first approximation to Keynes’s theory, and that care should be taken with attempts to do exercises involving shifts in the curves. But while Pasinetti’s schema, and the simple model it represents, certainly succeeds in simplifying the GT, it is really not a caricature. The original version of the schema can be found in Growth and Distribution, by Luigi Pasinetti, chapter II, Cambridge University Press, a 1974 collection of generally lucid essays (publisher’s book site).