Indeed, Krugman's presentation doesn't incorporate any of the more sophisticated arguments about the financial system of such old-line, hard-core Keynesians as James Tobin. He moreover completely ignores any possible complications arising from Ricardian Equivalence, essentially knocking down straw-men objections to fiscal policy. No other Krugman article has come closer to convincing me that John Cochrane is in fact right: Krugman doesn't actually know or understand much modern macroeconomics, as Krugman himself comes close to admitting at the article's beginning.
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Nor do I think, if you really want to get a perspective on Krugman's article, that the way to go is to get into Talmudic distinctions between Say's Law and Say's Identity, as Pete [Boettke] suggests. Instead I would recommend slogging through Don Patinkin's massive classic, Money, Interest, and Prices: An Integration of Monetary and Value Theory, the second edition of which was published way back in 1965. It had become the standard fare in all graduate monetary theory classes before the New Classical revolution swept the profession with dynamic stochastic general equilibrium models. Patinkin actually considered himself a Keynesian, which is why his careful, rigorous, and exhaustive comparisons between classical and Keynesian approaches are so telling and insightful.