One of the constant themes in Keynesian (and Krugmanian) economics is the evil of savings, and how government must manipulate the currency and the banking system in order to discourage people from saving money. On a number of occasions in his columns and blog posts, Krugman has invoked the hoary "paradox of thrift" which uses the Fallacy of Composition to declare that while it might be OK for a few individuals to save a few bucks here and there, it is disastrous if everyone saves at once.
In a recent blog post, Krugman once again claims that if the rate of savings goes up, GDP automatically goes down and the economy plunges into recession. (The post is primarily about the methodology of comparative statics, which all economists use in one way or another, but nonetheless his example is very telling. It is one thing to use comparative statics to demonstrate the effects of a tax on coffee and quite another to use the same method for savings and GDP, as they are not the same thing even though Krugman wants us to believe that we examine these things in exactly the same way.)
This example "proves" that if people save money, then GDP must fall. When people save money, Keynesians argue, not all of it is invested immediately, so when some current spending is eliminated but is not immediately spent as investment, there is a lull in which the economy is dragged down. Furthermore, they argue, once the economy starts to plunge, unless government immediately disrupts the pattern by spending and also inflating (which undermines savings), then aggregate demand will fall and investors will fail to create new capital, since they don't anticipate demand for the products it will help produce.
The Keynesian Multiplier, along with graphs such as what Krugman trots out, are shown as "proof" of this point. The Multiplier is expressed as 1/savings rate (Marginal Propensity to Save) which also can be expressed as 1/(1 - Marginal Propensity to Consume).
For example, say the MPC is 80 percent (or 0.8) and the MPS, then would be 20 percent (or 0.2). In other words, people in an economy would spend 80 percent of their income and save 20 percent. Thus, the Multiplier would equal 1/0.2 or 5. However, if people saved only one percent of their income, then the Multiplier would be 1/0.01 or 100, which "proves" that the less we save, the more prosperous we will be.
(I must admit that this reminds me of the saying we had when I was in high school, which began with "The more you study, the more you know," and finally was able to end, after some "logical" progressions, to "The less you study, the more you know. So why study?")
An obvious questions arises: If savings is bad, why not have a zero savings rate, which then would give us a multiplier of infinity? Keynes, when faced with that same question, declared that at that point, inflation would skyrocket, although he did not explain why that would be a bad thing, given that Keynesianism is based upon the "magic" of inflation, anyway.
This economic viewpoint, however, is based upon a nuanced view of capital, that it is homogeneous AND that the value of capital formation is in the spending that takes place, not with capital itself. And, Keynesians argue, because increased savings lower the value of the Multiplier, that the "solution" is for people not to save (or save as little as possible) and depend upon government or the central bank (or both) to manufacture the money needed for capital investment out of thin air.
All of this crashes, however, if capital is heterogeneous. Furthermore, if capital can be malinvested -- and Austrians argue that will be the case when capital is created via inflation -- then the Keynesian scheme is destined to end in disaster.
That is what we are seeing now. For more than two decades, the government has followed the pattern of inflating, running into malinvestments, inflating the economy into "recovery," and then dealing with future crashes that are larger. We have seen the Tech Bubble and collapse, the Housing Bubble and collapse, and now the governments around the world have created the Sovereign Debt Bubble which is destined to collapse.
Krugman can use all of the graphs and math that he wants, but he cannot get around the sticky problem of heterogeneous capital, nor does he have an answer for malinvestments. His M.0. has been to state his case and then attack anyone who disagrees, claiming that their disagreement is based upon their fundamental desire for people to suffer and to be out of work. That is not economics, but then Keynesianism is not economics, either.