The Pardox of Thrift

I'm trying to understand Keynesian business cycle theory. I think I get this much. There's a shock to the system that causes consumers to worry about the future. In order to smooth consumption, consumer spend less and save more. Spending less decreases the demand for goods and services. The resulting drop in demand for goods and services causes a drop in demand for people providing those goods and services, resulting lower GDP and unemployment.

Classical economics says that the creators of goods and services will respond to lower demand by lowering prices, and at the lower price they will be able to sell what they could have earlier. Similarly, workers will respond to lower demand by working for less.

Keynesians believe that prices and wages are sticky--that it takes time for people to understand that the labor that used to be worth more in nominal dollars, is actually worth less now in nominal terms. Thus, the necessary adjustment does not take place for some time, and that results in prolonged periods of unemployment and depressions.

Keynesians view the solution to this problem as increasing aggregate demand, or the total demand in the system for goods and services. If demand falls because of some shock to the system, it can be restored by government stepping in to supplement the demand, by spending money.

I'm having a hard time understanding the idea that saving reduces consumption, also called the paradox of thrift. Russ Robert and Steve Fazzari go a couple rounds on this point, here. I've now listened to this podcast twice, and I still don't quite get it. And I've been thinking about this occasionally since I first studied Keynes in college some years ago.

I do understand on one level that if a dollar comes to me, and I put 20 cents under my mattress, and spend 80 cents, and then someone else does the same thing (saving 20% and spending 80%) that will result in X number of dollars of economic activity. If you "save" less, and spend more, like say you save only 10%, and spend 90%, there will be more economic activity.

But "saving" in this instance is putting the money under your mattress. Saving, at least in common parlance, also means putting the money in the bank. The bank, however, is going to lend all but a small portion of that money out. So suppose you put a dollar in the bank instead of spending 90% of it, the bank will lend most of it out, and the person who get that loan will spend the money on consumption. It seems to me that, saving, then is actually mostly investing, which is also a specific type of consumption, which does not, in fact, reduce consumption, triggering the paradox of thrift.

So despite Fazzari's efforts, I don't understand the paradox of thrift.

UPDATE: ask and ye shall receive. Here is an article about Keynes by Richard Posner. Still not sure I understand the paradox, though.