1. Logically, insufficient demand for goods implies excess demand for money, and vice versa.
2. Causally, excess demand for money (i.e. an increase in liquidity preference or a fall in the money supply) is what leads to insufficient demand for goods.
3. The solution is for the monetary authority to increase the supply of money.
Quasi-monetarists say that 2 is true and 3 follows from it. Kaspar says that 2 doesn't imply 3, and anyway both are false. And Krugman says that 3 is false because of the zero lower bound, and it doesn't matter if 2 is true, since asking for "the" cause of the crisis is a fool's errand. But everyone agrees on 1.
Me, though, I have doubts.
An overall shortfall of demand, in which people just don’t want to buy enough goods to maintain full employment, can only happen in a monetary economy; it’s correct to say that what’s happening in such a situation is that people are trying to hoard money instead (which is the moral of the story of the baby-sitting coop). And this problem can ordinarily be solved by simply providing more money.For those who don't know it, Krugman's baby-sitting co-op story is about a group that let members "sell" baby-sitting services to each other in return for tokens, which they could redeem later when they needed baby-sitting themselves. The problem was, too many people wanted to save up tokens, meaning nobody would use them to buy baby-sitting and the system was falling apart. Then someone realizes the answer is to increase the number of tokens, and the whole system runs smoothly again. It's a great story, one of the rare cases where Keynesian conclusions can be drawn by analogizing the macroeconomy to everyday experience. But I'm not convinced that the fact that demand constraints can arise from money-hoarding, means that they always necessarily do.
Let's think of the baby-sitting co-op again, but now as a barter economy. Every baby-sitting contract involves two households  committing to baby-sit for each other (on different nights, obviously). Unlike in Krugman's case, there's no scrip; the only way to consume baby-sitting services is to simultaneously agree to produce them at a given date. Can there be a problem of aggregate demand in this barter economy. Krugman says no; there are plenty of passages where Keynes seems to say no too. But I say, sure, why not?
Let's assume that participants in the co-op decide each period whether or not to submit an offer, consisting of the nights they'd like to go out and the nights they're available to baby-sit. Whether or not a transaction takes place depends, of course, on whether some other participant has submitted an offer with corresponding nights to baby-sit and go out. Let's call the expected probability of an offer succeeding p. However, there's a cost to submitting an offer: because it takes time, because it's inconvenient, or just because, as Janet Malcolm says, it isn't pleasant for a grown man or woman to ask for something when there's a possibility of being refused. Call the cost c. And, the net benefit from fulfilling a contract -- that is, the enjoyment of going out baby-free less the annoyance of a night babysitting -- we'll call U.
So someone will make an offer only when U > c/p. (If say, there is a fifty-fifty chance that an offer will result in a deal, then the benefit from a contract must be at least twice the cost of an offer, since on average you will make two offers for eve contract.) But the problem is, p depends on the behavior of other participants. The more people who are making offers, the greater the chance that any given offer will encounter a matching one and a deal will take place.
It's easy to show that this system can have multiple, demand-determined equilibria, even though it is a pure barter economy. Let's call p* the true probability of an offer succeeding; p* isn't known to the participants, who instead form p by some kind of backward-looking expectations looking at the proportion of their own offers that have succeeded or failed recently. Let's assume for simplicity that p* is simply equal to the proportion of participants who make offers in any given week. Let's set c = 2. And let's say that every week, participants are interested in a sitter one night. In half those weeks, they really want it (U = 6) and in the other half, they'd kind of like it (U = 3). If everybody makes offers only when they really need a sitter, then p = 0.5, meaning half the contracts are fulfilled, giving an expected utility per offer of 2. Since the expected utility from making an offer on a night you only kind of want a sitter is - 1, nobody tries to make offers for those nights, and the equilibrium is stable. On the other hand, if people make offers on both the must-go-out and could-go-out nights, then p = 1, so all the offers have positive expected utility. That equilibrium is stable too. In the first equilibrium, total output is 1 util per participant per week, in the second it's 2.5.
Now suppose you are stuck in the low equilibrium. How can you get to the high one? Not by increasing the supply of money -- there's no money in the system. And not by changing prices -- the price of a night of baby-sitting, in units of nights of baby-sitting, can't be anything but one. But suppose half the population decided they really wanted to go out every week. Now p* rises to 3/4, and over time, as people observe more of their offers succeeding, p rises toward 3/4 as well. And once p crosses 2/3, offers on the kind-of-want-to-go-out nights have positive expected utility, so people start making offers for those nights as well, so p* rises further, toward one. At that point, even if the underlying demand functions go back to their original form, with a must-go-out night only every other week, the new high-output equilibrium will be stable.
As with any model, of course, the formal properties are less interesting in themselves than for what they illuminate in the real world. Is the Krugman token-shortage model or my pure coordination failure model a better heuristic for understanding recessions in the real world? That's a hard question!
Hopefully I'll offer some arguments on that question soon. But I do want to make one logical point first, the same as in the last post but perhaps clearer now. The statement "if there is insufficient demand for currently produced goods, there must excess be demand for money" may look quite similar to the statement "if current output is limited by demand, there must be excess demand for money." But they're really quite different; and while the first must be true in some sense, the second, as my hypothetical babysitting co-op shows, is not true at all. As Bruce Wilder suggests in comments, the first version is relevant to acute crises, while the second may be more relevant to prolonged periods of depressed output. But I don't think either Krugman, Kaspar or the quasi-monetarists make the distinction clearly.
EDIT: Thanks to anonymous commenter for a couple typo corrections, one of them important. Crowd-sourced editing is the best.
Also, you could think of my babysitting example as similar to a Keynesian Cross, which we normally think of as the accounting identity that expenditure equals output, Z = Y, plus the behavioral equation for expenditure, Z = A + cY, except here with A = 0 and c = 1. In that case any level of output is an equilibrium. This is quasi-monetarist Nick Rowe's idea, but he seems to be OK with my interpretation of it.
FURTHER EDIT: Nick Rowe has a very thoughtful response here. And my new favorite econ blogger, the mysterious rsj, has a very good discussion of these same questions here. Hopefully there'll be some responses here to both, soonish.
 Something about typing this sentence reminds me unavoidably of Lucky Jim. This what neglected topic? This strangely what topic? Summary of the quasi-what?
 Can't help being bugged a little by the way Krugman always refers to the participants as "couples," even if they mostly were. There are all kinds of families!