The Sweeneys describe an economy where goods (babysitting) are exchanged for money (scrip) at a fixed price level of one piece of scrip exchanges for one-half hour of babysitting. The system works well when there is the right amount of scrip to support the set price as the equilibrium price. When this isn't the case, things fall apart. When things work, people have scrip so use it to get babysitting, and then if they want more scrip, they must do some babysitting themselves. However, when there's not enough scrip in the system, we get a recession. That is, since the value of scrip can't rise due to the fixed prices, people find that one half hour of babysitting isn't worth the value of hoarding scrip in case of an emergency (scrip's value as a store of value means it's not used as much as a medium of exchange). This problem would go away if more scrip is injected into the system or if the value of scrip is allowed to rise, perhaps to one piece of scrip being worth an hour of babysitting. Then the real value of the (money) scrip supply would be great enough to handle the transactions needed. On the other hand, when there's too much scrip in the system, it would be good if the value of scrip were allowed to fall, perhaps to one piece of scrip being worth 15 minutes of babysitting. Since that isn't allowed, too much scrip in the system wrecks the economy also because people find that they've already got all the scrip they ever plan to need and so see no need to do any babysitting to gain more. In the case of the fixed price level in this economy, too much or too little scrip causes the amount of babysitting done to fall to overly low levels.
Joan and Richard Sweeney, "Monetary Theory and the Great Capital Hill Baby Sitting Co-op Crisis", Journal of Money, Credit, and Banking, February 1977 (Don't worry about the math of inflow and outflow of scrip)
Here is a PDF of the original article
For an interesting view on economies like those described by the Sweeney's and how they relate to this topic, see these articles by Paul Krugman: