Alice, Bob, and Sue have ten marbles between them. Whenever one kid wants another kid to take over a chore, she promises a marble in exchange. Alice doesn't like setting the table, so she promises Bob a marble if he will do it for her. Bob hates mowing the lawn, but Sue will do it for a marble. Sue doesn't like broccoli, but if she says pretty please and promises a marble, Bob will eat it off her plate when Mom isn't looking.
One day, the kids get together to brag about all the marbles they soon will have. It turns out that, between them, they are promised 40 marbles! Now that is pretty exciting. They've each promised to give away some marbles too, but they don't think about that, they can keep their promises later, after they've had time to play with what's coming. For now, each is eager to hold all the marbles they've been promised in their own hands, and to show off their collections to friends.
But then Alice, who is smart and foolish all at the same time, points out a curious fact. There are only 10 marbles! Sue says, "That cannot be. I have earned 20 marbles, and I have only promised to give away three! There must be 17 just for me."
But there are still only 10 marbles.
Suddenly, when Bob doesn't want to mow the lawn, no one will do it for him, even if he promises two marbles for the job. No one will eat Sue's broccoli for her, even though everyone knows she is promised the most marbles of anyone, because no one believes she will ever see those 17 marbles she is always going on about. In fact, dinnertime is mayhem. Spoons are placed where forks should be, and saucers used for dinner plates, because Alice really is hopeless in the kitchen. Mom is cross. Dad is cross. Everyone is cross. "But you promised," is heard over and over among the children, amidst lots of stomping and fighting. Until recently, theirs was such a happy home, but now the lawn is overgrown, broccoli rots on mismatched saucers, and no one trusts anyone at all. It's all a bit mysterious to Dad, who points out that nothing has changed, really, so why on Earth is everything falling apart?
Perhaps Mom and Dad will decide that the best thing to do is just buy some more marbles, so that all the children can make good on their promises. But that would mean giving Alice 19 marbles, because she was laziest and made the most promises she couldn't keep, and that hardly seems like a good lesson. Plus, marbles are expensive, and everyone in the family would have to skip lunch for a week to settle Alice's debt. Perhaps the children could get together and decide that an unmet promise should be worth only
a quarter some fraction of a marble, so that everyone is able to keep their promises after all. But then Sue, the hardest working, would feel really ripped off, as she ends up with a much more modest collection of marbles than she had expected. Perhaps Bob, the strongest, will simply take all the marbles from Alice and Sue, and make it clear than none will be given in return, and that will be that. Or, perhaps Alice and Bob could do Sue's chores for a while in addition to their own, extinguishing one promise per chore. But that's an awful lot of work, what if they just don't want to, who's gonna force them? What if they'd have to be in servitude to Sue for years?
Almost whatever happens, the trading of chores, so crucial to the family's tidy lawns and pleasant dinners, will be curtailed for some time. Perhaps some trading will occur via exchange of actual marbles, but this will not be common, as even kids see the folly of giving rare glass to people known to welch on their promises. It makes more sense to horde.
A credit crisis arises when many more promises are made than can possibly be kept, and disputes emerge about how and to whom promises will be broken. It's less a matter of SIVs than ABCs.
Update: Mark Thoma offers characteristically thoughtful comments. I also liked this, by Alex Whalen. (BTW, I don't have children, though my wife is urging we remedy that soon.) In the comments, Arun Garg is reminded of Paul Krugman's Baby-sitting Co-op, whose influence I'm happy to acknowledge. Krugman is a master of this sort of parable, see also hot dogs and buns.
Update 2: (Not for kindergarteners!) There've been comments here and elsewhere suggesting that the numbers in this story can't be made to work. They can. Note that the 40 marbles the children think they have is before netting. As the piece says, "They've each promised to give away some marbles too, but they don't think about that, they can keep their promises later, after they've had time to play with what's coming." That's realistic. It's why people who borrow from banks think they have cash, even though, if you net it out, that cash is offset by a liability to the bank. On idealized balance sheets, the promises made to us are represented as assets. The promises we've made are our liabilities, and the promises that can't be kept show up as negative equity. On net, across people, all promises sum to zero, and all equity sums to the real value of all the stuff. It's the distribution of gross numbers that gives rise to a credit crisis. It's an accounting identity that, on net, everything balances. But that doesn't help anybody.
For the very geeky among you, click the link below to reveal balance sheets that comport with this tale.
Physical marbles: 4
Marbles promised from Bob: 0
Marbles promised from Sue: 2
Total assets: 6
Marbles owed to Bob: 7
Marbles owed to Sue: 18
Total liabilities: 25
Physical marbles: 6
Marbles promised from Alice: 7
Marbles promised from Sue: 1
Total assets: 14
Marbles owed to Alice: 0
Marbles owed to Sue: 2
Total liabilities: 2
Physical marbles: 0
Marbles promised from Alice: 18
Marbles promised from Bob: 2
Total assets: 20
Marbles owed to Alice: 2
Marbles owed to Bob: 1
Total liabilities: 3
Update 3: (Only for very neurotic grownups!) The balance sheets posted in "Update 2" miss a constraint implied by the tale. It is claimed that, if promises were devalued to a quarter marble, everyone would be solvent. But given the posted balance sheets,, Alice would still be underwater. One can come up with balance sheets consistent with the constraint, but in doing so one runs afoul of another implication of the text, that Bob owes Sue more than Sue owes Bob. I don't think that both constraints can be satisfied. So, I'm changing the text, from "a quarter" to "some fraction", because it's the right thing to do. I think everything works out now, and the balance sheets previously posted are fine.
- 20-Mar-2008, 1:30 p.m. EDT: Added update re Thoma, Whalen, and Garg comments, Krugman acknowledgement.
- 20-Mar-2008, 6:40 p.m. EDT: Added update 2 with balance sheets.
- 20-Mar-2008, 6:40 p.m. EDT: Added sentence about bank loans to update 2. Changes a "the" to an "a" and added "not for kindergarteners" to same update.
- 24-Mar-2008, 2:05 p.m. EDT: Added update 3, struck "a quarter" and replaced it with "some fraction".
|Steve Randy Waldman — Thursday March 20, 2008 at 3:18am||permalink|