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Follow the Money

Brian Hayes

The Price Is Right

The economy being simulated in these models is a rather special one, based on pure, free-market trading. The exchange of assets is all that ever happens here; there is no production of new wealth, and no consumption either. Leaving out so much of the real economy is an obvious weakness, but there is a compensating advantage: What remains is a closed system. In the model, wealth is a conserved quantity, like energy or momentum. Because the total amount of wealth never changes, one person can get richer only if another grows poorer.

I find it helpful to think of this miniature economy in terms of a yard sale, where all the participants put their goods out on the lawn Saturday morning, then stroll up and down the street making trades with their neighbors. At the end of the day, after all transactions are completed, an auditor reviews everyone's inventory and calculates their new net worth.

Many economic models assume that all transactions occur at precisely the right price. Indeed, prices are correct by definition in such models: Whatever price is agreed to by a willing seller and a willing buyer is the value assigned to an asset. Given such perfect pricing, nothing interesting could ever happen in the yard-sale economy. I might trade my old toaster for your broken VCR, but if we negotiate the terms of the deal correctly, my net worth will not change in the slightest, and neither will yours.

In practice, the assumption of perfect pricing seems a little unrealistic. Some buyers are more discerning than others, and some sellers are more persuasive. There are bargains to be had, and there are bad deals—concepts that could hardly exist if we did not agree that merchandise has a true and proper value, which does not always correspond exactly to the price paid.

Even slight departures from perfect pricing bring a new dynamic to the yard-sale model. If I buy your rusty wheelbarrow and pay more than it's worth, I am left slightly poorer after the transaction, and you are a little richer. Conversely, if I pay less than fair value, I gain a little, and you lose. In either case there has been a transfer of wealth, typically a small fraction of the price paid. These transfers are where the action is in the modeled economy; as a matter of fact, the model can ignore the transaction itself—there's no need to talk about toasters and wheelbarrows—and simply consider the net transfer of wealth.

The question is: What happens when this process is repeated many times? If some of the traders are shrewder than others, you would certainly expect them to do well in the long run; likewise the perennial suckers are going to lose their shirts. But suppose that everyone is equally skillful, so that who wins and who loses is purely a matter of chance. The amount of gain and loss is also determined at random—but it's always less than the total wealth of the poorer agent, so that traders never risk losing more than they own.

Before reading on, you might try to predict what will happen in such an economy. If everyone starts out with the same bankroll, how will the assets be distributed after many random exchanges? Will the levels of wealth remain uniform? Perhaps the system will evolve toward a Gaussian distribution, with most people having a middling amount of money, while a few are very poor and a few are rich?

Figure 1. Wealth flows through a model economy . . .Click to Enlarge Image

Here is the answer given by the computer experiment: If trading continues long enough, essentially all the wealth winds up in the hands of one person. The yard-sale economy, as formulated in this model, is a winner-take-all lottery. The traders might just as well put all their goods in one big pile, and then roll the dice to decide who keeps it all. (Strictly speaking, one trader gets all the goods only if wealth is quantized—if there is some smallest unit of value below which one's worth falls to zero. If wealth can be subdivided indefinitely, the winner's share comes arbitrarily close to 100 percent but never quite gets there.)

This condensation of all property in the hands of one individual is an economic catastrophe—something like the formation of a black hole in astrophysics. It's obviously bad news for the majority of the people, who are left penniless. But even if you happen to be the big winner, your victory may prove hollow. Although you have all the riches in the world, you can't buy a thing, because no one else has goods to sell. And you can't sell anything either, because no one has money to buy with. The whole economy is frozen.

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