Barter -- Why Bother?

From: Dan Fabulich (daniel.fabulich@yale.edu)
Date: Thu Mar 09 2000 - 09:09:49 MST


I'm going to raise the argument here that a complex barter economy is
economically less efficient than an economy with only one (or only a few)
currencies by suggesting how and why a barter economy would develop a
single currency and something like paper money.

I'll break this into four sections:

Why Trade is Good -- showing the obvious and defining my terms
Why Having Only One Currency Is Good -- the cost of complex barter
Why Having Paper Money Is Good (and Bad) -- (dis)advantages of credit
Why Did We Want Barter, Anyway? -- some possible objections

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Why Trade is Good (If you already know why trade is good, you may be able to skip this part.)

Imagine, if you will, a society consisting of people which has agreed that the enforcement of private property is morally legitimate. Imagine also a wide variety of different goods being held by these persons, and that people have different, independent ideas of the value of these goods. Barter becomes an obvious means by which people can maximize the value of their goods: if Alice has got Apples and Bob has got Bananas, and Alice values Bananas more than she values Apples, and Bob values Apples more than he values Bananas, they can efficiently trade to acquire more of what they value. Call this a "direct" trade.

You can see this more clearly if we imagine an actual utility function behind these valuing schemes, measuring "utility", something akin to happiness or satisfaction. Let UA(X) be the utility Alice has when she has X, and let UB(X) be the utility Bob has when he has X. Let UA(Apples) = 5, UA(Bananas) = 10, UB(Apples) = 10 and UB(Bananas = 5). So UA(Alice's property = Apples) initially is 5, and UB(Bob's property = Bananas) is initially 5. Suppose they trade. Now UA(Alice's property = Bananas) is 10, and UB(Bob's property = Apples) = 10. So the utility of both parties has increased. In general, Alice will be willing to undergo a particular trade whenever her utility after the trade will be higher than her utility before the trade; a voluntary trade will take place, then, if and only if the utilities of both parties increases (though this will not necessarily maximize "overall" utility).

Of course, we can also trade "indirectly." Suppose this time that Alice has got Apples, Bob's got Bananas, and Carol has Cantaloupes. Suppose that Alice values Cantaloupes more than she values Apples, but she values Apples more than she values Bananas. Suppose Bob values Apples more than he values Bananas, as before, and Cantaloupes less than both. Finally, suppose Carol values Bananas more than she values Cantaloupes, and Apples less than both.

In this case, no voluntary direct trade between will be possible between any two parties. Alice will not voluntarily trade with Bob, because she values her own Apples more than she values Bob's Bananas. Carol will not voluntarily trade with Alice, be she values her own Cantaloupes more than she values Alice's Apples. Bob will not trade with Carol because he values his own Bananas more than Carol's Cantaloupes. However, an indirect trade is possible: if Alice consents to trade with Bob and then trades Bob's Bananas for Carol's Cantaloupes, everyone gets what they value most. Bob gets Apples, Alice gets Cantaloupes, and Carol gets Bananas.

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Why Having Only One Currency is Good

Having shown that indirect trading can be advantageous, we can now start to get into a few more details.

First, notice that in the above case, in order for Alice to trade with Bob and then go on to trade with Carol, she has to know that Carol would be willing to trade Bananas for Cantaloupes. If Alice is ignorant of this fact, she has no reason to trade Bob for Bananas. Thus, Alice needs to know Carol's utility function before this trade becomes reasonable. The most obvious solution would be for all three participants to declare their own utility functions, thus settling the matter. While this might not appear a problem in a society consisting of only three persons, the problem becomes monstrously more complex when you consider the case of a thousand people, or millions or billions. This problem, as Billy Brown has pointed out, is on the order n^2, since the utility functions must be declared in terms of willingness to make a trade given by the ordered pair <X, Y> where X and Y are Apples, Bananas or Cantaloupes.

There is a better way. If each person declared only their willingness to trade for a SINGLE good, Bananas, the same result could be derived. Alice would declare that she would be willing to give up Apples or Cantaloupes for Bananas, Bob would declare that he would be willing to give up Bananas for Apples but not Cantaloupes, and Carol would declare that she would be willing to give up Apples or Cantaloupes for Bananas. Bob, who has Bananas, would examine only n = 2 pieces of information, (Alice's and Carol's willingness to trade for Bananas,) and notice that only one person has the goods he's looking for and is willing to trade for them: Alice. Alice would then compare only n = 2 pieces of information (Bob's and Carol's willingness to trade for Bananas) and notice that only one person has the goods *she's* looking for and is willing to trade them: Carol. After that trade, Carol would compare only n = 2 pieces of information to find that no further trading was possible.

A barter system in which only direct trades take place may be considered "simple barter," whereas a system in which simultaneous indirect trades take place, by a group of people simultaneously declaring their entire utility functions in terms of all of the goods held by one another and then computing the efficient outcome, may be considered "complex barter."

The point of that little exercise was to demonstrate that given a barter system, declaring one's preferences in terms of a *single standard good* and engaging in simple barter is information-wise efficient relative to complex barter. Call this standard good "money."

There are other good reasons to do it this way. If the money is, for the most part, a portable good, then transactions are easier, since that way the trade doesn't require as much physical work on the part of the traders. (Though this advantage is mitigated by the use of credit; see the next section.) In addition, if money keeps relatively well, it can be saved and traded later. This is useful if the desired non-standard good is not available now, or if it will require less money in the future in order to acquire it. Thus, we should prefer rare gems and metals for our money, since they tend to keep relatively well and are quite valuable (in terms of the willingness of others to trade for them) relative to their weight.

In the last section I'll talk about reasons not to do it this way.

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Why Having Paper Money Is Good (and Bad)

We might desire one further step, however, towards "paper" money or something like it. Despite common belief, a move to paper money in no way requires the influence of government; it can be economically efficient in the total absence of government. To do this, we simply create a storehouse of money, a "bank," who accepts money in exchange for unforgeable articles of credit; these will normally be written on paper and signed by the bank (though they needn't be). These articles of credit can then be exchanged back from the bank for hard money at any time, so people can trade these articles for non-standard goods almost as easily as they can trade the standardized good which we call "money."

While this allows for added portability of money, it is also advantageous to the bank, since it grants the bank the power to loan that money out to others in exchange for interest. This is *so* advantageous, in fact, that the bank itself voluntarily pays interest to people who put their money in the bank, though less interest than the bank derives from lending the money. The bank also pays interest to mitigate risk, since the bank loans out more money than it has on hand, in the hope that not too many people will demand hard money back for their credit simultaneously, putting a "run" on the bank. (Note that the more hard money in the bank relative to the money it loans out, the lower the likelihood of a run on the bank, and thus a lower risk to both the bank and those who save at the bank.)

Next, we notice that since exchanges with the bank are voluntary, the expected utilities of the bank and those who save at the bank increase whenever someone saves there; moreover, the capacity of the bank to lend out money to voluntary borrowers also increases the expected utility of both the bank and the borrower. In particular, it allows the borrower to invest the money in the creation of capital, earning more money from this capital than was borrowed from the bank. This earning of money, when voluntary, also increases the utility of both the borrower and the borrower's customers. Thus, the existence of a voluntary bank tends to maximize the expected utility of the bank, those who save there, as well as those who borrow from it (in the form of investment).

Notice as well that much of this can take place only if society is willing to trade the bank's articles of credit for real goods; otherwise, the bank cannot pay any more interest or loan any more money than the hard currency which the bank currently has on hand. However, by accepting some risk in loaning out more money than the bank has on hand, expected utility (utility modified by risk) increases. Thus, the expected utility of people in society increases when we allow for the existence of banks which can loan out more money than they have, thus allowing for the existence of a money market in which the money supply increases and decreases (according to what the bank estimates to be acceptable risk, the amount of money which people save in the bank, and the rate of returns on investment available to borrowers).

There are risks, however. When the bank has underestimated the likelihood of a run, the lending is inefficient, as the savers would yield greater utility from holding hard money instead of articles of credit. For this reason, the government has gotten involved. (Rightly or wrongly.)

The US government specifies a maximum legal ratio of money-lended to money-on-hand for banks, thus determining the money supply directly. It also acts as a "bank" itself, accepting gold in exchange for articles of its own credit (legal tender). It requires by law that its articles of credit be accepted wherever debts are owed, and that its citizens pay taxes only in the form of its own articles of credit or articles of credit from other banks, who now serve more or less as "second order" banks, accepting articles of credit from the government bank instead of hard currency. Libertarians have argued that the government need not serve this role, that the banks themselves can determine the money supply as efficiently as the government, according to their own independent evaluations of the risk of runs, and as people avoid trading articles of credit from banks who manage their money supply poorly. There may be historical counterexamples to this claim, though the debate rages on.

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Why Did We Want Barter Anyway?

I have attempted to show in the last few sections that, in a barter system, participants will tend to declare their utility functions according to a single portable non-perishable good and switch to a credit currency thanks to the advantages of added investment which are passed on to everyone who saves at banks.

However, there are good reasons not to standardize on just one currency, but to maintain several and to declare utility functions in terms of all of them. Multiple currencies can help to increase the stability of an economy, since traders can switch to a stable currency if another currency is destabilized, by, for example, minimizing the risk that someone could control the entire money supply by controlling the means by which it is created (perhaps by controlling many or all of the gold/diamond mines). Certainly, by the time we get banks involved, we'll want to be able to trade credit from at least two or three different banks, in case one of the banks has a run and one of the others does not, though their articles of credit might all be exchangeable for one hard currency. Also, we might want/expect the money supply in a given market or geographical region to expand and contract relative to the demand for investment in that market/area. (This is part of the reason why many nations have their own individual currencies instead of standardizing on one world currency.)

If the advantages of stability are great, and the cost of computation/information transport small, we might imagine declaring our utility functions in terms of increasingly more goods, until *all* goods (or, at least, all articles of credit which are easily exchangeable for any good) are currencies; at that point, we're back to complex barter. This is already the case in the international money market, where the relative value of each nation's currency is determined by declaration of its value relative to many other currencies, though even there we find exceptions, as currencies are traded in for the Euro, or as foreign currencies are compared to a relatively stable currency like the dollar.

However, there are many, many goods in a given economy, and it is fairly clear that though the number of "currencies" (that is, portable non-perishable goods in terms of which people will declare their utility functions) will increase as the cost of computation and information transport decreases, this number of currencies will probably never become so large that *every* article of credit for *any* good in the economy can be thought of as a currency, since the stability advantages of adding a new currency diminishes fairly quickly whereas the computation/information transport cost increases fairly rapidly.

So we should expect the number of currencies to increase as computation and information transport become cheaper, but we'll probably never see an economy fully run by complex barter. (My own shot-in-the-dark opinion is that if/before the point where computational power gets anywhere near high enough to try something like that, some technological Singularity will likely take place.)

If I have one further point to make, it's this: if we're moving towards barter at all, nobody needs to set up a server or perform any infrastructure whatsoever to make it happen. All it takes is people declaring "complex prices:" declaring the price of their goods in terms of many other goods which they would be willing to accept. As has been stated quite bluntly by those on the list, barter is no tax dodge (and even if it were, it could be easily closed). I see no adavantages to moving towards barter at this time. Let the market work this one out.

-Dan

-unless you love someone- -nothing else makes any sense- e.e. cummings



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