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
---
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.
---
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.
---
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.
---
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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