1 Analysis‎ > ‎Economics‎ > ‎01 Value and Price‎ > ‎

02 Exchange

When any bodies meet they can exchange things that they have for things that they value more, in other words they can move themselves into a more valuable circumstantial position through exchange.

For example somebody who is thirsty but has food meets somebody who is hungry but has water, they exchange some water for some food and they are both better off as a result.

Coincidence of Wants Problem

Exchange has its difficulties in that some body offering X and biding for Y in exchange for it, must find some other body offering Y and bidding for X, they both must want what the other has for the exchange to take place. This is the problem of "coincidence of wants". In principle the chance of finding another body with the complimentary bid offer pair, is very slim.

Another serious problem is that not every class of thing is divisible and so one cannot exchange a sheep for some fraction of a cow.

Higher Order Exchanges

Although most exchanges involve only two bodies, there can be higher order exchanges which cannot be reduced to a series of two body exchanges and which overcome the "coincidence of wants" problem to some degree.

A man needing water has food, a man needing food has a tool, a man needing a tool has water. In this circumstance there is no two body exchange where both bodies benefit i.e. where their wants coincide with what the other has. However if all three meet a three body exchange can be made that benefits everybody.
Putting it more abstractly if;
  • person 1 wants item A,
  • person 2 wants item B,
  • person 3 wants item, C,
but;
  • person 1 has item B, 
  • person 2 has item C, 
  • person 3 has item A.
Only a three body exchange benefits all parties to the exchange, yet there is no two body exchange that benefits both parties to the exchange.

It should be apparent that there may also be viable four body exchanges where there is no viable three body exchange and so on.

Generalising, there may exist a viable N body exchange where there is no viable N-1 body exchange.

Exchange Rings & Chains

All viable exchanges form rings, in that if each body puts his hands on the shoulders of the body who has what he wants, if a ring will form,  there is a viable exchange possible i.e. a coincidence of wants, but would these bodies ever meet at the same time in reality?

The exchange ring above is an example of a simple exchange ring formed of a chain of giving that simply connects back to its self to form a complete ring.

What if two things are given in exchange for one, there is no requirement that the two things must be given to the same body. Similarly if one thing is given in exchange for two, there is no requirement that the two things must be taken from the same body.

The action of giving two things for one will split the exchange chain, while the act of giving one thing for two will join two exchange chains. The first act may split a ring while the second act may rejoin it. Thus the exchange ring may be split but still complete.

The action of giving any number of things for any other number of things can split exchange rings in the most complex ways yet at long as splits rejoin, the ring is complete and so the exchange is viable.
 
Finding high order split exchange rings is finding a needle in a haystack but the rings are opportunities where complex exchanges can benefit all involved.

Many bodies will not have their exchanges performed as they will not find a viable exchange ring to take part in.



(C)2010 Tom de Havas. The information under this section is my own work it may be reproduced without modification but must include this notice.







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