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# Mises's Regression Theorem and a Logical Proof

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447 Posts
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Micah71381 posted on Mon, Apr 18 2011 7:29 PM

Premise: A thing must be valued for one or more non-exchange purposes by one or more people before it can be used for indirect exchange. (regression theorem)

Given: A specific thing is used for indirect exchange in a market of 3 or more people.

Conclusion: The specific thing must have been valued by one or more people for one or more non-exchange purposes at some point in history.

Is my premise incorrect or arguable?  Have I committed a logical fallacy in drawing my conclusion?

The premise is discussed here: http://mises.org/Community/forums/t/23938.aspx

The specific thing can be any object that is used for indirect exchange in a market of 3 or more people.  The market size of 3 comes from the above linked thread as well where it was established that one person must value a good and the market must be of size 3 or more in order for indirect exchange to occur.  It was touched on that technically 2 or more could result in indirect exchange but for the sake of this proof I went with the generally accepted market size of 3.

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4,248 Posts
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Smiling Dave replied on Thu, May 3 2012 10:00 PM

Very good point AJ.

Unfortunately, it's not me who originated the vagueness, it's in Mises and Rothbard. I imagine the reason for the vagueness is that what number would not be arbitrary?

My conception of generally accepted is "you can get anything you want" with X. Food, clothing, cars, everything.

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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Micah71381 replied on Thu, May 3 2012 10:13 PM

Unfortunately, even "you can get anything you want with X" is still a bit arbitrary.  By that definition, most currencies of the world don't qualify, except the big name first world ones.  Even those have things that you can't buy with them (e.g., you may not be able to buy a particular food from a street vendor in some particular country with USD).

This means that you still have to apply an arbitrary threshold of "you can get almost anything you want with X".

I think it's easiest to just accept that "money" isn't a well defined term and it will always be vague.  In a logical debate, it would be best to hardline define it up front and work with that definition just so the debate can move on.

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Smiling Dave replied on Thu, May 3 2012 10:28 PM

Micah,

I am talking about dollars in the USA, small country money in the small country, etc. You certainly can get anything you want, just go to the stores.

What are you unable to buy in the USA with dollars, or with Luxemburg money in Luxemburg?

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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Micah71381 replied on Thu, May 3 2012 10:34 PM

So if I am in a small amish village (entirely self contained) and I can get anything I want within the comumnity using twigs, does that mean twigs are considered money?

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Smiling Dave replied on Thu, May 3 2012 11:16 PM

Sure.

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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AJ replied on Thu, May 3 2012 11:19 PM

Well what happens if I can trade something for half the things I want? 10% of the things I want? (No need for precision, but without even a wildly conservative lower bound how can these terms even make sense?)

If some people won't accept twigs because they both have no personal use for twigs and, more to the point, they are simply ignorant of the fact that they can buy butter, bread, clothes and other things with the twigs, twigs might only be accepted within a limited sub-population until more people figure out that it is beneficial to accept twigs as payment.

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Smiling Dave replied on Thu, May 3 2012 11:25 PM

In the sparsely settled American colonies, money, as it always does, arose in the market as a useful and scarce commodity and began to serve as a general medium of exchange. Thus, beaver fur and wampum were used as money in the north for exchanges with the Indians, and fish and corn also served as money. Rice was used as money in South Carolina, and the most widespread use of commodity money was tobacco, which served as money in Virginia. The pound-of-tobacco was the currency unit in Virginia, with warehouse receipts in tobacco circulating as money backed 100 percent by the tobacco in the warehouse.

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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Micah71381 replied on Thu, May 3 2012 11:27 PM

Does the "community" have to be contained geographically?  Or would a virtual (but self contained) community count?

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Smiling Dave replied on Thu, May 3 2012 11:37 PM

Not sure what your point is. Make up whatever lower bounds makes sense to you.

Here's Bob Murphy, saying that it's not just Mises and Austrians, it's all economists from all schools:

Austrian economists generally follow Mises in defining money as a "generally accepted medium of exchange." Mises felt that this was the essence of money, and that its other "functions" (as described in mainstream textbooks) flowed naturally from this.

To be clear, all economists would agree with the Austrians that money is a generally accepted medium of exchange, though they might not choose such terminology. But standard texts may say that money has other functions, that it (for example) serves as a store of value and as a unit of account. But in Mises's view, these functions are an outgrowth of the fact that money is a generally accepted medium of exchange; that's why it can also serve as a store of value, a unit of account, and so on.

More from Murphy, in the same article:

Money is the commodity or good that everybody in the community is willing to accept in trade.

Note his use of the word everybody. Does he mean if one person in the communtiy insists on being paid in wampum instead of dollars that dollars are no longer money because of that one person?

OK, we can learn from that article  that...

1. generally accepted means everybody, or almost everybody.

2. everybody means everybody in a given community [not the whole world or even a whole country. A community]. One may ask how big is a community? Again, i leave thatto you to decide.

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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AJ replied on Thu, May 3 2012 11:43 PM

Insofar as there is nothing requiring the transactions to take place in a contained geographical region, it cannot matter whether the community is so contained.

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AJ replied on Fri, May 4 2012 12:11 AM

So to be generally accepted, we could say 80% acceptance for all the goods that most people want is a bare minimum. That pretty much settles it: bitcoin is not money, not even in the bitcoin circles.

However, two things have been being discussed simultaneously. What does it take for something to be money, and what does it take for something to *become* money. "People value X for non-exchange uses" is held to be the standard prerequisite for the latter, but - taking gold, wampum, shells, or feathers as examples - this "people" by no means refers to almost everyone, and in fact may be a small minority.

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Smiling Dave replied on Fri, May 4 2012 9:18 AM

this "people" by no means refers to almost everyone, and in fact may be a small minority.

You forgot the proviso, "In a given community". For example, I imagine all the Indians in the region where wampum had value accepted it, even though nobody in Europe or Africa did.

My humble blog

It's easy to refute an argument if you first misrepresent it. William Keizer

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AJ replied on Fri, May 4 2012 2:02 PM

"...for non-exchange purposes"

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Seraiah replied on Thu, Jun 28 2012 12:30 PM

Micah71381:
Premise: A thing must be valued for one or more non-exchange purposes by one or more people before it can be used for indirect exchange. (regression theorem)

Your premise is just entirely wrong.

A medium of exchange does not need to be used for other purposes, by any number of people*, before being used as a medium of exchange.

A medium of exchange can gain value the same way everything in the universe gains value: Through mutual voluntary transactions in a free market. Supply and demand will adjust the price until it reaches equilibrium. If the price of the currency is too high, there will be a surplus, if it is too low there will be a shortage.
The initial price of the medium of exchange could be a total shot in the dark, the Invisible Hand will work just the same.

The reason that the Regression Theorem exists is because fiat money is made from a commodity that typically trades far far lower on the free market than justifies its purchasing power.

Bitcoins are a medium of exchange that gained all of its value through voluntary transactions in a free market. There is no discrepency for the Regression Theorem to explain; proving that a medium of exchange does not need to have any purpose other than to be used as a medium of exchange.

The utility of a medium of exchange in and of itself is valuable. In fact, the vast majority of gold's market price is due to its use as a medium of exchange. Most gold is not intended for any industrial purposes, it is simply hoarded until it is one day exchanged for something else.

*Well, at least three, but a negligable amount.

"...Bitcoin [may] already [be] the world's premiere currency, if we take ratio of exchange to commodity value as a measure of success ... because the better that ratio the more valuable purely as money that thing must be" -Anenome
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MMMark replied on Sat, Jun 30 2012 10:27 AM

Sat. 12/06/30 11:27 EDT
.post #186

Does the "community" have to be contained geographically? Or would a virtual (but self contained) community count?

community
a social, religious, occupational, or other group sharing common characteristics or interests and perceived or perceiving itself as distinct in some respect from the larger society within which it exists (usually preceded by the): the business community; the community of scholars.

Origin:
1325–75; < Latin commu-nita-s, equivalent to commu-ni(s) common + -ta-s -ty2; replacing Middle English comunete < Middle French < Latin as above

To your questions, I would answer "no" and "yes," respectively.

It seems to me that what defines a "community" is the thing, or things, that is, or are, common.
A community is a group of people who all have some thing, or things, in common.

From this viewpoint, then, I can sensibly talk about "the bitcoin community":
It is the group of people for whom bitcoin is a medium of exchange.

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