# [OPE-L:7403] Fwd: RE: RE: Commodity money in a Sraffian system

From: Gil Skillman (gskillman@mail.wesleyan.edu)
Date: Wed Jul 03 2002 - 13:05:25 EDT

```Gary--

>Double hmm.  Since the point of my comments has been to support your claim
>below that the differences identified by Fred are more apparent than real,
>it seems I'm still not making myself clear.  How's this:  your
>interpretation of invoking a numeraire good is as follows:  Having
>specified an n-dimensional vector of commodity prices, (P1, P2,...., Pn),
>denominated in terms of nothing in particular, select one commodity, say
>commodity j, and then divide all prices by Pj, yielding a new vector of
>relative prices (P1/Pj, P2/Pj,....1,..., Pn/Pj), in which the "1" is the
>normalized price of good j.  This procedure is understood as a purely
>analytical exercise motivated by the fact, which you've noted, that only
>relative prices matter in this system.
>
>Fred makes a "real-world" objection to this, citing Marx, on the basis
>that in fact the money commodity doesn't  exchange with itself, and thus
>doesn't really have an exchange ratio with itself, and thus "has no
>price."  Perhaps, but my point is that this "practical" observation has no
>*analytical* significance, because one can acknowledge it with a procedure
>that is *mathematically identical* to the one described above, to
>commodity j.  Specify the non-money commodity prices Pi, i not equal j,
>understood as exchange ratios with the money commodity.  The money
>commodity doesn't have a price, per se, but one can still coherently
>define an "augmented" price vector (P1, P2,..=1,...P(n-1)), with the
>"1"  in the jth position having the interpretation (not as a price!) given
>in my previous post.  Another way of putting this is that there is no need
>to go through the initial charade of positing the existence of prices that
>aren't denominated in terms of anything.
>
>But the main point is that the latter procedure exactly satisfies Fred and
>Marx's "real-world" concerns, and yet is mathematically identical to the
>procedure indicated by your interpretation of what it means to identify a
>numeraire good.  Conclusion:  the apparent difference highlighted by Fred
>is not analytically meaningful, and may thus be ignored.
>
>>Hmmm.  This prompts two questions, Gil.
>>
>>1. What difference does this make to your argument?  It seems like a bit of
>>hair-splittlng to me. This in fact was what I wanted to nudge Fred into
>>answering in my last post. I am surprised to find you and him on the same
>>side
>>of this issue,
>
>Not really--see above.
>
>>since that doesn't seem consistent with your other posts on the
>>topic.
>>
>>2.  Besides, I must disagree, or anyway ask you to say what you mean by
>>numeraire.  I understand it to mean the standard in which prices are
>>measured.
>>  Well then, the price of good x measured in terms of itself cannot be
>> anything
>>but one.
>
>And that's where Fred (if I may presume....), following Marx, would
>immediately object that this statement is meaningless, because by the
>nature of what "prices" are, they are not measured "in terms of
>themselves."  I'm saying, fine, but even if one were to incorporate this
>proviso analytically, it makes no analytical difference.
>
>>  In effect, when one expresses prices in terms of a numeraire one is
>>posing the question, how many units of the numeraire good can be swapped for
>>one unit of any other good?
>
>Yes, that, *and* that there exists a price out there of the numeraire good
>in terms of itself.
>
>>  On reasonable assumptions about human rationality
>>we may suppose that under normal circumstances no more nor less than one
>>unit
>>of the numeraire can be swapped for one unit of the numeraire, whatever the
>>numeraire happens to be.
>
>Marx insists these swaps don't in fact happen.  Whether or not you agree
>with that assertion, I'm saying you could grant this point and end up at
>the same place, in other words, it doesn't signal a difference that makes
>a difference, i.e. it's hair-splitting.  So I'm agreeing with you.
>
>>   It seems to me entirely irrelvent whether there is a
>>market for the numeraire in terms of itself, as long as there is a market
>>for
>>it in terms of other goods.  And I'm not even sure there needs to be a
>>market
>>for it in terms of other goods if its function is purely to serve as a
>>standard of measuring prices. So what is the harm, or the mistake of saying
>>that the price of the numeraire is one.
>
>Agreed. Perhaps the problem with my point is that it seems so elaborate
>yet yields a very simple conclusion that's identical to yours:  clearly
>there *is* no harm, because even if you grant the "real-world" point, you
>can still proceed analytically in a manner that is mathematically
>indistinguishable from what you've proposed.
>
>
>
>
>
>
>
>>Gary
>>
>>
>>
>> >===== Original Message From Gil Skillman <gskillman@mail.wesleyan.edu>
>> =====
>> >Gary, you wrote in part
>> >
>> >
>> >>Gil reminds us of Marx's remark that "gold has no price." It is
>> >>interesting to
>> >>me that Gil interprets that to be equivalent to what a modern economist
>>means
>> >>by "gold is the numeraire and therefore its price is 1."
>> >
>> >"therefore" comment you attribute to me here, and for a
>> >reason:  identifying a commodity as the numeraire good in an exchange
>> >system *can* mean the same thing as "normalizing its price to one," but it
>> >doesn't have to.  And in my second post, I was arguing that in the specific
>> >case of commodity money, it is both economically appropriate to call the
>> >single money commodity the numeraire good and economically implausible to
>> >say that it has a price--i.e., an exchange ratio with itself--that happens
>> >to be equal to one, since as Fred and Marx rightly point out, the money
>> >commodity isn't exchanged for itself.
>> >
>> >Instead, the Sraffian "price of production equation" equation for the money
>> >commodity, say,
>> >
>> >1 = [p(c)*a + w*l] (1+r)
>> >
>> >
>> >is more in the nature of an accounting relation given that the law of one
>> >price obtains, indicating that each unit of gold produced must be just
>> >sufficient to cover the associated physical and labor production costs
>> >(measured in gold), augmented by the rate of profit common to all sectors.
>> >
>> >The math is the same as in the standard normalization procedure, of course,
>> >but the interpretation is different.
>> >
>> >Gil
```

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