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

[Gil Skillman <gskillman@xxxxxxxxxxxxxxxxx>]

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
> wit:  start with n-1 non-money commodities and a money commodity, say
> 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@xxxxxxxxxxxxxxxxx>
> > =====
> > >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."
> > >
> > >I wasn't any too clear about this, but I want to note that I didn't add the
> > >"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