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@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." >> > >> >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
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