Well, if I have not completely lost all my readers, even Magpie, who seems to have a taste for this sort of arcana, let me continue. Re-reading what I wrote yesterday, I realize that by referring to some random commodity as "a," I invite confusion. Indeed, when I re-read the last sentence from yesterday's episode, it looked at first as though I had ended in the middle of a sentence. So henceforth I shall use "A" rather than "a." I hope that makes things a trifle clearer. Anyway, here we go.
X's possessions are simply the totality of all the ownable goods towards which, at the specified time, X bears the relation of owner. If we assume -- as classical political economy does -- that the goods of which we speak are commodities, which is to say goods partitioned into categories, treated as interchangeable within categories, and quantifiable therefore within categories along natural physical dimensions [so many bushels of wheat, so many tons of iron, so many power looms, etc.], then we may define an economic agent's holding as a vector, the ith element of which is the naturally measured quantity of the ith type of good [according to some conventional ordering] toward which the agent bears the relationship of owner as defined by the ruling legal system. I add the phrase "along natural physical dimensions" to make it clear that at this point I am talking about things, not quanta of value. [A vector is a list, but "list" does not sound impressive at all, and "vector" makes it manifest that I am a very serious person. Much of modern economic theory consists of such like maneuvers.]
Economic agents, of course, own specific determinate physical goods [this bushel of wheat, that pair of shoes], but this fact is abstracted from in the concept of a holding. I am now going to try to put all of this into symbols. Be patient. This is easy if I am writing by hand, but rather daunting if I am using WORD. I have never done this before in WORD, and it may take me several days to type in WORD what it took me a few minutes to write by hand. So much for technological progress. [RATS. I solved the problem of inserting a summation symbol into WORD, and then, when I tried to copy it into this benighted blog framework, it simply disappeared! I give up. In future I shall write in long hand and then send mimeographed copies of what I have written by perswonal courier to anyone who wants them! Phooey.]
Let hi = (hi1, hi2, ... hin) = the holding of economic agent i, where hiq = the quantity of commodity q owned by individual agent i, with i = 1, 2, ...., s.
If H = the sum, from 1 to s, of the h sub i
[This is where I tried to put in a summation symbol] and β = (β1, ...., βn) = the
vector of gross outputs.
Then H = β during the period of exchange between cycles of production.
In other words, the totality of all the stuff produced by the economy is equal to the totality [divided up differently] of all the stuff owned by economic agents. Doh. Why on earth spend the better part of the morning scrabbling around in WORD to type that? Why not just say it. Ah, grasshopper, it will become clear in time.
Notice that the equality implies that every bit of output is owned, and that nothing is owned save the output of this cycle. There are no fixed capitals in our model yet, and not even any durable personal possessions.
When a market exchange takes place, economic agents make a legally enforceable agreement, the effect of which is to accomplish a mutual transfer of ownership of some non-zero portion of each party's possessions. This mutual transfer alters the holding of each agent in such a way, obviously, as to leave the sum of their holdings unchanged. During the interval of exchange between cycles of production, therefore, H = β is constant, regardless of the number of transactions their frequency, or the prices [ i.e., exchange ratios] that govern the magnitudes of their exchanges.
Since a market exchange is a mutual transfer of ownership, the effect of which is to alter the composition of individual possession vectors, and thereby to alter holdings, it is a matter of no importance whether any physical change takes place in the location and arrangement of the ownable goods being exchanged. We can imagine that the agents carry their goods about on their backs. like the Balnibarians encountered by Gulliver on his third voyage; or we can suppose them to conduct their affairs entirely on chits of paper, the goods having been left elsewhere. Also, it is clear that whatever has had the status of ownable good ascribed to it by the appropriate legal procedures can become an element in a commodity exchange: a bushel of wheat, a bolt of cloth, the performance of a Bach cantata, a trademark, a scientific idea, or a municipal office.
Now [I am creeping up on the idea of money, be patient], Let us suppose that a private party who has hitherto engaged only in transfers and exchanges of such commodities as gold and silver, now offers as a service [for a nominal fee] to store and care for its customers' gold. [Other parties might offer the same service for wheat or iron, but never mind that.] The owner of a quantum of gold who decides to avail herself of this service can transfer legal possession of the gold to the bank [as this service provider now becomes]. In return, she receives a certificate of entitlement [regardless, by the way, of whether the gold is physically moved from the owner's strong box under her bed to the imposing building maintained by the bank]. The certificate announces that its owner, the depositor, has the legal right, whenever she [or he, or they, or it] may choose, to present the certificate to the banking house and receive in return the amount of gold indicated thereon.
What effect has this new banking service on the structure of possessions and holdings? If the depositors are entitled, by their certificates and by the laws governing them, to recover identically the same particles of gold that they placed on deposit, then the answer is clearly none at all. The gold is,, as it were, in safe deposit, just as one agent's wheat may be in a warehouse, or another's beef in a rental meat locker.
But since we are assuming a homogenization of commodities sufficient to permit their classification, categorization, and aggregation within categories, we may suppose that it is a matter of indifference to the depositors whether they receive back physically the same gold which they have deposited, as opposed to gold of the same quality [category] and quantity. This assumption rules out, as instances of our analysis, such goods as a specific painting by Rembrandt, or a performance of the Beethoven violin concerto by Hillary Hahn. It is scarcely plausible that an art collector who had deposited Rembrandt's painting of Aristotle Contemplating a Bust of Homer would accept, on presentation of the deposit certificate, an equal number of paintings, or an equal number of Dutch Old Masters, or an equal gold-value of paintings, or even another Rembrandt. The depositor would demand back the specific painting she had deposited. Nor would a music connoisseur be satisfied with an alternative performance of an alternative concerto for an alternative instrument by another composer!