Friday, December 31, 2010

Expansion of the Exchange Media in a Closed Economy with no Production

What follows is a piece of correspondence I sent to a friend regarding money expansion and price changes. It is meant to suggest that money inflation may not show up in price inflation for all goods.

"The purpose here is to consider the effects on nominal prices of goods and services when exchange media expand in a closed economy with free exchange. I choose prison as an adequate metaphor here, with cigarettes as the media of exchange.

Suppose that there is a prison where the inmates provide goods and services to each other, and some goods are delivered from outside the prison. These latter can be considered to be ‘endowments’ from a neoclassical point of view. In fact, in prison, the endowments are likely to be the dominant goods available. The endowment includes cigarettes. Every day, the prisoners will be endowed with goods, (e.g. food, cigarettes, books) and then they may consume, store, or trade with each other.

Services are traded within prisons too. One of the most important services may be protection. This is not endowed, although the guards may provide some protection among inmates. Thus the inmate-provided protection is on the order of extra protection that may be purchased.

Now, consider a prison after all endowments have been made. Trade will occur, facilitated by cigarettes, and prices of various goods and services in terms of cigarettes will be set. These prices will reflect each prisoner’s value scale, including the consumption value of cigarettes, not just the exchange value. Note that cigarettes, then, are basically commodity money.

Imagine that cigarette endowments are now restricted to the ‘replacement’ level, such that when a cigarette is used up or wears out, it will be replaced. This assures the current arrangement of prices will not change unless the prisoners’ value scales change. So as new endowments (sans cigarettes) occur, trade occurs using a constant price matrix. We should expect no inflation or coordination problems in this case, assuming value scales are stable (constant).

Suppose now that one inmate is given an endowment of cigarettes that is reasonably large given then amount of cigarettes currently available. This could be from visiting family, for example. Now what will happen to the prices of available goods and services?

Suppose the inmate really enjoys small powdered cake doughnuts, the kind made by Hostess and other companies. The first thing, then, our inmate (call him A) might do is go and locate some doughnuts and procure them. He may already have some that he purchased previously. So he might go back to the same person (call him B) he traded with before to get the doughnuts. If that person (B) still has some doughnuts, then A will offer some cigarettes in exchange for the doughnuts. There are two possible outcomes here. The first is that B accepts A’s offer and an exchange is made. The second is B rejects A’s offer and no exchange occurs.

Remember now that all trading had ceased prior to the injection of new cigarettes. Thus, the last price offered to B was too low to trade any more doughnuts. So if A wants some of B’s doughnuts, A will have to offer a higher price than B accepted before in order to induce B to sell doughnuts to A. Alternatively, A can seek someone else from whom to buy doughnuts (person C). But since trade had ceased, the higher price required by B will also be required by C, although B’s price may be higher than C’s price, both prices will be higher than the previous market-clearing price.

Now, A might go on like this buying more things he likes. The prices of the things he likes will go up. But notice, too, that his trading partners will have more of the medium of exchange, so that they can buy more of the things they like. Thus one may  trace from A’s increase of exchange media a price increase in a variety of goods, according to the desirability of goods from the perspective of A and his initial trading partners.

A benefits the most from the increase in exchange media, and the benefit declines as the trading partners increase. A benefits more than others because he is using the new media before any of the other inmates are aware of the new media and so they have not yet adjusted their prices. In fact, it is A that causes the initial price adjustment and so he faces the minimal adjustment required to get his doughnuts, for example. Anyone coming after A to get doughnuts will have to pay a higher price than even A paid.

Note that if A hoards his new media of exchange and only uses a bit to get a small edge in trading whenever new endowments are delivered, the price effects will be minimal. But, if A exchanges all his new media quickly after receiving it for goods, price effects will be very rapid and may be large, depending on other inmates’ trading behavior.

After A’s new media have entered and circulated in the system, prices will have changed permanently. The price of doughnuts has gone up. Perhaps also the price of protection services, or books, has increased. We cannot know ahead of time. What is important to note is that i) prices didn’t increase immediately; ii) prices didn’t increase uniformly. In fact, a different pattern of trade may exist after prices change, assuming inmates’ value scales haven’t changed.

 If no new media are injected, the current price pattern will be constant. If new media are injected, two events are possible. If the media are injected by B (or C, D, whomever) then the price pattern will change to reflect first B’s most desired goods, and then his trading partners’ desires, and so on. However, consider what would happen if A were given the endowment of media again, and this became common knowledge. Then, as A were to go out and spend his new cigarettes, he would find B’s price of doughnuts already adjusted to (close to) the new market-clearing price. Since B wouldn’t know exactly what the new market-clearing price would be, he would estimate it but it would be, in any case, higher than the previous market-clearing price and likely higher than A’s initial offer would have been, since B anticipated A’s desire. This anticipation of higher market-clearing prices would move through the system in this case, and clearing prices would be reset much more quickly than when new media injections were unknown.

However, what would happen if A changed his pattern? Suppose A decided doughnuts were no longer on the menu. Then the anticipated price changes would be all wrong and have to go through a re-coordination process as A’s new media moved through the prison markets. This would likely through a lot of planned exchanges, perhaps ones that had already been agreed to (a forward exchange), out of whack and cause them to be less desirable than anticipated. Those plans that could be called off would be, and those that could not may result in value losses for those involved. At any rate, likely there would be less value gained than anticipated. A new price pattern would emerge, but now if A got another endowment and it was common knowledge, prices would not likely adjust since the other inmates cannot predict A’s behavior.

Finally, what would happen if the same size endowment of exchange media was given, but it was divided among 2 or more inmates? Unless the inmates had the exact same value scale, the exchange media would enter the prison economy more quickly than if just one inmate received the endowment, but the resulting price pattern would look different, since the inmates have different value scales. We cannot know, a priori, if the pattern would be a more or less general increase in prices than if just A got the endowment, although it is likely to be so. We do know, however, that as N becomes large, where N is the number of inmates receiving an endowment, the probability of a uniform increase in prices goes to 1."


  1. As a finance prof, you seem to focus most of your posts on economic matters. Do you find that economic posts provide more stimulating thoughts and conversations than would finance matters?

  2. Actually, I'm working on a short piece right now about which measure of inflation should we use in calculating the equity risk premium. So in some ways, this is a finance topic for me.

    The point that I'm trying to get to is incorporating Austrian insights into Finance. So right now I'm really trying to understand the Austrian econ perspective, which (I think) is why so much here is economics.

    I can do some finance stuff if you like, though.

  3. Let's suppose that our government had no real debt. We use T-bills and such to determine the risk-free rate. Absent this government instrument, what would take its place? Would we just use highly rated corporate debt and other AAA rated instruments in its place? But I can see problems with this too.

  4. I'm not sure. That's certainly a possibility. Another is that methods of pricing equities that dispense with a risk-free rate might have arisen.

  5. Thanks for the post at Cafe Hayek. Boom-Bust cycles - instigated by the Fed. Another reason to have free banking.

    Here's a direct quote from DanielK. Do you have any idea what he means here? This is a few posts above yours. I asked DK to expound as well.

    "I'm not exactly sure why we should expect the profit maximizing supply of money to be the full employment supply of money."

    I'm trying to get my head around the "profit maximizing supply of money" part. The "Full employment supply of money" makes no sense to me either.

  6. DK answered my question - although I'm leery of his opening statement.

  7. Brad,

    I'm not real sure about DK's position. It's straight-up outta the Keynesian playbook.

    I'll look it up in some of my textbooks later on and see what I can dig up.

  8. Brad,

    Btw, I think DK is thinking about the supply of currency. Most money (M1, M2, whatever) is made up of deposits and money market mutual funds and stuff like that. Deposit banking is "free" after a fashion. "free banking" is about note issuance.

  9. DK says "there is a quantity of money consistent with full employment." I don't understand how the supply of money (M1, M2) affects employment, other than money or currency is needed for investments and payment to workers.

    I think I need to do some reading on the matter. Clearly I can't speak intelligently on the matter.

  10. I have a standard macro textbook for grad students and couldn't find anything in there. It might be some Keynesian thing other schools don't bother with. Anyway, let me know the results of your research on the matter.

    You may want to start here: