Questions on Mises VIII: The Paradoxical Value of Cake. And Pennies.
Jason Kuznicki on Dec 15th 2006
Below the fold, a cakey conundrum. And pennies for your thoughts.
Let us suppose that the scale of values of the possessor of an apple, a pear, and a glass of lemonade, is as follows:
1. An apple
2. A piece of cake
3. A glass of lemonade
4. A pearIf now this man is given the opportunity of exchanging his pear for a piece of cake, this opportunity will increase the significance that he attaches to the pear. He will now value the pear more highly than the lemonade. If he is given the choice between relinquishing either the pear or the lemonade, he will regard the loss of the lemonade as the lesser evil. But this is balanced by his reduced valuation of the cake. Let us assume that our man possesses a piece of cake, as well as the pear, the apple, and the lemonade. Now if he is asked whether he could better put up with the loss of the cake or of the lemonade, he will in any case prefer to lose the cake, because he can make good this loss by surrendering the pear, which ranks below the lemonade in his scale of values. The possibility of exchange introduces considerations of the objective exchange value of goods into the economic decisions of every individual; the original primary scale of use-values is replaced by the derived secondary scale of exchange values and use-values, in which economic goods are ranked not only with regard to their use-values, but also according to the value of the goods that can be obtained for them in exchange. There has been a transposition of the goods; the order of their significance has been altered. But if one good is placed higher, then—there can be no question of it—some other must be placed lower. This arises simply from the very nature of the scale of values, which constitutes nothing but an arrangement of the subjective valuations in order of the significance of the objects valued.
But the analysis in the foregoing paragraph seems to turn the linear hierarchy of values into a mobius strip: If we accept that the free exchange of a pear for a piece of cake means that the two are equal in value, and that the one has risen just as the other has fallen, then where do the two terms of this equality stand in relation to lemonade?
Every time I look at (lemonade versus [cake or pear]), I am convinced that I see an inequality. It’s just a different inequality every time I look. It is clear, I think, that outside the market I still prefer the cake to the lemonade, in that I fear the loss of the former more keenly. Within the market, this reverses. Likewise, I introspectively prefer the lemonade to the pear, and again, within the market, this reverses.
This conflict, between the exchange values set in the market and the values I hold within myself, is arguably what impels the individual into the market in the first place. Yet from where I stand, it also creates confusion in my values, for once I enter the market, have I not reached a self-contradictory position: How, after all, can we construct a hierarchy of values in which I desire a piece of cake and a pear both equally, but in which I desire a glass of lemonade some intermediate amount, with the cake above and the pear below?
I suspect, by the way, that I know the answer to this question, one that my husband Scott suggested to me last night. Assuming he is correct, here are two hints:
Hint 1: The solution does not rest on the division between use and exchange values.
Hint 2: It’s surprising that Mises of all people would have missed this one.
Thanks: Discussion continues on Question VII; commenters AMW and Quasibill — both clearly know their economics — have been tremendously helpful in particular, and I thought I would take the opportunity to thank the many commenters who have contributed so far. Without you, I’d be talking to myself.
As to returning to a commodity currency, it appears that in some cases we already have: Both nickels and pennies now have more commodity value than they do exchange value — that is, melting them down for their metals is a profitable proposition (n.b.: Yes You Can Do This At Home. “Wow,” notes the author of the page, who recommends using a blast shield).
Unaccustomed to handling real money, the U.S. Mint is floundering:
Effective today, the U.S. Mint has implemented an interim rule that makes it illegal to melt nickels and pennies, or to export them in mass quantities…
“We are taking this action because the Nation needs its coinage for commerce,” said U.S. Mint Director Edmund Moy in a statement. “Replacing these coins would be an enormous cost to taxpayers.”
How big a cost? Moy told ABC News that if just 1 percent of all the nickels and pennies that are in circulation were melted down, taxpayers would have to foot a $43 million bill.
This is rubbish. The “nation” clearly does not need this coinage for commerce. We cannot possibly need the small change if we’re willing, collectively, to melt down our coins and turn a profit. What the market tells us here is that we need the coins for copper and zinc (note that both of these are, perhaps obviously, articles of commerce as well). Whatever the case may be, we don’t need these coins chiefly for their exchange value, or — if we did — we’d still be using them for money.
Also, I fail to see how taxpayers need to foot any sort of bill here: The U.S. Mint should simply decline to issue coins of these commodity values. It’s become a losing business proposition, and any sane business would refrain from throwing its money away in this manner. Perhaps the U.S. Mint could take the opportunity and re-denominate the lowest tiers of the currency, creating a two-cent piece and a ten-cent piece out of the erstwhile penny and nickel. Or they could let the value of the coins float in relation to the dollar, which should solve the melting problem overnight.
All of this raises an interesting point:
The public can offer comments to the U.S. Mint on the regulations for the next 30 days. Moy will take those comments into consideration and then issue the final rule within 120 days.
Given that my formal economics training amounts to a single undergraduate micro class, I’m not exactly qualified to make a recommendation. But I’m sure that some of my readers are.
[Crossposted at Liberty & Power.]
Filed in The Boardroom
We cannot possibly need the small change if we’re willing, collectively, to melt down our coins and turn a profit.
This is faulty reasoning. At the outset, let me say that I am agnostic as to the value of small change. I rarely use it myself, as I typically consider it a burden to carry (any change I get usually ends up in the Save A Starving Child tray, or in a jar back home until I can exchange it for real money). Moreover, the ubiquitous use of credit and debit cards means that for all practical purposes “cents” could be nothing more than a mental concept. As long as you’re willing to make your transactions without cash (as I do 99% of the time) small change is of absolutely no worth.
But let’s say just for the sake of argument that the exchange value of small change (that is, it’s usefullness in facilitating exchange) does indeed exceed its commodity value. Suppose further that the commodity value of small change does, however, exceed its face value. Would we expect this to prevent individuals from melting down small change?
I would argue that we would not. Consider the individual who undertakes to melt down the small change. For $1, he can acquire 100 pennies whose commodity value is worth, say $1.15. (For simplicity, let us suppose he can melt the coins with the power of his mind, so that doing so is essentially costless to him.) If he proceeds to melt down the pennies, he nets 15 cents all to himself, and his 300 million fellow citizens will each help to pick up the tab for purchasing the copper to make another 100 pennies to replace the ones he melted. The effect on his tax bill is essentially nil. Assuming that he is rationally self-interested and not hung up on the morality of netting 15 cents at the expense of his compatriots, he will melt the pennies.
But what if his compatriots would not replace the melted pennies? In all likelihood this doesn’t change his value calculus at all. Let’s face it: there are a lot of pennies out there, and his diminution of the total probably hurts the penny’s exchange value to him by less than 15 cents.
What we have here is an artificial (and unending) arbitrage opportunity for anyone willing to skirt the law. One dollar will always be fungible for 100 pennies by government fiat. But pennies (now) are worth more than 1/100 of a dollar on the open market. The government’s commitment to preserve the supply of pennies means that 1) the impact on the exchange value of pennies by melting them down will be nil 2) the cost of replacing the pennies will be barely felt by the arbitrageur and 3) the gap between the market value of the copper in a penny will continually exceed one cent.
AMW,
I’ve read and reread your comment here, and I do not see how what you have written reveals any fault in the section you quoted. Indeed, it seems self-evident to me that if someone is willing to melt down a quantity of his small change, then he clearly does not need it for exchange; his satisfaction is maximized, as in the web page I linked, by using it as a metal and casting into useful objects.
“Cents” could in time become fully a unit of accounting, true, but this says nothing one way or the other about pennies and their commodity value. But you cannot say “small change is of absolutely no worth,” since, after all, a metals dealer may want them for scrap.
I have to say, though, that I am unclear on the distinctions you draw among “commodity” “exchange and “face” values. The first two are clear to me; the third seems only a restatement of the second, at least under the present legal regime.
You are entirely correct, I think, when you write, “What we have here is an artificial (and unending) arbitrage opportunity for anyone willing to skirt the law.” The way do this is simply to obtain a quantity of pennies, melt and sell them, turn the money you get into pennies again, and repeat the process on a larger scale.
Jason,
First, some definitions. (I should have made this more clear from the outset.)
Commodity Value: The value of the physical elements that make up a coin. (If an oz. of copper is worth $1.15 in the copper market, and there is 1/100th of an oz. of copper in a penny, the penny’s commodity value is $0.0115.)
Face Value: The relationship between the coin and a dollar as dictated (or defined) by the governing authority. (The government sets the face value of one penny as 1/100th of a dollar.)
Exchange Value: The usefulness of small change in facilitating transactions of low-valued goods. (Ask yourself, “how many fewer of my wants would be satisfied if I had to barter low-valued goods because all existing cash denominations were too high?” The difference between your answer and the status quo gives you the exchange value of small change.)
The arbitrageur’s opportunity for profit comes from the disconnect between the commodity and face values of small change. In carrying out his arbitrage, he (infinitesimally) degrades the exchange value of small change in general, as there is less of it to facilitate low-value transactions after he has melted some of it down.
Now, I will attempt to clarify where I find your reasongin faulty. Your argument in the body of the post seems to say that no one would melt down small change if its exchange value exceeded its commodity value. Indeed, in your response to my post you reiterate this argument quite clearly:
it seems self-evident to me that if someone is willing to melt down a quantity of his small change, then he clearly does not need it for exchange; his satisfaction is maximized, as in the web page I linked, by using it as a metal and casting into useful objects.
What you are not taking account of here is that even if the exchange value of small change exceeded its commodity value (i.e., even if being able to carry on some small transactions with his own stock of small change exceeded the price he could get by melting it all down), the existence of a set exchange rate between dollars and pennies makes the melting down of the small change a profitable proposition nonetheless.
Suppose the following. Our arbitrageur has 100 pennies. He could use them to buy 100 1-cent gumballs, whose cumualative value to him is $1.20. He could also melt them down and sell the resulting bar of copper for $1.15. I think we can agree that the purchase of the gumballs has the higher ordinal ranking. But then our arbitrageur recalls that he can take any $1 bill into any bank (and most stores), and exchange it for 100 pennies. He realizes that the Federal Government has given him an unparalleled opportunity.
He melts down the coins and sells them on the copper market for $1.15 - one dollar bill and 15 pennies. He then exchanges the bill for 100 pennies, melts them down and sells them for $1.15. Lather, rinse, repeat. After seven iterations, our arbitrageur has a dollar bill and 105 pennies. He may now buy his 100 1-cent gumballs and still have the equivalent of 105 pennies. His position is more than twice as good as it was previously.
Of course, in doing this he has deprived the world of 700 pennies. Small change is now very slightly harder to come by, and therefore its exchange value to society as a whole is diminished. But although our arbitrageur will feel a small portion of that loss, his gain has more than made up for it.
Hopefully this has clarified my position. What is optimal behavior to the arbitrageur is sub-optimal to the whole economy. The opportunity for him to practice this behavior comes from the fact that there are actually two copper markets: one has a fixed price and the other does not.
Now, if the world’s supply of pennies was only 700, he might not carry out this arbitrage, because the absolute loss of a small-value transaction medium of exchange could exceed his profit from the arbitrage. But given that no arbitrageur could ever hope to eliminate more than a small fraction of the world’s small change, he has little to fear from his actions. He lowers the exchange value of small change to everybody, but brings in a profit sufficient to offset his share of this loss.
And now let me respond/clarify regarding the following statement:
But you cannot say “small change is of absolutely no worth,” since, after all, a metals dealer may want them for scrap.
First, note my qualifier, that small change (i.e., pennies & nickels) is of absolutely no worth if one makes all (or nearly all) of his transactions via electronic currency (i.e., credit and/or debit cards). I might like a nickel so that I can purchase a single-wrapped Jolly Rancher with it. But if the 7-11 owner takes credit cards (and has no minimum size of purchase) the nickel is just taking up space in my pocket.
Second, allow me to confess to sloppy wording. What I meant was that if electronic currency may be used as a substitute, then the exchange value of small change is nil. You are obviously correct that it retains its commodity value. But even what I meant to say is not strictly accurate. Legal tender laws ensure that small change cannot actually lose its exchange value. However, the existence of electronic currency renders the act of carrying loose change essentially useless. You can get all the exchange value you need from plastic cards, so why go jingling about with metal discs in your pockets? (Especially when their commodity value exceeds their face value.)
Third, in a sense small change as it exists today represents a negative value. Copper and nickel markets are telling us that elements in a nickel and penny are worth more than 1/20th and 1/100th of a dollar. We have a natural substitute through electronic currency. So why lock up all that nickel and copper?
This comment has gone on for too long by half. I certainly hope it has added some clarity. If it has not I will despair of that objective and refrain from posting again on this particular thread.
Oh, and share Scott’s wisdom with us, already.
Seems quite clear to me that the problem with pennies lies in the fact that the exchange value is dictated to be 1/100th of a fiat dollar. It’s not that copper has become “more in demand”, or become more valuable, it’s that the fiat dollar has become “less in demand”, or less valuable, due to increased supply, and since the penny is artificially pegged to that standard, such ridiculousness ensues. It’s really one the paradoxes that only a state can create, and should be cause enough for quite a bit of discontent, if only enough people really understood even basic economics - it’s an indication of just how poorly the Federal Reserve is fulfilling its purported mission.
The value of copper as currency is unlikely to ever fall below its value as a commodity under free market conditions - the increase in commodity value would coincide with (yes, over time, allowing for short term speculation) an increase in currency value - perhaps to the point where it exceeded the currency value of some other common metal, but it would take an amazing increase in commodity value for it to lose its currency value because it became too dear.
I second AMW’s call for Scott’s wisdom - to me it IS as simple as a distinction between use and exchange values: currency evolves specifically because it has greater exchange value than use value. I’d like to know what I’ve missed here.
[...] In part VIII of the ongoing series, I quoted an example given by Ludwig von Mises, and I suggested that it created a paradox in the ordinal theory of value. Mises wrote, Let us suppose that the scale of values of the possessor of an apple, a pear, and a glass of lemonade, is as follows: 1. An apple 2. A piece of cake 3. A glass of lemonade 4. A pear [...]
[...] Once a money had been arrived at — let’s hypothetically call it silver — things would be very different, all without anyone intending these differences at the outset. Money allows us to adjust our value hierarchies in precisely the way we discussed in part VIII of the series; it allows us to trade things we desire less for those that we desire more. [...]