A Brief Story of Money, Part 2
In this article, the so-called "equation of exchange" is introduced and used to explain inflation in an example. As with the first installment, bloggers are pressed into service as the actors in this drama. Their performances are herewith noted: BlondeSense Liz of BlondeSense and Misty of expostulation are thanked for their performances as castaways on a deserted island, and Peter of Lone Tree, also of BlondeSense, is graciously thanked for a cameo appearance.
Among the definitions of inflation are some that don't explain a whole lot. One such nice but somewhat uninformative definition is this: Inflation is a rise in the aggregate price level. Well, yes, but that doesn't really do much to explain why the "aggregate price level" rises.
Perhaps a better, working definition of inflation might go something like this: Inflation is the erosion of purchasing power per unit of the currency. Not much better, huh? Read on and see how this one fits into the story told below, a story about two women trapped on a deserted island where they must engage in trade with one another, exchanging clams for pineapples.
Several years ago, an ugly storm came out of nowhere during a cruisea three-hour cruiseon which were two hearty women, BlondeSense Liz and Misty. The storm capsized their boat; and of the five passengers who had set sail that day with the crew of two, only Misty and Liz had survived, each of them floating away from the doomed ship on the drowned remains of one of their more corpulent fellow shipmates.
After several days at sea, they beached on a tiny, deserted island paradise in the South Pacific. Shortly after they came ashore, there was something of an ugly scene about whether to eat their corpse/life rafts uncooked or to do so after roasting them on a spit for several hours, and the two stranded castaways finally decided that it would be best if each went her own way and followed her own culinary preferences.
They did stay in touch. Although they didn't speak to each other, they did send smoke signals on special occasions like birthdays and Halloween. They also traded.
Liz lived on the south side of the island, where pineapples and man-eating plants grew. Fortunately for Liz, the man-eating plants didn't eat women, but she stayed clear of them anyway, putting her daily efforts into cultivating the pineapple trees. She could eat or trade them with Misty, whose side of the island had no pineapples at all but did have the occasional really big clam wander onto the beach to get a tan or answer nature's call, at which time Misty would nail the sucker either to eat or to trade for a pineapple from Liz.
After much wrangling on the matternegotiations made particularly tricky because of the lack of oral communicationLiz and Misty had worked out an exchange rate of one clam for one pineapple, and this equivalence relationship had remained stable for all of the three long years the two of them had been stranded on that beautiful if somewhat harsh little plot of land in the Pacific.
One day, Misty had a brilliant idea. She noticed that there were a whole lot of empty clam shells on the beach, so she decide to take a real clam she had just beaten senseless, open it up, split the meat in two, and put half of the clam meat into one of the empty shells.
She went as usual to make her trade with Liz; but instead of the usual deal, Misty handed her two clams, each of course containing only half the meat of an original, single clam. Liz suspected nothing and wouldn't have been able to verify the clam's worth, anyway, since she had no immediate access to a clam shell prying tool. Liz did look a little surprised at the escalation of the economic activity Misty was proposing but acknowledged that Misty would get two pineapples that day. Obviously, Liz had to work harder thereafter because of what appeared to her as real, extra currency flowing her way. In economics terms, Liz's real output increased, and it did so because the clam-based money supply increased.
Over time, however, once Liz had eaten some of these clams, she realized that it was taking twice as many to fill her up. Without a full stomach, Liz just didn't have the energy she needed to keep up the pace of her work on the pineapple groves.
Exhausted one day, Liz met Misty for their daily trade. As had become usual, Misty produced her two clams, and Liz handed her one pineapple. Liz had worn herself out producing twice as much for what was really the meat of only one real clam. She never did quite come to know that there was only half as much meat in each clam she was getting, but that didn't matter at all: it was purely a matter of capacity to produce under the circumstances of the standing terms of trade.
In terms of economics, this story is about the equation of exchange. Specifically, it is about three different equilibrium states of that equation as it went from its initial configuration to a short-term re-alignment and then to a long-term stability.
The equation of exchange looks like this:
Money Supply × Velocity of Money = Aggregate Price Level × Aggregate Output Level,
Now, you're probably saying, "Ah, yes, that's exactly what I was thinking when I read that tragic story about Liz and Misty." Of course, what you're probably thinking is something like, "Dude! That's some g-o-o-o-d stuff you're smokin' if you think that equation has anything to do with anything."
Okay, fine. Let's step through the equation piece by piece. On the left side, M is the supply of money: the amount of it in circulation.
V is the velocity of each unit of the currency: how many times each unit is used in a given period. We usually assume the velocity of money doesn't change during the periods we analyze, which means the number of times a unit of the currency is used doesn't increase or decrease during our scenarios.
So the left side of the equation is M×V: the amount of money in circulation multiplied by the number of times each unit of it gets used per period. M×V is just the total expenditures of an economy in a given period of time. For example, if there are ten one dollar bills in circulation, and on average each of them gets used twice in a year, then the total expenditures in the economy would be $10 × 2 times per year = $20 per year in total expenditures.
The right side of the equation is just the total nominal value of the goods and services of an economy. The word "nominal" means price-denominated, as opposed to "real," which means the actual counting of the units of the goods, themselves, without putting prices on them.
On that right side, P is the aggregate price level, or just the price of the average good (in a simplified way). Q is the aggregate real output of the economy (and notice that the Q by itself is "real" since it's a count of actual, physical things instead of a dollar value of them). As an example for the right side, let's say the economy produces a single good, which has an initial price level of $5 per unit, and the economy creates four of those per year. That means the total nominal (price-denominated) output of the economy is $5 per unit × 4 units per year, or $20 per year.
The equation of exchange simply states that the total expenditures, M×V, must be the same as the total nominal product, P×Q, of the economy in a given period of time.
In the situation on the island, the clams had originally been circulating at the rate of one per period, which would mean that the velocity of clams was exactly one, so we have V=1.
The money supply was one clam in each period of trading, so we have M=1.
On the other side when our story began, the real output of pineapples was one per period, so Q=1.
The agreed-upon equilibrium price for a pineapple was one clam, so P=1.
Hence, the equation of exchange captures this situation by stating that
or without the units to obscure the numbers,
But look what happened when the clams got watered down. For a while, something very cool was going on. The velocity of each clam stayed the same: each one of the clams was still being traded only once per period, so V stayed at a value of one. However, there were now two of the clams in circulation in each trading period, so the left side of the equation, M×V, which describes expenditures, became
so the M×V side became
Now for the right side of the equation. The price per pineapple was still one clam, but Liz selling the pineapples had to come up with two of them to meet Misty's clam-driven demand. The price stayed firm, but real output rose. In other words, P×Q became
hence P×Q became
Thus, we have a new equilibrium of the equation of exchange:
Notice that the equation of exchange is not in some sense "forcing" the situation; instead, it's merely explaining how the parts of an economy fit together.
What we've just seen was the short-run effect of an increase in the supply of clams that was not matched by any actual change in the fundamental dynamics of production of pineapples. Liz on the pineapple side of the island really didn't have any greater "capacity" to create pineapples, and she didn't have some new technology or anything like that. All she was doing was responding to what she saw as an increase in money she could make for bringing pineapples to market.
Now comes the long run. Liz was harvesting pineapples at a rate higher than she normally could, given the rate at which pineapples grew to harvestable size and given her own ability to gather pineapples in any period of time. Ultimately, the fact that she wasn't getting any more real meat in those two clams than she originally had in the one clam simply forced her to return to a real output of one pineapple. She simply could not produce two, actual pineapples per day, not in the long-run, anyway. But the only way she could then accommodate two clams being handed to her is if she were to revert to what it actually takes in terms of clam meat to deliver a pineapple. Those two clams have the meat of one of the original clams, and that was how much meat it really took for Liz to be able to harvest a single pineapple. Hence, she's going to have to charge Misty two of her watered-down clams for each actual, honest-to-goodness pineapple.
So here's what happened in the long run to the equation of exchange. The left side, M×V had already moved to its new configuration: that happened in the short run when the clam supply went up to two (while the velocity stayed at one). Thus, the left side of the equation hangs at
which means the left side of the equation will be 2×1, or 2.
The right side of the equation for the long-run scenario has changed. The price for each pineapple has risen to two clams, and the real output of pineapples has reverted back to one per period. Hence, the right side of the equation of exchange, P×Q, is in the long run going to be
which means the right side of the equation is now 2×1, or 2.
The long-run equilibrium configuration of the equation of exchange is this:
works out its equilibrium (the equation is in balance) as
Well, look at that. It really is still in equilibrium: the left side equals the right side, just as it did at the very beginning and just as it did in the short run. Not only that, look closely at the three states of equilibrium:
Ah. An increase in the money supply in the short run causes an increase in real output; but in the long run, the only effect is that real output reverts to what it was originally while the price of the output goes up.
In short-hand notation, it might look like this:
Notice something about that island economy. If Liz had actually been able to really produce more pineapples, she couldn't have sold them to the Misty unless Misty had more real (undiluted) clams. As an example, there was an brief incident where the hapless Peter of Lone Tree came ashore on the island, and Liz forced him to serve as her slave labor. With his help, Liz was able to produce two pineapples per period, but she couldn't sell both of them to Misty because she didn't have two real, undiluted clams. In other words, real growth rate of an economy requires a matching growth rate of the money supply. Frustrated by the lack of real money to reflect the real growth in output, Liz was planning to cast Peter back out to sea, where he would eventually be picked up by the floating Republican fund-raising cruise liner Washington HO! and made to serve as bartender under the tutelage of the earstwhile Tom Delay. As fate would have it, though, Peter was eaten by one of those man-eating plants that lived on Liz's side of the island.
Anyway, the point of that last paragraph was that it's not that a central bank should never increase the money supply; in fact, it must, but it should do so only at the rate at which the real output of the economy needs that extra money.
That makes the job of a central bank really hard. Think about it: if the central bank prints money too fast, real output would go up in the short run. That would give the central bank the impression that this real growth required even more money to be printed. But the first round of extra money would eventually be causing inflation and real output would be tending to revert back to its original level. But the central bank would have been printing even more money because it saw the real output of the economy growing from its first excess punch of money, and this would lead to a scenario something like a horse watching its wagon go by in front of it and thinking that it had to run faster to catch up with its cart, not realizing that it was actually pushing the cart to go faster and faster. That could be the beginning of a run-away horse and buggy as well as run-away inflation. The central bank erroneously thinks the economy is really growing well, but it's the central bank that's causing it to happen, and the way it's happening won't last.
And that's why a central bank should never, ever contemplate being in the business of helping (or hurting) an economy: short-run versus long-run effects of accommodative or punitive monetary policy simply cannot be foreseen with the clarity to distinguish between fundamental economic growth and mere reaction to the money supply manipulation.
In conclusion, returning to the story of the women on the island, the lesson should be clear and obvious. In summary, it is stated as such:
Inflation has one cause: too many clams chasing too few pineapples.
The Dark Wraith has thus delivered the tropical goods.
of this series.