Thursday, January 22, 2009

Today's lesson, the equation of exchange

In today's Senate confirmation hearing, Treasury Secretary Timothy Geithner talked about how restoring the banking system could require spending "trillions of dollars." The result of such a large scale increase in the money supply is that inflation will occur due to the formula known as the Exchange of Equation. This formula, MV=PQ states that the number of dollars in circulation(M) times the number of times they change hands in a year(V) is equal to the average price of all goods sold during the year(P) times the number of goods sold during the year(Q). By definition velocity is relatively constant and only moves greatly during a recovery or a depression when people are afraid to spend money.

Using this formula, by increasing the money supply X dollars means that those X dollars are spread out by the percentage change in the money supply equalling the percentage change in price. The previous statement presupposes that Q is unchanged or drops, which is likely given the economic slowdown occurring. As a result, those trillions of dollars in new spending will end up translating into fractions of dollars and cents on goods to spread out the increased money supply over the goods produced and sold in the country. (If Q increased it would be simple arithmetic to find if P rose or fell by having %(delta)M=%(delta)P+%(delta)Q) A little inflation is a given in an economic system because goods are scarce so over time the value should rise do to increasing marginal costs to produce.

When the money supply greatly increases relative to GDP growth, however that is when problems occur. When that happens the costs of doing business increase faster than a firm can deal with so people get laid off or their real wage falls.

5 comments:

John Médaille said...

This equation is not nearly so neat as it appears. V is not constant, nor even nearly, as Volker found out when he was at the Fed; the speed kept changing faster then he could adjust the rates. Nor is M so neat, since what counts as money covers a range of instruments, some with more "V" than others. And when trillions of paper "wealth" have been wiped out, the value of M is always ambiguous.

Further, distributional issues are left out of the equation. If, for example, you printed up a trillion dollars and gave it to me (God-willing) it would have no effect on inflation, because I simply couldn't spend or invest it fast enough to make a difference. If you distributed it evenly among the population, the effect would be greatly different, but even here there is a pitfall.

For if it were evenly spread, this would affect both V and Q; the initial result would be inflationary, but Q would rise rapidly in an effort to capture more of the M, and investments funds would likely be more available to help this along.

Further, it depends on where the money goes. Creating vast amounts of credit for the housing market leads to housing inflation, as we have seen, but does not equally affect all prices. Further, the funds that go to mere speculation return as profits to a few, or as losses. They may not have a simplistic relation with inflation.

The bottom line is that the formula describes too little and predicts nothing. Even Friedman, at the last, had to agree that he got it wrong. In the highly intentional world of exchange, it is always suspicious to see neat formulae with have little relation to the way humans act, the way things are distributed. As a distributist, I recognize a central function for both distributive justice and distribution functions. These are not merely moral, but technical requirements.

John said...

Let me address each of your points individually.

1)V is not constant, that is correct but it is within a small band of movement outside of a period of economic collapse. The problem that is arising from traditional macroeconomic theory is that the traditional money supply is being supplanted by paper assets which may or may not be on the books, which brings me to:

2)The value of the total money supply is always ambiguous to the extent that there are monetary instruments that are not recorded or kept hidden from the official M number. This has become especially obvious now that the "value" of stocks and bonds has readjusted to the reality that the issues were only valuable because people believed them to be, and not because they held an intrinsic worth due to their utility. Credit default swaps and margin purchases would be two areas where this disconnect between the market value and the real asset value occurred.

3)If the M were evenly spread it would not necessarily change the rate of V, since that would depend on the marginal propensity to consume by a society. If the MPC is low, then the money will not circulate quickly as it is put into savings and may circulate slower than the current money stock. In a high MPC society such as this nation, however, your statement is true in the short term. This kind of rapid infusion of capital into investment markets causes bubbles as money flows into one sector on the belief that because some firms may be making a profit now, others should also try ot make a profit. Thus the margins shrink from competition driving down price and many firms fail.

John Médaille said...

I think the assumption of a near constant V is much too simplistic, especially since it is affected by MPC/S. But it would seem to me problematic to make any statements about V is you don't know where all the M is, is different kinds of M move at different rates at different times. Nevertheless, these critiques would only affect the usefulness of the formula, not its validity.

More important is the fact that the relationship between M and Q is dynamic, not static. A change in M will affect Q (and likely V, as well). Moreover, the change is not symmetric to the sign of the change; that is, inflationary and deflationary changes act in different ways.

These considerations affect the very validity of the formula. The basic problem is that even a primitive economy cannot be described by static formulas. A dynamic formula needs to capture the relationships with V and the MPC/S, as well as its relationship with M, and M's relationship with Q. This would not be a simple formula.

SassyDefiance89 said...

Dear Mr. Economist (Invisible Boot) and Mr. Distributist (JM),

Yes, I've been following this particular discourse... I understand the "ambiguity" of the factors in the equation and their inconstancy and that a lot of factors can influence the outcome of such "seemingly" simple equation -- I am fully aware that you are both highly cultured and highly intelligent and highly educated.

Actually I admire and give kudos to both of you...

But for the sake of educating and enlightening an ordinary citizen -- such as myself who does not have any background on high finance or the advance or even a beginner's background in the field of Economics - may I please ask you that you relate the equation with our present crisis.

I will understand if you will both concur that my request can not be accommodated -- but I need a legitimate and logical reason as to the why it's not doable or if my request can't be granted.

Mr. John Medaille, I thought I recognize your name... I checked Eiusdem Generis and now, I remember - Cattus Vobiscum (CV) sort of recommended you as sort of a person who is versed with DISTRIBUTIVISM together with 2 more gentlemen...

I'm glad that you found John's (Mr. Economist's) blog and finally shared your point of view and wisdom.

Now, my next question or request is this, (I have asked Mr. Economist this already and he has truly tried to answer my question -- to the best that he pssibly can).

So, dear Mr. John Medaille I am addressing these questions to you--- How do we interject or introduce MORALITY into the field of Economics? How do we factor in -- freewill?

How do we factor in the consequences of those myriads of dizzying yet magical Economics equations and algorithms when we know that human lives (human beings' source of livelihood) are at stake when these Economics equation/s and theorem have and will be applied and pushed to the EXTREME?


I am well aware that the male and female brains have a different sort of tackling and looking at problems... I do not wish to change anyone of you and that goes without saying that I am banking that you will not wish to change mine... LoL.

But gentlemen, if we do not address the issue fairly and squarely and grab it by its sharp and slippery horns -- we are not going to solve anything -- we are just going to be stuck with our fancy Economics algorithms and theorem... great for highly and intellectually stimulating fodder and looks good on paper... but I want us (lead me,--- educate me... guide me --- inspire me - and when I say "me" I mean me--- as representing the future generation or as an ordinary citizen fed- up with the system who is corrupt to its core)

So, yes, give me those fancy equations -- I can do research.... I will ask pertinent questions... I may find it dizzying and overwhelming and it may take time for me to grasp it or there will be lots of times that I may not even grasp it at all --- But with God's grace I've decided that no one and nothing will intimidate me! If I don't understand it --- I will search, I will ask for help and clarification and if my brain has reached its maximum potential --- I'll stop and surrender --- LoL.

So, please... I beg on bended knees... stop divorcing or detaching Economics from Morality.

Because gentlemen -- IDEAS/IDEALS ultimately have CONSEQUENCES when people decide to act upon them... especially --- most especially when some highly intelligent and corrupt/evil-minded group of individuals or even an individual decide/s to implement or apply such fancy Economic equations and theorem to the extreme!

John Médaille said...

Dear Sassy, I am sorry I haven't gotten back to this; I didn't know anybody but me and the IB were reading this or would be interested in my critique.

But to answer your question, you do not inject morality into economics; economics IS morality at the level of practice. Willy-nilly, want it or not. If the social order believes in a dog-eat-dog morality, their economics will reflect that. If it believes that some men are made to be masters and others slaves, their economic system will reflect that. So economics is practical morality.

The question really is, "What should the economics of a Christian be?" (or at least, that is my question, as a theologian.) The answer is simple: "What you take out of the economy by consumption should be equal or less than what you put in by production." That's it.

That's the whole science. But as with other sciences that have a simple principle (e.g., hydrolics: water seeks its own level) the actual practice can be difficult. Nevertheless, we can state the obvious: that where there is wealth without work, there must also be work without wealth. When one consumes more than he produces, another must produce more than he consumes. Where what we get approximates what we give, there is justice; when it does not, there is inequity.

Inequitable economics cannot reach equilibrium, by definition. There will be great imbalances between supply and demand. There are ways to cover up the imbalances--for a time. Two ways (other than charitable redistribution) are one, government redistribution or spending ("stimulus"), and usury (consumer credit.) In the first the govmint manages demand through various means; in the second, the people with more than they can spend lend to those with less then they need, or think they need.

But both are unlikely to last for long. The first has worked for 60 years, but I don't think it will work for much longer. The second is a ponzi-scheme from the start, always subject to sudden collapse. Both are failing at the same time, and there may not be a way out.

Or rather, the only way out is to re-establish justice, and that is what distributism is all about.