I have a young friend whose husband just got back from Afghanistan. He was offered a promotion which he took, but was then assigned to a different unit (reserves) who are being deployed to Africa this summer.

Does anyone have leads as to the size of our troops in Africa? I believe Africa theater has its own command structure now.

“Based in Stuttgart, Germany, Africa Command has only about 2,000 military and civilian personnel assigned to coordinate U.S. defense programs in about 38 African countries, although 5,000 or more U.S. troops are frequently on the continent for operations and training missions.”

Jerry Critter, I am currently reading “Chosen Soldier” a book following a Special Forces class during early Iraq actions. Even then Nat Guard and Reserve Units were very active components.

Active Duty Special Operations (SO) operators can expect to be deployed ~ 75% of the time, and Reserve and Nat. Guard units are close behind.

Afghanistan is a case study in how to perform small unit asymmetrical actions using SO tactics and units. Today’s world is a growing Hot Bed of these actions. Most of the African activity will never be publicized, let alone which units partook.

SO operators are all volunteers and the best of the best of an all volunteer military. Reservists and Nat Guard units would naturally want in on that kind of action.

Sounds like OUR CIA buddies are about to get a little “indiscreet” again. Gitmo has some empty beds that need filling. (Black people being held prisoner for torture in Cuba. What a novel idea!)

On a related note, and longer term, the U.S. is the only superpower and has a world empire to defend, somewhat similar to the Roman empire, which lasted hundreds of years.

The American empire will also likely last hundreds of years. This depression is only a “soft-patch.”

Nero followed Claudius, like Obama followed Bush. The Roman Empire lasted for hundreds of years even after Nero.

After the Roman Empire fell, there was a thousand years of economic stagnation, called the “Dark Ages.”

Some people underestimate the value of the Fed. Before the Fed, per capita real GDP growth averaged 1.38% a year from 1814-1912, and after the Fed, it averaged 2.16% per year from 1914-2010. Of course, there are other factors that contributed to faster growth, including fiscal policy and the establishment of the minimum wage. Also, it should be noted, large economies tend to grow more slowly than small economies.

In the equation MV = PT, if M and P are constant, then V = T, i.e. V, the velocity of money, or the number of times money is exchanged, equals T, the number of transactions, or the quantity of goods exchanged. T can be represented by real GDP.

The goal of monetary policy is to keep actual GDP close to potential GDP, which smooths-out business cycles creating sustainable growth, which is optimal growth. The fact that there are monetary tightening and easing cycles, to close output gaps, are attempts to smooth-out T in the short-run. V and T fluctuate in the short-run, which require adjustments in M to stabilize P and smooth-out T. For example, if people decide to hoard money, then V and T will fall (in the short-run). So, M needs to rise (higher than a constant growth rate).

Changes in fiscal policy can change the velocity of money. However, in the long run, V and T are constant. So, M equals P.

Moreover, there are positive and negative shocks to the system in the short-run that require adjustments in the money supply, e.g. in recent years, technology (at the height of the Information Revolution), Y2K, 9-11, oil shocks (or commodities in general), the creative-destruction process (mostly from 2000-02), the financial crisis, etc..

When the Fed targets prices, output fluctuates little. When the Fed targets output, prices fluctuate a lot, which leads to instability. I suspect, if the Fed targeted the money supply, that would also lead to instability, because of shifts in the foreign exchange market or changes in the velocity of money in the short-run. However, the money supply determines prices in the long-run.

The Fed doesn’t micromanage the economy, e.g. to determine winners and losers or redistribute wealth. It creates or destroys money, to smooth out business cycles.

Before the Fed, there were many periods of economic booms and busts.

List of recessions in the United States – Wikipedia

Recessions in the Industrial Revolution – 1871-1914

I agree that if M and P are constant, their derivatives are zero. However, this says nothing about the values of V and T, and certainly does not require that V = T.

If you think I am wrong, where is the error in my example that proves that M and P are NOT equal when T and V are constant and not equal?

Assuming that M and P are constant and equal to “a” (a = P/M )

Then V=aT.

Now if you wanted to know about the rate of change of V as a function of T, then you would take the first derivative of “aT”. What you end up with is not that V = T, but rather that the rate of change of V is equal to the rate of change of T. Quite a different thing.

Its been a while, and my understanding may be rusty, but I think that is how it works.

You are almost right Linnus. The only correction to what you said is at the end. If you take the derivative of aT, you get “a” times the derivative of T, so that the rate of change of V is equal to “a” times the rate of change of V.

PT: May I point out, from 1812-1914people road a horse to work or walked and ALL communication was a letter or a hootnaholler. Today WE compute&jet commute.

In Fisher’s Quantity Theory, if the money supply changes, the price level must change by the same percentage. This is so because

V and T are fixed, with respect to the money supply.

MV = PT where V and T are constant means that

[Change in P]/P = [Change in M]/M

In this model, changes in the money supply have no effect on the volume of transactions or velocity. In fact, changes in the money supply have no effect on anything except the price level.

Increasing the money supply can only cause higher prices.

Fishers variable T, which does not change in the short run, is represented in modern economics by “natural” or potential real GDP.

Oh, PT. In one of your comments above (the long one) you said that T fluctuates in the short term. Now you are saying that it does not change in the short term.

Not only have you not clarified your earlier math errors, now you are changing what one of the variables does in the short term.

You first made an assertion that Jerry “obviously doesn’t understand math,” and then demonstrated that if there is someone in the conversation who doesn’t understand math it is not Jerry. You made an incorrect mathematical assertion, which Jerry pointed out, and you do not have the intellectual honesty to own up to it.

The economic theory you are promoting may or may not be correct. I am still trying to understand your point. But your mathematical assertions are, at a grade school level, incorrect.

Linus, you and Jerry are creating unnecessary math, which don’t contradict the succinctness of my math. Actually, your math is like high school math at best. I’ve shown Jerry’s math is incorrect and ignored your math attempts.

I don’t disagree with the rate of change. It’s unnecessary, because the equality still holds, which you seem to disagree:

I stated before:

In the equation MV = PT, if M and P are constant, then V = T, i.e. V, the velocity of money, or the number of times money is exchanged, equals T, the number of transactions, or the quantity of goods exchanged.

Also, I may add, there are many math shortcuts in economics. I just happened to know beforehand V = T, which you both stated is incorrect, even after doing some math.

Moreover, in using real numbers, estimates are made. For example, what’s 231 / 7? You can do it in your head:

7 X 10 = 70, then 70 X 3 = 210 (10 X 3 = 30), with 21 left over, and then 21 / 7 happens to be 3.

So, the answer is 33.

Normally, I would go directly to 7 X 30 = 210. However, there are several ways.

You are continuing to insist that “In the equation MV = PT, if M and P are constant, then V = T”, even when shown a case where that is not true.

In answer to my questioning your statement, you replied, “If M and P are constant, the derivative of a constant is zero. So, V = T”.

Both Linus Bell and myself pointed out to you that even though the derivative of a constant is zero, it does not prove that V = T, and in fact showed that it does not.

V = T only for the case where M = P. And in this case, M and P do not even have to be constant. They simply have to vary at the same rate, so that they are always equal.

In fact I gave you an example where M and P are constant and V does not equal T. However, you chose to conveniently ignore my example.

So it is time for you to prove what you say is true. Don’t just say it. Don’t just say you know it. Prove it mathematically. Let me get it started for you.

Given:
MV = PT
and M and P are constant.

Prove that V = T.

Like our math teachers use to say, “Show your math.” Show me mathematically how you go from MV = PT, and M and P are constant to V = T. And don’t give me the trivial solution that M = P, because all you said was that M and P are constant. You did not say they have to be equal.

And don’t give me any double talk about math shortcuts. If you are going to use math to justify your statements, you must use it correctly or state your short cuts so that the readers can evaluate them for themselves.

If you want to be taken seriously on this blog, your math and mathematical statements and mathematical conclusions must be correct.

I don’t think you can do it, at least do it mathematically correctly. I think what we are looking at is,

See! For V = T, M must equal P, but you did not say that. What you said was the M and P were constant, not that they were equal. In fact they must be equal in order for V to equal T. They don’t even have to be constant, just equal.

The fact that you resorted to M = P, shows that your original statement that when M and P are constant, V = T is wrong. In other words, you are not able to prove that V = T without resorting to the special case where M = P, a condition you just now admit.

And, of course, your statement,

” If M and P are constant, the derivative of a constant is zero. So, V = T.”

is just crap, unless you once again add the condition that M = P, a condition you failed to mention. And once you add M = P, M and P no longer need to be constant, making your statement irrelevant.

If you are going to use math, use it correctly. Otherwise, just give your opinions and leave the math to people who know how to use it. As has often been said by others, you are entitled to your own opinions, but you are not entitled to your own facts.

I have a young friend whose husband just got back from Afghanistan. He was offered a promotion which he took, but was then assigned to a different unit (reserves) who are being deployed to Africa this summer.

Does anyone have leads as to the size of our troops in Africa? I believe Africa theater has its own command structure now.

http://articles.latimes.com/2014/mar/07/world/la-fg-usmil-africa-20140308

“Based in Stuttgart, Germany, Africa Command has only about 2,000 military and civilian personnel assigned to coordinate U.S. defense programs in about 38 African countries, although 5,000 or more U.S. troops are frequently on the continent for operations and training missions.”

Dan, AFCOM is a Special Forces hot bed, so its personnel count is very, very fluid and and only a handful would know any count.

Seems to me that this should be a deployment for Regulars nor Reserves. What gives?

Jerry Critter, I am currently reading “Chosen Soldier” a book following a Special Forces class during early Iraq actions. Even then Nat Guard and Reserve Units were very active components.

Active Duty Special Operations (SO) operators can expect to be deployed ~ 75% of the time, and Reserve and Nat. Guard units are close behind.

Afghanistan is a case study in how to perform small unit asymmetrical actions using SO tactics and units. Today’s world is a growing Hot Bed of these actions. Most of the African activity will never be publicized, let alone which units partook.

SO operators are all volunteers and the best of the best of an all volunteer military. Reservists and Nat Guard units would naturally want in on that kind of action.

Sounds like OUR CIA buddies are about to get a little “indiscreet” again. Gitmo has some empty beds that need filling. (Black people being held prisoner for torture in Cuba. What a novel idea!)

On a related note, and longer term, the U.S. is the only superpower and has a world empire to defend, somewhat similar to the Roman empire, which lasted hundreds of years.

The American empire will also likely last hundreds of years. This depression is only a “soft-patch.”

Nero followed Claudius, like Obama followed Bush. The Roman Empire lasted for hundreds of years even after Nero.

After the Roman Empire fell, there was a thousand years of economic stagnation, called the “Dark Ages.”

ALL WE need now is an emperor.

Some people underestimate the value of the Fed. Before the Fed, per capita real GDP growth averaged 1.38% a year from 1814-1912, and after the Fed, it averaged 2.16% per year from 1914-2010. Of course, there are other factors that contributed to faster growth, including fiscal policy and the establishment of the minimum wage. Also, it should be noted, large economies tend to grow more slowly than small economies.

In the equation MV = PT, if M and P are constant, then V = T, i.e. V, the velocity of money, or the number of times money is exchanged, equals T, the number of transactions, or the quantity of goods exchanged. T can be represented by real GDP.

The goal of monetary policy is to keep actual GDP close to potential GDP, which smooths-out business cycles creating sustainable growth, which is optimal growth. The fact that there are monetary tightening and easing cycles, to close output gaps, are attempts to smooth-out T in the short-run. V and T fluctuate in the short-run, which require adjustments in M to stabilize P and smooth-out T. For example, if people decide to hoard money, then V and T will fall (in the short-run). So, M needs to rise (higher than a constant growth rate).

Changes in fiscal policy can change the velocity of money. However, in the long run, V and T are constant. So, M equals P.

Moreover, there are positive and negative shocks to the system in the short-run that require adjustments in the money supply, e.g. in recent years, technology (at the height of the Information Revolution), Y2K, 9-11, oil shocks (or commodities in general), the creative-destruction process (mostly from 2000-02), the financial crisis, etc..

When the Fed targets prices, output fluctuates little. When the Fed targets output, prices fluctuate a lot, which leads to instability. I suspect, if the Fed targeted the money supply, that would also lead to instability, because of shifts in the foreign exchange market or changes in the velocity of money in the short-run. However, the money supply determines prices in the long-run.

The Fed doesn’t micromanage the economy, e.g. to determine winners and losers or redistribute wealth. It creates or destroys money, to smooth out business cycles.

Before the Fed, there were many periods of economic booms and busts.

List of recessions in the United States – Wikipedia

Recessions in the Industrial Revolution – 1871-1914

Period – Percent Decline of Business Activity

1873-79 – 33.6%

1882-85 – 32.8%

1887-88 – 14.6%

1890-91 – 22.1%

1893-94 – 37.3%

1895-97 – 25.2%

1899-00 – 15.5%

1902-04 – 16.2%

1907-08 – 29.2%

1910-12 – 14.7%

1913-14 – 25.9%

Recessions in the Information Revolution – 1982-2007

Period – Percent of Contraction

1990-91 – 1.4%

2001 – 0.3%%

PT — “In the equation MV = PT, if M and P are constant, then V = T,”

And

“However, in the long run, V and T are constant. So, M equals P.

Sorry, PT, those statements are completely wrong. V and T are equal only if M and P are equal. It doesn’t matter if they are constant.

For example, let’s assume they are constant and V=1 and T=2. Then M= 2P.

Jerry, obviously, you don’t understand math. If M and P are constant, the derivative of a constant is zero. So, V = T.

The same for the derivatives of V and T.

I agree that if M and P are constant, their derivatives are zero. However, this says nothing about the values of V and T, and certainly does not require that V = T.

If you think I am wrong, where is the error in my example that proves that M and P are NOT equal when T and V are constant and not equal?

PeakTrader,

I am sitting here scratching my head trying to understand why you are talking about derivatives at all. Please explain.

MV = PT.

Then V=PT/M, or V=(P/M)T

Assuming that M and P are constant and equal to “a” (a = P/M )

Then V=aT.

Now if you wanted to know about the rate of change of V as a function of T, then you would take the first derivative of “aT”. What you end up with is not that V = T, but rather that the rate of change of V is equal to the rate of change of T. Quite a different thing.

Its been a while, and my understanding may be rusty, but I think that is how it works.

You are almost right Linnus. The only correction to what you said is at the end. If you take the derivative of aT, you get “a” times the derivative of T, so that the rate of change of V is equal to “a” times the rate of change of V.

You are correct that it does not say V = T.

PT: May I point out, from 1812-1914people road a horse to work or walked and ALL communication was a letter or a hootnaholler. Today WE compute&jet commute.

Jerry,

Thanks… d(cu)/dx = c(du/dx).

Linus, I’m showing the equation has some usefulness in determining real GDP or MV / P = T and nominal GDP or M = PT / V.

You may want to see this link from Rutgers University (at bottom of page):

http://ctaar.rutgers.edu/gag/NOTES/macnotes7.html

In Fisher’s Quantity Theory, if the money supply changes, the price level must change by the same percentage. This is so because

V and T are fixed, with respect to the money supply.

MV = PT where V and T are constant means that

[Change in P]/P = [Change in M]/M

In this model, changes in the money supply have no effect on the volume of transactions or velocity. In fact, changes in the money supply have no effect on anything except the price level.

Increasing the money supply can only cause higher prices.

Fishers variable T, which does not change in the short run, is represented in modern economics by “natural” or potential real GDP.

Obviously, the assumption is the economy is already at full employment.

Or a long run assumption.

Oh, PT. In one of your comments above (the long one) you said that T fluctuates in the short term. Now you are saying that it does not change in the short term.

Not only have you not clarified your earlier math errors, now you are changing what one of the variables does in the short term.

Why should we believe anything you are saying?

Jerry, that’s untrue, and I made no math errors.

Moreover, T fluctuates in the short-run, not in the long-run.

T is potential output in the long-run and actual output in the short-run.

In the long run, potential output = actual output, not necessarily in the short-run.

PeakTrader,

You first made an assertion that Jerry “obviously doesn’t understand math,” and then demonstrated that if there is someone in the conversation who doesn’t understand math it is not Jerry. You made an incorrect mathematical assertion, which Jerry pointed out, and you do not have the intellectual honesty to own up to it.

The economic theory you are promoting may or may not be correct. I am still trying to understand your point. But your mathematical assertions are, at a grade school level, incorrect.

T representing “natural” or potential real GDP doesn’t change in the short-run.

T representing actual real GDP changes in the short-run.

Potential real GDP = actual real GDP in the long-run, not necessarily in the short-run.

See the difference?

Also, I may add, PT is nominal GDP.

Linus, you and Jerry are creating unnecessary math, which don’t contradict the succinctness of my math. Actually, your math is like high school math at best. I’ve shown Jerry’s math is incorrect and ignored your math attempts.

And, I responded to your question before above.

PeakTrader,

Q.E.D

Unbelievable!

Jerry,

I am in awe.

Jerry and Linus, you haven’t contradicted any of my math and economics. Yet, your responses indicate you believe you did.

I don’t disagree with the rate of change. It’s unnecessary, because the equality still holds, which you seem to disagree:

I stated before:

In the equation MV = PT, if M and P are constant, then V = T, i.e. V, the velocity of money, or the number of times money is exchanged, equals T, the number of transactions, or the quantity of goods exchanged.

Also, I may add, there are many math shortcuts in economics. I just happened to know beforehand V = T, which you both stated is incorrect, even after doing some math.

Moreover, in using real numbers, estimates are made. For example, what’s 231 / 7? You can do it in your head:

7 X 10 = 70, then 70 X 3 = 210 (10 X 3 = 30), with 21 left over, and then 21 / 7 happens to be 3.

So, the answer is 33.

Normally, I would go directly to 7 X 30 = 210. However, there are several ways.

You are continuing to insist that “In the equation MV = PT, if M and P are constant, then V = T”, even when shown a case where that is not true.

In answer to my questioning your statement, you replied, “If M and P are constant, the derivative of a constant is zero. So, V = T”.

Both Linus Bell and myself pointed out to you that even though the derivative of a constant is zero, it does not prove that V = T, and in fact showed that it does not.

V = T only for the case where M = P. And in this case, M and P do not even have to be constant. They simply have to vary at the same rate, so that they are always equal.

In fact I gave you an example where M and P are constant and V does not equal T. However, you chose to conveniently ignore my example.

So it is time for you to prove what you say is true. Don’t just say it. Don’t just say you know it. Prove it mathematically. Let me get it started for you.

Given:

MV = PT

and M and P are constant.

Prove that V = T.

Like our math teachers use to say, “Show your math.” Show me mathematically how you go from MV = PT, and M and P are constant to V = T. And don’t give me the trivial solution that M = P, because all you said was that M and P are constant. You did not say they have to be equal.

And don’t give me any double talk about math shortcuts. If you are going to use math to justify your statements, you must use it correctly or state your short cuts so that the readers can evaluate them for themselves.

If you want to be taken seriously on this blog, your math and mathematical statements and mathematical conclusions must be correct.

I don’t think you can do it, at least do it mathematically correctly. I think what we are looking at is,

“Garbage in, garbage out”!

Jerry says: “Given:

MV = PT

and M and P are constant.

Prove that V = T.”

MV = PT, or V = PT / M

In the long run, M = P. So, V = T.

See! For V = T, M must equal P, but you did not say that. What you said was the M and P were constant, not that they were equal. In fact they must be equal in order for V to equal T. They don’t even have to be constant, just equal.

The fact that you resorted to M = P, shows that your original statement that when M and P are constant, V = T is wrong. In other words, you are not able to prove that V = T without resorting to the special case where M = P, a condition you just now admit.

And, of course, your statement,

” If M and P are constant, the derivative of a constant is zero. So, V = T.”

is just crap, unless you once again add the condition that M = P, a condition you failed to mention. And once you add M = P, M and P no longer need to be constant, making your statement irrelevant.

If you are going to use math, use it correctly. Otherwise, just give your opinions and leave the math to people who know how to use it. As has often been said by others, you are entitled to your own opinions, but you are not entitled to your own facts.