Y=(a+b)(c+d)=(ac+ad+bc+bd)
If Q = ( 4 chairs + 4 tables+ 7 barrels of oil + 32 hours)
and
P= ( $7.5/chair + $20/table + $72.5/barrel + $130/counsel)
then
PQ=(4 chairs x $7.5/chair + 4 chairs x $20/table + 4 chairs x $72.5/barrel + 4 chairs x $130/counsel) + ( 4 tables x $7.5/chair + 4 tables x $20/table + …
You can fill in the rest…
If that’s all you have to say, I’ll take it as a concession.
Okay, so assuming PxQ has only $ as unit then what are the units of M and V ?
M [$] x V [$/time] = [$] ?
its true juan, some amount of money, does equal that same amount of money. A is A. maybe eventually scineram and the others will want to discuss economics…
to expand on my point, another qoute:
In Fisher’s “equation of exchange” version of the theory the critics
have pointed out other defects. In his The Value of Money
Mr. B. M. Anderson noted the following:
(a) The equation is an identical proposition. There are not a goods
side and a money side, as Fisher claims, but two money sides. “On one
side of the equation we have M, a quantity of money, multiplied by
V, an abstract number; on the other side of the equation, we have
P, a quantity of money, multiplied by T, an abstract number. The
product, one each side, is a sum of money. These sums are equal be-
cause they are identical. The equation asserts merely that what is paid
is equal to what is received.” There is, of course, no objection per se
to an identical equation. It is only the value of such an equation as a
revelation of causal relations that is questioned by Anderson.
Well, MV=PQ is, or at least tries to be, an equation - it’s not an identity in the strict mathematical sense. (a+b)^2 = a^2 + 2ab + b^2 OTOH is an identity.
You are right in the example of an exchange equation per a single good, but for the aggregage exchange equation, it is mathematically invalid.
scineram had to ignore basic algebra by doing (a+b)(c+d)=(ac+bd). This is clearly incorrect.
I already told you P and Q are vectors. Ever heard of scalar product?
M is the money supply, simply $. V then is unitless, a number.
A car has speed of 100 miles per hour. What distance does the car cover in half an hour ? …
distance traveled = speed x time.
[miles] = [miles/hour]x[hour] (that’s an identity).
hours cancel out and you get [miles] = [miles]
distance traveled = speed x time. That’s an equation which gives ‘real’ information about a physical phenomenon.
What category does MV=PQ belong to ?
It is not - V is an amount of money changing hands in a given period - it must be denominated in $/time.
I anticipated that excuse.
You mean dot product! A scalar product has a vector for its resut.
(4 chairs + 7 tables +…) is now a vector? Why? because this it is the only way you can perform the multiplication.
Now let me get this straight. A real economy should have millions or even billions of dimensions for such vectors.
You are now telling me that economists are hypothetically using a multi-billion demensional vector as a mental construct?
A mental construct with billions of dimensions?
Anybody who says he can mentally grasp more then 3 dimensions is not human. multi-dimensional vectors (more then 3) exist in the hard scienses but they are useful not as mental aids, but because they predict causal events.
No, that is given by the product PQ. You could say V is how many times 1 dollar changes hands on average.
It’s an analytical tool, just as the ERE is. And if fact, the exact same point could be made about the ERE. In a developed economy the sheer number of exchanges that would go on in the ERE defy human understanding, this doesn’t mean it’s not valid as a concept. Seriously, this whole topic amounts to nothing more than an ad hoc rejection of anything the looks remotely mainstream.
UH OH. How many times IN A GIVEN PERIOD.
Scalar and dot product are synonims, also with inner product. You confuse them with cross product.
Only you wrote (4 chairs + 7 tables +…), I never did that in this thread.
Hahahahaha. This is clearly a lost cause for you.
Yes, on average during, say, a year.
Just like your attempt to deny that V must be denominated in $/time is a lost cause.
If $1 changes hands 3 times in a year then you have :
velocity = $1 x 3 IN A YEAR = $3 PER YEAR. Units : [$] x [unitless factor] / [time]
You can’t get around the fact that velocity is defined as rate of change with respect to TIME.
No, the whole equation refers to a given period. P and Q contain the prices and volumes of all exchanges during the time, M is the nominal money supply, the amount of gold coins available. Therefore V is indeed unitless.
can you explain how this ‘equation’ is ‘useful’ to economists?