<p>Assume there are two agents in an economy, $A$ and $B$, (and some costless transaction mechanism). Per time period, agent $A$ produces alone quantity of intermediate good $q_A$. Agent $B$, thorugh a company where it is shareholder, buys this quantity, the company inputs also some other intermediate good , say $q_B$, and the two together through a production function result in a final good quantity $(q_A,q_B) \to Q$. $Q$ is then bought by agent $A$ and agent $B$ as consumers, at price $P$. $PQ &gt; p_Aq_A$ since it embodies a larger amount of productive resources (assume no inflation, which is not essential here).</p>

<p>Now, for the first transaction to take place, the buying of intermediate good $q_A$, we need quantity of money $M_A=p_Aq_A$. This quantity of money is now held by agent $A$. How much money we want, in order to facilitate also the purchasing by both consumers of the final good? </p>

<p>It will depend on what kind of transactions we envisage to the end of the cycle.  Agent $A$ already has $M_A = p_Aq_A$ with which he can buy part of the final good. If $B$ buys the good pior to any other interaction with $A$, then $B$ must also hold quantity of money equal to $M_B = PQ - p_Aq_A$.  So the total quantity of money needed, in this scenario, is $PQ$, and the intermediate goods do not enter the final equation of the quantitative theory of money.  </p>

<p>Assume now that the only quantity of money available is $p_Aq_A$. What can we do to facilitate all transactions? Well, agent $A$ can buy first a part of the final good from company belonging to $B$, then the company will give the money to $B$ as dividends, and then $B$ will give the money to the company as consumer buying the rest of the final product. But in order for the transactions to happen <em>sequentially</em> as described, and be completed within the same time period as previously, money must "move faster". So in such a situation, the velocity of money will be higher than unity. </p>

<p>$$PQ = \left(\frac{PQ}{p_Aq_A}\right) \cdot M$$</p>

<p>where the term in the parenthesis is $\left(\frac{PQ}{p_Aq_A}\right)\equiv \mathbf v$, the velocity of money. But again, the "product" side of the equation will be $PQ$. No counting of intermediate goods. </p>

CC BY-SA 3.0
2017-12-05T14:27:38.787Z
The definition of v is residual. Of course, you can define Q as the final output, but that will change the definion of v. Denesp is correct. Pa*Qa is used twice.
chatGPT
CC BY-SA 3.0
2017-12-05T19:36:47.690Z
I liked your explanation but I don't think it supports your actual conclusion. Let us consider two radical examples. Case 1. Firm $A$ buys resources worth \$1 mill, makes a product worth \$1 mill 100 and sells it.  What is $PQ$ and what is $v$ $M$ in this case? Case 2. There are two firms. Firm $A$  buys resources worth \$1 mill, makes a product worth \$1 mill 1 and sells it to firm $B$, who increases its worth to \$1 mill 2 and sells it to $A$, who incr. value to \$1 mill 3 and sells it to $B$, etc. In the end $B$ sells product for \$1 mill 100. What is $PQ$ and what is $v$ $M$ in this case?
Giskard
CC BY-SA 3.0
2017-12-05T19:38:09.873Z
@denesp Where is consumption in your examples?
Alecos Papadopoulos
CC BY-SA 3.0
2017-12-05T19:38:31.193Z
The end product worth \$1 million 100 is consumed in both cases.
Giskard
CC BY-SA 3.0
2017-12-05T19:47:22.870Z
@densep In your first example, that's $PQ$ (in reality $PQ$ is consumption plus investment in nominal terms). Then, tell me the quantity of money available in the economy and the velocity is determined residually. In your second example, it is not clear whether there are third parties or not. From whom does $A$ makes the initial buy?
Alecos Papadopoulos
CC BY-SA 3.0
2017-12-05T19:54:48.950Z
My handle does not include the word 'dense'. (It's a popular misconception.) I understand that only $v \cdot M$ can be determined, not the separate values, that is fine. If you wish assume $M = \$ 5$ mill. 
Firm $A$ in case 2 makes the initial buy from the same people as the firm in case 1. If it helps assume people in same country.
Giskard
CC BY-SA 3.0
2017-12-07T11:52:35.207Z
Alecos I don't mean to rush you but I am wondering if you saw my last comment and if yes what the answer would be. ($PQ$ in the second case, $v \cdot M$ in both cases?)
Giskard
CC BY-SA 3.0
2017-12-08T01:25:56.243Z
@denesp I cannot find a satisfactory response at comment-level... I had intended with my answer to provide some micro-level intuition about the matter but I feel I may have made matters worse... I have to rethink my answer from scratch.
Alecos Papadopoulos
CC BY-SA 3.0
2018-01-01T01:02:42.157Z
@AlecosPapadopoulos I have thought some more about this question and I am pretty sure that your answer is incorrect, intermediate goods do matter when calculating $\nu$. Please tag me if you make an edit and I will remove my downvote.
Giskard
CC BY-SA 3.0
2017-12-05T13:55:05.553Z
2017-12-05T19:38:04.553Z
2017-12-05T19:38:04.553Z
Alecos Papadopoulos
<p>Yes, this is supposed to be the GDP. You can interpret it as being the sum of all aggregate value in the economy, so all intermediary goods and services are already in there. </p>

CC BY-SA 3.0
2017-11-04T22:17:33.033Z
2017-11-04T22:17:33.033Z
python_enthusiast
<p>Money has to be used in all transaction. So Q refers to all transactions. In the early literature Q refered to commodities. This includes everything, from inputs to outputs. So you should include not only GDP but also intermediate transactions.</p>

<p>Using only GDP is like thinking that only final goods were bought using money! This is plainly wrong.</p>

CC BY-SA 3.0
2017-12-05T13:57:19.927Z
This answer is wrong. The same money, the same paper bill, is used to facilitate multiple transactions, depending on its velocity. So we count only the nominal value of final output.
Alecos Papadopoulos
CC BY-SA 3.0
2017-12-05T20:34:27.343Z
The velocity depends on the definition of Q. And you can use different money. Do not forget bank credit. This is created and destroyed, without need to use paper bill.
chatGPT
CC BY-SA 3.0
2017-12-05T20:53:32.380Z
@user92817217 We are talking about the basic quantity theory of money here, nothing so fancy as bank credit, fractional reserve banking etc etc
Alecos Papadopoulos
CC BY-SA 3.0
2017-12-06T14:18:10.650Z
But M1 includes bank deposits, out of which credit is created. https://en.wikipedia.org/wiki/M1_(money_supply_measure) So if johnjohnny wants to use M1, bank credit must be acklowledged.
chatGPT
CC BY-SA 3.0
2017-12-05T11:26:38.997Z
2017-12-05T11:26:38.997Z
chatGPT
<p>I am testing the quantitative theory of money for South Africa. QP = Mv. It is fairly clear what M and P are (broad money, or M1, price index, etc). But I am puzzled with Q. Is it GDP or does it include also intermediary inputs?</p>

<p>The idea of the theory is that prices depend on the amount of money and the quantity of "goods and services". But since companies and people also pay for intermediate goods and services, I think I need to consider also intermediate inputs and not only final goods and services, as in GDP.</p>

<p>Any ideas? Thank you very much!</p>

<gdp><money><empirical-methods><quantity-theory-of-money>
What is Q in the quantitative theory of money?
johnjohnny
# What is Q in the quantitative theory of money?

(Asked by: username_0 on 2017-11-03)

I am testing the quantitative theory of money for South Africa. QP = Mv. It is fairly clear what M and P are (broad money, or M1, price index, etc). But I am puzzled with Q. Is it GDP or does it include also intermediary inputs?

The idea of the theory is that prices depend on the amount of money and the quantity of "goods and services". But since companies and people also pay for intermediate goods and services, I think I need to consider also intermediate inputs and not only final goods and services, as in GDP.

Any ideas? Thank you very much!

**Tags:** gdp, money, empirical-methods, quantity-theory-of-money


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## 3 answers

### Answer by username_1 on 2017-12-05. Score: 1

Assume there are two agents in an economy, $A$ and $B$, (and some costless transaction mechanism). Per time period, agent $A$ produces alone quantity of intermediate good $q\_A$. Agent $B$, thorugh a company where it is shareholder, buys this quantity, the company inputs also some other intermediate good , say $q\_B$, and the two together through a production function result in a final good quantity $(q\_A,q\_B) \to Q$. $Q$ is then bought by agent $A$ and agent $B$ as consumers, at price $P$. $PQ > p\_Aq\_A$ since it embodies a larger amount of productive resources (assume no inflation, which is not essential here).

Now, for the first transaction to take place, the buying of intermediate good $q\_A$, we need quantity of money $M\_A=p\_Aq\_A$. This quantity of money is now held by agent $A$. How much money we want, in order to facilitate also the purchasing by both consumers of the final good?

It will depend on what kind of transactions we envisage to the end of the cycle. Agent $A$ already has $M\_A = p\_Aq\_A$ with which he can buy part of the final good. If $B$ buys the good pior to any other interaction with $A$, then $B$ must also hold quantity of money equal to $M\_B = PQ - p\_Aq\_A$. So the total quantity of money needed, in this scenario, is $PQ$, and the intermediate goods do not enter the final equation of the quantitative theory of money.

Assume now that the only quantity of money available is $p\_Aq\_A$. What can we do to facilitate all transactions? Well, agent $A$ can buy first a part of the final good from company belonging to $B$, then the company will give the money to $B$ as dividends, and then $B$ will give the money to the company as consumer buying the rest of the final product. But in order for the transactions to happen *sequentially* as described, and be completed within the same time period as previously, money must "move faster". So in such a situation, the velocity of money will be higher than unity.

$$PQ = \left(\frac{PQ}{p\_Aq\_A}\right) \cdot M$$

where the term in the parenthesis is $\left(\frac{PQ}{p\_Aq\_A}\right)\equiv \mathbf v$, the velocity of money. But again, the "product" side of the equation will be $PQ$. No counting of intermediate goods.

> **Comments:**
> **username_2**: The definition of v is residual. Of course, you can define Q as the final output, but that will change the definion of v. Denesp is correct. Pa*Qa is used twice.  
> **username_3**: I liked your explanation but I don't think it supports your actual conclusion. Let us consider two radical examples. Case 1. Firm $A$ buys resources worth \$1 mill, makes a product worth \$1 mill 100 and sells it.  What is $PQ$ and what is $v$ $M$ in this case? Case 2. There are two firms. Firm $A$  buys resources worth \$1 mill, makes a product worth \$1 mill 1 and sells it to firm $B$, who increases its worth to \$1 mill 2 and sells it to $A$, who incr. value to \$1 mill 3 and sells it to $B$, etc. In the end $B$ sells product for \$1 mill 100. What is $PQ$ and what is $v$ $M$ in this case?  
> **username_1**: @denesp Where is consumption in your examples?  
> **username_3**: The end product worth \$1 million 100 is consumed in both cases.  
> **username_1**: @densep In your first example, that's $PQ$ (in reality $PQ$ is consumption plus investment in nominal terms). Then, tell me the quantity of money available in the economy and the velocity is determined residually. In your second example, it is not clear whether there are third parties or not. From whom does $A$ makes the initial buy?  
> **username_3**: My handle does not include the word 'dense'. (It's a popular misconception.) I understand that only $v \cdot M$ can be determined, not the separate values, that is fine. If you wish assume $M = \$ 5$ mill.  Firm $A$ in case 2 makes the initial buy from the same people as the firm in case 1. If it helps assume people in same country.  
> **username_3**: username_1 I don't mean to rush you but I am wondering if you saw my last comment and if yes what the answer would be. ($PQ$ in the second case, $v \cdot M$ in both cases?)  
> **username_1**: @denesp I cannot find a satisfactory response at comment-level... I had intended with my answer to provide some micro-level intuition about the matter but I feel I may have made matters worse... I have to rethink my answer from scratch.  
> **username_3**: @username_1 I have thought some more about this question and I am pretty sure that your answer is incorrect, intermediate goods do matter when calculating $\nu$. Please tag me if you make an edit and I will remove my downvote.  

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### Answer by username_4 on 2017-11-04. Score: 0

Yes, this is supposed to be the GDP. You can interpret it as being the sum of all aggregate value in the economy, so all intermediary goods and services are already in there.


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### Answer by username_2 on 2017-12-05. Score: 0

Money has to be used in all transaction. So Q refers to all transactions. In the early literature Q refered to commodities. This includes everything, from inputs to outputs. So you should include not only GDP but also intermediate transactions.

Using only GDP is like thinking that only final goods were bought using money! This is plainly wrong.

> **Comments:**
> **username_1**: This answer is wrong. The same money, the same paper bill, is used to facilitate multiple transactions, depending on its velocity. So we count only the nominal value of final output.  
> **username_2**: The velocity depends on the definition of Q. And you can use different money. Do not forget bank credit. This is created and destroyed, without need to use paper bill.  
> **username_1**: @user92817217 We are talking about the basic quantity theory of money here, nothing so fancy as bank credit, fractional reserve banking etc etc  
> **username_2**: But M1 includes bank deposits, out of which credit is created. https://en.wikipedia.org/wiki/M1_(money_supply_measure) So if username_0 wants to use M1, bank credit must be acklowledged.  

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