<p>Money demand is fixed because it depends on the real economy....that's an assumption. 
So when M changes only P can change. That's the theory. It's not really a theory. Just an accounting equality, since V is never defined exogenously. It's bad economics. :/</p>

CC BY-SA 4.0
2019-03-22T16:30:55.853Z
2019-03-22T16:30:55.853Z
RN_174_b
<p><span class="math-container">$M\cdot V=P\cdot Y \Leftrightarrow M=\frac{P}{V}\cdot Y\\
\frac{1}{V}=k \Leftrightarrow M=kPY$</span>
So suppose we keep <span class="math-container">$V$</span> and <span class="math-container">$Y$</span> fixed and vary <span class="math-container">$M$</span>, <span class="math-container">$P$</span> varies as well and this means <span class="math-container">$kPY$</span> also varies (because of P). More specifically when money supply goes up while keeping velocity and output constant, the price level has to rise,(raising money demand to equal money supply). </p>

CC BY-SA 4.0
2019-03-22T10:44:29.147Z
In my text book, Macroeconomics 7th edition by Gregory Mankiw, it says V = 1/k, there's no P there. What am I missing?
dolco
CC BY-SA 4.0
2019-03-22T11:48:53.027Z
i have edited the answer
user18214
CC BY-SA 4.0
2019-03-22T09:58:29.243Z
2019-03-22T12:24:19.880Z
2019-03-22T12:24:19.880Z
user18214
<p>I'm the OP. I've solved it. What I was missing was that the fixed supply is nothing but the 'real supply'.</p>

<p>1.real demand = kY (fixed)</p>

<p>2.real supply = M/P (fixed)</p>

<p>When they said "the central bank controls the money supply", it meant it manipulate the M only. So P should also change by the same rate to make the whole 'real' supply, M/P, equal to kY. It was so easy. I kind of feel stupid now :D</p>

CC BY-SA 4.0
2019-03-23T07:00:47.180Z
2019-03-23T07:00:47.180Z
dolco
<p>I'm not a native speaker so please excuse my English.</p>

<p>When they draw the result that the central bank's monetary supply determine the inflation rate, didn't they suppose many variables sticky?</p>

<p>With <strong>money supply</strong> matching up with the <strong>demand</strong>, they start their train of logic as follows. <strong>MV = PY</strong>, here the <strong>Y</strong> is fixed since it's exogenous, and <strong>V</strong> is fixed for the convenience of computation, so <strong>M</strong> controls the <strong>P</strong>... Okay I get that part, but what I wonder is that, when you fix the <strong>V</strong>, doesn't that make the <strong>k</strong> also fixed, which means <strong>kY</strong>, <strong>the money demand function</strong> is eventually fixed.</p>

<p>Then, how can they manipulate the <strong>M</strong> when they assumed <strong>M</strong> equals to the <strong><em>fixed</em></strong> <strong>demand of money</strong>?</p>

<quantity-theory-of-money>
I don't understand the MV = PY
dolco
# I don't understand the MV = PY

(Asked by: username_0 on 2019-03-22)

I'm not a native speaker so please excuse my English.

When they draw the result that the central bank's monetary supply determine the inflation rate, didn't they suppose many variables sticky?

With **money supply** matching up with the **demand**, they start their train of logic as follows. **MV = PY**, here the **Y** is fixed since it's exogenous, and **V** is fixed for the convenience of computation, so **M** controls the **P**... Okay I get that part, but what I wonder is that, when you fix the **V**, doesn't that make the **k** also fixed, which means **kY**, **the money demand function** is eventually fixed.

Then, how can they manipulate the **M** when they assumed **M** equals to the ***fixed*** **demand of money**?

**Tags:** quantity-theory-of-money

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## 3 answers

### Answer by username_1 on 2019-03-22. Score: 3

Money demand is fixed because it depends on the real economy....that's an assumption.
So when M changes only P can change. That's the theory. It's not really a theory. Just an accounting equality, since V is never defined exogenously. It's bad economics. :/


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### Answer by username_2 on 2019-03-22. Score: 2

$M\cdot V=P\cdot Y \Leftrightarrow M=\frac{P}{V}\cdot Y\\
\frac{1}{V}=k \Leftrightarrow M=kPY$
So suppose we keep $V$ and $Y$ fixed and vary $M$, $P$ varies as well and this means $kPY$ also varies (because of P). More specifically when money supply goes up while keeping velocity and output constant, the price level has to rise,(raising money demand to equal money supply).

> **Comments:**
> **username_0**: In my text book, Macroeconomics 7th edition by Gregory Mankiw, it says V = 1/k, there's no P there. What am I missing?  
> **username_2**: i have edited the answer  

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### Answer by username_0 on 2019-03-23. Score: 1

I'm the OP. I've solved it. What I was missing was that the fixed supply is nothing but the 'real supply'.

1.real demand = kY (fixed)

2.real supply = M/P (fixed)

When they said "the central bank controls the money supply", it meant it manipulate the M only. So P should also change by the same rate to make the whole 'real' supply, M/P, equal to kY. It was so easy. I kind of feel stupid now :D


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