<p>You can make $P$ the subject of the equation:
$$P=\frac{M-L} {ky} $$ then find the derivative $$\frac{\mathrm d P} {\mathrm d M} = \frac 1{ky}&gt;0$$ to show there is a positive relationship (when $M$ increases, $P$ increases). The elasticity answers your question about proportionality: \begin{align*} 
\frac{\mathrm d P} {\mathrm d M} \cdot \frac MP &amp;= \frac 1{ky}\left( \frac {kPy} P + \frac {L \cdot ky} {M-L} \right) \\
&amp;= 1 + \frac L{M-L} \end{align*} shows that $P$ increases more than proportionally (because the elasticity is greater than 1).</p>

CC BY-SA 4.0
2018-06-24T12:58:42.337Z
2018-06-24T13:13:17.020Z
2018-06-24T13:13:17.020Z
ahorn
<p>Consider a macroeconomy defined by following equations:<br>
<span class="math-container">$$M = kPy + L(r)$$</span> 
<span class="math-container">$$S(r) = I(r)$$</span> 
<span class="math-container">$$y = m $$</span><br>
 Where <span class="math-container">$M$</span> is money supply, <span class="math-container">$P$</span> is price level, <span class="math-container">$y$</span> is output, <span class="math-container">$r$</span> is interest rate, while <span class="math-container">$k,m$</span> are constants. <span class="math-container">$S(r)$</span> is saving function with <span class="math-container">$S'(r) &gt;0$</span>, <span class="math-container">$I(r)$</span> is investment function with <span class="math-container">$I'(r) &lt;0$</span>,  and <span class="math-container">$L(r)$</span> is speculative money demand function with <span class="math-container">$L'(r) &lt;0$</span>. </p>

<p>Now how an increase in M affects P? Does P decrease or increase more than proportionately or less than proportionately or proportionately? </p>

<p>I am more interested in approach than in solution. I am not able to understand how to approach this problem. </p>

CC BY-SA 4.0
2018-06-21T12:34:40.410Z
How are $L(r)$, $S(r)$, and $I(r)$ related? You could solve for the equlibrium $r$ from the second equation and then differentiate the first, maybe.
Weierstraß Ramirez
<macroeconomics><supply-and-demand><money>
Effect of money supply on price level
Amit Sharma
# Effect of money supply on price level

(Asked by: username_0 on 2018-06-19)

Consider a macroeconomy defined by following equations:  
$$M = kPy + L(r)$$
$$S(r) = I(r)$$
$$y = m $$  
Where $M$ is money supply, $P$ is price level, $y$ is output, $r$ is interest rate, while $k,m$ are constants. $S(r)$ is saving function with $S'(r) >0$, $I(r)$ is investment function with $I'(r) <0$, and $L(r)$ is speculative money demand function with $L'(r) <0$.

Now how an increase in M affects P? Does P decrease or increase more than proportionately or less than proportionately or proportionately?

I am more interested in approach than in solution. I am not able to understand how to approach this problem.

**Tags:** macroeconomics, supply-and-demand, money
> **Comments:**
> **username_1**: How are $L(r)$, $S(r)$, and $I(r)$ related? You could solve for the equlibrium $r$ from the second equation and then differentiate the first, maybe.  

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## 1 answers

### Answer by username_2 on 2018-06-24. Score: 2

You can make $P$ the subject of the equation:
$$P=\frac{M-L} {ky} $$ then find the derivative $$\frac{\mathrm d P} {\mathrm d M} = \frac 1{ky}>0$$ to show there is a positive relationship (when $M$ increases, $P$ increases). The elasticity answers your question about proportionality: \begin{align\*}
\frac{\mathrm d P} {\mathrm d M} \cdot \frac MP &= \frac 1{ky}\left( \frac {kPy} P + \frac {L \cdot ky} {M-L} \right) \\
&= 1 + \frac L{M-L} \end{align\*} shows that $P$ increases more than proportionally (because the elasticity is greater than 1).


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