Effect of money supply on price level 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 $S'(r) &gt;0$, $I(r)$ is investment function with $I'(r) &lt;0$,  and $L(r)$ is speculative money demand function with $L'(r) &lt;0$. 

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.
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).