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.