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 ? whether P will 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.