# IS-LM - Effect of interest rate on price level

I'm starting to study the Keynesian theory, and I have just read that the increase of interest rate ($$r$$) will lower the price level ($$P$$). I tried to understand this using the IS-LM model (I mean, visually through the curves or through the equations), but I am stuck at this reasoning.

If I consider the LM curve and its idea, we will eventually see the following curve:

This represents the interest rate in the y-axis and real money in the x-axis. Now, if I want to know the effect of an increase in $$r$$ (from $$r_1$$ to $$r_2$$), I can say that the real money will be lower, and considering $$M$$ constant, this implies that $$P$$ increases. I am aware that this result is obviously not correct, how could I understand this change in $$r$$ in terms of the IS-LM curves correctly?

• You can't find a rationale for this using an IS-LM, because prices are assumed fixed in it. You should try with an AS-AD model. – Patricio Jan 4 '19 at 11:16