Are Real and Nominal Interest Rates Identical in Monetary Policy Analysis?

[Bipolarity]

In the Money Supply-Money Demand curve, the equilibrium interest rate is the real or nominal interest rate?

Or are they the same thing for the purposes of evaluating monetary policy?

BiP

 

[John Creighto]

If monetary policy worked (which it doesn't) then they should be identical (in shape not necessarily in value) as inflation should be constant.

 

[Bipolarity]

If monetary policy worked (which it doesn't) then they should be identical (in shape not necessarily in value) as inflation should be constant.

I see. What confuses me is that even if the shape is the same for both of them, once you change the money supply then price levels change, and that causes nominal interest rate to change but not real interest rate, effectively distorting the original curve in the context of real vs nominal interest rates.

BiP