Stable prices are an unachievable mythical goal in the real world.

It stems from deficient mathematical understanding, economists need to do some research into stationary fixed points of dynamical systems, strange attractors and the like. A non-linear dynamic, multi-variable system like a money market is never going to produce stable prices. A vibrant system needs a kernel of instability to retain flexibility and robustness, as a resistance to stagnation, corruption and large external disturbances (shocks).

With a more modern mathematical basis "stable prices" would be recognised as unattainable and anyway not desirable, imho.