Question about misperception in IS-MP model Why is these steps happens one after another in IS-MP Model if MP curve is a horizontal line? Also, is this preventable?

a) Policymakers believe the slow-down in growth is caused by a
negative aggregate demand shock...

(b) ...so they lower the Real interest rate R.

(c) In truth, the IS curve never shifted...

(d) ...so the great inflation happened.
Consider the standard IS-MP model with horizontal MP. According to (c), the IS remains in the original level. Therefore, the fall in the real interest rate $R_t$ leads to an increase in the output gap $\tilde{Y}_t$. This happens because the opportunity cost of investing is lower. As such, for an unchanged marginal return to capital $r$, investment increases, leading to a deviation of actual output from potential output, and therefore to a positive short-term output gap $\tilde{Y}_t$.

In the IS-MP-PC model, inflation follows a simplified Phillips Curve, which is:

$$\Delta \pi_t = v\tilde{Y}_t + \bar{o}$$

(notation borrowed from Jones, Macroeconomics, 3rd edition).

Therefore, in the absence of a cost-push (or supply) shock ($\bar{o}$), deviations in inflation from the target are given by the positive output gap $\tilde{Y}_t$. In consequence, inflation increases.

I don't really get your second question (is this preventable?). Clearly, a first best is for central banks to correct their models in order to avoid mistakes. This is of course difficult. It requires to identify potential output and to distinguish between aggregate supply and aggregate demand shocks. Not an easy task.