Figure 13.12 shows what happens if the AE curve shifts out temporarily and the central bank raises

Question:

Figure 13.12 shows what happens if the AE curve shifts out temporarily and the central bank raises the real interest rate. Now suppose the same shock occurs but the central bank keeps the interest rate constant. Assuming lags in the AE and Phillips curves, show over time what happens to output and inflation. Discuss the pros and cons of raising the interest rate in response to the shock.