Assume that an economy is in the long run equilibrium and inflation is equal to the inflation target. Using the graph of the DAD-DAS model, answer the following questions:

a) In period t+1 the central bank changes its estimation of the natural real interest rate . The new estimation is not correct: the estimated natural real interest rate is higher than the true rate ( > ). This mistake lasts for two periods (period t+1 and t+2). In the period t+3 the central bank reestimates the value of the natural rate and this time makes no mistake. How will the mistake of the central bank affect inflation and output in the periods t+1 and t+2? Show this situation in a graph.

b) Show the adjustments to the long run equilibrium in this economy. Explain the shifts of the curves.