Consider the Dynamic Aggregate Demand (DAD) is

Yt=(/(1+Y))(t*)+(1/(1+Y))t

and the Dynamic Aggregate Supply (DAS) is

t = _t-1 + (Yt-)+vt

The potential level of output and the central bank's target for the inflation rate are assumed to be constant.

Assume the following parameter value = 0.2 , = 1 , = 0.5 and Y = 0.5

The central bank's target is * = 2% We know that at time

t-1,t1=t2=* andYt1=

Assume that at timetthis economy is hit by a large wave of optimism, which is captured by a demand shock t = 2% This wave of optimism only lasts for one period (i.e., the demand shock is equal to zero at time t+1, t+2 and all future periods). Assume that the supply shock is always equal to zero. Compute the responses of the output gap and inflation rate from timet to t+3

(Yt- ) and t; (Y_t+1- ) and _t+1 ; (Y_t+2- ) and _t+2 and (Y_t+3-) and _t+3