Suppose that the Phillips curve is given by pi subscript t $=$ pi$^$e subscript t $+0\mathrm{.}1-2*$u subscript t and expected inflation is given by pi$^$e subscript t $=(1-$theta$)*$pi bar $+$ theta$*$pi subscript t$-1$ and suppose that is initially equal to $0,$ and that is given and does not change. It could be zero or any positive value. Suppose that the rate of unemployment is initially equal to the natural rate. In year t$,$ the authorities decide to bring the unemployment rate down to $3\%$ and hold it there forever. Determine the rate of inflation in periods t$+1,$ t$+2,$ t$+3,$ t$+4,$ t$+5.$ How does pi bar compare to pi$?$