In the augmented$-$Phillips curve given as

${}_t={}_t^e+0\mathrm{.}15-3u_t$

Originally, suppose that people believe that ${}_t^e=0\mathrm{.}02.$ If the government implements a monetary policy leading to ${}_t=0\mathrm{.}04$ and people change their expectation to ${}_t^e=0\mathrm{.}04,$ what will happen?

$($A$)$ The augmented$-$Phillips curve shifts down and the unemployment rate is less than the natural unemployment rate

$($B$)$ The augmented$-$Phillips curve shifts down and the unemployment rate is greater than the natural unemployment rate

$($C$)$ The augmented$-$Phillips curve will shift down and the unemployment rate is equal to the natural unemployment rate.

$($D$)$ The augmented$-$Phillips curve will shift up and the unemployment rate is less than the natural unemployment rate.

$($E$)$ The augmented$-$Phillips curve will shift up and the unemployment rate is greater than the natural unemployment rate.

$($F$)$ The augmented$-$Phillips curve will shift up and the unemployment rate is equal to the natural unemplovment rate.