Suppose that the Phillips curve is given by

pi Subscript t equals pi Subscript t Superscript e Baseline plus $0\mathrm{.}1$ minus $2$ u Subscript tt$=$et$+0\mathrm{.}12$ut

and expected inflation is given by

pi Subscript t Superscript e Baseline equals left parenthesis $1$ minus theta right parenthesis pi overbar plus theta pi Subscript t minus $1$et$=(1$$)$$+$t$1,$

where

theta

is equal to zero and

pi overbar

$=$

$0\mathrm{.}010\mathrm{.}01$

and does not change.

The economy is initially at the natural rate of$$ unemployment, which is$5\%,$ when the authorities decide to bring the unemployment rate down to$3\%$ and hold it there forever. With

theta

equal to$$ zero, this will yield a

$5\%$

rate of inflation every year.

Now suppose that in year

$($tplus$+6),$

theta

changes to $1.$

theta

might increase in this way because

A$.$

inflation expectations adapt to persistently positive inflation.$$

Your answer is correct.

B$.$

inflation expectations always adapt immediately to the last$$ period's inflation.

C$.$

government policy would mandate inflationary expectations.

D$.$

inflation expectations change constantly.

Part $2$

In year

$($t

$+6),$ the inflation rate will be

enter your response here$\%.$

$($Enter

your response as an

integer$.)$

In year

$($t

$+7),$ the inflation rate will be

enter your response here$\%.$

$($Enter

your response as an

integer$.)$

In year

$($t

$+8),$ the inflation rate will be

enter your response here$\%.$

$($Enter

your response as an

integer$.)$