Suppose that the Phillips curve is given by

pi Subscript t Baseline equals pi Subscript t Superscript e Baseline plus $0\mathrm{.}1$ minus $2$ u Subscript t

Given this equation find the natural rate of unemployment.

Part $2$

The natural rate of unemployment is

$$

enter your response here$\%.($Enter your response as an integer$.)$

Part $3$

Assume that

pi Subscript t Superscript e Baseline equals left parenthesis $1$ minus theta right parenthesis pi overbar plus theta pi Subscript t minus $1$

and suppose that theta is initially equal to $0$ and pi overbar $=0\mathrm{.}01$ and does not change. 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.

In year $($t $+1),$ the inflation rate will be

$$

enter your response here$\%.($Enter your response as an integer$.)$

In year $($t $+2),$ the inflation rate will be

$$

enter your response here$\%.($Enter your response as an integer$.)$

In year $($t$+5),$ the inflation rate will be

$$

enter your response here$\%.($Enter your response as an integer$.)$

Part $4$

This expectations structure is probably not realistic because it implies that

A$.$

inflation expectations adapt very quickly.

B$.$

inflation expectations are always wrong.

C$.$

inflation expectations are always right.

D$.$

the natural rate of unemployment is too low