JNU SSS 2018 Question 41: Inflation, unemployment and the Phillips curve

Suppose in an economy $p_t = p^e_t + 0\cdot01 - 0\cdot2u_t$ and $p^e_t = 0\cdot75p_{t-1}$, where $p_t$ is the rate of inflation in period $t$, $p^e_t$ is the expected rate of inflation in period $t$ and $u_t$ is the rate of unemployment in period $t(t = 1, 2, 3, \cdots)$. Suppose in period 1 expectations regarding inflation are realized and the unemployment rate in the economy remains constant from period 1 onwards. Answer the following questions :

(a) What is the value of the inflation rate in period 3 if $p_0 = 0\cdot128$?

(b) What happens to the value of the inflation rate as $t \to \infty$?

(c) For what value of the inflation rate in period 0, will the inflation rate in the economy remain constant from period 2 onwards?