Question

Consider the Phillips curve: pi(t) = Epi(t) - 0.5(u(t) - 8), where pi(t) is inflation rate at t, Epi(t) is expected inflation for t, and u(t) is unemployment at t.

Now suppose the public has adaptive expectation: Epi(t) = pi(t-1), Epi(t+1) = pi(t), and so on. Inflation at time t-1 is pi(t-1) = 3%; the rate of unemployment u(t) at time t is at the natural level. The authorities decide to bring the unemployment rate to 6% from time t+1 on. What is the rate of inflation at t+3? (hint: derive inflation rate for t+1 and t+2 first)

Answer 1

Consider the given problem here the Phillips Curve is given by.

=> Pt = EPt - 0.5*(ut - 8), where expectation is adaptive, => EPt=Pt-1, where EPt = 3 for all “t”. In “period t” the “ut” is at its natural rate”, => “ut=8”, => “Pt=EPt”.

=> Pt = Pt-1 = 3”. So, the inflation of “period t” is “3%” and the unemployment rate at “8%”.

Now, for the period “t+1” the inflation is given by.

=> Pt+1 = EPt+1 - 0.5*(ut+1 - 8) = Pt - 0.5*(ut+1 - 8) = 3 - 0.5*(6 - 8) = 4, => Pt+1 = 4%. So, the inflation of “period t+1” is “4%” and the unemployment rate at “6%”.

Now, for the period “t+2” the inflation is given by.

=> Pt+2 = EPt+2 - 0.5*(ut+2 - 8) = Pt+1 - 0.5*(ut+2 - 8) = 4 - 0.5*(6 - 8) = 5, => Pt+2 = 5%. So, the inflation of “period t+2” is “5%” and the unemployment rate at “6%”.

Now, for the period “t+3” the inflation is given by.

=> Pt+3 = EPt+3 - 0.5*(ut+3 - 8) = Pt+2 - 0.5*(ut+3 - 8) = 5 - 0.5*(6 - 8) = 6, => Pt+3 = 6%. So, the inflation and unemployment rate of “period t+3” are “6%”.