Assume , and suppose that is initially equal to 0. Suppose that the rate of unemployment is initially equal to the natural rate. In year , the authorities decide to bring the unemployment rate down to 3% and hold it there forever. b. Determine the rate of inflation in years , , , and . c. Do you believe the answer given in (b)

The question is incomplete. The complete question is :

Suppose that the Phillips curve is given by :

[tex]$\pi_t=\pi_t^e+0.1-2u_t$[/tex]

a). What is the natural rate of unemployment ?

Assuming [tex]$\pi_t^e=\theta \pi_{t-1}$[/tex] , and suppose that [tex]$\theta$[/tex] is initially equal to 0. 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.

b). Determine the rate of inflation in years t, t+1, t+2 and t+5.

c). Do you believe the answer given in (b)? Why or why not?

Solution :

Given the equation :

[tex]$\pi_t=\pi_t^e+0.1-2u_t$[/tex]

a). At [tex]$u_N$[/tex],  [tex]$\pi_t = \pi_t^e$[/tex]  (Inflationary exponents are constant)

      [tex]$0.1 = 2u_N$[/tex]

    ∴  [tex]$u_N=0.05$[/tex]

               = 5%

b). [tex]$\pi t^e=\theta \pi_{t-1}$[/tex]

   Let [tex]$\theta = 0$[/tex], then [tex]$\pi t^e = 0$[/tex], [tex]u-u_N=3\%[/tex]

    Now for year t [tex]$\pi t^e=0, \pi_t= 0.1-2(0.03)=0.04=4\%$[/tex]

     [tex]$(t+1) : \pi (t+1)^e=0, \pi (t+1) = \pi t = 4\%[/tex]

                                                      [tex]$= \pi (t+2)= \pi (t+5) = 4\%$[/tex]

c). No, I do not believe as

    [tex]\pi t^e=0[/tex], but πt comes out to be 4%, [tex]$\pi (t+1)^e=0$[/tex] but [tex]\pi (t+1)= 4 \%[/tex].

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