Question

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)

Answer 1

The question is incomplete. The complete question is :

Suppose that the Phillips curve is given by :

`$\pi_t=\pi_t^e+0.1-2u_t$`

a). What is the natural rate of unemployment ?

Assuming
`$\pi_t^e=\theta \pi_(t-1)$` , and suppose that
`$\theta$` 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 :

`$\pi_t=\pi_t^e+0.1-2u_t$`

a). At
`$u_N$`,
`$\pi_t = \pi_t^e$` (Inflationary exponents are constant)

`$0.1 = 2u_N$`

∴
`$u_N=0.05$`

= 5%

b).
`$\pi t^e=\theta \pi_(t-1)$`

Let
`$\theta = 0$`, then
`$\pi t^e = 0$`,
`u-u_N=3\%`

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

`$(t+1) : \pi (t+1)^e=0, \pi (t+1) = \pi t = 4\%`

`$= \pi (t+2)= \pi (t+5) = 4\%$`

c). No, I do not believe as

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

If inflation is consistently positive, why to make the expectations of zero percentage.