Question

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The economy is at the natural level of unemployment of 6% and is described by the following equations: 1. oyt (a) How does a 2 year long disinflation from 8% to 4% inflation look like? (b) How does a 4 year disinflation from 8% to 4% look like when the Central Bank commits to lower inflation?

Answer 1

Answers

a) From Phillips Curve(PC):

a) From Phillips Curve(PC): pi_t - pi_t - 1 = -2(mu_t - mu_n) and from given Okun's law(OL) we have: mu_t - mu_t - 1 = -0.4(g_yt - 0.03) for year 1, given pi_t = 4% pi^e_t = 8 % and mu_n = 6% Based on PC, mu_t = pi_t - pi_t - 1- 2mu_n/2 = 8% Now, substituting mu_t value in OL equation we will get g_yt -0.04_gyt = mu_t - mu_t - 1 - 0.012 -0.04g_yt = 0.08 - 0.06 - 0.012 -0.04g_yt = 0.008 g_yt = -0.2 Similarly, we will solve for 2nd-year b) The value for inflation, expected inflation, the natural rate of unemployment is given. We will calculate first mu_t based on PC equation. There after we will calculate in g_y^t the similar fashion as done above. Output Shortfall as mentioned in notes: (g_y^t - gnt) = 2.5 (mu_t - mu_n) Substituting the values we will derive gnt here. There after the output shortfall can be calculated.

and from given Okun's Law(OL) we have: $\mu_t - \mu_t_-_1 = -0.4(g_y_t - 0.03)$

For Year 1,

Given $\pi_t = 4$ %, $\pi_t^e= 8$ % and   $\mu_n = 6$ %

Based on PC, $\mu_t =\frac{\pi_t - \pi_t_-1-2\mu_n}{2}$ = 8%

Now, substituting $\mu_t$ value in OL equation we will get $g_y_t$

$-0.04g_y_t = \mu_t - \mu_t_-_1 - 0.012$

Similarly, we will solve for 2nd-year

b) The value for inflation, expected inflation, the natural rate of unemployment is given.

We will calculate first $\mu_t$ based on PC equation. Thereafter we will calculate in $g_y_t$ the similar fashion as done above.

Output Shortfall as mentioned in notes: $(g_y_t - g_n_t) = 2.5(\mu_t - \mu_n)$

Substituting the values we will derive $g_n_t$ here. Therafter the output shortfall can be calculated.