Assume that an economy is governed by the Phillips curve: pi = E pi - 0.5(u - 0.

Question

Assume that an economy is governed by the Phillips curve: pi = E pi - 0.5(u - 0.06), where pi is the inflation rate, E_pi is the expected inflation rate, and the natural rate of unemployment is 6%. Also, note from Okun's law that 1 percentage point of unemployment translates into 2 percentage points of lost output. Suppose that today, pi = 0.05 and E_pi = 0.05. The government wants to lower inflation to 2%. Assume that people have adaptive expectations. How much cyclical unemployment does the economy have to experience to have inflation rate of 2%? What is the sacrifice ratio? Assume that the government announced its plans to lower inflation before the workers and firms form their expectations. The workers and firms form their expected inflation by the following rule: E_pi = alpha pi^a + (1 - alpha) pi - 1 where pi_1 is the inflation rate in the previous period, pi^1 is the announced inflation, and alpha [0, 1] is the weight workers and firms put on the announcement (credibility of the government). Suppose that households and firms fully trust the government, and thus alpha = 1. How much cyclical unemployment does the economy have to experience to have inflation rate of 2%? Suppose alpha = 0.5. How much cyclical unemployment does the economy have to experience to have inflation rate of 2%? What is the sacrifice ratio? How does a affect the sacrifice ratio?

Explanation / Answer

a) To reduce inflation, the equation of the Phillips Curve (PC) suggests that unemployment must lie above its natural rate wnich is fixed at 6 percent. With adaptive expectations, write the PC equation in the form: - -1 = 0.5(u-0.06). We need inflation to fall by 5 %, which implies

- -1 = -0.05.

-0.05 = 0.5(u - 0.06)

-0.1 = u - 0.06

u = 0.16.

Hence, a total 10 % per year of cyclical unemployment is needed above the natural rate of 6 percent.

b) Okun's law says that a 1% increase in unemployment requires a 2% lost GDP. A 10 percent increase in unemployment needs 20 percent lost GDP. This makes the sacrifice ratio = 20/5 = 4.

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