Suppose that an economy has the following Phillips curve pi = (pi)^2 - 2(u-u^n).

Question

Suppose that an economy has the following Phillips curve pi = (pi)^2 - 2(u-u^n). Suppose the natural rate of unemployment is 5 percent (0.05), and that expectations about inflation are adaptive. Suppose the central bank targets inflation to be 2 percent (0.02) in the coming year.

a) If inflation over the past year has been 4 percent, what will total actual unemployment have to be in the coming year for the central bank to achieve its inflation target?

b) If the central bank plans to keep inflation at 2 percent again the following year, what must total actual unemployment be in that following year? Explain why your answer is different from part ( a) above.

Explanation / Answer

The economy has the Phillips curve: p = p-1 - 2(u-0.05).
a) The natural rate of unemployment is the rate at which the inflation rate does not deviate from the expected inflation rate.
Here, the expected inflation rate is just last period's actual inflation rate. Setting the inflation rate equal to last period's rate, that is, p = p-1, we find that u =0.05. Thus the natural rate of unemployment is 5 percent.

b) To reduce inflation, the Phillips Curve (PC) tells us that unemployment must be above its natural rate of 5 percent for some period of time. We can write the PC in the form: p - p-1 = 2(u-0.05). Since we want inflation to fall by 3 percentage points, we want p - p -1 = 0.03. Plugging this into the above equation gives us u = 0.065. Hence, we need 1.5 percentage point-years of cyclical unemployment above the natural rate of 5 percent. According to Okun's law, a 1% increase in unemployment requires a 2% drop in GDP. Thus, a 1.5 percentage point increase in unemployment requires a 3 percentage point drop in GDP.

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