15. Suppose that the relationship between inflation rate (π) and unemployment rate (u) is described by the following equation: πt – πte = (m + z) – αut   where m = 0.05, z = 0.04, and α = 2. In this economy, the authorities keep unemployment rate at 4% forever.   a.  If the modified Philips curve describes the relationship between π and u correctly, how should “πte” be specified? Rewrite the equation using this specification. Assume that πt–1 = 1%. Compute πt, πt+1, and πt+2.   b.  Do you believe the answer in part (a)? Why or why not?   c. Derive the natural rate of unemployment.

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