Let the Symbol $\pi$ Stand for the Rate of Inflation,with $E$ $\pi$

question 93

Essay

Let the symbol $\pi$ stand for the rate of inflation,with $E$$\pi$ the expected inflation rate,both measured in percent.The letter u is the unemployment rate and uⁿ is the natural rate of unemployment.Suppose the short-run Phillips curve u = uⁿ - $\alpha$ ( $\pi$ - $E$$\pi$ )applies in a certain economy.The central bank's loss function L(u, $\pi$ )= u + $\gamma$$\pi$ ².The analysis in the appendix to textbook Chapter 14 shows that if the central bank minimizes its loss function under the assumption that $E$$\pi$ is fixed and "rational" private agents know this,the expected inflation rate will be $E$$\pi$ = $\alpha$ /2 $\gamma$ ,and this will also be the inflation rate the government chooses.a.Suppose that $\alpha$ = 0.5 and $\gamma$ = 0.05.What are the expected and actual inflation rates?
b.Suppose $\alpha$ = 0.5 and $\gamma$ = 0.50.In this case,does the central bank have greater or lesser relative distaste for inflation than in part a? What are the expected and actual inflation rates with $\gamma$ = 0.50? Why do they differ from the inflation rates in part a?

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