Let the Symbol π Stand for the Rate of Inflation

question 37

Essay

Let the symbol π stand for the rate of inflation, with πe 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 - α(π - Eπ) applies in a certain economy. The Fed's loss function is L(u, π) = u + γπ2. The analysis in the appendix to textbook Chapter 15 shows that, if the Fed minimizes its loss function under the assumption that Eπ is fixed and
"rational" private agents know this, the expected inflation rate will be Eπ = α/2γ, and this will also be the inflation rate
the government chooses.
a. Suppose that α = 0.5 and γ = 0.05. What are the expected and actual inflation rates?
b.Suppose α = 0.5 and γ = 0.50. In this case, does the Fed have greater or lesser relative distaste for inflation than in part a? What are the expected and actual inflation rates with γ = 0.50? Why do they differ from the inflation rates in part a?

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