Let the Symbol π Stand for the Rate of Inflation

Essay

Let the symbol π stand for the rate of inflation, with Eπ the expected inflation rate, both measured in percentage. The letter u is the unemployment rate and uⁿ is the natural rate of unemployment. Suppose the short-run Phillips curve is u = uⁿ - α (π - Eπ) applies in a certain economy. The Bank of Canada's loss function is L (u, π) = u + γπ². The analysis in the appendix to textbook Chapter 16 shows that if the Bank of Canada 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 Bank of Canada 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?