Suppose that the Phillips curve is given by
πt=πₜᵉ−α(uₜ−uₙ)
where the estimated value of the natural rate of unemployment, uₙ=4.5% and α=0.4. The expectations are myopic (i.e. fully backward), thus πₜᵉ =πt−1.
a) What is the sacrifice ratio in this economy? Explain in words. Suppose that at time t=0 unemployment is initially equal to the natural rate (i.e. u₀=4.5%) and π₀=7.5%. The central bank decides that 7.5% inflation is too high and that starting in year 1 it will decrease inflation to 3.5%.
