Final answer:
In an economy described by the given Phillips curve πₜ = πₜᵉ − α(uₜ − uₙ), with α = 1 and backward-looking expectations, the sacrifice ratio is 1, meaning a 1% rise in unemployment is expected to reduce inflation by 1 percentage point.
Step-by-step explanation:
The 'sacrifice ratio' refers to the percentage of a year's real GDP that must be forgone to reduce inflation by 1 percentage point. The formula for the sacrifice ratio in the context of the Phillips Curve is S = -(Δu / Δπ), where S denotes the sacrifice ratio, Δu is the change in the unemployment rate, and Δπ is the change in the inflation rate.
Since we have the Phillips curve equation πₜ = πₜᵉ − α(uₜ − uₙ), with α being equal to 1, and also given that the expectations are myopic or backward-looking (πₜᵉ = πₜ₋₁), we can rearrange the equation to find the change in unemployment rate for a given change in inflation rate. The unemployment rate would need to increase by 1% to decrease inflation by 1 percentage point (since α = 1 and uₙ = 4.5%). Therefore, the sacrifice ratio in this economy is 1, indicating that a 1% increase in unemployment would be needed to reduce the inflation rate by 1 percentage point.