The Phillips curve describing an economy takes the form u = un - α(π - Eπ). The central bank directly sets the inflation rate to minimize the following loss function, L(u, π) = u - γπ2. The symbol u denotes the unemployment rate, un is the natural rate of unemployment, π is the inflation rate, Eπ is the expected inflation rate, and α and γ are behavioral response parameters of the economy. Private agents form their expectations rationally before the central bank sets the inflation rate. Compared to making monetary policy with discretion, the optimal inflation rate will be under a fixed rule and the unemployment rate will be .

Question

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Under a fixed rule, private agents would have a clearer understanding of how the central bank would respond to changes in economic conditions. This would reduce the scope for them to form mistaken expectations about future monetary policy, leading to smaller forecast errors and reduced variance in actual inflation. Consequently, the expected inflation rate (Eπ) would be more stable and closer to the target rate set by the central bank. As a result, the cost of reducing inflation would be lower and the central bank would set a lower optimal inflation rate, which would lead to lower unemployment in the long run. Therefore, compared to making monetary policy with discretion, the unemployment rate will be lower under a fixed rule.

The Phillips Curve Describing an Economy Takes the Form U