The Phillips Curve Describing an Economy Takes the Form U $\alpha$

The Phillips curve describing an economy takes the form u = uⁿ - $\alpha$ ( $\pi$ - E $\pi$ ) . The central bank directly sets the inflation rate to minimize the following loss function, L(u, $\pi$ ) = u + $\gamma$ $\pi$ ². The symbol u denotes the unemployment rates, uⁿ is the natural rate of unemployment, $\pi$ is the inflation rate, E $\pi$ is the expected inflation rate, and $\alpha$ and $\gamma$ 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 ______.

A) higher; lower
B) higher; the same
C) lower; lower
D) lower; the same