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.The optimal inflation rate when the central bank operates using a fixed rule will be ______.The optimal inflation rate when the central bank operates with discretion will be ______.

A) uⁿ; 0
B) 0; uⁿ
C) 0; $\alpha$ /(2 $\gamma$ )
D) $\alpha$ /(2 $\gamma$ ) ; 0