Given That the Philip Curve Defines an Economy As $u = 6 - 0.4 ( \pi - E \pi )$

Essay

Given that the Philip curve defines an economy as $u = 6 - 0.4 ( \pi - E \pi )$ where u is the unemployment rate and $\pi$ is the inflation rate, and the loss function which tells the social cost of unemployment and inflation is $L = u + 0.05 \pi ^ { 2 }$ ,calculate the optimal level of inflation for the economy.