Assume that the central bank has the utility function: U =u2 0.52 where U is utility, u

Assume that the central bank has the utility function:

U =−u2 −0.5π2 where U is utility, u is unemployment and π is the inflation rate. Assume that the economy imposes a constraint in the form of the Phillips curve. Let this be:

u = 5−0.1π

Derive the optimal values of u and π. Compare these optimal values with those under a credible pre-commitment to zero inflation.