Loss Function

Suppose a macroeconomic 'loss-function' of the form L = an + (x - 2)2 where It is inflation and x is the output gap. a is a fixed parameter. Suppose also a Phillips Curve, It = i + 0.5x where i is expected inflation. Wages are set before policy is set and inflation expectations are formed rationally. Assume firstly that the government sets monetary policy and in doing so sets the inflation rate, with a = 1. Calculate the equilibrium inflation rate. Briefly discuss whether policy should be delegated to an independent central bank and what the optimal value for a might be