PLZ PLZ HELP

QUESTION 1

Suppose a macroeconomic 'loss-function' of the form L = an2 + (x - 2)2 where IT is inflation and x is the output gap. a is a fixed parameter. Suppose also a Phillips Curve, It = me + 0.5x where Tre 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.An individual begins her working life at date twith no non-human wealth. Her labour income grows at rate 9 per year. assumed to be 3% (or 0.03) per annum: thus her income in year t + j is yr.\" 2 yt(1 + 9);. Her income is received at the end of each year so that the present value of income received in year t + j is iL where r is the constant real rate of interest assumed to be 5% (0.05) (1+r)j+1' per annum. Assume an innite planning horizon and assume that she consumes her permanent income. Calculate the ratio of consumption to income at the start of her working life. Briefly discuss why her consumption will initially be substantially greater than her income