Using the 3-equation a) Derive the optimal interest rate rule and carefully explain il. Show that if it is at the policy target, then output must be at the medium-run equilibrium level, using lhe optimal inlcrcst rate rule. (b)Suppose that a = \ a = 2 and fl =. what is the required adjustment in lhe real interest rate to bring inflation to policy target if inflation is currently 3% above the policy target? By how much should nominal interest rate be increased to achieve the desired increase in real interest rate. Explain. (c)In modem monetary policy framcworii. the central bank adjusts lhe inlcrcst rate lo keep intlaiion target through tbur major channels. Explain how lhe exchange rate channel transmits to inflation. Modem monclary policy set out two conditions that must hold if monetary urgeting will succeed in controlling inflation. Briefly explain these two conditions and why they were violated during the Thatcher experiment with monetary targeting