Suppose the economy is described by the system:

= 1 + ( ),(1)

= ( ),(2)

= ( ),(3)

where > 0, > 0, > 0, represents equilibrium output, represents the equilibrium real interest rate, and represents the inflation target. Equation (3) is a special case of what is known as a Taylor rule and describes a rule for conducting monetary policy.

6.1.Suppose that the economy is hit by an unanticipated temporary negative

aggregate demand shock. Beginning from a point of equilibrium, explain carefully and use diagrams to illustrate how the economy responds to the shock and how it transitions back to equilibrium. (Hint: combine equations (2) and (3) to express the policy rule in terms of the output gap and inflation gap.)

6.2 Suppose that the shock described above initially pushes inflation two percentage points below the inflation target. If = 0.5, = 0.5, = 2.0, and = 1.0, then determine how many periods it is expected to take before inflation is within half a percentage point of target. Explain whether higher values for increase or decrease the speed at which inflation returns to target.