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.

question: 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.)