Q9 chapter 13 from the macro barro book:

Rules vs discretion

2.- Assume that the monetary authoritys preferred inflation rate is zero, but the authority also wants to reduce unemployment by making inflation surprisingly high

a) show how the equilibrium rate can be high. Is the rate surprisingly high? Does the result depend on the authority's having the wrong objective or being incompetent?

b) Can the results improve if the policymaker has the power to bind himself in advance to a specific inflation rate? If so explain why this constrain can improve matters.

c) Might the policymaker's reputation be a satisfactory alternative to a formal rule that prescribes future policies?