11.17. Other equilibria in the Barro–Gordon model. Consider the situation described in Problem 11.16. Find the parameter values (if any) for which each of the following is an equilibrium:

(a) One-period punishment. πe t equals ˆπ if πt−1 = πe t −1 and equals b/a otherwise; π = πˆ each period.

(b) Severe punishment. (Abreu, 1988, and Rogoff, 1987.) πe t equals ˆπ if

πt −1 = πe t −1, equals π0 > b/a if πe t −1 = πˆ and πt −1

= πˆ, and equals b/a otherwise; π = πˆ each period.

(c) Repeated discretionary equilibrium. π = πe = b/a each period.