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MBFM III - Week 12 Tutorial Questions

The objective of this problem set is simply to force repetition in solving the Barro- Gordon model of commitment in monetary policy.

1. Explain the difference between a Nash Equilibrium (NE), that is used to charac- terize a solution of a simultaneous move game, versus the concept of a Subgame Perfect Nash Equiilbrium (SPNE) which is used to characterize the equilibrium of a dynamic game (in which at least one player moves before another)? Make specific reference to credibility and rational beliefs regarding the play of the second mover in the game.

2. Consider the commitment case of the Barro-Gordon model.

• Write down the Central Bank’s (CB) objective function and constraint(s) as well as that of the Private Sector (PS).

• Using the concept of backward induction in solving for the Subgame Perfect Nash Equilibrium (SPNE) of the commitment game, define the strategy space of the CB and the PS.

• Solve the model by backward induction. Derive the PS’s optimal strategy and then derive the CB’s optimal strategy.

• Once you have both the players’optimal strategies, derive the values for in- flation and output gap that arise in the SPNE.

• Identify the marginal cost and benefit from inflation for the CB in this com- mitment case.

3. Consider the discretion case of the Barro-Gordon model.

• Using the concept of backward induction in solving for the SPNE of the com- mitment game, define the strategy space of the CB and the PS.

• Solve the model by backward induction. Derive the CB’s optimal strategy and then derive the PS’s optimal strategy.

• Once you have both the players’optimal strategies, derive the values for in- flation and output gap that arise in the SPNE.

• Identify the marginal cost and benefit from inflation for the CB in this com- mitment case.

4. Why are the marginal benefits and costs from inflation different between the com- mitment and the discretion cases?