This exercise (which concerns commitment in monetary policy) considers a central bank which…

This exercise (which concerns commitment in monetary policy) considers a central bank which chooses the level of the money supply as in the discussion of “time consistency” in chapter 3. The new wrinkles here are that the bank’s preferences are private information and that the link between the money supply and inflation is stochastic. Specifically, suppose that the central bank’s payoff in each period is θN – π2/2, where N is the level of cmployment, π is the rate of inflation, and θ is a taste parameter.

The payoff functions of the “public” generate a link between employment and inflation given by a “Phillips curve,”

Phillips curve corresponds to the short-run reaction correspondence of the unmodelled economic agents.

The realized level of inflation depends on the central bank’s action and a random disturbance ε:

(c) Suppose that the game is repeated infinitely often with discount factor near 1, and that θ has a finite support including θ = 0. Suppose that type 0 always sets a = 0. Characterize each type’s equilibrium payoff. (This exercise is based on Cukierman and Meltzer 1986. See Cukierman 1990 for more on central banks’ reputations.)