Suppose an economy is characterized by the following three equations: where the first equation is an aggregate-supply function written in the form of an expectations-augmented Phillips curve, the second is an IS or aggregate-demand relationship, and the third is a money-demand equation, where ∆m denotes the growth rate of the nominal money supply
Suppose an economy is characterized by the following three equations:
where the first equation is an aggregate-supply function written in the form of an expectations-augmented 
Let the central bank implement policy by setting i to minimize the expected value of 
Assume that the policy authority has
a. Assume that the central bank can commit to a policy of the form 
prior to knowing any of the realizations of the shocks. Derive the optimal commitment policy (i.e., the optimal values of c0, c1, c2, and c3).
b. Derive the time-consistent equilibrium under discretion. How does the nominal interest rate compare to the case under commitment? What is the average inflation rate?
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