Prices and aggregate-supply shocks can be added to Poole’s analysis by using the following model:
Assume that the central bank’s objective is to minimize 
and that disturbances are mean-zero, white noise processes. Both the private sector in setting Et-1 πt and the monetary authority in setting its policy instrument must act prior to observing the current values of the disturbances.
a. Calculate the expected loss function if it is used as the policy instrument. (Hint: Given the objective function, the instrument will always be set to ensure that expected inflation is equal to zero.)
b. Calculate the expected loss function if mt is used as the policy instrument.
c. How does the instrument choice comparison depend on
i. the relative variances of the aggregate-supply,
ii. the weight on stabilizing output fluctuations l?
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