Question: In the New Keynesian model suppose that in the short

In the New Keynesian model, suppose that in the short run the central bank cannot observe aggregate output or the shocks that hit the economy. However, the central bank would like to come as close as possible to economic efficiency. That is, ideally the central bank would like the output gap to be zero. Suppose initially that the economy is in equilibrium with a zero output gap.
(a) Suppose that there is a shift in money demand. That is, the quantity of money demanded increases for each interest rate and level of real income. How well does the central bank perform in relative to its goal? Explain using diagrams.
(b) Suppose that firms expect total factor productivity to increase in the future. Repeat part (a).
(c) Suppose that total factor productivity increases in the current period. Repeat part (a).
(d) Explain any differences in your results in parts (a)-(c), and explain what this implies about the wisdom of following an interest rate rule for the central bank.

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