policy itself is set after the cost shock is known The central bankers p ay is

Policy itself is set after the cost shock is known

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policy itself is set after the cost shock is known. The central banker’s p ay is determined by his/her success at keeping inflation low: CB Pay = ? 0 − ? 1 ? 𝑡 where ? 0 , ? 1 > 0 . The central banker cares both about his/her pay and the social loss associated with his/her policies. His/her loss can be written: 𝐿 ?? = ω𝐿 𝑆 − (1 − ω)(? 0 − ? 1 ? 𝑡 ) where 0 < ω < 1 . b. What is the first-order condition characterising the optimal choice of ? 𝑡 in terms of 𝑥 𝑡 and what are the associated equilibrium values of ? 𝑡 and 𝑥 𝑡 ? Are there values of ? 0 and ? 1 that support the first-best policy rule in part (a) as an equilibrium? Explain. c. Why do you think that central bankers pay is in practice rarely related explicitly to inflation outcomes in this way?
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2 2 . Optimal preferences of central banker Suppose the loss function of society from inflation and output gap fluctuations is: 𝐿 𝑆 = 1 2 ? 𝑡 2 − λ𝑥 𝑡 where ? 𝑡 is inflation and 𝑥 𝑡 is the output gap. (The term in the output gap is linear here rather than quadratic, but like the loss function of the lectures when 𝑥 > 0 it has the property that the loss is reduced if output is pushed above its natural rate.) The Phillips curve is given by ?
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