ECON 3350 Exam III - Page 2 of 5 12/7/2021 1. (60 points) Consider the model of monetary policy and time inconsistency. There is a central bank with the objective function 1 U = {(– yn) - (1) and the public have the following Expectations Augmented Phillips Curve for Output given by yt = yn + a(TTY – E[74]) + (2) (a) (12 points) Substitute the right hand side of Equation 2 in for yt in Equation 1. (b) (12 points) Differentiate the result from part a with respect to 74 and set the deriva- tive equal to zero. (c) (12 points) What is the optimal rate of inflation? 1. (60 points) Consider the model of monetary policy and time inconsistency. There is a central bank with the objective function U = 4(4 – yn) - (1) and the public have the following Expectations Augmented Phillips Curve for Output given by yt = yn + a(+14 - E[74]) + € (2) (a) (12 points) Substitute the right hand side of Equation 2 in for yt in Equation 1. (b) (12 points) Differentiate the result from part a with respect to Ty and set the deriva- tive equal to zero. (c) (12 points) What is the optimal rate of inflation?

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