Give answer for c and D only Exercise 1Consider the following scenario.Aggregate output y at date t is specified as follows,Yt = Tt – T +ỹwhere the trend level of output is represented by y.The central bank's loss function is captured byL2(y: – k)² +(T)2Where b> 0, and where k > 0 is a given parameter reflecting the normal level ofaggregate production or the target level of output. The central bank takes the public'sexpectations as given. The society loss function is the same as the central bank lossfunction.Notation: y;: output/production; T: inflation rate; n: expected inflation rate; L:loss function; b, k: constant parameters; t: time index. Exercise 2Consider a modified aggregate supply function which takes account for the emergence ofrandom business cycle shocks (&t) with E&t] =O in the sense thatYt = Tt – T + ÿ +&tThe loss function is the same as in exercise 1:(yt – k)? +(72)?Notation: Et: random shock; E[e,]: expected value of €t; b: constant parameter; allother variables see Exercise 1.Having considered the scenario above complete the following tasks:a) Derive the central bank's preferred inflation rate and explain.b) The result in a) reads asb(k – 9) – H5ɛbExplain the economic intuition of this result.c) Consider a more conservative central banker whose lossfunction is represented byL = (4 – k)² + } (Tt)²Apparently, the preferred inflation rate would read6(k – 9) –||1+ôWhat can you say about the relationship between ô and b? Is ilarger or smaller than b? Provide an explanation.d) Given the above output function and yYt = Tt – T +€4, the inflation rate and the loss-function in c), itcan be shown that the loss function can be expressed as a:0, such that||function of bz (1) – }{* (* » +) + 1}():3),2 (6² + ô) + E [=*]}(1+8')Assuming that L represents the social welfare function, thesocially optimal level of conservatism b can be obtained from thefirst-order condition of L(ô) with respect to 6. Show from thiscondition whether b is larger or smaller than b.

A conservative central banker is sets discretionary monetary policy in discretionary fashion and is…

c) Consider a more conservative central banker whose loss function is represented by L = ½ (yt − k)² + ½¼½ (π₁) ² - Apparently, the preferred inflation rate would read Eb 1+6 What can you say about the relationship between 1 and b? Is în larger or smaller than b? Provide an explanation. π£ = ô(k − y) - - d) Given the above output function and y = 0, such that Yt = πt − π£ + &, the inflation rate and the loss-function in c), it can be shown that the loss function can be expressed as a function of L (6) − } { x² (8² + 6) + (6 +6³ 7 B [2]} = b+ô² E (1+6³) [e²] Assuming that I represents the social welfare function, the socially optimal level of conservatism ô can be obtained from the first-order condition of L(1) with respect to ĥ. Show from this condition whether ☎ is larger or smaller than b.

c) Consider a more conservative central banker whose loss function is represented by L = ½ (yt − k)² + ½¼½ (π₁) ² - Apparently, the preferred inflation rate would read Eb 1+6 What can you say about the relationship between 1 and b? Is în larger or smaller than b? Provide an explanation. π£ = ô(k − y) - - d) Given the above output function and y = 0, such that Yt = πt − π£ + &, the inflation rate and the loss-function in c), it can be shown that the loss function can be expressed as a function of L (6) − } { x² (8² + 6) + (6 +6³ 7 B [2]} = b+ô² E (1+6³) [e²] Assuming that I represents the social welfare function, the socially optimal level of conservatism ô can be obtained from the first-order condition of L(1) with respect to ĥ. Show from this condition whether ☎ is larger or smaller than b.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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