. a) Derive the socially optimal inflation rate and explain.b)Derive the central banks preferred inflation rate and provide an explanation Consider the following scenario.Aggregate output y at date t is specified as follows,Yt = T - nị +ỹwhere the trend level of output is represented by g.The central bank's loss function is captured byL= ( - k)° +(r)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; 7;: inflation rate; n: expected inflation rate; L:loss function; 6, k constant parameters; t: time index.

Output Equation in the economy - yt = πt - πte + y⏞ Where πt = Actual inflation rate , πte =…

Consider the following scenario. Aggregate output y at date t is specified as follows, where the trend level of output is represented by g. The central bank's loss function is captured by L=(-k) +(m) Where b> 0, and where k > 0 is a given parameter reflecting the normal level of aggregate production or the target level of output. The central bank takes the public's expectations as given. The society loss function is the same as the central bank loss function. Notation: y;: output/production; 7: inflation rate; n: expected inflation rate; L: loss function; b, k: constant parameters; t: time index.

Consider the following scenario. Aggregate output y at date t is specified as follows, where the trend level of output is represented by g. The central bank's loss function is captured by L=(-k) +(m) Where b> 0, and where k > 0 is a given parameter reflecting the normal level of aggregate production or the target level of output. The central bank takes the public's expectations as given. The society loss function is the same as the central bank loss function. Notation: y;: output/production; 7: inflation rate; n: expected inflation rate; L: loss function; b, k: constant parameters; t: time index.

ENGR.ECONOMIC ANALYSIS

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Chapter1: Making Economics Decisions

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Question

. a) Derive the socially optimal inflation rate and explain.

b)Derive the central banks preferred inflation rate and provide an explanation

Consider the following scenario.
Aggregate output y at date t is specified as follows,
Yt = T - nị +ỹ
where the trend level of output is represented by g.
The central bank's loss function is captured by
L= ( - k)° +(r)²
Where b > 0, and where k > 0 is a given parameter reflecting the normal level of
aggregate production or the target level of output. The central bank takes the public's
expectations as given. The society loss function is the same as the central bank loss
function.
Notation: y;: output/production; 7;: inflation rate; n: expected inflation rate; L:
loss function; 6, k constant parameters; t: time index.

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