a) Draw indifference curves
B) Derive the pre-commitment ( or non-discretionary) equilibrium

Question

a) Draw indifference curves
B) Derive the pre-commitment ( or non-discretionary) equilibrium

David · Accepted Answer

Answer to 1: 
Social objective function: S(xt, ut) = –  ut – (xt
2/2) ……… (1) 
Subject to the Phillips curve constraint: ut = u* - λ(xt-xt
e) …….. (2) 
Substituting (2) in (1), we social objective function as 
S(xt, ut) = u* - λ(xt-xt
e) - (xt
2/2)  ………………………… (3) 
(a) 
Along indifference curve welfare remains constant. Suppose the fixed welfare be 
‘S*’. Given this, the equation of indifference curve is can represented as: 
S* = –  ut – (xt
2/2) or xt
2 = -2(ut-S*). It can be mapped as follows;
(b) 
Substituting (2) in (1), we social objective function as 
S(xt, ut) = -u* + λ(xt-xt
e) - (xt
2/2)  ………………………… (3) 
Non-discretionary equilibrium: 
Under non-discretionary equilibrium, actual inflation rate equals expected inflation 
rate i.e.

a) Draw indifference curves B) Derive the pre-commitment ( or non-discretionary) equilibrium

Solution

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