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Category > Management Posted 17 Jan 2018 My Price 8.00

Taylor model

(This follows Ball, 1994a.) Consider a continuous-time version of the Taylor model, so that

 where T is the interval between everyone’s price changes and x (t−τ) is the price set by individuals who set their prices at time t − τ. Assume that φ = 1, so that p∗ i (t) = m(t); thus

(a) Suppose that initially m(t) = g(t) (g > 0), and that Etm(t + τ) is therefore (t + τ)g. What are x (t), p (t), and y(t) = m(t) − p (t)?

(b) Suppose that at time 0 the government announces that it is steadily reducing money growth to zero over the next interval T of time. Thus m(t) = t [1 − (t/2T)]g for 0 < t="">< t,="" and="" m(t)="gT/2" for="" t="" ≥="" t.="" the="" change="" is="" unexpected,="" so="" that="" prices="" set="" before="" t="0" are="" as="" in="" part="">

(i) Show that if x (t) = gT/2 for all t > 0, then p (t) = m(t) for all t > 0, and thus that output is the same as it would be without the change in policy.

(ii) For 0 < t="">< t,="" are="" the="" prices="" that="" firms="" set="" more="" than,="" less="" than,="" or="" equal="" to="" gt/2?="" what="" about="" for="" t="" ≤="" t="" ≤="" 2t="" given="" this,="" how="" does="" output="" during="" the="" period="" (0,2t)="" compare="" with="" what="" it="" would="" be="" without="" the="" change="" in="">

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Maurice Tutor
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Status NEW Posted 17 Jan 2018 05:01 PM My Price 8.00

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