ADVANCED MACROECONOMICS Lecture 7 Micro Foundations of Incomplete Nominal Adjustment 电子科大经管学院马捷
ADVANCED MACROECONOMICS Lecture 7 Micro Foundations of Incomplete Nominal Adjustment 电子科大经管学院 马捷 1
Outline -The Lucas Incomplete-Information model With perfect information With imperfect information Time dependent price adjustment ·Fischer model .Taylor model State dependent price adjustment 。Caplin-Spulber Model 电子科大经管学院马捷 2
Outline The Lucas Incomplete-Information model • With perfect information • With imperfect information Time dependent price adjustment • Fischer model • Taylor model State dependent price adjustment • Caplin—Spulber Model 电子科大经管学院 马捷 2
Lucas Model with Perfect Information Personal production: Personal consumption:C=P;Q;/P=PL/P Personal utility: U,=c,-↓Ly=fc,iy>1 2 PL/P--L 电子科大经管学院马捷 3
3 Qi Li Lucas Model with Perfect Information Personal consumption:Ci PiQi P Pi Li P Personal production: i i P L P L U C L f c L i i i i i i 1 ( , ), 1 1 Personal utility: 电子科大经管学院 马捷
U,= PL-LL→ Y FOC: aU1=0→ D L-1=0 aLi 1 →nL,= 1(In P-InP) ,- 1 电子科大经管学院马捷 4 一一元 元元元元元元元元
4 i i i i L PP L U 1 FOC: ( ) 1 1 ln ln 1 1 ( ) ln 0 0 1 1 1 l p p L P P P P L L P P L U i i i i i i i i i i （ ） 电子科大经管学院 马捷
Demand for good i: 9:=y+2;-7(p,-p),7>0 The aggregate demand:y=m-p In equilibrium,demand supply, i.e.9,=l→ P-p)=y+:-n,-p) 电子科大经管学院马捷 5
5 Demand for good i: The aggregate demand: y = m - p In equilibrium, demand = supply, i.e. i i i i i i y q p p z q y z p p 0 ( ), 0 电子科大经管学院 马捷 qi li ( ) ( ) 1 1 p p y z p p i i i
In equilibrium: n-p)=y+n-p)9 2-1 (y+2;)+p 1+7y-7 y-1 p= y+p 1+7y-7 y=0? → m=p? y=m-p 电子科大经管学院马捷 6 元元元元
6 In equilibrium: ( ) 1 1 p p i y zi ( pi p) ? 0 ? 1 1 ( ) 1 1 m p y m p y p y p p y z p i i 电子科大经管学院 马捷
2 P,-p= 1 +门 y-1 21 y:= y-1 (D.-B)= +(y-1)m 电子科大经管学院马捷 7 5元元元元元元
电子科大经管学院 马捷 7 1 1 i i z p p 1 ( 1) ( ) 1 1 i i i z y p p
Lucas Model with Imperfect Information Relative price of good i:=p,-p Two assumptions: (1)Certainty equivalency. (2)Rational expectation. Supely -1E(:) y-1 电子科大经管学院马捷 8 元元元
8 Relative price of good i: Two assumptions: (1) Certainty equivalency. (2) Rational expectation. ( | ) 1 1 ( ) 1 1 Supply : i i i pi l p p E r 电子科大经管学院 马捷 Lucas Model with Imperfect Information ri pi p
Assume m and =are independent and normally distributed,E[z]=0,so p;and r;are independent and normally distributed. up,), v.Ip:-Elpll if p,=E[p],EIrp]=0; if pi>E[p],E[rpi]>O; if p;<E[p],E[r,p ]<0. 电子科大经管学院马捷 9
9 Assume m and zi are independent and normally distributed, E[zi]=0, so pi and ri are independent and normally distributed. ( | ) [ p E[ p]] v v v E r p i r p r i i if [ ], [ | ] 0. if [ ], [ | ] 0; if [ ], [ | ] 0; i i i i i i i i i p E p E r p p E p E r p p E p E r p 电子科大经管学院 马捷
Lucas Supply Curve 1 Vr y-Ivr+vp (p,-E[p]) =b(p,-E[p])→ Aggregate supply y=b(p-E[p]), b>0 Price surprise 电子科大经管学院马捷 10
10 ( [ ]), 0 Aggregate supply : ( [ ]) ( [ ]) 1 1 y b p E p b b p E p p E p v v v l i i r p r i 电子科大经管学院 马捷 Lucas Supply Curve Price surprise