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Complement to ‘rationing macroeconomics: A graphical exposition’: Aggregate demand and supply
COMPI.EMENT ‘Ratking
Jean-l’ierrc
TO
Macroecoqw min: A Graphical Exposition’: Aggregate Demand and Supply DANTHINE
and Michel
PEYTRl(iNI~.l
L fiOIW.W.V ($ Louwnfw.1015Luuwwr-Doript?-. Fmal +crsinn waived
.SHIlrcrlcrnd
July 10x4
I. The ohjectiv: of this no:e Is to cornplcment Sncesscn~ I lQx.11 1-1 iwoviding a graphical exposikicn of his four market macroeconwllc not~:zl with zommwlity Irices ;rnd wages in the price quantity sp~c, 2 In mosr macloecona>mic textbooks, the IS.-LM model is comrlctcd l-q I~I ;timrcg3tc demard-aggregate supply (AE-AS) diagram. Sec. For ~4 I\’IL’. Branson-, Lirvack ( 19%. p. IX).
rhls IS Y downw;\rc? doping schedule. The model is completed by an upu.-ard 4qwg AS WI\C oC which there exist many varieties. Sat. for cx,~mplc. Branwn Lltkack (197h1. Gordon ( 1981). The usual approach then r:on~l~;s in fc\tiwq on the Intersection of these schedules. i.e.. on the price equilib-rtlrn in the goods market. Typi~lly, however. because of wage rigidities or ITI.IIIC~, d,udun. this is nd a full Waltasian gencrd equilibrium.
YF= F[NSW(~f)J, ?S = tin [ YS*, YFJ. The same model with other
labor supply hyp&W is worked out in Danthinc-Peytriguet (1981) and PcytrigM (1934). Assuming, as Snccsscn $ that the financill markets clear instantly. our general demand equation is
where R, amtc incxlmc, can be one of three things ming on the nature of the equilibrium. First, if R = 1 D, wt &ad :hc traditional AD curve (1) above. However, this scfrcd-3k will bc meaningful only if quililxium national income c&cicks with aggrcgmtc ckmand (i.e.. c AI_ if YT = YD). As this will turn out to bc the tax only in a Keynesian ummployamt situation WClabel this Atcduk as YD”a YDyZ,?,
Ad).
&con& it will lx tbt a3e that in arttin equilitium configunrlon. fTNDw( W P)J. fn tti situdistributed income will be R = YSwj W/f)= ations the rtkvant demand &uk will be YD~.Z+CD[YS”(WIf)J+ID[nrtP.
Because this will be the case rn situation rewrite (2) as Yocs
YDyZ,P.H:
YSw(H’f),,U)).
of cl.a&cal unemployment
t3
we
M).
YD=Z+CD[YF{WIP)J+
lD(II(P. YF(I+‘, P). Ad,].
This schcduk will be mcaniagful if Ibd only if distribu~al ~ncamc quals (i.e., YT= YPj. As this will be the ca3c in a rcpre4 inflatltm +nc wrile (3) a!4
YF *,c
m.w
Jct~~lcd cxpwtitw
lilf ano illustrations of other types ol’ cquilihria labr supply ‘- are in Danthine Pqt~ igrlet ( 19X ! 1.
rhc CUC or ;d fir&l SufFicxnt car&ions for the slopv of the dimerent schedules to he as +hotbn m fi* 1 can bc found in the appendix. ‘\ the nominal wage-price pair corrzspondinp to ;I In fig. 1. I H& P,) 1, -aI WdrGsn equilibrium (GWE). That the three demand csves crozs rt (U& PO) is easily verikd.
(I)
If YT=YD.
avfF --* dP
YqZ.P.w!M)=YmZ.r’,uI lht,
-_.
I -CD’-lDm,
A
If (Cf~+fD’lrr,~>O,
(3)
If YT=
YF.
and
lD’m, <(Cl?‘-+ fD’m,)FNDw(W/f*2)
W(Z,P,W,M)=
YD*‘(Z,P,W,Ml.
.-..t
tvD”’ 2P
li(CD’+ID’rn.~kCl
- [ rD’ + lD’m,)FNSW
_ -
then
0
?YDR’.‘?P
W
PL
+ IDhI,.
Jean-l’ierrc
TO
Macroecoqw min: A Graphical Exposition’: Aggregate Demand and Supply DANTHINE
and Michel
PEYTRl(iNI~.l
L fiOIW.W.V ($ Louwnfw.1015Luuwwr-Doript?-. Fmal +crsinn waived
.SHIlrcrlcrnd
July 10x4
I. The ohjectiv: of this no:e Is to cornplcment Sncesscn~ I lQx.11 1-1 iwoviding a graphical exposikicn of his four market macroeconwllc not~:zl with zommwlity Irices ;rnd wages in the price quantity sp~c, 2 In mosr macloecona>mic textbooks, the IS.-LM model is comrlctcd l-q I~I ;timrcg3tc demard-aggregate supply (AE-AS) diagram. Sec. For ~4 I\’IL’. Branson-, Lirvack ( 19%. p. IX).
rhls IS Y downw;\rc? doping schedule. The model is completed by an upu.-ard 4qwg AS WI\C oC which there exist many varieties. Sat. for cx,~mplc. Branwn Lltkack (197h1. Gordon ( 1981). The usual approach then r:on~l~;s in fc\tiwq on the Intersection of these schedules. i.e.. on the price equilib-rtlrn in the goods market. Typi~lly, however. because of wage rigidities or ITI.IIIC~, d,udun. this is nd a full Waltasian gencrd equilibrium.
YF= F[NSW(~f)J, ?S = tin [ YS*, YFJ. The same model with other
labor supply hyp&W is worked out in Danthinc-Peytriguet (1981) and PcytrigM (1934). Assuming, as Snccsscn $ that the financill markets clear instantly. our general demand equation is
where R, amtc incxlmc, can be one of three things ming on the nature of the equilibrium. First, if R = 1 D, wt &ad :hc traditional AD curve (1) above. However, this scfrcd-3k will bc meaningful only if quililxium national income c&cicks with aggrcgmtc ckmand (i.e.. c AI_ if YT = YD). As this will turn out to bc the tax only in a Keynesian ummployamt situation WClabel this Atcduk as YD”a YDyZ,?,
Ad).
&con& it will lx tbt a3e that in arttin equilitium configunrlon. fTNDw( W P)J. fn tti situdistributed income will be R = YSwj W/f)= ations the rtkvant demand &uk will be YD~.Z+CD[YS”(WIf)J+ID[nrtP.
Because this will be the case rn situation rewrite (2) as Yocs
YDyZ,P.H:
YSw(H’f),,U)).
of cl.a&cal unemployment
t3
we
M).
YD=Z+CD[YF{WIP)J+
lD(II(P. YF(I+‘, P). Ad,].
This schcduk will be mcaniagful if Ibd only if distribu~al ~ncamc quals (i.e., YT= YPj. As this will be the ca3c in a rcpre4 inflatltm +nc wrile (3) a!4
YF *,c
m.w
Jct~~lcd cxpwtitw
lilf ano illustrations of other types ol’ cquilihria labr supply ‘- are in Danthine Pqt~ igrlet ( 19X ! 1.
rhc CUC or ;d fir&l SufFicxnt car&ions for the slopv of the dimerent schedules to he as +hotbn m fi* 1 can bc found in the appendix. ‘\ the nominal wage-price pair corrzspondinp to ;I In fig. 1. I H& P,) 1, -aI WdrGsn equilibrium (GWE). That the three demand csves crozs rt (U& PO) is easily verikd.
(I)
If YT=YD.
avfF --* dP
YqZ.P.w!M)=YmZ.r’,uI lht,
-_.
I -CD’-lDm,
A
If (Cf~+fD’lrr,~>O,
(3)
If YT=
YF.
and
lD’m, <(Cl?‘-+ fD’m,)FNDw(W/f*2)
W(Z,P,W,M)=
YD*‘(Z,P,W,Ml.
.-..t
tvD”’ 2P
li(CD’+ID’rn.~kCl
- [ rD’ + lD’m,)FNSW
_ -
then
0
?YDR’.‘?P
W
PL
+ IDhI,.