Reinha d , Paul G.
A icle
Is he Neoclassical G ow h Economy a Ma ke Economy?
Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de
Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik
P o ided in Coope a ion wi h:
Duncke & Humblo , Be lin
Sugges ed Ci a ion: Reinha d , Paul G. (1981) : Is he Neoclassical G ow h Economy a Ma ke
Economy?, Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de
Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik, ISSN 0342-1783,
Duncke & Humblo , Be lin, Vol. 101, Iss. 4, pp. 441-443,
h ps://doi.o g/10.3790/schm.101.4.441
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Is he Neoclassical G ow h Economy a Ma ke Economy?
By Paul G. Reinha d
This pape in oduces ime explici ly in o he neoclassical g ow h model.
I c ea es a p oblem in he p icing o p oduc ion and consump ion lows,
on he one hand, and o he physical quan i ies ansac ed, on he o he .
I appea s ha he explici in oduc ion o a ma ke in o he neo-
classical g ow h model c ea es an inconsis ency in he p icing o i s
good.
The p ope y equi ed o he ma ke is ha i ansac s non-in ini es-
imal -physical quan i ies Q ( ) o he good a he model's p ice p (i) a
any ins an in con inuous ime. The analysis is in con inuous ime, o
ollow Samuelson's s abili y equi emen ha imeless economic mag-
ni udes mus be ea able as special alues o unc ions o con inuous
ime.1
Now i is no ed ha an indi idual's ma ke decision a ime emains
a discon inuous decision. The quan i y Q ( ) he sells will ha e acc ued
a ins an aneous a es Q' ( ) a he model's p ices p ( ) o e he p oduc-
ion pe iod — e < < , whe e e is he leng h o ime be ween ans-
ac ions. The buye will consume Q ( ) a he ins an aneous a es Q' ( )
ha a e p iced a p ( ) o e <
<C
+ e.
I all decisions now we e o occu pe iodically, e ime uni s apa , a
he same ins an s =
U
i = 0,... n, p ( ) would be cons an be ween
ansac ions. Time would pass as a sequence o s a ic s a es ha would
me ely da e con inuously.
Bu as Hahn has poin ed ou : "Fi s , i mus be admi ed ha pe iod
analysis is highly a i icial since while people may ake decisions dis-
con inuously, no all people ake decisions a he same ime".2 Tha is,
he iming o an indi idual's decision, and o ansac ions mus be
unc ions o con inuous ime. I can occu a any a bi a y poin in
ime and canno be aken o coincide wi h he e minal poin o a
p ocess ha is assumed independen , in i s iming, o con inuous ime.
This means a selle 's decision a , o a buye 's decision a — e,
in ol e an in e empo al p ice 77 (i) o a low ac oss ime a ime , o
1 Samuelson (1970).
2 Hahn (1955).
28 Zei sch i ü Wi scha s- und Sozialwissenscha en 1981/4
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DOI h ps://doi.o g/10.3790/schm.101.4.441 | Gene a ed on 2023-04-04 11:59:17
442 Paul G. Reinha d
1 1
— / Q' ( ) d ha is no longe equal o p (i). Ra he , 77 ( ) is he
e -e
a e age3
77( ) = -i- / p( )d .
e -e
In he g ow h model p ( ), he p ice o he good ela i e o he wage
a e, declines a he cons an p opo iona e a e
—
g om an ini ial
alue Po as he unc ion
PW = P0e-9* .
Thus,
ege — i
n ( ) = p
( )
o
e
>
0
,
9s
i.e. he p ices o p oduc ion and o consump ion and he model's p ice
all di e a ansac ion ime .
As a de ense, i may be a gued ha , i he discon inuous decision
in e al we e elima ed, he in e empo al p ice would disappea be-
cause as s 0,77 ( ) = p ( ).
Howe e , as s -> 0, Q ( ) 0, also. Tha is, his a gumen des oys he
ma ke as a mechanism ha is capable o ansac ing non-in ini esimal
physical quan i ies a a p ice. In wha sense can he ma ke , as we
know i , and as we like o a ionalize i , be an alloca i e de ice?
Summa y
Con inuous ime en e s he g ow h model h ough he s abili y equi e-
men s on he model. I s p esence c ea es a p oblem o ans o ming he
ansac ion p ice o he good, which can only be a p ice o physical uni s o
he good a a poin in ime, in o he p ice o a low o he same good ac oss
ime, as i en e s in o a ansac o 's decision, a a poin in ime. G ow h
models ea hese p ices as in e changable. The p esen pape ies o show
ha hese p ices di e ge in he g ow h model.
Zusammen assung
Kon inuie liche Zei wi d du ch S abili ä sbedingungen in das Wachs ums-
modell au genommen. Sie üh zum T ans o ma ionsp oblem des T ansak-
ionsp eises de Gü e — ausged ück in physischen Einhei en zu einem be-
s imm en Zei punk — in den P eis eine S omg öße, die in die En schei-
3 The cos o a low o a uni acc ues a p ( ) a o e
—
e < < and i
will o al -e y M d a . The alue pe uni o ime a ime o he low
o one uni o e
—
e < < is, hus,
77
( ).
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DOI h ps://doi.o g/10.3790/schm.101.4.441 | Gene a ed on 2023-04-04 11:59:17
Is he Neoclassical G ow h Economy a Ma ke Economy? 443
dung des Wi scha ssubjek s zu einem bes imm en Zei punk eingeh . Die
A bei e such zu zeigen, daß diese P eise in Wachs umsmodellen di e gie-
en.
Re e ences
Clowe , W. R. and J. F. Due (1972), Mic oeconomics. Homewood, Illinois,
Hahn, F. (1955), The Ra e o In e es and Gene al Equilib ium Analysis.
Economic Jou nal, 65 (1955), 64.
Samuelson, P. A. (1970), Founda ions o Economic Analysis. New Yo k.
Solow, R. M. (1956), A Con ibu ion o he Theo y o Economic G ow h. Qua -
e ly Jou nal o Economics, 70 (1956), 65 - 94.
OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/
DOI h ps://doi.o g/10.3790/schm.101.4.441 | Gene a ed on 2023-04-04 11:59:17