Roskamp, Ka l W.
A icle
A Neo-Classical Mac o-Economic Model: En ep eneu s,
Banke s, Inno a ions and Exess P o i s
K edi und Kapi al
P o ided in Coope a ion wi h:
Duncke & Humblo , Be lin
Sugges ed Ci a ion: Roskamp, Ka l W. (1979) : A Neo-Classical Mac o-Economic Model:
En ep eneu s, Banke s, Inno a ions and Exess P o i s, K edi und Kapi al, ISSN 0023-4591, Duncke
& Humblo , Be lin, Vol. 12, Iss. 1, pp. 42-55,
h ps://doi.o g/10.3790/ccm.12.1.42
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A Neo-Classical Mac o-Economic Model: En ep eneu s
Banke s, Inno a ions and Excess P o i s
By Ka l W. Roskamp, De oi
I. In oduc ion
In he his o y o economic analysis wo mac o-economic models we e
de eloped which deal wi h he co e p ocess o a neoclassical economy,
ye a e oday ela i ely li le used. They a e Schumpe e 's model o en-
ep eneu ial inno a ion and economic g ow h and Wicksell's model o
he "cumula i e p ocess."1 Bo h models we e s a ed e bally and hey
e eal p o ound insigh s in he wo king o a ma ke economy. In his
pape an a emp is made o b ing oge he a ious elemen s con ained
in hese wo models and o se up a dynamic neoclassical model. The
unde lying ideas a e he ollowing ones.
A compe i i e capi alis ma ke economy is a dynamic one. I i is o
unc ion well, i mus g ow. Acco ding o Schumpe e such an economy
is cha ac e ized by he p esence o en ep eneu s who ake he isk o
in oducing mo e e icien , cos educing inno a ions. I success ul hey
a e ewa ded o his h ough excess p o i s — un il he imi a ion o
hei inno a ion by o he s wipes excess p o i s ou and o ces hem o
look o new ones. En ep eneu s a e he d i ing o ce in a ma ke
economy. They p opel i o wa d in hei sea ch o excess p o i s; no
ou side impulses a e needed. Wi hou he en ep eneu ial d i e he
economy will go sideways. I alls back in o a dull, no-g ow h s a iona y
s a e, whe e he compe i i e equilib ium will awa d ac o s o p oduc-
ion wi h no mal a es o e u n only; a s a e much discussed in
economic analysis bu no a all cha ac e is ic o a ma ke economy.
1 Joseph A. Schumpe e , "The Theo y o Economic De elopmen ," Ha a d
Uni e si y P ess, Camb idge, Mass. 1934; and "Business Cycles," McG aw-Hill
Comp., New Yo k, 1939. Knu Wicksell's „Vo lesungen übe Na ional Ökono-
mie" which we e published in 1901 and 1906. The English ansla ion is
"Lec u es on Poli ical Economy," (Lionel Robins, edi o ) 2 olumes, London,
1934; especially olume 2, p. 190 .
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En ep eneu s, Banke s, Inno a ions and Excess P o i s 43
A second cha ac e is ic o a capi alis ic ma ke economy is a inancial
supe s uc u e wi h a banking sys em able o c ea e money. The
beha io o banke s, wi h espec o po olio choices — hei desi e
o s ay liquid o o acqui e ea ning asse s — has, as Wicksell showed
some 70 yea s ago, a g ea in luence on capi al o ma ion, u u e
p oduc ion and p ices. Inno a ions, he incen i es o in oduce hem by
in es ing in new capi al goods and he inancing o he la e in a
c edi economy, o m hus he co e o he neo-classical economy g ow h
p ocess. A i s cen e is he beha io o en ep eneu s and banke s wi h
espec o expec ed ea nings, isk- aking and liquidi y.
I will be shown ha he Schumpe e ian and Wicksellian app oaches
lead o a gene al dynamic neoclassical model which is help ul o he
unde s anding o he ac ual wo king o ma ke economies. The model
con ains as special cases a numbe o o he mac o-models, he simplis ic
se en equa ions "neoclassical model," he Keynesian model, F iedman's
"Simple Common Model" and Solow's neoclassical g ow h model.
II. The Neoclassical Model
We assume a compe i i e economy wi h upwa d and downwa d p ice
and wage lexibili y. The e a e wo ac o s o p oduc ion, capi al and
labo . The o me is owned by en ep eneu -capi alis s. Labo is sup-
plied by wo ke s.
The economy p oduces wo ypes o goods, consume goods and
capi al goods. Consume goods a e consumed by bo h wo ke s and
en ep eneu s. Capi al goods may ei he be used o ein es men s o
keep he exis ing capi al s ock in ac o o ne in es men s o enla ge
and/o deepen i . To simpli y ou model we assume ha he p oduc ion
unc ions o bo h ypes o goods a e he same, hus he agg ega e
p oduc ion unc ion is w i en as
(1) 0 = 0
(K,
L)
whe e: O is eal ou pu o consume goods and capi al goods
K is capi al s ock, in eal e ms
L is labo o ce
The p oduc ion unc ion shall be linea homogeneous, he e a e
cons an e u ns o scale, bu diminishing e u ns o each ac o o
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44 Ka l W. Roskamp
p oduc ion. The eal en al o capi al is equal o he ma ginal p oduc
o capi al
ÔO ÔO Ô 20
(2) R " ÔK ~SK>0 <5K2
whe e RR s ands o eal en al. The eal wage a e is equal o he
ma ginal p oduc o labo
ôO ô
<0 62
O ^
(3> "6L->0
The money wage a e is
(3a) Wm = PcW
whe e WM s ands o money wages, PC o consume goods p ice le el
and WR o eal wage a e.
The demand o new capi al goods shall be a unc ion o he a e
o e u n en ep eneu s expec o ob ain on hem and he bank a e
cha ged on loans o inance hese new capi al goods. We w i e he in-
es men demand unc ion he e o e as
dK _
(4) -¿ =9(nex ,RB)
M7-->0 "SRT«»
Z/exp is he expec ed a e o e u n on new capi al goods and RB he
bank a e. The expec ed a e o e u n on new capi al goods consis s
o wo componen s. The i s one is he "no mal a e o e u n." I he
economy is ini ially in a compe i i e s a iona y s a e, his a e is equal
o he ma ginal e iciency o capi al-^. Wi h his a e o e u n all
o
K
in es men s shall consis o ein es men s in capi al goods embodying
he gene ally known echnology o he s a iona y s a e. A he same
ime known o some en ep eneu s shall be ad anced echnologies,
which, when in oduced, will esul in mo e e icien , cos educing
p oduc ion. This gi es hose en ep eneu s a chance o b eak ou o he
"no mal p o i " ange. They may expec excess p o i s, p o ided hey
ake he isk o in oducing inno a ions. We w i e he expec ed a e o
e u n equa ion as
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En ep eneu s, Banke s, Inno a ions and Excess P o i s 45
(5) •^p n —
(d Q l
ÔO
dK
[ÔK)K+[ÔK +E^J~d
K + dK
d
In his Eexp is he expec ed excess p o i a e. We assume, o he sake
o simplici y, ha i is gi en exogenously. I Eexp should be equal o
ze o, he expec ed p o i /7exp e e s o he ma ginal p oduc i i y o
capi al.
In o de o ealize he excess p o i s, en ep eneu s ha e o make ne
in es men s in mo e e icien , new capi al goods. Ye o inance hese,
loanable unds a e needed. Thei amoun is equal o
'-MS)
whe e: F s ands o loanable unds needed
P/£ is he p ice index o capi al goods.
In he ully employed economy he loanable unds F can come om
wo sou ces, om mone a y sa ings and (o ) om money c ea ion by
he ac ional ese e banking sys em. We w i e he e o e
(7) M* = F - Smon
whe e
M*
s ands o new money c ea ed and
Smon
o mone a y sa ings.
I F >
Smon
en ep eneu s ha e o y o ob ain loans om he bank-
ing sys ems. On hese loans hey ha e o pay he bank a e o in e es .
We assume ha he banks conside h ee ac o s when hey de e mine
he bank a e o in e es . They shall o ien hemsel es on a long- un
s a iona y s a e a e o in e es
RQ.
In addi ion hey shall ake in o
dP
accoun inc eases in he p ice le el—-. Finally hey shall conside he
deg ee o which hey a e loaned-up. I
MS
is he heo e ical maximum
amoun o money hey could c ea e wi h gi en bank ese es, hey may
p e e o lowe his amoun , o isk and liquidi y, o aMs, whe e
a < 1. The smalle oc he g ea e he isk a e sion o he banke s, he
g ea e hei liquidi y p e e ence. Thus i is easonable o assume ha
banke s compa e he ac ual amoun o money supplied,
MS,
wi h wha
hey hink would be he desi able amoun supplied, namely a Ms. We
w i e he e o e he equa ion, de e mining he bank a e as
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46 Ka l
W.
Roskamp
(8) RB = H ( 0, , (MS - a MS) J
dP
The beha io o banke s shall be such ha i — > 0, ce e is pa ibus,
d
RB ises and ice e sa. A he same ime we ha e, ce e is pa ibus,
(MS - a MS) < 0, RB alls
(MS
— A
MS) = 0, RB unchanged
(MS
— A
MS) > 0, RB ises
I he demand o money in he ini ial equilib ium s a e was Mo
(be o e en ep eneu s ob ain loans equal o he amoun o M* om he
banking sys em) he new demand o money is
(9) MD =
M.q
+ M*
Fu he , he ac ual supply o money is equal o he demand o money
and we ha e
(10) MD = MS
The new p ice le el in he economy is he e o e, acco ding o he
quan i y equa ion
(11) -^
whe e P is he gene al p ice le el and V he eloci y o money, which
depends on paymen habi s and a i udes owa ds holding o money.
We shall conside i as gi en. Once he o al p ice le el is known he
consume goods p ice le el PC is equal o
(12)
(o-dK
d
Fu he mo e knowing P and PC he in es men good p ice le el PK
can easily be ob ained. We ha e
/ dK
dK
I emains o de e mine he mone a y sa ings in he economy. These
a e equal o
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(14)
(15)
En ep eneu s, Banke s, Inno a ions and Excess P o i s
{ iO, l
47
SO
a-BiJ-^ + a
o
(1 - B2)
O
+ (B2 SO
In (12) and (15) Bi and Bz may be conside ed a e age p opensi ies o
consume and hus cons an ,
(16a) Bj = Bj, B? = Be
Al e na i ely, Bi and B2 may be conside ed o be unc ions o he bank
a e RB and hus
(16b)
(16c)
Bl = Bi (R/j)
B2 =
Bg
(R^)
As a las equa ion we inally ha e he supply o he labo . This can
be ei he exogenously gi en,
(17a) dL
~d = nL
o be a unc ion o he eal wage a e
(17b) L = g (W )
The basic sys em consis s hus o 16 equa ions, namely (1), (2), (3),
(3a), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (15), and (17a) o (17b).
These su ice o de e mine 16 a iables, namely O, K, L, RR, WV, WM,
77exp, F, M*T Smon, RB, MD, Ms, P, PC and Pa> The sys em is hus de-
e mined. I he sys em is enla ged he e a e wo mo e a iables, Bi
and Bi2, and wo addi ional equa ions, namely (16b) and (16c). The
sys em con ains hen 18 a iables and 18 equa ions.
I is a pleasan ask o show now how he de i ed neoclassical model
is ela ed o o he , well-known mac o-economic models.
III. Rela ionship o o he Models
1. The Special Case o he Con en ional Se en
Equa ion Neoclassical Model
The widely used simple neoclassical se en a iable, se en equa ion
model can be w i en as,2
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48 Ka l W. Roskamp
(1*) O = F (L, R)
(2*)
(3*) L = L
S = S ( )
(5*) I = I ( )
I = S
(n O
The model is a special, simple case o he neo-classical model
p esen ed in Sec ion II. I e e s o a s a iona y s a e economy which
is in compe i i e long- un equilib ium. The e is no echnological p o-
g ess and he e a e no inno a ions and no excess p o i s.
Equa ion (1*) o his model is equal o (1) excep ha he capi al
s ock is gene ally conside ed cons an . Equa ion (2*) is he same as (3).
Equa ion (3*) is he same as (17b), and equa ion (7*) is he same as
equa ion (11).
The equa ion (4*) o eal sa ings is a special e sion o equa ion (15).
Because he classical model does no dis inguish be ween wo ke s and
en ep eneu -capi alis s, we may se in (15) Bi = Bg = B. Wi h his (15)
becomes
Fu he mo e, in he long- un classical model RB = R = -R. The eal
ou pu O is a maximum. Thus B de e mines wha will be sa ed. I B,
is in line wi h (16b), a unc ion o he a e o in e es , B = B ( ), eal
sa ings become a unc ion o he a e o in e es .
The in es men unc ion (5*) is iden ical wi h equa ion (4) i , he
expec ed excess p o i s a e Eexp is ze o. /7exp is hen equal o
RR — RB = R-
Equa ion (6*) s a es he equali y o eal sa ings and in es men . This
equa ion is con ained in he neoclassical model in Sec ion II, as a
2 See o ins ance: Ga dne Ackley, Mac oeconomic Theo y, The MacMillan
Company, New Yo k, 1961, p. 156.
^a- = (i-B)o
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En ep eneu s, Banke s, Inno a ions and Excess P o i s 49
special case. In he simple neoclassical model in es men s canno be
inanced h ough money c ea ion. Thus equa ion (7) becomes
Wi h his equa ion (6) becomes
Smnn dK
PK d
= I
The classical model does no dis inguish be ween consume goods and
in es men goods p ice le el. Thus
P = Pc = PK. Thus
c Smon _ dK _ T
S ~ P - d
2. The Special Case o he Keynesian Model
I we assume ha all p ices a e cons an and ha consume goods
p ices a e equal o in es men goods p ices, ha is PC = PK = P = 1,
we can w i e equa ion (12a) as
/ dK
dK
(13) p0 = p^O-—) + P —
Thus we ha e he Keynesian agg ega e demand equa ion
(1**) Y = C + I
F om equa ion (4) we ge he Keynesian in es men unc ion i
iZexp = RB = R = R. Thus
dK
(2**) I = — = g ( )
I he a e o in e es cha ged by banks depends solely on he amoun
o money supplied equa ion (8) simpli ies o
(3**) R = hi (Ms)
This is he Keynesian liquidi y p e e ence unc ion.
Finally, i wo ke s and en ep eneu s ha e he same p opensi y o
consume we ha e in (15) Bi = = B and
4 K edi und Kapi al 1/1979
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