A Neo-Classical Macro-Economic Model: Entrepreneurs, Bankers, Innovations and Exess Profits

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 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/292834 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. 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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 . 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/ccm.12.1.42 | Gene a ed on 2023-01-16 12:43:58 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 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/ccm.12.1.42 | Gene a ed on 2023-01-16 12:43:58 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 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/ccm.12.1.42 | Gene a ed on 2023-01-16 12:43:58 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 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/ccm.12.1.42 | Gene a ed on 2023-01-16 12:43:58 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 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/ccm.12.1.42 | Gene a ed on 2023-01-16 12:43:58 (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 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/ccm.12.1.42 | Gene a ed on 2023-01-16 12:43:58 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 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/ccm.12.1.42 | Gene a ed on 2023-01-16 12:43:58 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 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/ccm.12.1.42 | Gene a ed on 2023-01-16 12:43:58