Classical, Neoclassicaland Keynesian Viewson Growth andDistribution

Edited bv

Neri Salvadori

Professor ofEconomics, University of Pisa, Jtaly

Carlo Panico

Professor ofEconomics, (iniversity ‘Federico I!’, Napies, Italy

Edward ElgarCheltenham. UK Northainpton. MA. USA

\Cri ‘alsadorj and Carlo Panico 21)06

.\li rahts esersed. No pan Ot’ihis puhuication O.II be reproduced, oored iii areirlesai 0cm or transrnitred in anv fiarm nr En .in lrIean. elcctronjcmedianica) or photocop. ne. recording, “r cthera. ‘hout iie priorpermosion ofthe puhliher

ContefltsPubiished En

IE’dward Elgar Puhlishing E mited

i(ìlensanda E-louse

i itt oJ iigiiresMontpellier Parade

i itt of i’ables lxC heltenham

i itt f Contributors x(los6E 50 ll.L8

Introductioii by Carlo Panico and Neii Salsadori xi

[dward E lgar Publishing, Inc.SEC1 ION ONE: CLASSICAI. VIEWSI 36 est Street

Smie 202I Growth and distribunon: a retuni to the clasical tradition\ onhampton

I Renato Balducc’i\lasachuens 0)1)60I

2. Natural sage drnamic in a Ricardian groth model

I Dai’ide Fiosrhi ami RocIoI/o

3 (‘o—eolution of population and natural resources: a simple

I Ricardian modelSimone D ‘Alea sandro\ catalogue record t’or this book

is available from the British E ihra4. Some aspects of stnictural change in Masx’ s analysis 79

Maria L)an,ela GiammaneoI ibrary of Congress Cataloguing in Publication DataClassica), neo classical and Keynesian views on grossth and distribution / edited SECTION TWO: NEOCLASSICAL \‘IEWShy Neri Sahadorj and Carlo Panico,

p. cm,5 Gross th. ineorne distnbution and ‘ige heterogeneitv in thelncludes hibliographical references and nde

4 neoclassical econorn: a potentiai contlict betsseen dynarniciSBN 1-54542-309-7

efficiency and equiI. Economie development. 2. Distribution (Economie theo>. Classical

io and Pesa .EIciìi/3edisehool ofeconomics 4. Neoclassjcal school oUecjnomjcs 5. Kesnesjan 1 J.i Uileconomics, I. Sals adori, Neri Il. Panico, (‘ano, 952-

1276. Distribution and gro.s rIi in the neoclassica! traditionsHD75 C56X 20064 Mario Pomini339.2 -dc22

20050541T Ii “ Reconsidening de earl marginal productis ity Ueors nf

146

ISBN-I 3 9 ‘5 54s4’ 3004

1 distribution and intetectISBN-lO 1 84542 0Q 74rrtgo Opoi 6cr

Pninted and bound in Great Britain by MPG Books E Id, E3odmin, ( orna1l8 Pobin financial groth rnodels: a reconstructi )n 167

Mic hele Lima sani

1’

vi C 1a icaI, neocla skal and KL yneuun iews un growth and dK stubution

Figures

Relation (s) 14

Lahourshare q(s) 14

16

Relation s () 17

Labourshare q(s) 17

Growth rate g(s,) 17

Phase dìagram of the stahle nude equilibrium 41

Vector field of the stable node equilibnum 42

The effect on the equilibrium wage of different initial natura!wages 33

2.4 Different 1ongnm behasiours of tsso economics which arenot observationally different 44

Phase diagram of the stahle focus equilibrium 45

Vector field of the stable focus equilibrium 35

Example of trajectory for the stab!e node equilibrium 47

Example of trajectory for the stab!e focus equilibrium 47

Unsustainable regime (Case I) 63

Sustainable regime (Case 2) 64

Concentrated versus collectise land ownership 67

Concentrated versus diffused !and ownership 69

Typical population lractions as functions of the populationgrowth rate in a table population 107

5 2 The Soloss mode! with age ‘trueture’ CD and 1 f uffects asfunctions of the popu!ation growth rate in a stab!e popu!atìonor distinct ages of entry in the work age span () 109

5 3 The Solow mode! with ige strucrure’ balance of CD and ITaffects for distrnct ages of entry in the york age span (A):onset of OPGR and WPGR

SECTION THREE, KEYNESIAN VIEWS

9. Unemp!oyment and growth. a critica! survevEnrico Bellino

10. Growth, unemployment and wages’ disequilibrium modelswith increasing returnsLuciano Boggio

I! Behind Goodwin’s rea! wage function: which kind of !abourmarket?Giuaeppe Maarrornatteo

12, Entry and stationary equilibrium prices tu a post-Keynesiangrowth mode!Antonio D A gota

13. Are Kaleekian mnde! relevant for the !ng ruqPa,squale Commendarore

Inde s

191

227

243

266

288

I I

1.3

14

15

1.6

2,1

2.2

2.3

2,5

2.6

27

2.8

3!

3,2

33

34

5,!

109

li

Iin (7a.,i, n/. ,i ocla’ ‘i, al and K ne t’tu tieW un erou th ,ind ditrrihution

5.4 The Solow mode! with age structure: halance of (‘D rnd ITeffects for distinct levels of the capitai share, and onset ofOPGR and WPGR iii

.5 The humped fonn of the ì a) pwdutti it factur as afuncuon of the population grmsth rate under Miles’ 1999) Tablesproduetis itv profile b age 16

—

o The Solow mode! with age structure and heterogeneousI .1 Faxonomy ofdvnamicequilibriaproductivity Gìni’s mdcx of incorne distribution as a

funetion of the population growth rate: onset of MinIPGR 12 The typology of steadystate equihbria 18and MaxIPGR 120 1.3 Fhe mu!tiplicity of non cooperative equihhria 20

57 Incume per capita as a funetion of the population grorh rateunder the ame parameter constellation adopted in Figure 5.6 121

6. 1 Neoclassica! theory of grov th and distribution 130

9.1 Adjustmer t in the Solow mode! 197

9.2 Equiiihrium of a production unII 208

9.3 Steady state equilibrium 210

19.1 Fhe reaiage Phillips curve 230

19.2 Neoclassica! mode! with !earning-by-doing andtechnologicalspillovers 238

12. 1 The gcometry of programme (12.4 1) 27512.2 Steady state price vectors for different wage rates 277

I 13 Price vectors and growth rates 278

2.4 Steady prices and Inverse relationship between te and 28013.1 Pricing equation graph 297

13.2 Bifurcation diagram of p with respect to the shiftparameter a 298

13,3 Changes in the average wage sbare, average profii share andaverage mark-up as the shift parameter a is increased 299

I 3.4 The classical closure: changes in the average rate of growth.average rate of profits and a’ erage degree of capitalutilisation as the shift parameter a is increased 300

3.5 The Kaleckian elosure: ehanges in the average rate ofgrov th, average rate of profits arid ascrage degree of capitalutilisation as the shift parameter a is increased 302

Contributors lntroduction

I

Carlo Panico and Neri Salvadorino hak.uc.i. jq( i’iU’O e eeeers1cv ,f

Enrico Bcllino, (alIec Iii I nìereirv t tIifr a Ce»re

Lietano Boagio. Cathe1j ,erverìt o tiri a Cuore Fhe prohlem al cconomic groth and income distribution as a major.encern nt the classical econccmists, Rtcardo iugurnent ahout .shat he calledPaqteaIe Commendaicre, I eueraetC of \upicv I eJcreco lì the naturaF course of the ec000rna contemplated an economie ‘ste[n in

\ntunio DATata. Unircrsjrv ùi (aiaaia nhich capital accumulates. the population grows, bifi there is n technicalI progress. the latter is set aside. In Ricardo the rate of accumulation isSimone l)’\Ies’andro, Cri-cr Lv ccf5iena

cndoeenously determined. The demand 1cr Iahour is gas erned by the pace aiLuciano Fanti. I ceieercitv c P’to n hieh capiial aceurnulate%, shereas the limg terrn suppl al laboor

I reeulated by the ‘v1althusian Law ai Population’ The required Si/e ot theDat i le Fiaschi, Unc-n e ets a/Pi a I workforce is considered essentially generated by the accumulation processMaria Daniela Giammanco. Unecerntt ( itself. In other words. lahour power is treated as a kind ci producible

commodity. It differs from other commodities in that it is not produced in aMichele Lemo-,ani. (‘ceccvrerv ,.tMc .c!i(i apita1istic ay by a special indutry on a par with other indusiries, bui is thePicro Mantredi. Unir ersits o/Pe re sull 01 the interplay between the generative hehaviour of the working

populatuen md socio economie conditions. In the most ‘3mpleGctoeppe Mastrccniatteo. Cr1h,!ic [ee 11(3 ‘T tllicOC 5 t 11)1- eonceptualiiation possibie. Iabour poster is scen to be iO elastic supply at aArrigo Opocher. i i ìLc [P cLsu gisen real wage rate hasket. lncreasing the ournher al baskets asailahle in the

tupport ol workers involves a proportional increase in the workforce, In thisMario Poinmi, Lnivercity oJ Padua viess the rate ol growih of Iahour supply adjusts to any given rate of growthRcd Ifo Signorino, I ;eicv rdr’: f l’derma t Iabour demand o. ethout necessltatmg a ‘arianon in the real a age rate.

Lahour can rhus set no irne m groo.th because it is gencrated’ o.ithin thegrowth process. the oniy limit to groo.th cari come from other nomaccumulable factors al production: as Ricardo and athers made clear. thesefactnrs are natural resour..c in generai md iand in parteular. In other ue’rds.there o. onl endogenous groo.th in Ricardo. Thi grov1th o. hound Io losemomentum as the scarcits of naturai factors of production makes itsell felt in

ternìs of extensive and irtensive diminishing rcturns. (Fechnical chanee Is of.oeurc ens ‘aged te eounleract these icndencies. Il land ai he best quaiity

I nere asailable in abundance O o.ouid he a free gnccd ami no rent ‘scculd bepaid br jts ore In this case the ec sterTi couid grov. tor ever Recardo vlasperfectly ao. ire ai thit mplicatirrn (Rraardo, trarlo. Vi p 301 .

Contrar lo Ricardo. Adam Smith’s attenteon taeucd on the facu o.dctermining che groo.th of lahour prnductis cv. that o., the factars attrettng

26 C’lt o al, o’ ì /o i i al and Kt a ne non i ire, i on pro rh unii tliatrihittion

K,ildi’r. . (I ‘463 i. ‘Capita! acciimulatiiin an) eeiiiai ‘mie ci” ic,th’ in E’ A 1 ali ,mdi c e ci) i. i ; I h ‘i e ip (. api la), ‘5 en Y iirk’ Si \4 irtin Pieni, pp I 7

222Kaidor. 5 and I. 4. StorIe, i (I 91) 62), A new mode! d ,w i’nom e unni th Re i i,

f’,.,,,.u,i, ,iu ,. 29. “4 dii.

La ud. R. irid S. Si,. kel ‘tOW, li unciiipli’r mciii mii er il uniun— baicain ni ere in pioy reni 6 Quiirii e! e Jan toni i’! I’ imiti unii i 55, 1 97

ucas, R i I ‘48$ i, On the irechanici of economie dei i’loprnent loiirna/ u( ((unitariEi inor’id i. 22. 42.

Pa’, udii, I I 962 i.- Rate i’! pr i il aiuti inc,’mc djnu’i hutien ‘i ,.‘Iau un iii uhe itc ai

eCOnomie 9roni tU, Rei-i,’,, a /4 ituimo,- Sti,i/j,’,. 29. 26”- 1)9Per’mon I and (3. Fahellini ( ‘492) ‘(irowih di,trihution and politici’ /aaropeon

Econornii Ri cii i,, 36, 9 61)2.I”. hjola.Mi’ ‘ ‘494,. Thrc.uun md barcainine in captaiiieu. \ di(terenti.u! carne

i ‘ ii’. J’iii 111111 c E, liii,’ no,. I)i ii,, t’ui un,! (1’i’ti’o! 8. 20 mi 12.Rehcio. 5. f i 1991), 1.ong run polici anali il’, and lune_rulli crowth’, Iouom/ ot

Puliti I &ono,na 99, ‘tOO m2 I.Rii. ardo, D. m I ‘4 1 Go ‘l’e Pri,,, -,p e ,it’ Poit ti. ‘il 6,- ‘nomi i md T,i,ua’iun, edo..

L,’ndnn.Rom,’r. P. Il i, ‘ increan ne eturumi md inc—i o n crini tU. i, urna! i [6 u! iii, li!

6conorny, 94, 11)02 iRomer, P. 1990i, ‘Endogenotui iechnical change , Journol “1 Pi lidi a? 1u-onoma. 98.

71—102Roniihorn. R i 1046) ‘Capita! k,rma’ion ,ind i,nempt’in ment’. (0 t,’r’! [,o , *

la, 000titui’ Poluv. 11,26 39.Ronitliorn, R. (1999). ‘Unemployment, capital—Iahoi nuhstutution. and ‘conornir

gronith’. tIfF 11 iok?nri l’api r. Slarch, Vt P/99/43Sali adori, N (ed. I 2Otu3a i, 0)111 aju,I ., ii (jriiuiih Th,irira: Ao E i i, inii’flt.

.\lderihi,t. ( K .ind Niìrthamptien. MA. 1, SA. Edo .ad Elt,ìr.Saliadori 5. (ed ) (20)3h), The T!uroi-r 0/ Pci noniii (.,ri,u,ih, \ldci’,hot, UK and

Northampton, MA, USA. Edward ElgarSrnith, A. (I ‘771)) 4,u !i’/uirn- lttii the ‘100,0’ in’! I. .!i!lel , :1,,. 11 ,,l!r/, 4 \‘ifi’’fl’ -.1

cdii 1 7”6. ‘vo! li of ‘ the Glaeoni Edition al the ‘Aorks ,ind C’ ‘rrenpindence ot,\dam Smuu.h . cduted hy R H Carnph’tl 4 8 Stunter md W.i3. Tuidd, Oatiird:Onford Unuversit’1 Presi

W ipler. R. (2001). ‘Unioni, gran th and unemploc ment’. L’niversiti of F(ihineen,Discu’.ion Paper So. 206. Echruar -

2. Natural wage dynamics in a Ricardiangrowth modei

Da4ide Fiaschi ami Rodolfo Signorino

Ricaido] ueiained dii iut’4nirranr e’ rrniee p,niiipie tIni) un an’1 cii cui ‘ocial andultural cnn ir,inment thei-c un a ‘naiur,i/ i de ‘il’ e. ,ies’ ,it o iuueh alone population

,.‘iuuld reiuiain ntationai’y and t’u’om nnhuch w1uges can only devOte teunporarily. thehypothenis of ,in inhinitely elastie nupply etitie al lahour thus did noi neceinarilyunply that this suppir price nasi he equa! lo the bare minumum ai nuhsintence.

‘E ci th in aiurnption e. a, itiCi insintent ni ah ,inother i mi PI ied i t’calore il hin nude!duncusned heIow, mhat waee, ire mt onlc fumi ui terne, al ‘corn’ bui are entireh(im alunont entirelv) ipent on COrn (Kaldor, I 956, p. 95, tootnate I. I nt einphants

2.1. INTRODVCTION

In the last tu,ni decades a host al (ormai mode!’, have fuurnished Ricardo i

theoryol’ economie nron’ th and iticome distrihution n ith a unathemancaigaih. S’ve iefer Lo Kaldor (1956. Sainuelsoti (1959 and I 9’8 i, Paainetti(1960), Hicks and Hoilander (1977) md Casarosa (1978 and 1982). tornentiw l’nt thnse mi idels e,- ltjch hai e commanded mosi attentino Un taniRicardian modeis share a common feature: ihey reproduce the clasiicaldtstinction hetween a market rate of wages ,md a natural rate of agca andmakc E a cruciai eiement to anaiyse the di namic properties ot the economyunder study. According lo Sainueison’s 1978 canonica! cias’,icai triade!, therate ‘A grnsvth c’I the 1tbouring populatuon. JL/di i/la. mi un maeicaniuig

(unctuon i of the gap hetween the nuarket rate 01’ in ages (a’) md the naturalr’ute of wagen (uu , and a decreasing function of the scnsitivity of the growth)t the labourung populanon tu the in 1tge cap (E):

-dJE] —- At ii — li i:

di 1.

in ouirs).

‘,vith 1tIt_ 0, 2) )>0 mmd E li 1nCC Saunuclmn I QX p - 421. E:q. St,

S 7mskal. neo(las u al (lld K snesi,ir i a m r(sth an,l htnbution \‘aturul a a e dv,lulnl( in a Ra ardtan en iii 1/I rnadel 29

Rtcardian scholars differ as te their interpretation of Ricardo’s view on thealue ot parameter e. Seme authors assume that tor Ricardo the value of e

is zero: the Malthusian population mechantsm s t,rks so rapidl\ that aerowing economy may be anaffsed as if the market rate of uagcs uerea1was at hs historically determined natura> leve! (sec Pasinetu 1960, pp. 81and 87). .Accordingly. these authors graffi a prrvìleged posiuon to the netionut natura! wage in the anaiysis of the growth process.

By contrast. other authors assume that e is large enough far population tearow ‘on1 sloulv during a highwage era’ >Samuelson !78. p. 1421>.rhese authors generally make much of Ricardo’s admission thtnetuithstanding the tendency of w’iges te conform te their natural rate, their

narket rate ina3 in an impro\ ing societv, far un indefinIte pertud. beeonstantly ahoxe it’ (Work’s [s133—5, emphasis added). Accordingly. theyfocus on market ssage dynamics, with the natural wage playing only asuhsidiary role. In particular. for Casarosa a growing econom mas beanalysed cri zJ the market rate of wages acre ala ays serv dose >0 itsdvnamic equilibrium level’ de(ined as the rate of wages at which ‘the rate of

population increase and the rate of capita! accumulatien are equa> (Casarosa975, p. 41).2

Our aim in this chapter is noi te assess the hits and inises of the twernajor scheols of thought on Ricardo’s theory of uages in a growingeconorny. We rather concentrate on an ana1tica1 issue which hoth schoo!shave sO far failed te investigate in due detati. We refer io the relationshipbetween economie growth and the secular dynamics of the natura! wage rateBoth schools assume that natura! wage is a given and constant magnitude.The assumption of censlant natura! wage is a useful simpliffing assurnptienwhich helps draw many interesting growth results. Yet, models built on suchan assumptien do less than fuil justice te Ricarde’s and. more generally, theclassica! pomi of iew on the relationship hctween economie growth and thedynamics of natura! wage.3 Ricardo explicitly wams his readers that ‘thenatura! price of Iahour, esrtrnated ei en in food and necessaries, [is not te beundersteod asi absolutely fixed and constant. li iariea or difjrenr titnea inthe sarne country. and sery materially differs in different ceuntnes’ (WarksI,v.96, emphases added). Smith, Terrens and Malthus make similar clatms

To put it in a nutshell. classica! auihors maintain that the ainount andcompesition of the werkers’ normal consumption basket depends un socio-politica! facters generally Iabel!ed as the hahits and custems’ ruling in aaiven country in a gisen historical moment.4 Classica! economists contderhabits md eustoms Ss persistcnt phcnomena once they are generallyestahlished ameng the lahouring population.’ Nenetheless, classical authersdo nnt treat hahtts and customs as pure! exogenous magnitudes ‘s hich fa!!nutside the field of economie anai 515: indeed, elassical economists hold ihat

habits md customs ‘sre deeply tntluenced by economie factors, in particularhy the past .md present growth performance uf a given country.6 .As aconsequence, the historical eolution ci’ hahits and customs and the relatedd namics ci the natura! rate ci’ wages are a fit subjeet for economie analysis

Unfortunatelv. classica! economists fai! te explain in due detail the causa!mechanism thruugh ahich economie groath influences the dvnamics uf thenatura! wage. Perhaps the clearest and mest concise singie statemeni of theclassicai point ai vteu on the relationship betwcen habits and eustems,sverkers’ norma! censumptien basket. natura! wage and stages of economielevelopment may be found in Chapter I ( On the Generai Princtpies whichRegu!ate Wages’) Section 4 (‘The Minimum of Wages’) of Rehert Torrens’On lVages cmd Conibinarians. The passage in question is werth quoting infu!!:

The miniinum he!ew ahich wages cannoi permanentlv t’al!, consists in a quantityai’ the necessartes and convcniences ai’ life sufficient te preserse the lahourer inworking condition. and te induce him to keep up the rade of lahourers. The pomi,heloa ‘slnch wages cannot fa!!. is noi a fixed and inmutab!e point, but 5. an thecontrary. tiah!e to considerabie s .iriaton .. Ecco in countries. situated in theame climate. diff’erent habitsof luna i1l often oceasien variations in theminimum o! wages, as considerable as these which are produced by natura!causes, fite labeurer in Ire!and wi!I rear a family under eircumstances whtchssould not only deter an Eng!ish workman frum marriage. bui wouid force him enthe parish t’or persona! suppert. Now, il li certain, that a graduai introduction aicapita! mio Ireiand. accompanied by such a diffusion of instruction amongst thepeople. as wouid impari io them a tasSe fnr the comforts of lite. might raise therninimum ai’ wages in that countrv to an equality with their minimum in Enaiand

Aiterations, hoaever, in the niinimum of wages cannot be sudden!y cffectedSo far as this minimum ... li determined hy the habits ai hving, and thee’.tahlished scale ai comfnrt. it can be ei’fected en!y by those circumtance ai’prosperltv or deca, and h thosc moral L5u5e5 of rnstruction and ciui!ization,which are ever graduaI in their operation. Thc minimum af wages, therefore,though it uaries under ditferent climates. and with the different stages of natienal>mprovement. may. in any given time and piace. he regarded ai very nearistationary (Torrcns, 1833).

it is te be stressed that Toriens takes t’or granted that if lrish werkers lived ina growing ee000my (suh a’ Eng!and) instead ai’ a stagnant cconomy (suchas lreland) they would learn io appreciatc higher quality, non-suhsistenee,cornmedttics nd they weu!d start te en!ro! thetr fertility, Flence. in the !ightai’ Tarrcns remarks abose. sue reconsu’uet the basic tenets ef the classica!polnt ai’ view on the reiationship hetween economie growth and natura! wagedynamics as fe!!ows:

30 CIa dcal, neo las Cui ami Kcne s jan tea, un g ru i/i md dC ril’Uhi( a \aiu, al a age dynumft . n a RC arhau gran rh un del

i) v orkers i Is ing in countries IOL aied in diiferent tages uf tintinnaIimproement (such as Eng!and and Ireiand up tu the IX3Os) turn out todeve!op different ‘hahits ot living and diffcrent ‘estahIihed scale[s otomtort ks a consequence. ihey carri different natural v ages (Furrens‘minimum of wages,

li) orkers habits of iiving’ and workers estahlihed caie of c’mfortdepend on the ‘circumstances of prosperity or decay

fo put tt hriefly, we claim that for classica! eeonom1ts, workers normalconsumption choices and workers’ normal feruhtv choìces are the two basiechanne!s through vhich economie groth intìuences the dynamics of thenatural wage. Ori the one hand. workers eaming high’ market wage acquirethe economie possihility to hu higher-qua!ity. nun-suhsitence commodities.On the other hand. once workers become aware uf the tradeotf heteenchildren tu rear and ‘comforts of life to enjoy, their fertihtv decisions ceaseheing mled merely by the passion between the sexes’ (to use Malthus’favourite expression) ami siart being discip!ined hy rationa! economiereasonings. Grantecl that the growth proces goes un unimpeded and iiiat themoral causes of instruction and ci iliiation’ are at work. workers get

progressisely accustomed tu higher standards of !iving and thus permanentiyre ise their concept of subsistence both in terms of quantity and quaIit, Thenatura! wage slowIy but steadi!y rises.

Our argument unfolds in two stages. In the first stage Secuon 2.2) weinquire into the historìcal background of classica! analysis. We assess thecompatibihty of the classica! economists opmion un the rising trend nf thenatura! wage in eighteenth century Eng!and with the assumption of constantnatural wage. We propose as a so!ution to the puzile the possibi!ity thatworkers may take account, in their norma! consumption and fertihty choices,of some growth-induced changes. We refer to the rnovement of relati’.enatura! prices and the rise of wurkers’ real ineome provoked by the processof economie growth. In the second tage Section 2.3) we propose moreformai analysis. We elaborate a imple Ricardian growth model and wede’e1op an extension of the mode! in order tu anaiyse the dynamics of thenatura! wage rate in the !ight of our findings in the first stage

We are aware that a mu!n-commodity mode! is required in order tu takefu!! account of the impact of workers’ consumption and fertility decisions onthe dynamics of the natura! wage in a Ricardian growing eionomy. Yet. econtent uurse!ves in this chapter with the ana!ysis ut a more ,imp!e unecommodity Ricardian growth mode! in which se drop the assumptlon o! aconstant natura! wage. Ohvious!, mu decision tu work within a onecoinmodity framework means that the cIasica1 distinction hetweennecessaries and cunveniences is remos ed. whch m a scrious drawhack for a

mode! intended tu be a rattona! rcconsiru.tìon o! classieai ana!ysis, \ieedìesstu add. we postpone the ana!ysis of natura! wage dnamics in a mu!tieommoditv framework tu a further stage of our research.

In our mode! we show that a high market wage may attract the natura!wage. Maktng lise uf the !anguage of phvsics. ve c!aim that wage dynarnicsin a Ricardian growing economy may exhihit hysteresis. Apparent!y. suchfindings sound !ike a radical subversion nf the receised view un Ricardianeconomics which asserts that the market \sage is attraeted hy the natura!wage and not the other way round. As is ssc!! known. Ricardo maintains thathowever much the market pnce uf !abour tna’ deviate from its natural price.

it has, !ike commudities, a tendency to confortii tu it (Work,s Lv.94). Yet,what Ricardo ea!!s the tendency’ uf the market wage towards the natura!ss age requires that the workers’ norma! consumpriun hasket be assumed as agiven and cunstant magnitude. In uther wurds. the Ricardhm tendencv’ ufthe market wage tuwards the natura! ss age cannot be taken fur gran ted ineconomies where the growth prucess induces a drastic modificatiun uf thehahits and customs which shape workers nonna! consumption hasket.

22. HISTORICAL BACKGROUND: CLASSICALECONOMISTS ON THE DYNAMICS OF THENATURAL RATE OF WAGES

Classica! economists hasicai!y agree un defining the market rate uf ssages asa magnitude uriginating in the !abour market and determined by the interplayof the supp!y of and the demand for cummon !abour By contrast, c!assicalcconomists propose a few definitions of the natura! rate uf wages whichdiffer in many aspects buI share a commun feature: the natura! rate o! wagesis noI conceived as a direct!y ohservable magnitude (sec Pasinetti 1982, p.24O). As observabie proxies fur the natural rate of wages, c!assicaieconumists choose tu gaze at workers’ norma! patterns of cunsumption andfertility in different cuuntries and in different historical periods .As far aseighteenth centurv Fng!and is concerned. they broadly agree thut Engiishworkers

i) increased their nn\umption uf higher-qua!itv commodities thi’th.igncu!tura! and manufactured unes and

i!) learnt tu contro! their tertiiitv in the boom years characterized hy rapid!yincreasing demand for !abour and a high market wage

Fmm obsersations i) and n) abuse. classica! economists cunclude that thevery concept al subsistence drastically changed and that natural wage in

2 ( a ical. neoL la .sit il (md Ke ne sian iews 7)fl mn h UJUI ddtribudnn Narumal n age dx’namrc in a Rj€-ardian roa th model

England fcl!o’ed a marked!y rislng trend ‘n the period under ohserttionFhis conc!usion entails an interpretathve puzzie in so far as il clashes with the

twin Ricardian assumptiOils un natura! wage, that Is Io say,

the commodity composition of the natura! wage haskel is gi\en andconstant and

2. the natural wage-basket Is most!, nude up h suhsistence. iow quaht,agncnitura! commodities.

Ricardos weIl-knowfl prediction about the rising trend of natural nominaisage (and the reiated fai! of the rates of profits and capita! aLcumulatiofl) ishased on the twin assumptìons above. Indeed, according to Ricardo, wtththe progress of society the natura! price of !ahour has always a tendency torise. because one of the principal cornmoditie.s hv whzch its natural prrc e rs

regulated [foodj, has a tendency to become dearer, from the greater difficultyof producing it’ Works I.v.93. emphasis added), Obviously. if with theprogress of soeiety’, food ceases to be ‘one of the principai commodities’which regniate the natura! price of !ahour. nomina! natura! wage may notincrease and the rates of profits and capita! accumulatton may not decrease.

In our view, the key to the puzz!e above lies in workers reaction io thew ider consumptiOfl opportunities disclosed to them hy the growth process.Growth in a Ricardian framework opens up for workers the economiepossihihty of consuming a different wage-basket trom the natura! onedcterrnined by historically given habits and customs. The natura! wage staysconstanh ceteris paribus, if and only if workers do not modify their norma!hehaviour as regards consumption and ferttlity choices and thus do not takeadvantage of the growt1winduced new opportunitieS. As we sha!l see, thisproposition holds both in a Ricardian economy where the market and thenatura! wage always coincide and in a Ricardian economy where the marketwage is persistently above the natura! wage.10

Consider first a Ricardian economy where the market and the naturalwage a!ways coincide. For Ricardo, the workers’ norma! consumptiofl basketincludes both commodities produced hy the agricultura! sector of theeconomy (‘food and necessaries’) and commodities produced hy themanufactunng sector of the economy conveniences). In a c!osed econoinywithout technica! progress, agricu!ture is depicted hy Ricardo as a sectorwhose technology disp!ays decreasing returns to scale (the various qualitiesof land are in fixed supp!y), while manufactures are depicted as a sectorhose techriology disp!ays increasing retums to scale (thanks Io the SmithianproLess of division and specialization of !abour). To put tt briefly, inRicardo’ s tramcwork. agricultural commodities are increasing-pricecommodities, whfle manufactured commodities are decreasing-pricecotnrnodities. Thus, in a Ricardian growing economy relative natural prtces

re bound to change. Ricardo is pci fccdy aware of such natura] prtcemos ements. Re ss rites that. in the course of economie growth. agriculturalmommodities hae a tendency io become dearer, from the greater difficu!tyof prnducing [themj : whi!e the natura! price of tnanulactured commodities

has a tendenmy to fa!! far thuugh, on inc haiid, they are enhanced in rea! va!ue,frnm the mise in the natura! price of the raw materia! o! shich the are made. thisi’. more than coiintemhalanced 1w the improsements in mamhinery, by the betterdivision and distribution of iabour, and 1w the incr’asing skit!. hoth in science andall. nf the producems i lVarki L.s Q3...t)

Far Ricardo. the movement of relative natural priees. triggered hy theprocess of economie growth, a!lows workers to carry out substitutions inconsumption. Ricardo points oi.fl that from ‘manufacturedalways fa!ling. and raw produce always rìsing. ss ith the progress of society,such a disproportion in their relative value is at length created, that in richcountries a labourer, hy the sacrifice of a very smal! quantity on!y of bisfood, is ab!e to providc liherally for all his other wants’ (Works !.v,97). Thus,esen if the market rate of svages is always at iis historical!y determinednatura! lese!, the growth-induced tnovement of relative natura! prices al!owsworkers io consume a different wagehasket from that determined by theruling habits and customs. Warkers may thus revise thetr concept otsubsistence. provided that they deve!op a taste for higher-quality, nonsobsistence commodities.

Now consider a Ricarclian economy where the market wage is persistentlyahove the natura] wage. The range of workers’ consumption options isobviously wider than in the previous case since economie growth provokesnot only a movement of relative natura! prices but also a ‘high’ rea! income(esrimated in terms of subsistence eommodities). In such a scenario, it Ishighly probable that workers may change their normal consumption choicesaizd their norma! fertility choices. These two changes are noI independent butmay be seen as two sides of the same coin» Once a •high’ market rate ofwages has opened up for workers the possibi!ity to achieve higher standardsof hving, workers may hecome progressive!y aware of the trade-offbetweenthe consumption of higher-quality commodities and the maintenance of alarger family. Hence the Malthusian popu!ation mechanism may collapse inthe sense that population response Io the wage gap may decline: in terrns ofSamuelson’s 1978 canonìcal classica! mode! this means that the va!ue ofparameter E may increase. lf that is the case, the labouring popu!ationremains (alrnost) stationary in the face of a htgh’ market rate of wages.According!y. the tendency of a grow ing economy to generate a high’ marketrate of wages is, Ceteris paribus, strengthened. Since the high’ market rateof wage does noi cause an increase in the Iabouring population. the Ricardian

4 ( Im ij(aI, neocla su al md Keviu iuta vien.s Im trowth and distribunon Vatural unge dinamo, in o Ricor€han gran tu modei

naturalfmarket wage distinctlon makes sense oniy hy aying tbat the naturalrate of wages has increased.’2

Ricardo recognizes that ‘the increase of opuiation, and the increase offood wiil generaliy be the effeeL bui ,ioi the neiearv etfect of high isages’Wnrka I.xyxii.4O6,cmphasis addedj. Moreoser, he is perfectly aware that

the causai mechanism which Iinks ‘high’ ages, workers’ constimptiondcc isions and population growth has a circular nature:

The axnended condition of the Iahourer, in consequence of the increased valueahieh is paid h,m, does not necessarily oblige him to rnarry and take up’n him’elfthe charge of a farniiy he wilI, in all probahility, employ a portien if ho,increased wages in furnishing himself abundantly with food and necessanes hut

with the remainder he mav, if It please him. purchase any commod,ties that may

contribute to his enjoyrnentS — chairs, table%, and hardware: or hetter clothes,

sugar. and tabacco flìs increased wagm titen uil be attended with no nther eflect

than an increased demand Jdr mute oJ rhose commodities: and as the rane of

labourers will noi be ,nrnerially inereased, ha nagei il continue permanenuls

high tWorks I sxxii.406 7. emphasi added)

Malthus’ analysis of the subject is more detailed insofar as he ciaims thateconomIe growth has a direct influence on the formation and evolution ofworkers’ habits of consumption and fertility thanks to the growthinducedpossibility of buying higher-quality commodities:

The condition of the Iabouring classes of society must evidently depend. partlyupon the rate at which the funds far the maintenance of labour and the demand forabour are increasing; and partiy. on the hahits of the people in respect to their

food, clothing, and Iodging, .. It rareiy happens, however. that either of themremains tixed for any great iength of time together In generai, their tendencyis io change together. When the funds for the mamtenanCe of !abour are rapid1increasing, and the iabourer commands a large portion of necessarleS, e u to becxpected that if he has the opportunltv of erchanging his superfluous food far,onveniencea and comforti, he Wi/I acquire a utste far tlieae ,onveniences, and hiiI,abiis iii!! be formed uccordingly (Malthus, 1986, voI. V, pp. 182—3. emphasesadded).

As weil as Ricardo, Malthus investigates the link between consurnptiOnchoices and fertility choices in a growing ec000my characterized by ‘high’market wages. His basic view is that a change of consumption hablls may

imply a change of fertility habits:

From high real wages, or the poer of commandtng a arge porti00 aL thenecessaries of life. two very dtfferent results may follow; one, that of a rapidincrease of population. in sshich case the hìgh uages are ‘hief1 pent in ‘he

maintenance at ‘arge aol trequent families; and the othcr, ,hat of a decrded1lnpr iienu’nl in the ìnode of oh., atc,ute, ,,nd 1/le i onienicnce., tinI nomjortsi nìayi’d 4 rhaur a j’roportu’naie aireleration in the raui’ of increaìe (Malthus.19X6. sai ‘t p I s3 .mpha4i% added).

Malthus’ second resuit above comes true whenes er workers hecome able andwilling to reason from the past to the future’. and are not ‘ready toacqtiiesce, far the sake of present gratification, in a very low standard ofcainfort and rcspectahihty’ (Malthus. 1986. sai. V. p. 184). Once ‘theimprovemeni in the tnodes of ubsistence’ becomes a persisteniphenomenon. workers update. so to speak. thcir estahlished standards ofliving: the rate o! uages previously perceied as ‘high’ siarts beingconsidercd normal. This is the reason why Malthus critici/cs Smith who. forMaithus. fails Io appreciate the circular nature of the relationship between thenatura! rate of wages, on the one hand, and normal consumption and fertiiitychoiccs, on the othcr. Smith establishes a oneway causai relationshiphetween these two variahles: he maintains that English workers normallyconsume better food than their Scottish counterparts because the naturalwage in England is higher than in Scotiand (sec WN 1.viii.32). Malthus’reply to Smith is that the above relationship may also work the other wayround: far Malthus the natural wage in England is higher than in Scotlandbecause Engiish workers are accustomed to consuming better food than theirScottish coIleagues and thus they would refuse Io marry and be obliged Loconsume the iowqua1ity food which Scottish workers normally accept. Thus,far Malthus, the natura! svage dynamics and workers’ choices are strictlyinterrelated: ‘high’ wages induce a ‘high’ concept of subsistence and thus a‘low’ rate of marriage and popuiation increase which, in mm, keeps wages ala high’ leve!. By contrast, a ‘Iow’ concept of subsistence, generated by past‘iow’ wages indtices a ‘high’ rate of marriage and popularion increasewhich, in iurn. keeps wages al a ‘Iow’ leve!:

The efti’c:, in uhis noie cci in man oihers, certainly heiomes in ira mm a cause:and there is no doubt that if the continuance of Iow wages for some time, shouldproduce among the lahourers of any conntry habits of marrying with the prmpectonly al a mere subsistence, ‘,uch habits, by uppIying the quantity af Iabourrequired ai a low rate [of wages], would became a canstantly operating cause oflaw wages Malthus, 1986, voI. V. p 183, emphasis added).

To suns iip. classica! econamists agree that economie grawth maymfluencessorkers’ consumption and fertility choices and thus may aflect the seculardynamics of the natural wage. Since economie growth si idens the range ofcansurnption options available Lo workers. the dynamics of the natura! wagedepends an the workers’ decision whether or not to take advantage af the

6 ‘;aftui, i ,uu] Kci n i. vi ‘ a rn gr ai nnd diii, ibunon V itural ,‘ ae d» naoiu in a Ricordino aron ih inod 1

rr’ vth induced oppoitauitiia’ to ameliorate their tandard’ of hvingParaphraiiig Malthus, in a growing econorn si orkers ‘are really the arhtteis

f their oan destiny’ i \Ialthus, t >8n, ml V. p 226)

2.3. FORMAL ANALYSIS

In vhat tuIlo s we firt ketch a canonca1 .ne coinmodity Ricardian modclin subsection 231; then we extend the mode! io mvestigate market smagedynaniL nd the related dynarnics of the nturai smage in uheciion 2.3.2.sinee our model admits multiple steady state equilibna in terms of the vagerate and the lesel of the lahour force, suhsection 2.3. discusses the generaifeatures o! Iongrun equilibria and local tability. Finaliy. uhsection 2.3.3proposes an analysis of the dynamics generated 1w the mode! hen constanteiasricity ot substitution of labour is assumed.

2.3.1. ‘11w Canonical Ricardian Mode!

The canonica! one commodity Ricardian model demcrihes a very simpleagricoltura! economy mmith no foreign trade and no tcchmcal progress. Theonly conmodity produced. ‘corn, is produeed by means of itself and labour(paid in corn). Ihe amount and fertihty of the arious plots of land on whichcorn is cultiated are assuined as given and constant Thus the cornproducing technology is represented by means of an eqoation of the type

X=f(Nwithf{O)=O,Ì(N)>O,f(t)<w*f(O)andf(N)<O (2.1)

where X is the amount of corn yearly produced by ti’ labourers and w’ is thenatural rate of wages.

The analyticat skeieton of the mode! also ìncludes the followingequations:

x= w+P+T (2.2)

representing the distribution of the national product X among aggregatewages (W). profits (P) and rents (7’):

J=JtV) Vf’(tv)

representing the Ricardian theor\ al di) ferential rents,

represevtlflg the Rcardnin theory of ssagc.s ‘.shcre a a the ruiing rate of

P(2.5)

mm hich det’ines the rate of profits (r) as the ratio hetween aggregate profits andaegregate wages. K = W heing the aggregate capital. (In a onecommodity(ramemmork like the one we are considering, capita! is present only in theform of circulating capitai and coincides msith the total amount i) anticipatedwagegoods.)

Say’s Law of Markets holds: aggregate income is entirely spent.Aggregate profits are determmed as a residuu,n, while the two distributiveariab!es a’ and rare linked hy a relationship of the type

wR=f’(N),mmithR€(I +r) (2.6)

derived by equations (2.l)—(2.5).The mode! thus reproduces the tmmo fondamenta! propositions of the

Ricardian theory of income distribution:

i) for each given level of N and f o. the w—r reiationship is an inverse oneandas N increases, wR decreases. (This obsiously implies that, if w isassumed as given and constant at the subsistence leve!, the !aw otdiminishing returns causes a fai! in r.)

r0 make the mode! a dynamic one, we introduce three more cquations Thelamvs of motion of capital and labouring population are representeci by meansof tmsns equations of the type

wiwith a(O)=O and a’(.)>Ow* (2.7t

.i’K —k’(r» r*) with /YO)=O and fl(.)>O for r> r* (2.8)

where g and g are the rate of growth of K and ti’. We define r* as theminimum rate of profits compatible with entrepreneurs’ incentive io employIahour,t4 Fiere we foliow Casarosa (1Q82) by assuming that he!ow theminimum rate of profits r* there is no aceumulation af capital. FlenceK< Vf tN)/R’ with R* + r*).

The law o) motion nf the markct svage is deraed la’ the equationK = W = wN and represents labour market eqoi!ihrium.

1V = wN (2.4)

18 (la ss i, al, eoela s k al and Ke ne ian lie on growth and ,li ,ributu,n \arural age di na’nici in a Rù urdian gran rh rnodi’l

ss here g s the rate of erosi th of the naikct si age.8v ontrasI the mode! a’slimes si as a given :“d canstant magmtude:

e,. -0

si here g is the rate of growth ai 11*.

The mode! represented by equations (2!) (2.10) reproduces in astraightforward wa the two fundamental prOpositions of the Ricardiantheors ot growth (sec Casarosa, 1982):

a) the econorny i dris ing force is the accumulation o( capital whose pace isdeterrnined by the state of income distribution, gisen entrepreneurs’propensity to accumulate, and

ht the d’1namics of !ahouring population is cndogenous to the model: gisenthe Malthusian population mechanism the erowth of capital creates. so tospeak. the required grosith of laboor.

2.3.2. An Extension of the Mode!: the Dynamics of the Natural Wage

The ssc!! known Ricardian one-commodity mode! sketched above may Itegeneralized in a number of diiections (sec Freni, 1°98. in this chapter wemvestigate the dynamics generaied by the mode! when cquation (2.10) isrelaxed according to the suggestioni of Ricardo and other classica!economists. Thus we rep!ace equation (2.10) with equation (2.lOb):

11)g=y—— wtth y(0)—0 and /)>0w*

We have already defined

Rz1--, arai Ri=I,ri

which represent a linear transformation of r and r*. lt is ruiw consenient tudefine a new variahle:

il -

which represenis the ssage normiliied tu its natura! lese!.It is straightforssard (rom (2.6) that

-g forR R*

2 10

where 0(.Vl — (i V ,Ir”t .‘s tV . (1 measures the e!asiicl[s of the mareinalproduct curie of lahour ai dcfined hy tlicks and Ho!lander (1977. p. 356t. Inmanv economie applications such e!asticit is constam and greater than ICon’ider (or ciample the cxronentia! prcduction tunction ((V) — .V’ with

(0,1) sihere O !1 I ) I.) \Ve assume that dO/dN 0. Fromequations (2.12 -- 2.1 ) we hai e:

CR O( \)Ja(lD 1) (R R*) far R > R5. (2.! 4)

The growth rate of W1 15 given by:

(R_R*)_a(nj,_!)_sia_!)=(R R*) a(si,—!) (or R>R* (2.15

si here ( ii, -- 1) a( 01, I) ± y( ti’0 —1) has the ame eharacteristics as o).)and ;‘u. that is io sav. o(O) = O and o’(. >0

FmalIy we trace the dynamics of N in terms of the new variable w:

g a(wr,—!) (2.16)

Equations (2.! 4H 2.! 6t. together with the initial conditions

and is(0)= (2.17)Jo

fu!ly describe the dynamics of our economy. (iV1, K0 and w are respective!ythe initial va!ues of the labour force, the capita! stock and the natura! rate ofssages) In fact, any other variable, !ike capital and market wage. can bederived from the behavjour of a1>, V and R

2.3.3. Long-Run Equilibrium and [oca! Stability

The dynamical system (2.!4)—(2.!7) has ai least one equi!ibrium. that is. acoup!e of R and o’ ‘uch that g, =g.0=g5=0 (or R1 = R’ and a> = 10

The features of suut an equtlihrium are the usual ones: the rates of siagesand profits are at thetr natura! lese! svhile capital and lahouring populationare coflstant over orne. Floisever. sec note that the natura! ivage isendogenously determmed and depends un the initial conditions of theeconomy In the same manner, the equi!ibrium !esc!s of capita! and !abouringpopu!ation depend on the equilihrium leve! ot the natura) wage fo put ithriefly, our mode! admits multiple steadv-tatc equilibria in terms itt thesi age rate and the level of the labour force

(2.!Ob)

t2.i i)

12.12)

(2)3)

1i) ( f’ 1’. f’ff’if ai haI K’ v a.’!hn i a itf ‘Pi Iafl rh anfl ii’rribuiimaea / narnu. n a Ra anl:jn rr’nrh moficI 41

ri inti..reting question tè investigate is: whtch initial conditions can lead10 in equihhnum characieriied hy higher Iong-run natura! and market‘vige’.? Io answer this question sve tiro hase tè analyse the overail knamicsot the economv.

[be first step in the analysis of stahiltiv is tè check whether equilibritim(R w1 ) = (R. 1)15 !ocally stable. Fhus we linearize around the steady statethe dynamical system (2. 14)—(2, i?) and calculate the Collowingeigens alue’.. 17

2cr’(0)4.,L1’(0)R*

•1—

I E i+ 2

[(0) — fl(0)R * + 4fl’(O)R *a’(0)I (2.1 8a>

)Lf0. (2.18b)

The presence of a zero eigenvalue and two negative eigensalues (or withnegative rea! pari) makes the anaiysis inconciusive (sec Gandolfo, 1997, p.3628 The origin of the problem is that the dynamics of tV does not affectthe other variabies in the linearized system incIuding itseif, whereas N atfectsC* in the origmai, non-iinearized, dynamical system.

This suggests a useful simplifying assumplion: io reduce the analysis iothe (R, è’0) space,t9 Consider that if 6(N) 6, then the dynamics of thecconomy ts fully represenied by the dynamics of R and w0 oniy In this case

01 equation (2.18a) with O(V*)= O. represeni the eigenvalues ot thesimphfied dnamicaI system and therefore the system proes (o be Iocaliystabie (the real pan of boih eigenvalues are negative). Moreover, under thefoilowing condition.

O—4/J’(O)a(O)R*

=<- (219)4R */3l0la(0)R * 4-[o-’(0)—/3(0)R *j’f

both eigenvalues are negitive and rea! Therefore the equilihrium is a stablenode, Otherwise equilibrium (R5w1)=(R*,i) is a stablc focus,20

2.3.3. Dynamics with Constant Elasticity of the Niarginal ProductCurie of Labour

In the previous subsection we showed that, for a constant e!asticity of themarginal product curse ef Iabour, equiiibrium (Rw1,).=(R*.l) can be of twotypes’ either a stable node or a stabie foeus. in hai foi!ows ssc firsi analvse

the details nf these lwo polar va es in the suhections 2.3. 1.1 md 2.3.4.2,respcctiveiy. md then ‘.s e propose tss o mimerical eRainples in ,uhsection

2.3.4.1. Stable nude equilihriumThe fu!Iowing picturc rcproJuce the phase diaeiam of mur cconomy tòr6>6, where E is the stable node equiiihriun (in Figure 2.1 ssc assume that

In Figure 2.1 ssc drasv the mci where g5 0. e,.1 = O md g 1) in thepace R. li),) and ssc partition t’ne posiuse orthant in seven leglon’. inakingthe assurnption that functions a(.), ,8(.) and u(.) g are Iincar.21 Note thatthe existence of region IV is a noselty in relation tè the canonica! Ricardianmode!, where the bei 4.,, —0 and ,, O coincide.

Regions I and VII are nèt feasibie because of the consiraini on R. Inregion 11 ,g, >0. g,0 <O. TR <0 and g <O. in region III ,c,. >0,g, >0. g11 <0 and g5 >0, in region IV g, >0. g,,>0, g <O andg,, >0, in region V g <0, g,0 >0, g <0 and g5 >0. md final!y inregion VI ,, <0, g, >0, ,g5 >0 and g5 >0. The constraint on R worksas a barrier. sshich i’. absorhing (or w, < I and repeliing for ii, > I . Theoverai! dynamics indicates a convergence tossard E. that is. E is giohallystabie.22 Inspection of Figure 2. I highlights the taci rhat the convergence tuthe equiiihrium E can include a non-monotonic dynamics hoth for R and

To have a look at rrseraiI dynarnics in Figure 2.2 ssc reproduce anumerica! simuiation of the economy.23

v--b

VII— w v

(i

i 4 Il A

R

Fi5’ure 2. i Plvjz.,e dagrnin 0(1/10 sta bie node equìlrbriutn

4’ 1 lui u I zeoc lui ical and Kenesian iews un rowjh and djstrzhunun Vatu,c I n.aee dvnamk i in a Ri(ardian ‘,on.th nudd

Figure 2,2 Vectorjreld of the itable nude equihhrium

Fhe equihbrium E in Figure 2.2 is represented by (R*, u) = (1 2, 1) In thefigure we report an example of a trajectory for each region Il—VI (nonmonotonic convergence of the two variables tu equilibrium is evident).

The model shows just one globally stable equilibrium in the space (R, se1,);but multiple steady-state equilibria in tenns of the market wage, the naturalwage and the labour force. In fact, given the same initial levels of the marketa’age, the rate of profits and the labour force, the higher is the initial naturalwage, the higher is the wage in the long-run equilibrium and the lower thelevel of the labour force,24 A heuristic argument for sueh findings is thefollowing Consider two economies with the same rates of profits, marketwages and labour forces, but whose initial natural wages are below marketwages yet different. In particular, the first economy has a natural wage suchthat (R1, w) is a point over the g = O curve in Figure 2,1. that is, in regionV’ while the second economy has a higher natural wage, such that (R’, u,)is below the g, = O curve, that is, ìn region IV. Accordingly, the firsteconomy is characterized by an initial decrease in se; while the secondeconomy is characterized by an increase in w.

This different behaviour will lead the second economy to a higherequihbrium wage and a lower labour force (sec equation (2.6)). Suchfindings support the claim made by classicai economists according to whichan cconomy where workers have finer tastes will show a higher equilibriumwage. In other words, there exists hysteresis in the dynamics of the

cconoiny.2’Figurc 2.3 rcpioduces a numerical example of the tlajeCtOriLS of

the market wage (or the two economies, one starting from region V and theother (ram region FV which differ only in the mitial level ol their naturalwage (the initia level al market wage i 0 169) 6

0 ‘7

Figure 2 3 The ejfect un the equzlibrium wage of dzjferent initial natural

The multiplicity of equilibria has major implications for empirical analysis asweil. Consider two economies where si. and N are increasing while R is

decreasing. The first economy has a higher w*, such that it stays in regionII while the second economy stays in region IV Since we can observedirectly only R, w and N, but not w the two economies are notdistmguishable. However. they will have different equilibriurn wages andthey can show different dynamtcs to equilibrium. Figure 2.4 reproduces tsotrajectorles of the market wage far the two economies, one starting from

region III and the other from region IV. which differs only in the initial levelof their natural wage (a magnitude which, we stress again, is not directlyobservable).’7

The same differences are present in the equilibrium level of labour.

4

lv -— si,- I

Trajectory startrng from reginn 1’

0 77S

0.765

I) 20

2.3.4,2. Stable focus equilibriumThe dynamics far & e O i qualitative different. gain. under the assurnptionthat functions a(.), ,/.J(.) aisd (.) g are linear. the locus g - O has anegative slope. We know that E is locally stable, in particular a stable focus.therefore we cxpect possible overshootrng in the dynamic paths of R and wnear the equilibrium E. It may be proved that E is globally stable as in theprevic’us case.28 We aote that there also exists another equdibrium (point .4in Figure 2.5), bui it is unstable. Figure 2.5 reproduces the phasc-diagram forthis case

Dynamics in the various regions iFVI cari be easiiy calculated lrom thefigure. In particular. consider the interesting behaviour of the system inregion lI. In the latter hoth the rnarket rate of wages aid the rate of profits aremcreasing. e’.en if the rate of profits is oser its Iong-run equilibrium Level.Howeser, hen the ec000my enters region Il, only the market rate of wagescontinues io increase. while the rate of profit starts decreasing.Also in thisase w hasi. a multiplicio’ uf eqwlihria in terms of the rate of wages and the

leve I of lahour force, so that the very 5ame considerations rnade in suhsection2.3.4 1 appiy.

Figure 2 5 Pha.se dia gram o( the Itable /7cus equilibrrurn

Figure 2.6 rcproduces a numerical imulation, where the possibility ofovershooting in the dynamics of the tso variables is made manifest.29

11 /

/

.3 35 4

f iure 2 6 Vrt ter Fiehl 3f the ,tab!( fccai equi1iI’rrun (si’itbi’t cnn edering!he coatriint nii R he ti “jt ie flr, le ‘3feasihlr regi. ‘01 1 nd VII eredotted)

34 (1’o‘ .il, 0 o. / i’ -i, is) A . “, ‘o o nm’.l th .103/ fili, 3311(1011

I rsec’or, -ltfjfl tS in eiun I

I ajs..tor tarl,ne re, rsin. e I

ituii1 g ciSl dj1 .0 a R,cnrdian grnwrh in( a& /

4 ,‘,

+ 4vu t VI vI,

4 0

fflfl+

1? R

Figur, 2,4 Diff.-i cilt 1(3313 l’Uil bi’ha,’tours al t’i.’,) e,’ononl,es lrhft’h or,’ notci)) 3[fl (1)100011V different

3

-5

4i5 C1a sic,ii u’o hi Ss u sd and Ke’,nesjan vjen mi 7rms l/i ami dt rrihuiun.V tu rai iae d ,usmi i a a Ri lrillm 3r0B lii sn ide! 37

A proper cycie around the equilihrium b is not possible hccause al’ aciìnstraint un E, that is, the \vstem cannot reach regions I and VII (see Figure25).

A linal reniark concems the relationship between the market rate and thenatura! rate of wages during the transition to the equilibrium. a pomi whìchhas heen hotl dehated in the literature. in genera!. we tind that if the marketssage is higher than the natural wage, then the twu rates will beceme equa!only in equilihrium. sshi!e if the market wage is lower than the natura! wagethcn the former tends to hecome higher. Therefore, ii is not possible for amarket wage higher than the natura! wage te hecome Ioer than the latterHowever. this conclusion crucially depends on the assumption of theexistence of a Iower constraint un the rate of profits. in fact, without theconstraint un R. we could have a proper ccle around E if equilibrtum E s’verea focus. Therefore w cou!d be oscillating around I before the economyconverges te E. This can happen in Hieks and Hollander’s (1977) model,‘v’vhere E has te be on1 nonncgattve.

2.3.4.3. Seme numerica! examplesIn what fo!lows ‘v’ve prcsent two numerica! exampies. The first exampleconcems the stable nude equilibrium. In particular, we consider an econoinystartìng from region VI of Figure 2.1. Figure 2.7 reproduces a numerica!simulation with the same paramerers as in Figure 2.2, here the initial levelsof the lahour force. the natura! wage and the rate of profits are such that theeconomy is starting in region VI un particuiar the initiai conditions are ii(0),E(O), MO), w1(o)l = (0.7692. 1.3. 1. I.5)).

Figure 2.7 shows that in the initial periods the economy realizes adecrease in the market wage and ari increase in R econoiny is in regiOn VIwith respect tu Figure 2.1 . When the economy moves te region V. then Rstarts decreasing as well as the market wage. Then. the eeonomy entersregion IV. where the market wage starts increasing, whule R continues tedecrease, Finally. the ecunomy reaches the equilihrium. here R is equa! te

1.20 and w = w1’ = 0.66.The other eamp!e regards the case where the equilibrium E is a stable

I ocus. In Figure 2.8 we repreduce a numerica! simulation s’vith the amepararneters as in Figure 2.6 for an economy starting from region 11 (the initialcenditions are [w(0). E(O). N(0), w(0)j = (0.7692. 1.3. 1.0.5)).

Fuee 2.7 Example oJ’ rrajecu’rv uve the SlSIhfe viode equilibriuin (in fìtureIena ied hv E)

lnvtval ,tite

i tv4

Ri ,

56

fsi)

[iure 2.8 framplé a/’ frajm’tol’S’ far the table fra o quiìihrtuni (in ((giuri’deno,’ed hy E)

38 (‘t so al neoclai no al Onu Ketnu tuO Vitti (Yfl groo th nl dzntrubution tvatural suagu .ltnacnti o R ardian roeth model

\Ve ohsrr’ e that in the tnrltal penods the mccrkct a atte dOul the rate o! profttstre hoth increasing. When the eeonomy reaehes first region III and thenceeion IV. R starts deereasing. hiht wi alaavs inereasing. Firtallv. theCruit1Oiiii drTi’CS at eqitilthrrtm P- md i 44.1 1 Bothnumerica! simulations show that R and o have non linear dynamies. This isparticularly intercting for cumparative statiu anutlysis. heeause the fino!outcome could be ere ditferent trom the short-run hehaviour ot theercmom\.

24 FINAL REMARKS

Ricardian growth modek are generally huilt ori the (oftrn tacit) assumptionot a constmt natural wage. Siteh ari assumption. useful as it is in derivinginteresring grossth resuuts. csnceals the faci that classical econumists ssereperfeetly aware that in growtrtg economica (sueh as Engtand) ssurkersnorma! pattern nf eonumptinn ‘teadi! rise hoth in terms of quantity andquahty. shile in stagnant or declining economica (aueh as Ireland or China)wiirkers Iise remain hrutish and short.

In the tirst part uf the chapter we gathered some classica! hints un therelationship hetween economie growth and natural na ages in order to pros idea ational reconstruction of the eiasreai pomt ot iew un natura! wagedynamies. We elaimed rhat. within the classica! framework, economiegroth intluences the dynarnics of the natural ssage through orkersreactrons to the wider consumption opportunities disclosed to rhem hy thegrmth priacess While in a atagiunt econom the economie possihilit afeseaping from the Malthuaian povert trap is almost nil. in a grossineeconomy sorkers carri a high market wage and are thus ahle to buy nonsuhsistence commodities. Moreos er, v orkers become increasingiy aware ofthe tradeoff betwecn ehrldren lo rcar and omforts ot lifc tu enjoy. andthus revise their frtilit dcctsions it the igltt uf radunai economieteasonmgs as to their future standard of life In such a scenario a highmarket wage does not cause an increae in the lahouring population (as is thetase in the Mahhuaian poi ert) trap scenario) but an upv. ard re ision or the1habits and customs shich shape natura! wages.

in the second part of the chapter we proposed a tormai analysis. Weanalysed the implieation of a Rtcardian mode! ith endogenaus natura!o atte, lite eeunomv shus a ttlohalls utable d’namies. hut the longui,tne9i,ilthrium dependu un the tnttial etndittons ari eeonomy w ith a highcrtnttiai natura! wage show’ a bigher oqutlthrium market ssage and a looerlaborir forte Furthermore. the convergenee tu the long-run equilihrium carioccur liv eyetes tn he rnarket o ape, the tate ot profita and the iabottr torce.

iIhus shvri-run hehas ioui Is not neecssartiV a oiide tu deiernatning the lt’ngturi equihhrium Finally, since the naturai wage ts not ohservable, eeonomieswhieh appear tu be initialh identica! an hehave verv differentlv in the ringi un

NOTES

5 hderii aiihu Iuta unturc’a un R cardo’a ci citi ‘nit aas ru’jua nated hs Paio Sraifa a arieaut ‘d ‘diii un t lh tti r1 cuI 5 ai tu lt su / acd Re cri/o il ilse tana dada and

ha Su atta °60 pini ta aula e honk, Pr i/tu ti lu ‘I i ‘u’’uliiu i l’i 4fuui i ‘‘5 (nomi llt!iiuPean h i ‘$1 t 5 hapier i aiaI K! ingen i t ‘1951 pro te an oa eri ien uil roiiiempnrao dai, triuìatiiehaie uil Ri unto, i,, arai ui/e i 9551 lii nuga toeihei aome ui the i dci alti tu no ihiiiuona. Secala i tlotiandvr 1905, Pan 15; un Ricaudiaiu gino h noi/ei(a) and ihe debate un Ritardo

uf su uges. [or a hook tu ngth discuatian itt che riassumi itieory nt gran th sec FitnslitI 5i i

Rirardian ‘ah tlara ,,enerattv aeree thai iSa m,ui Sei note aruut the iuuiurat trage roma de in the‘uauionary siate su hen sue grous ih botti ot aaputat md lahoui ing population has moine io a hatili uardty tatdu uiueiaiuig ihat usai, al uiiiuuti,isia li oh ai [o tanonuity sidie ju»i a nuorepii ihit iuy iii the cr utisiarut tutore iii in usinO kuuuu o utuiniea I Se oniy riutable e ueepiu in a

5 una uutuich. ti a Sinith, hai atrr’adt ‘ui_9uu ired ihai tutt rompleineni aI ruches a’. bit h udtutore iii is dos and in ,iutiuiiiifla permii’ i io ucqui ire t il .\ la irl4).

We are at morse mare ihat the ihenreuicat uhjeri atted ‘ciassimat economucs us noi aui.noiih. due ‘i the many tifteuencea hu_ioeuuu the aaoua Ltassiaat auiiious, unii thai risatuiltrpreiaiioun e’i/’a ai ui the ‘atone and mnpe ii_la’-’iaat emoiuunits. Vei ‘ne uhinL uSai,

tu iterencea ot emphasus apant, taaiaal iiuttors uhLnoat Is s,iare a mommon poi o iS en

iii ihe ie (aoon’hip beta’. een emani mie gino th and the d_ naunius nt ihe utaturat a atte (in reali sinmu dui lei una),

‘1 oli iih dednes the h’. iuience o age ai the ‘ i’. i ai rate nt su ige’ I a’. hu[i i’. ti IO isteni a uil,:‘ln’nuie iumaiiuia ‘ 0.5 I ui I lii Rir,,rdo taum uSai uSi,’ naturat faVe uf ,uages dmpeitd athC’u,uuIiIli’i ci 5’. iii. iuemesaal ei, aiid tana cuneate’ e, tinte eauuutiat [ta i cr5 ur) trotti

liabii’ (rinrka I.’. .93). t-lence, ihe norinat haaket ot wage eoods ‘essentiatty depends on thehabits auet tOsi ma at lIte people’ (ltsi’rk I v.d6—97) Sturati (1994 i995 aol i 998) maO sestue ite plased h noilan’. it’ tairnesa and poser reiauicattips within the elusi/mal thutra’a ot

i,eti mal su im doti, nmiaati io,

5 ‘titubai iuuauniaiiu’. thau in att tasca onere panicu)ur modes nt arhsisuence, trom wttateserauses anising, bave heen tor any time estabtished ihoiugh such modes atways rcimiain

‘ci a eptibie of ituange, ce chan ce musi t’e itt cr5 nI i nie aiud ditt’uculty’ i Matthuu (956 ai‘.pp. 578.

O. [i CISC n’a inc esco te ‘ e ‘snuiih’’ stmiacted disiu’.’.ion ‘t ‘Se dutberent panermu ilauin’.uniption and Seni i O uuorkers O me in uuntnies ai dittereni stages nt Cenni-miedes ‘ti pnleni sm h as bneiand, Scoutand, “uuuuih \mcr’ca, ((I mia, B nga( tnd i inc ot theI,rugtu’h surii!emel,ts m the E.e’i Induca i c’iS I, iii iii

7 1 tie’narkc’i rr5e ci tahour a detjmued lì i. ,a’,ti, aa tue priae a Si/itt i’, Cui tu pait ti,

i ,uhaiant, Ram the lui u,ral iipcrauuon ccl due prs pentita’ ‘ I tue ucppls iO tre deuuiaiud’ Il ,i0

5 945 Siinutart, tor Slalihus the iaarkei truce ot lahour a itt aaiuat priVe un il e n,inkci,a hich (mm iemporana causea i’. 5 meiimeu hoae, unii su mennues nei/co, tubai is uuerr’aar

si siippta itir eiiei,tiuat demurcl ct ah’ ,‘ai,int Si i.ihs 1 isii t 5 t 81

50 (los twa! m’ce lasstcal aod Kepnevjan tews ce tlrcwth and dittrthution \ztu,aI taaa,’e dvnarnicr te a Rtcacltan airowth rncdel i

8 Smtth detmes the naturai rate 01 wagea at ‘the aardtnary e aserage rate atf wages ‘n a ttattttame and piace. I-le ettabliabea a connectmn between the natura! nage atad econtnticdeaclopment in m 0w at [the circumstances ehich narurali deterrnine the rate Ct aaage’Ite” at(eted h ‘he ichea tt po Cray, nt the ad’ ana in, atationa’ or dcc littmg ttate raI titesttctet (Wh i i t4 “e t a W 1. 0. ). The atate o( cc- nomi deselopmant o( a g acttcountra detemtinea orkers’ ormai cotttumpttott haakets and their ahtlim a:ttd economie,onaentence to rear a Famth tace Wh J.atti22 (fa. Ricardo emphaai/es the relattonahtpi’ctts cera the taatural aaage and aubaittence san the broad seme 01 the teran) (o clainting thathe ttaturai rate cI- wages O assoctated sa tth a stationary Iabouring popatiation (sec Worla

L •t5• Ricardo’, ttctton ci the nataral asage ltarahl’, .aitiieed h8 Malthus. In \lalthtcpinion, a stationary ahouring oepulatiort, ttsually associated lo a ‘tagnattt ert’ttomac

sttuatit’n. a a state cI- artairs al a great tlist-tnce te pomi ultime I-or IaI’htta temi c I- d’e

known economica have plenty of erowth opportuntties at ‘et unexplotted. He prefera tudefirte ‘he ttatural or eecea’,arv riee of abour’ a’ a ong-run eqatilabritana price. that O. at‘haI price -.ahich, o the acuta! citrumatancea cI-the societh. i’ necessary tu occasion an

aserage sttppIv o( labottrers. sttfficient to mcci the effecrttaI demand’ (Malthus 386. voI. ‘a’.

p 1823.O Stnith ciaints that the real recompense ci Iabour. the rea! quantitv cI-the necea-’aates and

conaeniencea al PI-e sahich il can procure to the Iahourer. itas, during the courae cI- thepreseni centurv increased perhaps in a stili greater proportion than itt ttaonea price litecommon comp!aint that luxttry extends itsett esco tu the towest ranks of the peopie, and thatthe !ahotaring poor ‘a iii t’at atow be content,d at ith Citi’ t,tt’tC !a’ttd, lt’uthin teatri 1 ‘J’inttahtih tana/Od rhem tu fdrrner timea. tnay cortaince sia that it is noi the tnoatey prtce att

Iabour oniy, bui ii.a rea! recompense. which has aaugnta’nted’ IWNT.siii.34, emphasis addedt.Ricardo piainiy adntits thal ‘rnany of the conveniencea nosa enjoyed in an English cuttage,wou!d haae been rhoueht lusaaries ai an eariier period rai cnr history’ Wr’rka I.v.Q7t. Ora therelaiionship betaeen asorker’. ferti!ity decìaions and saorkers male (or ltagher-qualit’acommodities he tnamtains that the ‘friends cI- httmaniiy cannot bui wtsh that in ali Countriesthe iabouring c!asses shouid bave a latte (or comforts and ettjoyments, and that they shouidne stimttlated (o ali legai means ttt their etertiona tu procure them. The re cwtntat beta b,-tter,ecurarr againsf a superahundaatt popuiatton. in those eountrtes, sshere the iahourtngctasses bave the (ewest wanis. and are contented ssith the vheapest food. the peopie areexposed to the greatest victssitudes and materica’ (lharkt l.s.100- 10!. emphasis ,,ddedi.Similarly. Mahhus writes that ‘tront 1720 io 175(1 the price of aaheat tn Eng!and] bari ‘oSaliera. ‘ahiie [moneyi asages had risen, iMi instead of t’ao thirds the labourer could purchasethe chole o) a peck of wheat with a day’s iabour, He adda that ‘the resuit was, ihat their [o)the lower classes cI- peoplej /ite reaaed corra acopea tnstcad of occaaiorring un in ‘rs’ate ra/topta1afion esciuslrelv. a ere va’ “apended at tr’,acca.si,t.a ai dectaicd clci-attton tu :Ite ,ran,iatcalat/n/teircoanforfxaiadrontcnieatres’ tMalthus 1986. so!. V. pp. 185-6. eanphasta addedt.

10. At stresaed in the lntreduction. lite market and the natura! nage aiways coincide ti,acoraSng lo Samueison’s 1978 canonica! s.lasstcai mode!, the value oI- parameler gas cero.By contrari, the naarket erige mav be persistent!y abose the natura! wage iI- the salate 01parameter sia positive.

11. More on this pomi in Fiaschi and Signorino (2003a and 2003bt.2 Remind that. un!ike the market wage, the natura! wage t’, t’tat a rttaer’itude o,ittch tttay (o

directlv obsrrseal Accardine tu Ricardo’’ definttìon cI- the ratttral sane, the aanO tara> fo-ascertain ‘ahether. te a gtaen time atari piace. the market ta-.me and the natural .vage di;a.reror coancade at to obaerve the re!ated dynattitcs oI- populatton. ihus, cx va tr’rmtati. any rttatketrate ci aages as’octated to a stattoflary popu!ataon musi be considered at a natura! rate raI

13 lI E acri v are assunaed aa gtven Rtcardo’s theorv ot wages ts in’erprcted a h’Iongtng tothe saage-Iund approach 0v ccntraat. ti iV and arare aa’ttmed at gtsen, Rtcardo’s theort ci-t tgcs a’. ‘nterpreted at belcttgang lo thc taatura! ssage or is acage .approach. In the I-irst case.rquation ‘24 determines the I-uil cmplotnient rate ‘ai saages: ti the ,ccottd case ttdetermtnes the leve! tal emp!oyment compattble wtth the state oI- capita! accumu!ation (OnceK = Pii ,tttd the ntlittg rate o( otturai acagea,

-t Since K — tE tori cR — tt.Vt the’t K Vf’t,VtiR: there esista tra iuserse reLationshaphetsaeen Kant! r, gtsen E and fi I.

i lIscI.> and Hollander (1977) write that surh elasttcity -,hould be decreasing in Vt inpartit,uiar. 5 ahould l’e a- 1cr E beitsg equal tu t) and 53 l’tr .V hOng aery large abati lesa lhan

Ft’r esatraple. the productatna functtaatt i(rV) aV—t’a - I-cr Ne [i),(a/e> “i -.hoass thompacaperties.

1 u A dtI-I-erettt equtlibrium ctauld exisi, depeoding n the aa,ssamptaons ora the shape cI- ai.),3i - t. 7).) atari Osi, characteriied ha ai a 0. Note thai the tnvta! equi!tbriumR = ,- = ti ts ttot (easahle.

i 7. tt’ae tgnore the constraint R 2 attace ti ts noi relesant Io our daacusstoaa.18 11 ts straightforssard te veri I-y that if the roots are real then hoth are negative, whi!e tI- tttey

are contpies. then lite rea! pari ts ttegatiaelt I-bis aastttvtptioat cara has e stnporrant elfecta. c’o the ata cmli 10 namics. bui t.e thtnk ai a taci

deci,ive I-or the study cI-luca! atabiiity ci equiiihnum.21). 4 simtlar condation 1cr the mode! 05 Hicks and Floilander 11477) a fottatd hy Gordon(i983).21. The inear representation o( nhe’.e oci i-a a simp!ifaing aaumptittn. depending ora lite

aelatiuoahtp’. betsaeen lIte first deriaataaes ci ,a3.l, /0.) and oi,t. lI- .a!l these fttnctaonscere nou-Itnear, then ssc aaould gel exact!y the same pieture lrom a qttalatative point ciiew. In lact, ativcn the ‘.onsiraittt R 2 Ra, then I I / O)a( ai’., - i) = /3i R R*) i’, the

at/tn ti atari tt’, aiope a’. given by 8’tR — tti. [li - I Ola’(w —1>] >0 forO> 1).10 the ‘ante ananater eisa-,, I — — R) O the loctis g,,, = 0 attd itt siope ts gtven b>d’tR R) ama, 1) (>0 a!ways) and a(w i) = ,d(R - Rt) is the 10cm g —0 andt’a alope is d° by /?‘(R R5) m’I-at lt I-> O alsaays, and greater ahan the slope o)

-ocnts e , t). lt a aratghttorsaard to check the relataattashaps hetsseen the ‘aiopes cI-thettiferent ce1 gi’-en the pcaitise sigtt of sali deria amaca and ‘dove ai a atj I-or ar-a.> 1

22. 1 hia statement can be ngorousiy proscd obsers ing that Ihere exists a reation sa here aoypossabie trajectory saarting I-rom il canotti leave ahe regton. This regioaa can be easi!y foundby taictttg an appropriate Rtt > RtO) > R” and aa- a sa’ 0) > i. and caanstdering the re’.ulitrtg.r.aa’tpact -‘ci formed hv ‘any pair tRa,,) -‘aach that R— [Rt, Rt] and sta, e)l. ‘a’,’,’ [. Thisrea,jon is posalive!y inaariant (sec Hirsch and Smale, 1974, p. 264). Moreover, the tegionrontattts tnly a singulaa pomi, the localiy stab!e equalabraum E (this i.s straightforward I-ramthe ligure). Finaiiy. ti is possable to show that d(dR/dfidR a aladva,Jdr)dR < 0 in ever) potraisaI- the piatte, su,th that in the region a cicsed paih, a e. a Iimat ‘.scle, cannoi cassa taceBettdixson’s negative t’ ertoo in GandolI-o 1997 p 438) Gte application oI- the P incaréBendisson i’hevtrem catrpltttes the proci (sec ‘Fhea’rem i in F!irs,h and Sattale. i971,

3 (la ortI, a ‘m’los s ut/ ,rnd A “ne si vi o ,“ rov iO ami i/i 5, rthts((,),i‘satur ti ti ar(e d’namu s in a Ra at dtan grao tu modei 53

ridi; cu,,t cx pa titani; ‘n the e’ O tt ‘‘a’ ti’ e. ‘ire htgher rhe erpt! libri’ l’a i mdctc’l,lre ,lx,r ne a,,tiiai esci ‘i ‘ret!,ne. i bis erenoillerlon o anali, alied xelÌ—inuiltIttr

‘speriarloll;.(‘ P anieter ,iiuts Sr’ lhe sante uxed far F eroe 2 2, ttittal ci ‘iditiorts ire [R(0, ‘(

VOI5J (1 3 I) 79), I (cc li’ ih ‘e ‘iro r e , api t’rc dotta! ,,atraai e, im, ho far rineCc! ‘fl,lfltS lx ‘Ct Ai t.602/ ,o r

“ 2 e a recati I 1 ‘cd far the otherlt”ho,t 2 (1r7 liiirCgi’’ti Vr.(-‘irimeter alrie are the ‘ante n’ed far 1 tenie 2 0 the initial Onditionx ,ee RtiI,, lt,‘rIO t (1 3. tJ.”692. i i I (or both econorntes, i ‘ept (or tatuai calori1 wage, that for s’ne

rnrtrny i ci at t 692J! .08 0 12 t i ti ecioii iVt md (or the othet AtO “tIPI, i 02 - O”41 Itt ix in teglon III)

‘e lite ciobai xtahiliix ,if equuiihri’im [ cari I’,” xc’,; ntt sub the ‘t’i” ‘ee”tu’e ‘“e’” 2-0 “-‘,hthe dillerence that R’ ha; io be aliai x ereater tirati ‘bit leel ct I? “rr’expciridritc io p”intin bigure 2 5.

“i itt he mtitation e agate a; in e ltat sci tuitction ‘i mar mcd ixed the ti litto talLtexd02.R* !,2,a-’ti,1,’=001 idO (35(0 OStIli

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(“irasale, (3 A. ledi I 10851. Pie Leeacv of Ru’,tr,li’, Oxtord’ Basi) BlackweII(‘axarosa, C. (1978) ‘A new formulation of the Ricardian system’. ()sford Itcono,nic

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