Health and Long-Run Economic Growth: A Fogel Approach

Transcription

1 Healt and Long-Run Eonomi Growt: A Fogel Approa Liutang Gong Guangua Sool of Management, Peking University, Cina Diai Wang Sool of Eonomis, Fudan University, Sangai, Cina Heng-fu Zou Resear Department, World Bank, USA Abstrat Based on Robert Fogel s resear, assuming tat onsumption not only raises agents utility but also inreases agents ealt, we take a new look at te relationsip between apital aumulation and onsumption and disuss te effet of ealt on eonomi growt in an extended Ramsey model. Tis paper as two important features: 1) te interation of ealt and onsumption, wi allows us to study ealt and long-run eonomi growt in an aggregate maroeonomi model; ) te existene of multiple equilibria of apital stok, ealt, and onsumption, wi speaks to te reality tat ri ountries may end up wit iger apital, better ealt, and iger onsumption levels tan poor ountries. Key words: Healt Human Capital; Consumption; Eonomi Growt; Poverty Trap JEL Classifiation: D990, E10, I Introdution Te relationsip between ealt and eonomi growt as long been attrating researers as well as pratitioners from many disiplines inluding eonomis, soiology, pysiology, and oters. Among te literature fousing on ealt and eonomi growt, tere is a set of fairly quantitative istorial ase studies (Fogel, 1994a, 1994b, Wangdiai: Sool of Eonomis, Fudan University, Cina. Wangdiai@gmail.om. 1

2 00, 004; Strauss and Tomas, 1998) laiming tat nutritional improvement is te driving fore beind improvements in te ealt omponent of uman apital (enefort referred to as ealt uman apital ) and ene te primary fore promoting eonomi growt in te long term. For instane, based on is series of studies, Fogel onluded tat ealt and nutritional improvements may ave aounted for more tan 50% of Britis annual per apita inome growt rate of about 1.15% in te 00-year period from 1780 to 1979 (Fogel, 1994a, 1994b, 00). Using a metodology similar to Fogel s, Son (000) argued tat improved nutrition as inreased available labor inputs in te Republi of Korea by one perent a year or more between 196 and Strauss and Tomas (1998) also indiated tat nutrition and alori intakes are positively related to ealt, measured in eigt and body mass index (BMI), in te ase of post World War II Ameria, Brazil and Vietnam. Tese studies indiate tat ealt improvements derived from onsumption inreases, and ene nutritional improvements, are te main fore tat enanes long-run eonomi growt. If an inrease in onsumption an improve ealt uman apital, an tis ategory of ealt uman apital be a driving fore tat motivates persistent long-run eonomi growt? If yes, ten wat is te meanism by wi ealt uman apital motivates long-run growt in te teoretial framework? If not, ten ow does ealt uman apital enane long-run eonomi growt? Tis is te first question tis paper addresses. Tere is an alternative view to Fogel s, owever. For te interation between ealt and inome, ealt is always regarded as anoter kind of uman apital, like eduation. Neverteless, ealt differs from eduation in many respets and te effet of ealt on eonomi growt is different from te effets of oter kinds of uman apital. First, sine ealt an generate positive utility of its own, using ealt servies is also a kind of onsumption (Grossman, 197).Tis implies tat ealt annot motivate long-run eonomi growt but is only a by-produt of su growt (Baumol, 1967, Zon & Muysken, 001, 003), wi seems to be ontrary to Fogel s result. One sould note ere tat Zon & Muysken (001, 003) only analyzed te ealt uman apital derived Strauss and Tomas (1998) laimed tat, at te miroeonomi level, tere are at least tree aspets tat distinguis ealt from most oter uman apital: first, ealt will vary over one s life ourse ompared wit eduation, wi is almost onstant in one s life yle. Seond, ealt is multidimensional, and it is important to differentiate among tese dimensions. Tird, measuring ealt is diffiult, and in many ases, measurement error is likely to be orrelated wit outomes of interest like inome.

3 from ealt investment but not tat from onsumption improvement and ene nutritional improvement. If Fogel s onlusion is true, does it imply tat te ealt uman apital derived from nutritional improvement embodied in te inrease in inome and onsumption an motivate te long-run eonomi growt? As a by-produt of eonomi growt, ow does te ategory of ealt beome one main fore improving eonomi growt in te long run? Tis paper aims to 1) explore ow and ow mu te ealt improvement derived from inreased inome and onsumption affets long-run eonomi growt and ) explain te rationality of Fogel s onlusion tat ealt improvements from inreasing nutritional intake affets long-run eonomi growt in a teoretial framework. In addition, tis paper seds ligt on te meanism of eonomi growt wen onsumption affets ealt and ene labor produtivity, and to see weter tis kind of uman apital will bring endogenous eonomi growt, like eduation uman apital, or weter it remains a by-produt of eonomi growt, like wat Baumol (1967) and Zon and Muysken (001, 003) ave onluded. Needless to say, in order to ompreend te effets of ealt on growt, it is a prerequisite tat we explore learly te ompliated interation meanism between te two sine tere are so many annels troug wi ealt and growt affet ea oter. For instane, ealtier populations tend to ave iger labor produtivity, wi failitates growt (Strauss & Tomas, 1998; Barro, 1996; Bloom, et. 004). Healt improvement is also inlined to inrease eduation uman apital and ene improve growt (Howitt, 000). In addition, ealt may influene eonomi growt troug mortality, longevity, fertility, and population omposition as well as oter annels (Kalemli-Ozan, Ryder & Weil, 000; Kalemli-Ozan, 00, 003; Morand, 004). On te oter and, growt is able to influene ealt troug inreasing inome. For example, eonomi growt inreases inome per apita, and people wit iger inome an inrease teir ealt investment (medial are and ure) and ene improve teir ealt (Grossman, 197). People wit iger inome are also able to improve teir nutritional intake, wi an improve teir ealt (Strauss and Tomas, 1998, Fogel, 1994a, 1994b, 00). It is beyond te sope of te present paper to explore all possible meanisms troug wi ealt and growt interat wit ea oter. Instead, we fous on one of te meanisms suggested by Fogel tat nutritional improvement an enane 3

4 te improvement of ealt uman apital and we analyze te effets of ealt improvement on long-run eonomi growt wen onsumption affets labor produtivity via ealt. By assuming onsumption not only inreases agents utility but improves agents ealt, we investigate te relationsip between onsumption, ealt, and apital aumulation, and disuss te effet of ealt on eonomi growt in an extended Ramsey model. Under te assumption tat onsumption improves ealt, tis paper sows tat, first, te ategory of ealt uman apital derived from onsumption improvement and ene nutritional improvement is not te ause but rater te by-produt of eonomi growt exept for te ase of a linear ealt generation funtion wit suffiiently large marginal ealt produtivity of onsumption, wi is suggested by Baumol (1967) and argued by Zon and Muysken (001, 003). Seond, ealt uman apital is able to magnify te eonomi growt driven by exogenous tenology, wi is onsistent wit Fogel s finding tat nutritional improvement is te main fore tat enanes ealt uman apital improvement and ene eonomi growt in te long term. We also formulate te proportion of eonomi growt from ealt improvement to total eonomi growt. By tis formulation, under some reasonable parameter values, te ontribution of ealt improvement derived from nutrition to te total eonomi growt is very lose to Fogel s (1994a, 1994b, 00) estimates. In addition, troug some speial ealt generation funtions, te paper displays te possibility of te existene of multiple equilibria of apital stok, ealt, and onsumption and te existene of te poverty trap, wi is onsistent wit te reality tat ri ountries may end up wit iger apital, better ealt, and iger onsumption tan poor ountries. Tis paper is organized as follows. Setion reviews te existing literature on ealt and growt. Setion 3 presents a teoretial model wit ealt generated by onsumption. Setion 4 analyzes te dynamis of pysial apital and ealt uman apital in an exogenous neolassial growt model. Multiple equilibria and a poverty trap ave been found in tis framework wit different ealt generation funtions. Setion 5 presents our onlusions. It is easy to prove tat ealt derived from onsumption improvement and ene nutritional improvement an motivate endogenous eonomi growt in te ase of a linear ealt generation funtion wit large enoug marginal ealt produtivity of onsumption, owever we do not inlude tis ase in tis paper. 4

5 . Literature Review Tere are inreasing teoretial and empirial investigations of te effet of ealt on eonomi growt. Te empirial studies mainly form tree ategories (Jamison, et al., 004). Te first omprises te istorial ase studies tat may be more or less quantitative (Fogel, 1994a, 1994b, 00; Strauss and Tomas, 1998; Son, 000). As stated above, tese studies all onluded tat nutritional improvement is te main fore tat enanes ealt uman apital improvement and ene eonomi growt in te long term. Te seond ategory is araterized by many miro studies wi involve eiter ouseold surveys tat inlude one or more measures of ealt status along wit oter extensive information, or te assessment of te impat of speifi diseases. Strauss and Tomas (1998) provided a major review (extensively updated by Tomas, 001), and Savedoff and Sultz (000) surveyed metods used in te ouseold studies and summarized findings of reent analyses from five Latin Amerian ountries. Reent studies inlude Liu et al (003) on Cina and Laxminarayan (004) on Vietnam. Tis literature onfirms tat ealt is positively assoiated wit produtivity on te miro level, wi is onsistent wit our assumption tat ealt uman apital onstitutes a type of prodution fator. Te tird ategory studied te relationsip between ealt and eonomi growt from a maroeonomi perspetive. Tese studies mainly rely on rossnational data to assess te impat of ealt at te national level, measured in life expetany, adult survival rates, adult mortality rates or oter indexes, on inome growt rates and most onfirmed tat ealt is positively related to growt (World Bank, 1980; Hiks, 1979; Weeler, 1980; Barro, 1996; Sas & Warner, 1997; Bloom and Williamson, 1998; Casas, 000; Mayer, et al, 000; Arora, 001; Bargava, et al, 001; Bloom et al., 004; Lorentzen, MMillan and Waziarg, 005; MDonald and Roberts, 006). On te miroeonomi and maroeonomi ontribution of ealt to eonomi growt and development, Surke et al. (006) reviewed reent evidene. Te teoretial studies on te relationsip between ealt and growt started to appear in te last 0 years and are beoming more frequent. Early teoretial studies on tis topi mainly foused on te provision of ealt servies from a miroeonomi demand perspetive and did not analyze te effet of ealt in te form of uman apital 5

6 driving eonomi growt and development (Grossman, 197; Muurinen, 198; Forster, 1989; Eril and Cuma, 1990; Joansson & Lofgren, 1995; Mertzer, 1997). Barro (1996) first studied te maroeonomi effets of ealt as one of te most important omponents in uman apital in a teoretial framework. In a tree-setor neolassial growt model inorporating a onept of ealt uman apital as well as sooling apital, Barro analyzed te effets of ealt uman apital on sooling apital and pysial apital and te interation between tese tree fators, and furter disussed te effets of publi poliy in te ase of ealt servies as a publily subsidized private good and as a publi good. Muysken, et al. (1999) also investigated te growt impliations of endogenous ealt on steady-state growt and transition dynamis in a standard neo-lassial growt framework. Extending te Luas (1988) endogenous growt model to inlude ealt investment and taking into aount tat ealt servies an provide utility, Zon and Muysken (001, 003) disussed te maroeonomi effets of ealt uman apital derived from ealt investment on eonomi growt. Compared to Barro (1996), besides te effet of ealt on labor produtivity, Zon and Muysken (001, 003) onsidered tree oter annels troug wi ealt influenes eonomi growt: 1) ealt inreases te aumulation of eduation uman apital; ) ealt servies inrease an agent s utility; and 3) ealt improvement inreases longevity and ene leads to an aging population. Wile te first two effets of ealt on labor produtivity and on eduation uman apital aumulation tend to failitate eonomi growt, te last two effets suggest tat ealt investment may be reaing beyond te optimal amount in wi te marginal ontribution of ealt investment to growt equals te marginal ost to growt. Tis will rowd out too mu pysial apital investment and uman apital investment. Aordingly, ealt investment may impede te progress of eonomi growt in te end. By introduing te effets of skill-driven tenologial ange (enefort SDTC) into Zon and Muysken (001, 003), in an endogenous growt model tat integrates SDTC and uman apital aumulation troug formal sooling wit ealt uman apital aumulation, Hosoya (00, 003) furter investigated te relationsips among eonomi growt, average ealt level, labor alloation, and longevity of te population. In addition, troug integrating te aumulation of uman apital, innovation in medial tenology, ealt 6

7 and longevity into a four-setor (eduation, onsumption goods, R & D setor devoted to ealt resear, and ealt goods) endogenous growt model wit keeping up wit te Jones preferenes and an altruism utility funtion, Sanso and Asia (006) also studied te bidiretional interation between ealt and eonomi growt and onluded tat ealt, by influening longevity, may beome an endogenous growt soure. In order to explain te real-world situation tat ri ountries may end up wit iger apital, better ealt, and iger onsumption tan poor ountries, te existene of multiple steady states and te poverty trap are also important issues in te literature on te relationsip between ealt and eonomi development. Cakraborty (004) and Bunzel and Qiao (005) introdued endogenous mortality risk into a two-period overlapping generations model to study te effet of ealt (measured in mortality) on eonomi growt and onfirmed te existene of multiple steady states. Hemmi, Tabata and Futagami (006) studied te interation between deisions about finaning afterretirement ealt soks and preautionary saving motives, and demonstrated tat, at low levels of inome, individuals oose not to save to finane te ost of after-retirement ealt soks. However, one individuals beome suffiiently ri, tey do oose to save to finane te ost of tese soks. Terefore, tis ange in te individual saving beavior may also give rise to multiple steady state equilibria and will result in te poverty trap. Te results of tose teoretial papers are important for understanding te results of te two latter empirial studies disussed above, and also for bot furter aademi resear and poliy. However, interpreting te results of te first empirial studies in te ontext of te teoretial framework and understanding ow ealt improvements derived from onsumption and nutritional improvement will influene te long term growt and ene eonomi poliy is not lear. Troug onsidering te effet of ealt improvements derived from onsumption and nutritional improvement on eonomi growt, tis paper fills te gap in te literature by proposing a arefully onstruted teoretial framework to study te relationsip between eonomi growt and ealt. We believe tat te teoretial models an elp us to analyze te relationsips of ealt and long-run growt effetively, ompreensively, and systematially. Given te importane of te issues investigated ere, our results will provide bot te publi and te private 7

8 setors wit poliy guidelines towards a better alloation of resoures to improve te ealt of a population, redue inome inequality, and at te same time maintain eonomi growt. 3. Te Benmark Model Te goal of tis paper is to onsider te effet of ealt derived from onsumption wi tus leads to nutritional improvement on inome and eonomi growt. Speifially, we mainly fous on te international meanism tat links ealt and eonomi growt were onsumption affets ealt uman apital. To tis end, we onsider an eonomy su as te following: tere is an agent wit infinite life in te eonomy. Te agent as a quantity of pysial apital and one unit of labor. Te agent s inome omes from is output wi is produed wit te use of two fators: pysial apital and te agent s labor. Labor ability is determined by agent s ealt uman apital. Te agent deides ow to divide te output between onsumption and investment. Wen te agent onsumes te produt, e an attain utility. At te same time, as per Fogel s studies (1994a, 1994b and 00), more onsumption brings more nutrition to te agent (assuming te agent onsumes food), and ene te agent also attains ealt uman apital troug onsumption, wi an improve is produtivity in te next period. Wen te agent uses is produt to invest, e an inrease pysial apital, wi also makes im inrease is prodution in te next period. Suppose te instantaneous utility funtion is u (.), and te subjetive future disounting rate β (0,1), ten te agent lifetime utility funtion is given by t ut (()) e β dt, (1) t= 0 Witout loss of generality, we assume u (.) > 0 and u (.) > 0. Te main annel troug wi ealt affets te eonomi growt lies in te prodution funtion, in wi ealt an improve te effiieny of labor produtivity. In te paper, te prodution funtion is assumed as follows y = f( k, l), () were y denotes te agent s produt, k denotes pysial apital, denotes ealt uman apital, and l labor supply. Compared wit te ommonly used neolassial prodution 8

9 funtion, te uniqueness of te above prodution funtion lies in te fat tat we inlude ealt uman apital in te prodution funtion. In fat, te existing literature points out several annels by wi better ealt will raise produtivity and output. Most diretly, ealtier workers ave more energy and endurane and are able to work arder and longer. People wit ealtier bodies tend to be less suseptible to disease and ave lower absenteeism. Te fat tat labor produtivity is positively assoiated wit ealt as been onfirmed bot in empirial miro- and maro-eonomi studies, espeially in lowinome settings (Strauss and Tomas, 1998, Bloom, et al, 004). In addition, tere are some indiret annels troug wi ealt influenes produtivity. For instane, improvements in ealt raise te inentive to aquire sooling, sine investment in sooling an be amortized over a longer working life. Healtier students also ave lower absenteeism and iger ognitive funtion, and tus reeive a better eduation for a given level of sooling (Howitt, 005; Kalemli-Ozan, et al., 000; Weil, 006). All tese fators lead to ealtier people wit iger produtivity. Terefore, it is rational and natural for te ealt variable to enter te prodution funtion, just as Barro (1996), Issa (003), Hosoya (00, 003), Muysken, et al. (1999), Zon and Muysken (001, 003), Weil (006) and oters ave argued. Furtermore, just as Fogel observed (00, p.4), te ontribution of nutrition and ealt to eonomi growt may be tougt of as laborenaning tenologial anges. Zon and Muysken (001, p. xiii) also onsidered te ontribution of ealt uman apital to prodution ability as Harrod-neutral tenial ange. In addition, we assume tat f > 0, f > 0, f < 0, f < 0, k kk fkk f fk > (3) wi implies tat te marginal produtivity of pysial apital and ealt uman apital are positive but diminising, and te prodution funtion exibits onvex tenology in and k. Te seond main aspet of te interation meanism between ealt and eonomi growt in tis paper lies in te effet of inome on ealt troug onsumption and ene troug nutritional improvement. As most eonomists observe, tere are tree main ways of improving individuals ealt: First, suffiient nutrition is indispensable to maintaining a ealty body. Fogel (1994a, b, 00) and Strauss and Tomas (1998) indiate tat-- 9

10 measured in life expetation, in eigt, and in te ratio of eigt to weigt--an inrease in nutrition is te main fator wi improve populations ealt in te long run in many ountries, inluding England, Frane, te United States, Vietnam and oters. In te ase of te underdeveloped periods of developed ountries or te presently low- and middleinome ountries, te main approa to improve ealt is still to inrease nutrition and alori intakes wi are mainly embodied in food onsumption. Te seond approa to improving ealt is ealt investment (Grossman, 197; Strauss and Tomas, 1998; Zon and Muysken, 001, 003). Aording to Grossman (197), ealt investment inludes te onsumer s time devoted to ealt are and market goods su as medial are, diet, exerise, rereation, and ousing, wi is obviously inluded in total onsumption. Moreover, ealt investment may also inlude individuals medial ure ativities wen e/se is striken wit disease or infetion, sine tese ativities an sorten te duration of ill ealt and avoid aidental deat aused by illness (Zon and Muysken, 003). Te tird way of improving ealt may be related to te individual s knowledge of ealt protetion and life beavior (Howitt, 005; Sanso and Asia, 006). Sine te goal of tis paper is to study te relationsip between ealt and growt in te long term, we mainly fous on te ealt derived from improvements in nutrition and onsumption. In te long term, as Fogel (1994a, 1994b, 000) and Strauss and Tomas (1998) indiated, inome and ene total onsumption exert te greatest fore on motivating improvements in ealt. To tis end, we assume tat ealt is mainly determined by agents onsumption, and people wit more onsumption will be mu ealtier, altoug oter important fators also determine ealt quality. Furtermore, we assume tat te ealt generation funtion is as follows = () (4) We assume tat marginal produtivity of onsumption is nonnegative and noninreasing, namely () 0, () 0 (5) Here we assume tat te funtion () is nondereasing. Tus, wit te inrease of onsumption, te ealt will at least not derease. Alternatively, we an assume tat it Note tat in equation (3), ealt is onsidered as a flow variable rater tan a stok variable and ene no depreiation is allowed. However, even if in te ase tat ealt is a stok variable and tere exists ealt apital depreiation, te general onlusion of tis paper is not affeted. 10

11 is not a monotoni funtion. For example, tere exists a onsumption level, > 0, su tat () inreases wen onsumption is greater tan ; and () remains onstant wen onsumption is less tan. Tat is to say, we ave () 0, wen > ; and () = 0, oterwise. We will disuss tis type of ealt generation funtion involving a minimum onsumption level in setion 3.. If we furter assume tat te agent supplies unit labor inelastially at any time, ten l equals 1. By te above assumption, te agent s pysial apital aumulation equation is k& = f( k, ( )) δ k (6) were δ denotes te pysial apital depreiation rate. A dot over a variable denotes te derivative of te variable wit respet to time. Te agent s optimization problem is tat, given te initial pysial apital, by oosing is onsumption pat,, and is apital aumulation pat, k, te agent maximizes is lifetime utility, i.e. max ( ( )) βt ut e dt k, t= 0 st..: k& = f( k, ( )) δ k given k 0 In order to solve te onsumer s optimization problem, we define te Hamiltonian assoiated wit te optimization problem H = u() + λ[ f(, k ()) δ k] (8) were λ is te ostate variable representing te marginal utility of pysial apital investment measured in utility. By te Pontryagin s Priniple, we obtain te first-order onditions λ = u () + λ f (, k ()) () (8) [ f ( k, ( ))] t and te transversality ondition lim λke β = 0. & λ = λ β + δ (9) t Proposition 1: under te above assumptions on te utility funtion, prodution funtion and ealt generation funtion, if and only if a pair of real numbers, ((t), k(t)), satisfies k 1 > f ( k, ( )) ( ) (10) ten te pair ((t), k(t)) satisfying equations (6), (8), (9) and te transversality ondition maximizes te objetive funtion. 11

12 Proof: (see appendix A) Equation (8) asserts tat te marginal value of pysial apital investment equals te marginal value of onsumption, wi is te sum of te marginal utility of onsumption and te ontribution of onsumption to prodution. From equation (8), we an express λ as a funtion of onsumption and apital stok, λ(, k). u () λ = 1 f ( k, ( )) ( ) (11) In equation (11), f ( k, ( )) ( ) denotes te inrease in prodution brougt by inreasing te unit onsumption troug inreasing ealt uman apital and ene improving produtivity, and 1 f ( k, ( )) ( ) denotes te ost of inreasing te unit onsumption measured in onsumption goods, te rigt side of equation (11) represents te marginal value of inreasing te unit onsumption or/and te marginal ost of inreasing te unit investment measured in utility. Te left side of (10) represents te marginal value of investment. Terefore, Equation (11) implies tat te agent divides is/er inome between investment and onsumption subjet to te ondition tat te marginal value of investment equals te marginal ost. Compared wit te standard Ramsey model, te uniqueness of tis onsumption optimal ondition is tat tere is an additional f ( k, ( )) ( ) in te denominator of te rigt side in te equation (11). If te onsumption as no effet on ealt, i.e. ( ) = 0, ten equation (11) is te same as in standard Ramsey model. By equation (11), we an understand wy it must be tat 1 > f ( k, ( )) ( ) for equation (10) wen an agent s investment is optimal. Given any positive investment, as we an see from equation (11), if 1 f ( k, ( )) ( ), ten te marginal value of investment measured in utility will be negative or zero. Sine te marginal utility of onsumption, u ( ), is definitely positive, a derease in investment or/and an inrease in onsumption always inreases te utility. Terefore, if 1 f ( k, ( )) ( ), te agent wo maximizes lifetime utility will keep inreasing is/er onsumption and dereasing is/er investment till te marginal value of investment beomes positive and equals te marginal ost of investment. 1

13 By te equation (11), we ave te following sort-run effets of onsumption and apital stok on te marginal value of apital u f k u f k f k λ = < 0 [1 (, ( )) ( )] + [ (, ( ))( ( )) + (, ( )) ( )] [ 1 f ( k, ( )) ( ) ] u fk( k, ( )) ( ) λ = < 0 k [ 1 f ( k, ( )) ( ) ] From equations (1) and (13), it is lear tat wen onsumption inreases, te marginal value of investment will derease, wi is te same as te standard Ramsey model. Te differene between te two models is tat te marginal value of investment dereases more in tis model tan in te standard Ramsey model, wi results from te dereasing marginal ealt produtivity of onsumption ( u f ( k, ( ))( ( )) ) and te dereasing marginal produtivity of ealt ( u f ( k, ( )) ( ) ). However, wen apital stok inreases, te marginal value of investment will inrease, ompared wit being onstant in te standard Ramsey model. Te intuition of tis result is very obvious: in te standard Ramsey model, sine te marginal ost of investment, u (), as no relation to apital stok, te marginal value of te optimal investment, wi equals u (), as no relation to apital stok. But in our model, te marginal ost of investment, u ()[1 f (, k ()) ()], is determined not only by onsumption but also by apital stok. Wen apital stok inreases, te marginal produtivity of apital will inrease, and ene te derease in prodution brougt by inreasing te unit onsumption will derease. Consequently, wit apital stok inreasing, te marginal value of te optimal onsumption and/or te marginal ost of te optimal investment will derease, wi results in te inreasing marginal value of te optimal investment, λ. By equations (6), (8), (9) and (11), we derive te dynami equation of apital stok as follows λ & = [ f(, ( )) ] k k k δ β λ [ f( k, ( )) δk] λ λ (14) Equations (6) and (14) determine te aumulation pats for apital stok and onsumption. In te following setions, we analyze te dynami beavior for te pysial apital aumulation, onsumption, and ene ealt uman apital aumulation. (1) (13) 13

14 4. Dynamis of Pysial Capital, Consumption and Healt Human Capital By equations (6) and (14), te onsumption and te apital stok approa te steady-state value wen & = k& = 0. It an be araterized as f( k, ( )) δ k = 0 (15) f ( k, ( )) δ β = 0 (16) k Under te assumption of te neolassial prodution funtion, te existene of a steady state is obvious, but we annot guarantee its uniqueness. We will give examples for te existene of a unique steady state and multiple steady states in te following setion. About te stability of te steady state, we ave te following teorem: Teorem 1: If and only if te steady state (, k ) satisfying equations (15) and (16) satisfies β f k + f k f k <, (17) ( ) k(, ( )) [1 (, ( )) ( )] kk (, ( )) 0 ten te steady state (, k ) in te eonomy is saddle-point stable. Oterwise, te steady state is divergent. Proof: see Appendix B. In general, owever, we still annot determine te stability and te uniqueness of te steady state. In order to furter analyze te dynami araters of te eonomy, we need to take furter assumption on te form of te prodution and ealt generation funtion. Witout loss of generality, we assume te prodution funtion is a linearly omogeneous funtion in k and, i.e. y = f( k, ) = Ag( k, ), (') were A represents a tenology parameter. Funtion g(k, ) satisfies te following arateristis: ωgk (, ) = g( ωk, ω), for ω > 0, (18) By assumption (3), te prodution funtion (') satisfies g > 0, g > 0, g < 0, g < 0, g g > g (3') k kk kk k 14

15 g(0, ) = g( k,0) = 0,lim g( x, x ) =+, lim g( x, x ) = 0, i= 1, (3'') xi xi + Furtermore, we an rewrite te prodution funtion as follows yˆ = y = Ag( k,1) Agˆ( kˆ ), (19) A at over a variable denotes te ratio of te variable to ealt. Obviously, gk ˆ( ˆ) satisfies gˆ(0) = 0,lim gˆ( x) =+, gˆ (0) =+,lim gˆ ( x) = 0 (3''') x x Terefore, we an rewrite te equation (15) and (16) as follows Agˆ( kˆ) ˆ δ kˆ= 0 (0) gˆ ( kˆ ) = ( δ + β) A (1) k Under te assumptions of ('), (3') and (3''), we ave te following teorem and proposition : Teorem : Under te assumptions of ('), (3') and (3''), tere exist unique satisfy equations (0) and (1). Proof: (Omit) ˆk and ĉ tat Proposition : Under te assumptions of ('), (3') and (3''), te steady state ( k,, ) of te eonomy satisfying equations (15) and (16) is saddle-point stable if and only if Oterwise, te steady state is divergent. Proof: (See appendix C) < < ( ) ( ) ε ( ) ( ) 1 () By Teorem and Proposition, under te assumption of a linearly omogeneous prodution funtion, te stability and te uniqueness of te steady state are totally determined by te ealt generation funtion. In te following setion, we will disuss tese questions in te ontext of te various forms of te ealt generation funtion. 4.1 Unique Steady State: te Effet of Tenology Progress on te Healt and Labor Produtivity. 15

16 In tis subsetion, we assume tat te ealt generation funtion is a neolassial funtion tat satisfies (0) = 0, ( ) 0, ( ) 0,lim ( ) =+, lim ( ) = 0 (5') By tis assumption, we ave, following Teorem and Proposition : Teorem 3: Under te assumptions of ('), (3'), (3'') and (5), tere exists one and only one equilibrium of ( k,, ) wi satisfies equation (15) and (16) and tis steady state is saddle-point stable in te eonomy. Proof: (See appendix D) Te eonomi intuition of Teorem 3 an be understood easily by looking at Figure 1. In Figure 1, Beeline OE denotes tat te ratio of onsumption to ealt uman apital is onstant and equals ĉ and Curve OEB denotes te ealt generation funtion. By Teorem, in te steady state, te ratio of onsumption to ealt uman apital equals and ene te equilibrium of (, ) must be on te Beeline OE. At te same time, equilibrium (, ) also must be on te ealt generation funtion OEB. Aording to Figure 1, it is obvious tat tere exists one and only one equilibrium of ( k,, ) wi satisfies equations (15) and (16). Furtermore, Figure 1 also indiates tat tis steady state is stable. Insert Figure1 ere ĉ Teorem 3 indiates tat te ealt uman apital derived from nutrition and onsumption an not drive te long-run persistent eonomi growt if tere is no exogenous tenology progress, altoug onsumption an improve te ealt uman apital and ene improve produtivity in tis model. Te ategory of ealt uman apital, owever, an magnify te eonomi growt derived from exogenous tenology progress. Te eonomi intuition of te result an be explained easily troug Figure. Insert Figure ere 16

17 Figure (A) indiates te determination of equilibrium (, ), wi is te same as in Figure 1 exept tat Beeline OE 1 denotes te equilibrium of ĉ under te tenology level A 1 and Beeline OE denotes te equilibrium of Figure (B) indiates te determination of equilibrium of ĉ after tenology progresses to A. ( k, ) and y. Isoquant urve is used to represent ombination of ealt and apital tat provide te same ratio of output to tenology. In figure (B), Curves I, II and III denote tree isoquant urves, wose level of output per unit of tenology is y 3 /A, y /A and y 1 /A 1, respetively. Beeline OA and OC in figure (B) denote tat te ratio of pysial apital to ealt uman apital equals to ˆk 1 and ˆk, wi are te equilibrium of ˆk in te tenology level A 1 and A, respetively. Wen te tenology level is A 1, te steady state in Figure (A) is Point E 1 and te equilibrium of (, ) is (, ), and te steady state in Figure (B) is Point A and te equilibrium of (k, ) is ( k, ), orrespondingly. Terefore, te level of output per unit of tenology under te tenology level A 1 is y 1 /A 1. Wen te tenology level improves from A 1 to A, by equations (0) and (1), te ratio of onsumption to ealt uman apital will improve from ĉ 1 to ĉ and te ratio of pysial apital to ealt uman apital from ˆk 1 to ˆk. As a result, te steady state in figure (A) will ange from Point E 1 to Point E and ealt uman apital will improve from 1 to. In Figure (B), orrespondingly, te prodution state will ange from Point A to Point C and pysial apital will improve from k 1 to k. Terefore, te equilibrium level of output per unit of tenology will improve from Curve III to Curve I. From Figure (B) we an see, owever, tat if te ealt uman apital remains unanged, te prodution state will ange from Point A to Point B and ene te level of output per unit of tenology will only improve from Curve III to Curve II. Sine te ealt uman apital improves, te prodution state ontinues to ange from Point B to Point C and te level of output per unit of tenology ontinues to improve from Curve II to Curve I. Tereby, te differene between Curve I and Curve II is te ontribution of ealt uman apital to te output growt. 17

18 Aording to te above results, we an understand Fogel s results on ealt and long-run eonomi growt. Fogel as laimed (in 1994a, 1994b, 00) tat te ombined effort of te inrease in dietary energy available for work, and of te inreased uman effiieny in transforming dietary energy into work output, appears to aount for 50 perent of Britis eonomi growt sine 1790 (Fogel, 1994a, p388), and e furter onsidered tat te impat of nutrition on long-term eonomi growt aounts for most of te previously unmeasured inrease in Britis total fator produtivity. (Fogel, 00, p7) By te above analysis we know tat, altoug ealt derived from onsumption and ene nutritional improvement annot motivate long-run endogenous eonomi growt, te ategory of ealt uman apital an magnify te eonomi growt from exogenous tenology progress and ene ontribute to long-run eonomi growt. We an even estimate te ontribution of ealt on eonomi growt by te following analysis. By equation ('), we obtain x = y& y = x + ε x + ε x (3) y A y yk k were x i denotes te growt rate of variable i, ε yk denotes te partial elastiity of output wit respet to pysial apital and ε y denotes te partial elastiity of output wit respet to Labor. In equation (3), te total fator produtivity in te Solow model is x A and te Solow residual is xa + ε ykxk. By equations (4), (0) and (1), we obtain x k x [ 1 δ ( δ + β) ] = x εg ˆ 1 εyk δ ( δ + β) (1ε 1) A [ ] 1 εyk δ ( δ + β) (1ε 1) + 1 δ ( δ + β) = εg ˆ 1 εyk δ ( δ + β) (1ε 1) were ε ='()/() denotes te elastiity of ealt output wit respet to onsumption and ε ˆ ˆ ˆ ˆ ˆ ( ) ˆ g = g kk g ( k) denotes te elastiity of marginal pysial apital produtivity wit respet to pysial apital. Sineε g ˆ < 0, by equation (4), if tenology level improves, ealt uman apital and ene te produtivity of labor will also inrease. Te ratio of eonomi growt derived from ealt uman apital improvement to te total growt rate of per apita inome, R y, and te ratio to Solow residual, R S, respetively are R y x A (4) (5) ε yx ε y = (6) xa + εyx + εykxk ( εyk εgˆ )(1 ε 1) 1 εyk δ ( δ + β) [ 1 δ ( δ + β) ]

19 R S [ 1 ( + )] εyx εy δ δ β = xa + ε yx ε gˆ 1 εyk δ ( δ + β) (1ε 1) + εy 1 δ ( δ + β) [ ] By equations (6) and (7), we an ompare te ontribution in our model of ealt uman apital improvement to eonomi growt to Fogel s results. In order to illustrate te effet of ealt uman apital derived from onsumption and ene nutritional improvement on te long-run eonomi growt wen tere is exogenous tenology progress, by equations (6) and (7), some estimated values of R y and R S for various onstellations of te parameter values are given in Table 1 and, respetively. In tese two tables, aording to te real eonomy, we take te apital depreiation rate (δ) and te disount rate (β) to bot equal 0.1. Te partial elastiity of output wit respetive to pysial apital (ε yk ) varies from 0.1 to 0.75, te partial elastiity of output wit respet to labor (ε y ) from 0.1 to 0.9, and te ealt output elastiity of onsumption (ε ) from 0.1 to 1. (7) Insert Table 1 ere Table 1 indiates tat te ontribution of ealt to eonomi growt (R y ) inreases wen te elastiity of ealt generation wit respet to onsumption (i.e. ε ) inreases and first inreases and ten dereases wen te elastiity of output wit respet to apital (i.e. ε yk ) inreases. If te elastiity of output wit respet to apital is taken as 0.35, wi is very lose to te real level in developed ountries, and ε anges from 0.1 to 0.9, R y will ange from to Espeially, if ε is taken 0.9 and ε yk is taken from 0. to 0.6, te estimate of R y in our model is less tan but mu loser to Fogel s estimate of R y. Sine te assumption in te above estimate tat only tenology levels inrease and oter parameters remain unanged is not onsistent wit te progress of real eonomi growt, te estimate of R y in our model may be even loser to Fogel s if we inlude tose fators in our estimate. Table indiates te ontribution of ealt in explaining te Solow residuals (R S ) wi inrease bot wit inreases in te elastiity of ealt generation wit respet to onsumption (i.e. ε ) and wit inreases in te elastiity of output wit respet to apital By te assumption of te Cobb-Douglas prodution funtion, we use ε ˆ = ε 1 in te table 1. g yk 19

20 (i.e. ε yk ). If te elastiity of output wit respet to apital is taken as 0.35 wi is very lose to te real level in developed ountries, and ε anges from 0.1 to 0.9, R S will ange from 0.03 to Speifially if ε and ε yk are very large, te ontribution of ealt to eonomi growt an explain most of te Solow residuals, wi is idential to one of Fogel s onlusions. Insert Table ere 4. Te Existene of Multiple Steady States: Healt and Poverty Traps In tis subsetion, we onsider te ase of an eonomy wit multiple steady states, a ase tat lends itself to explaining te presene of poverty traps in te real world, tat is, ow ri ountries may end up wit iger apital, better ealt, and iger onsumption tan poor ountries. Tis irumstane will appear in te presene of te minimum onsumption requirement in te ealt generation funtion. In te subsetion 3.1, we assume tat te ealt generation funtion is a new lassial funtion, wi implies tat an agent wit any level of onsumption possesses ealt uman apital tat an provide labor produtivity. In fat, just as Fogel (1994b) laimed, an individual always needs to obtain a minimum amount of energy required to maintain is/er basal metabolism, su as to maintain body temperature and to sustain te funtioning of te eart, liver, brain and oter organs. For example, for adult males aged 0-39 living today in moderate limates, te basal metaboli rate (BMR) normally ranges between 1350 and 000 kal per day. Furtermore, sine BMR does not allow for te energy required to eat and digest food, nor does it for essential ygiene, an individual annot survive on te alories needed for basal metabolism. Fogel regarded tat a survival diet is 1.7 BMR, wi is not suffiient to maintain long-run ealt but represents te sort-term maintenane level of totally inative dependent people (Fogel, 1994b, p.6). By tese onlusions, in a word, only by taking in nutrition above te minimum amount of onsumption and nutritional requirements, an an individual maintain a level of ealt uman apital tat an provide labor produtivity. Terefore, in a ealt generation funtion, tere is a possibly minimum onsumption requirement 0

21 below wi te agent s ealt will be zero, namely we assume tat te ealt generation funtion is () if> = and ( ) 0, ( ) 0, lim ( ), lim ( ) 0 0 if =+ = (5'') + + were is te minimum onsumption requirement tat provides te amount of energy required to maintain te individual s basal ativity. Te oter assumption is te same as in subsetion 3.1. Under te assumptions of ('), (3') and (3''), similar to subsetion 3.1, we an prove tat tere exist unit ˆk and ĉ satisfying equations (0) and (1). By tis result, we ave Teorem 4. Teorem 4: under te assumptions of ('), (3') and (3'') on te prodution funtion and of (5'') on te ealt generation funtion, if and only if 1 1 ( (1 ˆ )) > (1 ˆ ) ˆ, (8) tere exist two equilibria in te eonomy. Were ' -1 (.) denotes te inverted funtion of '(.) and ĉ is determined by te equations of (0) and (1). Furtermore, te lower steady state is unstable and te iger steady state is stable. Proof: We prove Teorem 4 based on Figure 3. In Figure 3, Beeline E 1 E denotes tat te ratio of onsumption to ealt uman apital is onstant and equals ĉ and Curve E 1 BE denotes te ealt generation funtion. At point B orresponding to wi per apita onsumption is 1, te tangent of te ealt generation funtion as te same slope as te Beeline E 1 E, i.e. 1 ˆ 1 = (1 ). ( ) = 1. Terefore ˆ 1 Insert Figure3 ere First, by Teorem, in te steady state, te ratio of onsumption to ealt uman apital equals ĉ and ene equilibrium of (, ) must be on te Beeline E 1 E. Furtermore, equilibrium of (, ) must also be on te ealt generation funtion E 1 BE. It is obvious tat tere exists an equilibrium in te eonomy if and only if Curve E 1 BE and Beeline E 1 E ave a point of intersetion. By geometry, Curve E 1 BE and Beeline 1

22 E 1 E ave two points of intersetion if and only if 1 ˆ 1 ( ) >, i.e. 1 1 ( (1 ˆ )) > (1 ˆ ) ˆ. Seond, sine in te lower steady state E 1, te slope of te ealt generation funtion E 1 OE is greater tan Beeline E 1 E (i.e. ( ) < ( ) ), and in te ig steady state low low low E 1, te slope of ealt generation funtion E 1 OE is less tan Beeline E 1 E (i.e. ( ) < ( ) ), by Proposition, it must be tat te lower steady state is unstable and low low low te iger steady state is stable. Teorem 4 implies tat wen an eonomy is above te lower steady state, te eonomy will eventually onverge to te iger steady state and enter te developed pase. However, if an eonomy is below te lower steady state, ten te eonomy will eventually onverge to te zero point and ene fall into te poverty trap in wi an agent as lower and lower onsumption and olds poorer and poorer ealt uman apital. Terefore, tere is a poverty trap in te eonomy wen tere is a minimum onsumption requirement in te ealt generation funtion. Tis onlusion implies tat even being faed wit te same tenology level, tese ountries wit ealt uman apital less tan a ertain lever will always be in tis poverty trap unless some exogenous fators improve te people s ealt to above te ritial ealt level. By tis result we onlude tat te way to elp tese ountries to get away from te poverty trap is to elp tese ountries to improve te people s ealt. Insert Figure4 ere We will sow te impat of tenology progress on eonomi growt and te poverty trap troug Figure 4. In Figure 4, Curve E 1 low E low E 1 ig E ig denotes te ealt generation funtion, Beeline OE 1 low E 1 ig denotes te equilibrium ratio of ealt to per apita onsumption in te ase of te tenology level A 1, and OE low E ig in te ase of te tenology level A. Figure 4 indiates tat, wen tenology is A 1, te stable steady state is E 1 ig and te unstable steady state is E 1 low, wi implies tat an eonomy above E 1 low will onverge to te developed state E 1 ig and an eonomy below E 1 low will fall into te poverty trap. Wen te tenology level improves from A 1 to A, first, te stable steady state will improve from E 1 ig to E ig, te eonomi impliation of wi is te

23 same as in subsetion 3.1 (we won t explain it furter ere). Seond, te unstable steady state, i.e. te boundary of te poverty trap will derease from E 1 low to E low. Tis implies tat an eonomy above E low but below E 1 low, wi falls into te poverty trap before tenology improvement, will esape from te poverty trap and enter te development pase after tenology level improves from A 1 to A. Tese results provide te seond metod in wi te ountry in poverty an get away from poverty: to improve its own tenology level. Insert Table3 ere Te above results of tis subsetion ave an eonomi impliation for explaining ealt and poverty traps in developing ountries and polarization in te real eonomy, wi is displayed in Table 3, and for eonomi poliy advie in developing ountries. By te above analysis, if te initial apital stok of an eonomy is below te lower steady state, tis eonomy definitely falls into te poverty trap, in wi te eonomy as a lower per apita onsumption and a lower ealt state. Te o-existene of low ealt and poverty results from te interation of some eonomi fores: low apital stok wi leads to low per apita output makes people unable to obtain adequate onsumption and nutrition, wi results in low ealt uman apital and low labor produtivity and ene low apital aumulation and eonomi development. Tis viious irle between ealt poverty and low development will ontinue forever unless tere are some oter fores to break te ain between low ealt, te produtivity and low eonomi development. By te above analysis, we know tat tere are two ways to break te viious irle: to improve te people s ealt state or to improve te tenology level. 5. Conlusions and Extensions of te Model In tis paper, based on Fogel s resear and assuming tat onsumption not only raises agents utility but also inreases agents ealt, we study te relationsip between apital aumulation and onsumption and disuss te effet on long-run eonomi growt of ealt uman apital derived from onsumption in an extended Ramsey model. 3

24 First, tis study indiates tat ealt uman apital derived from onsumption an neiter motivate endogenous eonomi growt nor be te driving soure promoting long-run eonomi growt. Tis result is te same as onlusion reaed by Baumol (1967) and Zon & Muysken (001 and 003). However, te study also finds tat tis ategory of ealt uman apital an enane eonomi growt troug exogenous tenology progress. Furtermore, omparing te results of tis paper to Fogel s work, te degree to wi ealt enanes eonomi growt is onsistent wit Fogel s estimates on te effet of ealt from nutritional improvement on long-run eonomi growt in England. Seond, in te presene of a minimum onsumption requirement in te ealt generation funtion, te study argues tat multiple steady states appear in te eonomy, wi lends itself to explaining te presene of te poverty trap in te real world in wi ri ountries may end up wit iger apital, better ealt, and iger onsumption tan poor ountries. Tese results imply tat a poor state of ealt may be one of tose key fators tat make ertain poor ountries relapse into or remain in a poverty trap. Te study suggests tat tere are two metods to break off a poverty trap: improving te state of te people s ealt or/and improving te tenology level. Terefore, in te ase of a onstant tenology level, improving people s ealt in poor ountries is te only way to elp poor ountries break out of te poverty trap. Referene [1] Arora, S., 001. Healt, uman produtivity, and long-term eonomi growt, Te Journal of Eonomi History, 61(3), [] Baumol, W.J., (1967), Maroeonomis of Unbalaned Growt: te Anatomy of Urban Crisis, Amerian Eonomi Review, 57, pp [3] Barro, R. J., Healt and eonomi growt, paper presented at te Senior Poliy Seminar on Healt, uman Capital and Eonomi Growt: Teory, Evidene and Poliies, Pan Amerian Healt Organization and Inter-Amerian Development Bank, Wasington, DC. [4] Bargava, A., Jamison, D.T., Lau, L.J. and Murray, C.J.L., 001. Modeling te Effets of Healt on Eonomi Growt, Journal of Healt Eonomis, 0, [5] Bloom, D. E., D. Canning and D.T. Jamison, 004. Healt, Wealt and Welfare. Finane and Development, 41, [6] Bloom, D. E., D. Canning, and J. Sevilla, 004. Te Effet of Healt on Eonomi Growt: A prodution Funtion Approa, World Development, 3, [7] Bloom, D. E. and J. G. Williamson, Demograpi Transitions and Eonomi 4

25 Mirales in Emerging Asia, Te World Bank Eonomi Review, 1, [8] Bunzel, H. and X. Qiao, 005. Endogenous Lifetime and Eonomi Growt Revisited, Eonomis Bulletin, 5, 1 8. [9] Casas, J. A., 000. Investment in Healt and Eonomi Growt: A Perspetive from Latin Amerian and te Caribbean, Pan Amerian Healt Organization, Wasington, DC. [10] Cakraborty, S Endogenous Lifetime and Eonomi Growt, Journal of Eonomi Teory, 116(1), [11] Eril, I. and H. Cuma, 1990, A Model of te Demand for Longevity and te Value of Life Extension, Journal of Politial Eonomy, 98, [1] Fogel, Robert W., 1994a. Eonomi Growt, Population Teory, and Pysiology: Te Bearing of Long-term Proesses on te Making of Eonomi Poliy, Amerian Eonomi Review, 84(3), [13] Fogel, R. W., 1994b. Te relevane of Maltus for te Study of Mortality Today: Long-run Influenes on Healt, Mortality, Labor Fore Partiipation, and Population Growt, NBER working paper [14] Fogel, R. W., 00. Nutrition, Pysiologial Capital, and Eonomi Growt, paper presented at te Senior Poliy Seminar on Healt, uman Capital and Eonomi Growt: Teory, Evidene and Poliies, Pan Amerian Healt Organization and Inter-Amerian Development Bank, Wasington, DC. [15] Forster, B.A., Optimal Healt Investment Strategies, Bulletin of Eonomi Resear, 41, [16] Grossman, M., 197. Te Demand for Healt: A Teoretial and Empirial Investigation, NBER, Oasional Paper 119, Columbia University Press. [17] Hemmi, N., K. Tabata and K. Futagami, 006. Te Long-term Care Problem, Preautionary Saving, and Eonomi Growt, Journal of Maroeonomis, In Press, Correted Proof, Available online Deember 006, [18] Hiks, N. L., Growt vs. Basi Needs: Is tere a Trade-off? World Development, 7, [19] Hosoya, K., 00. Healt, Longevity, and te Produtivity Slowdown, Projet on Intergenerational Equity, Institute of Eonomi Resear, Hitotsubasi University, Disussion Paper Series, No. 5. [0] Hosoya, K., 003. Tax Finaned Government Healt Expenditure and Growt wit Capital Deepening Externality, Eonomis Bulletin, 5(14), [1] Howitt, P Healt, Human Capital, and Eonomi Growt, In Healt and Eonomi Growt: Findings and Poliy Impliations, edited by G. Lopez- Casasnovas, B. Rivera and L. Currais. Cambridge, MA: MIT Press, 005, [] Issa, H., 003. Human Capital, Demograpi Transition and Eonomi Growt, CGBCR Disussion Paper Series. University of Manester, Manester. Download paper from: Disuss. tm. [3] Jamison, D. T., Lawrene J. Lau and J. Wang, 004. Healt s Contribution to Eonomi Growt in an Environment of Partially Endogenous Tenial Progress, Disease Control Priorities Projet, Working Paper No. 10. [4] Joansson, P.O., and K.G. Lofgren, Wealt from Optimal Healt, Journal of Healt Eonomis, 14, [5] Jones, C., 001. Was an industrial revolution inevitable? Eonomi growt over te 5