NOT FOR DISTRIBUTION. 6 Alternative models of growth and distribution with a simple formulation of endogenous technological change

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1 6 Altenative models of owth and distibution with a simple fomulation of endoenous technoloical chane Intoduction Amitava Kishna Dutt hee have been a numbe of attempts to show how altenative models of economic owth and the distibution of income between waes and pofits can be developed usin a common famewok, which have auably been useful in uncovein the essential featues of these diffeent models and showin how these featues compae with those of othe models. he altenative models include those will full employment of labo and the full utilization of capital, as in othodoxneoclassical models, those with owth based on savin and capital accumulation as in the classical-maxian appoach, and post-keynesian ones in which owth depends on aeate demand. hese attempts, howeve, have typically assumed exoenously-iven technoloy in the fom of iven input output elations, focusin instead on owth due to facto accumulation, especially capital accumulation. he pupose of this chapte is to extend the altenative-models appoach to owth and distibution by incopoatin technoloical chane usin a simple theoy of theoy of endoenous technoloical chane. he main motivation fo this extension is to allow technoloical chane to inteact with othe deteminants of owth and distibution in the models developed fom the common famewok, in line with the eate attention iven to endoenous technoloical chane in altenative models of owth, both othodox-neoclassical (especially in what ae called new o endoenous owth models) and heteodox (includin post- Keynesian and classical-maxian appoaches). An additional motivation is to see whethe new theoies of owth and distibution emee when endoenous technoloical chane is incopoated into the common famewok, and whethe the diffeences between the theoies based on the famewok without technoloical chane pesist in this extended famewok. he est of this chapte poceeds as follows. he second section pesents the basic eneal famewok of the pape. he thid section pesents simple vesions of some altenative models based this famewok. he fouth section pesents vaiants of some of these models to moe fully exploe the ole of technoloical chane in diffeent appoaches to owth and distibution.

2 68 Amitava Dutt he eneal famewok We examine a eneal famewok of a closed economy in which one ood is poduced with two homoeneous factos of poduction, capital and labo, with a fixed coefficients technoloy epesented by the equation Y = min [BK, AL] (6.) whee Y is the level of output, K is the stock of capital, L is the level of labo employed, and A and B ae labo and capital poductivity. Labo poductivity is assumed to be iven at a point in time, and capital poductivity is assumed to be constant thouhout. Income fom poduction oes to waes and pofits. We assume that fims hie only the wokes they need fo poduction but have to hold on to the capital they have aleady installed. We can expess the division of income into waes and pofits in tems of the wae pofit elation w K = + A Y, (6.2) whee w is the eal wae and is the ate of pofit. he two tems on the ihthand side of this equation ae the wae and pofit shaes in income. We will hencefoth denote the labo shae, w/a, with the symbol ω, so that we can wite it as = ω + u, (6.2 ) whee u = Y/K, the actual output-capital atio, is a measue of capacity utilization. he actual output-capital atio has an uppe bound iven by B, so that u B. (6.3) We assume that wokes, who ean wae income, consume all thei income, and a faction, s, of pofits is saved. Savin is theefoe iven by S = sk. (6.4) Fims hie wokes, poduce, sell thei poduct at a pice P, and invest. Ou altenative models will specify the pecise behavio of fims. Ove time, capital ows accodin to the level of investment, I, assumin away the depeciation of capital fo simplicity, so that we have = I K. (6.5)

3 Altenative models of owth and distibution 69 Ove time employment ows accodin to the equation l = y a, (6.6) whee lowe case lettes denote the time-ates of owth of the vaiables denoted by uppe case lettes, fo instance, y = (dy/dt) /Y. We assume that labo supply ows at the exoenously iven ate n. he ate of owth of labo poductivity, a, is a vaiable in ou model. he theoy of endoenous technoloical chane adopted in this chapte assumes that labo poductivity ows popotionately with the capital employment atio, so that A = θ K, (6.7) L whee θ > 0 is a fixed paamete. his equation implies, in owth-ate fom, a = l. (6.8) his simple fomulation is the same as, o closely elated to, a numbe of appoaches to endoenous technoloical chane available in the owth-theoetic liteatue. It is closest to the appoach used in seveal new neoclassical owth theoy models used to deive the so-called AK poduction function, which has poved to be a popula appoach in that liteatue to depict poduction conditions without diminishin etuns to capital and theeby eneate endoenous owth with a neoclassical full employment settin. Fo instance, if fim i has the Cobb- Doulas poduction function iven by Y i = ξk iα (AL i ) α (6. ) with A, the efficiency facto of labo, common to all fims and epesentin extenalities, is iven by equation (6.7), whee this facto depends on the oveall capital/labo atio of the economy. With the assumption that all fims ae identical, the poduction function of the epesentative fim takes the fom Y = ξ θ α K, which takes the AK fom with constants etuns to capital. his is basically the appoach used in Rome (986), with the diffeence that labo poductivity is popotional to capital stock pe woke athe than to the capital stock, unde the easonable assumption that what affects poductivity owth is not the total amount of capital but capital pe woke. his appoach is consistent both with leanin by doin, whee leanin is measued by cumulative investment, o with investment in eseach and development. he appoach is also elated to Aow s

4 70 Amitava Dutt (962) theoy of technoloical chane due to leanin by doin, which assumes that labo efficiency depends on capital stock but, athe than assumin diminishin etuns to leanin, takes leanin to be popotional to capital stock with the additional diffeence, noted ealie, that it is the capital labo atio, athe than total capital, which measues leanin. It is also elated to Kaldo s (957) technical poess function, which elates labo poductivity owth to the ate of owth of the capital employment atio, althouh hee ou fomulation implies that labo poductivity owth is equal to the ate of owth of the capital employment atio, so that thee ae no diminishin etuns to capital deepenin in tems of poductivity owth. We define an equilibium position fo the economy as a state of the economy in which the followin conditions ae satisfied. Fist, the oods maket cleas, so that Y = C + I, whee I efes fom now on to both the actual and planned levels of investment by fims, o that S = I, o, usin equations (6.4) and (6.5), = s. (6.9) Second, the vaiables,, ω, u, l, y and a all attain stationay values. It may be noted that we do not equie that the economy eithe attains full capacity utilization o full employment o even a constant ate of unemployment, in equilibium. Since u attains an equilibium value, fo equilibium we must have y =, (6.0) that is, that output and capital ow at the same ate. he eneal famewok descibed so fa is compised of equations (6.2 ), (6.6), (6.8), (6.9) and (6.0), that is, five equations in seven unknowns, ω,, u,, l, a and y. Howeve, it can be seen that the five equations ae not independent equations. Substitutin equation (6.6) into (6.0) implies equation (6.8), that is, substitutin the equilibium condition that output and capital ow into the definitional equation fom the owth ate of employment implies the equation epesentin the theoy of endoenous technoloical chane. his esult is not a eneal one, but holds fo ou specific theoy of endoenous technoloical chane iven by equation (6.7) which, as we have seen, has some populaity in the owth liteatue. he eneal famewok can be epesented aphically as shown in Fiue 6.. he uppe left quadant shows equation (6.9), the elation between the ate of owth of capital and the ate of pofit: it epesents the savins function of the economy. he economy will be on this iven line, but we do not know whee exactly it will be. he neatively-sloped solid line in the lowe left quadant shows the elation between the wae shae and the pofit ate when u = B, that is, the economy is at full capacity utilization, so that = ω +. (6.) B

5 Altenative models of owth and distibution 7 ω u = s Fiue 6. he eneal famewok B he economy, of couse, does not have to be at full capacity utilization, since (6.3) may be satisfied as an inequality. hus, the economy may lie within the solid line, fo instance on the dashed line fo which the level of capacity utilization can be shown by the hoizontal intecept of the line. Not only do we not know at which point on a iven line the equilibium will lie, but also which line it will be on. he positively-sloped line in the uppe iht quadant shows the elation between the ate of owth of capital stock and the ate of labo poductivity owth when employment ows at the ate l, and is iven by = l + a. (6.2) he line has a vetical intecept of l and a slope of unity. his equation is deived fom equations (6.6) and (6.0) and also equation (6.8). Not only do we not know whee the economy will be on this line in the fiue but because the value of l is unknown, even its intecept is unknown. Clealy, thee is insufficient infomation to detemine the equilibium values of the vaiables of the model. Altenative models of owth and distibution o deive fully specified models of owth, distibution and technoloical chane, we need to add additional infomation to ou eneal famewok to obtain additional equations. We may seek to obtain this additional infomation fom majo altenative taditions in the theoy of owth and distibution, that is, neoclassical, classical-maxian and post-keynesian theoies, as discussed in Malin (984) and Dutt (990). he neoclassical appoach assumes pefect competition and full employment owth, and can thus be epesented by the additional equations l a

6 72 Amitava Dutt u = B (6.3) and l = n, (6.4) whee n, the ate of owth of labo supply, is exoenously iven. Equation (6.3) states that the economy poduces at full capacity, which follows fom the assumption of pefect competition, which ensues that as lon as fims make positive pofits, they will poduce as much as they can. Equation (6.4) is necessay fo full employment owth, althouh not sufficient, because it is consistent with any iven ate of unemployment. he esultin model is not econizable as a standad neoclassical model because, unlike standad neoclassical models which do not make distinctions between the savin behavio out of pofit and wae income and allow fo facto substitution in poduction, ou famewok assumes diffeences between the savin behavio out of waes and pofits and assumes that the input output elations in poduction ae fixed. No is it a fully detemined model, since addin these two equations to ou eneal famewok meely fixes the wae pofit elation in Fiue 6. to be the one iven by the solid line which epesents full capacity utilization, and the line as one with a vetical intecept of n. he ates of capital accumulation and technoloical chane, and the wae shae and the ate of pofit cannot be detemined fom this model. he model, howeve, can be completed by assumin that the savin ate out of income is constant and does not depend on the distibution of income (because of diffeences in savin behavio out of waes and pofit, as assumed in ou famewok), so that S = σy, (6.5) whee σ is the constant savin ate out of income, and allowin fo capital-labo substitution and cost-minimization by fims. he fome assumption implies that equation (6.9) must be eplaced by = σu. (6.9 ) he implications of the latte assumption can be examined by assumin that the poduction function is of the Cobb-Doulas fom iven by equation (6. ) athe than the fixed-coefficients fom iven by equation (6.). In minimizin costs fims take A to be iven, althouh it is, in eneal equilibium, it is detemined by equation (6.7). Cost minimization and the use of equation (6.7) implies that α ω = αθ, (6.6)

7 and Altenative models of owth and distibution 73 u = ξθ α, (6.7) which eplaces equation (6.3). Equations (6.9 ) and (6.7) detemine the ate of capital accumulation. Since this is iven by the paametes of the model and independent of, the savin cuve fo the economy in the uppe left hand quadant of Fiue 6.2 is a hoizontal line. ω α αθ Fiue 6.2 = σξθ α ξθ α Equation (6.2 ), usin equation (6.7) ives the elationship between the wae shae and the pofit ate in the lowe-left quadant whee the value of ω is detemined by equation (6.6). he model is now fully detemined: the ate of pofit is detemined in the lowe left quadant, the ate of capital accumulation in the uppe-left quadant (independently of ), and the ate of technoloical chane in the uppe-iht quadant, with the vetical intecept of the line fixed at n. Havin detemined the equilibium values of the vaiables of the model, we may examine the effects of chanes in paametes. A ise in the savin ate, σ, will shift up the hoizontal savin line upwads and incease the ates of capital accumulation and technoloical chane (and hence pe capita output owth), but leave the wae shae and the ate of pofit unchaned. A ise in oveall poductivity, epesented by a ise in ξ, will shift the savin line up and otate the wae-shae pofit ate line out, inceasin both the ate of pofit and the ates of capital accumulation and technoloical chane, leavin the wae shae unchaned. A ise in θ, the labo poductivity paamete, will have a simila effect on the two cuves, and theeby incease the ate of pofit and the ates of capital accumulation and technoloical chane, but educe the wae shae. he model may also be modified to obtain an upwad-isin savin cuve, usin at least two modifications. One is to assume that the savin ate depends positively on the ate of pofit. Anothe is n a

8 74 Amitava Dutt to etun to ou assumption that savin is iven by equation (6.4), so that we et the usual savin cuve fom ou eneal famewok. With these chanes, an upwad otation o shift in the savin cuve (due to an incease in the oveall savin ate at a iven pofit ate o a ise in the savin ate of capitalists) will incease the ates of capital accumulation and technoloical chane without chanin the distibution of income o the ate of pofit. 2 he classical-maxian appoach assumes a iven wae shae, detemined by the elative baainin powe of wokes and fims owned by capitalists, o the state of class stule, so that ω = ω, (6.8) and that fims poduce at full capacity, so that equation (6.3) is satisfied, eithe due to the assumption of pefect competition, as in the neoclassical appoach, o due to the popensity of fims to poduce as much as possible to compete actively aainst othe fims fo makets. Othewise we etun to the eneal famewok of the pevious section. When we add these two equations to ou eneal famewok, we find that althouh we can detemine and (and y), we cannot detemine l and a, that is, we cannot detemine the way in which the inceases in the demand fo effective labo will be decomposed into inceases in employment and technoloical impovements. his is shown in Fiue 6.3, whee the position of the cuve, and hence, l and a ae indeteminate. Fiue 6.3 A classical-maxian model o close the model we can assume that equation (6.4) is satisfied, so that employment owth is at a ate equal to the ate of owth of labo supply, which is exoenous. his fixes the position of the cuve at in the fiue, and detemines the value of a, iven by a = n.

9 Altenative models of owth and distibution 75 In this modified model, we find that owth is consistent with fully employed labo o at least a constant ate of unemployment. he equilibium ate of capital accumulation and output inceases if s (o B) inceases and if ω falls, and this is accommodated by an incease in the ate of owth of effective labo supply due to endoenous chanes in the ate of labo poductivity owth without ceatin a shotae of labo. If thee is an exoenous fall in the ate of owth of labo supply, n, the equilibium ates of capital accumulation and output owth will be unaffected, but a will incease, which will imply a hihe ate of owth of the eal wae. wo post-keynesian models of owth and distibution have been examined in the liteatue, which have been called the neo-keynesian and the neo-kaleckian (o Kalecki-Steindl) models. Both stess the ole of aeate demand by depatin fom the assumption that all savin is automatically invested, as in the neoclassical and the classical-maxian owth models, by assumin an independent desied investment function, makin desied investment depend positively on the ate of pofit o the ate of capacity utilization, the position of the cuve detemined by business confidence o animal spiits. he neo-keynesian model assumes that the economy is at full capacity, so that equation (6.3) is satisfied, and that planned investment and savin ae bouht to equality, as equied fo oods maket equilibium, by vaiations in the wae shae. In this appoach, followin Robinson (962), it is assumed that desied investment depends positively on the ate of pofit, so that = ( ) = γ + γ (6.9) 0 whee a linea fom is assumed fo simplicity, with γ i > 0. he Kalecki-Steindl model assumes, followin the adjustment mechanism stessed by Kalecki (97), that fims typically hold excess capacity, and set thei pice as a fixed makup on pime o labo costs, so that P = ( + z) W / A. (6.20) he makup facto, z, epesents the deee of monopoly, and depends on factos like the deee of industial concentation, the impotance of fixed o ovehead costs, and the state of class stule between wokes and fims. his equation implies that the labo shae is iven by ω =, (6.2) + z and that the ate of pofit is iven by z = + z u. (6.22) Since thee is excess capacity in the economy, this appoach assumes that oods maket adjustment occus thouh chanes in the levels of output and capacity

10 76 Amitava Dutt utilization, iven the distibution of income. Since excess capacity exists in the economy, this appoach typically follows Steindl (952) and assumes that desied investment depends positively on the ate of capacity utilization, so that we have = ( u) = u (6.23) whee, aain, γ i > 0. 3 Rathe than examinin both vesions of the post-keynesian model, we examine the second, Kalecki-Steindl one, which allows excess capacity to exist. 4 Substitutin equation (6.22) into (6.23) we obtain + z = γ 0 + γ 2 z ω + z u B s Fiue 6.4 A post-keynesian model I/K which is epesented by the I/K in the uppe left quadant of Fiue 6.4, assumin that it is flatte than the savin line. 5 he ates of investment and pofit ae detemined at the intesection of the savin and investment lines in the uppe left quadant. he lowe left quadant shows the value of ω detemined by equation (6.2), and the point inside the wae shae-pofit fontie in that quadant shows the wae shae and pofit ate fo the economy (to ensue that thee is excess capacity in equilibium). he ate of capacity utilization is shown by the hoizontal intecept of the dashed line thouh this point and the point at which ω =. In eneal, fo this model, since l is undetemined, so is a, as in the classical-maxian model: the extent to which output owth is accommodated by labo supply owth and labo poductivity owth is undetemined. It may be noted that, in this model, an incease in animal spiits o business confidence, epesented by an incease in γ 0, o a fall in the makup, z, will incease the ate of capital accumulation n 0 a

11 Altenative models of owth and distibution 77 (by shiftin up the investment line) and the ate of pofit. he fall in the makup also inceases the labo shae, implyin that capital accumulation in this model is wae led. A ise in the savin ate of capitalists otates the savin line up and theefoe educes the ate of pofit and ate of accumulation: we et the paadox of thift. If we assume that the model is closed with equation (6.4), the position of the cuve is fixed in the uppe iht quadant, so that l(=n) and a ae detemined. his model is a post-keynesian model in which in equilibium labo supply and labo demand ow at the same ate, so that we have full employment owth. he effects of the paametic shifts in this modified model ae the same as those discussed fo the basic model, which did not detemine the ate of technoloical chane. Hee, with endoenous technoloical chane, chanes in aeate demand due to chanes in autonomous investment, the makup and the savin ate have an effect on capital accumulation and technoloical chane even if we assume full employment owth in equilibium: when the ate of owth of output and labo demand chane in this model, the ate of labo poductivity owth chanes endoenously to accommodate these chanes. 6 owad an expanded ole fo technoloical chane A featue of technoloical chane in the heteodox models discussed in the pevious section is that it has a athe passive ole in the owth pocess. Althouh in the neoclassical model the ates of capital accumulation and output owth ae affected by the technoloical chane paamete θ, as shown by equations (6.9 ) and (6.7), as is distibution, as shown by equation (6.6), in the heteodox classical-maxian and post-keynesian models, these vaiables ae independent of technoloy and technoloical chane: all that endoenous technoloical chane does, in the modified models with full employment owth, is to allow technoloical chane to accommodate owth without ceatin a labo shotae. In Fiues 6.3 and 6.4 the ate of accumulation and the distibution of income ae detemined in the left-hand quadants, in which thee is no mention of a technoloical chane paamete. It can be aued that the appoach adopted in these models does not ive technoloical chane its due. A majo eason fo this inadequate teatment of technoloical chane in these models is that the only way it entes the model is by affectin the ate of owth of labo poductivity. he eleation of technoloical chane to this ole in these models a ole which is emphasized in neoclassical models does an injustice to the ich ole that technoloical chane is iven in heteodox owth taditions. In these taditions technoloical chane can affect investment, income distibution and othe featues of the economy. o illustate these effects we conside the effect on income distibution in the classical-maxian model and the effect on investment in a post-keynesian model. Fo the classical-maxian model we assumed in the pevious section that the wae shae, ω, is exoenously iven, which implies that wokes ae able to incease thei eal wae in step with labo poductivity owth, maintainin thei

12 78 Amitava Dutt shae of the fuits of technoloical chane. If this is not the case, we may fomalize the dynamics of the wae shae by notin that ˆ ω = wˆ a (6.24) whee the ovehat denotes the ate of owth of the vaiable, and assumin that wˆ = λ ( ω ω) + λ a, (6.25) 2 whee λ i ae positive, finite, paametes and λ 2 <. his equation shows that the ate of owth of the eal wae depends on the ap between the taeted wae shae and the actual wae shae, and incompletely on the ate of labo poductivity owth. Substitutin equation (6.25) into (6.24) and solvin fo the equilibium value of the wae shae, at which ˆ ω = 0, we obtain ω λ 2 = ω a λ. (6.26) his equation shows, iven ou assumptions, that a hihe a implies a lowe equilibium level of ω, since the eal wae fails to keep up with the ate of poductivity owth. his elationship is shown in the lowe iht quadant of Fiue 6.5. his appoach can be seen as followin Max s analysis of technoloical chane which involves the adoption of labo-displacin machines as a weapon in the hands of capitalists in class stule (see Max, 867, ch. 5.5), which educes the shae of wokes in oveall income. If we modify the classical-maxian model by eplacin equation (6.8) with equation (6.26), while assumin full employment owth in equilibium, that is, makin equation (6.4) hold, we et the model shown in Fiue 6.5, in which the wae shae is endoenous. Combinin the thee lines in the lowe two quadants and the uppe-left one, we obtain the AG cuve, which is deived fom equations (6.9), (6.) and (6.26), which yields λ 2 = s( ω) B + Ba λ. (6.27) he fiue assumes that s( ω ) B > n, that is, the ate of capital accumulation which esults fom a ate of pofit implied by the taeted wae shae (which ives an uppe bound to the wae shae) exceeds the ate of labo supply owth, and λ2 B <, that is, the eal wae la behind poductivity owth is not too lae. λ he intesection of the AG cuve and the cuve which has n as its vetical intecept detemines the equilibium levels of and a. he est of the fiue solves fo the equilibium values of the othe vaiables. Since AG incopoates infomation fom the line in the lowe iht quadant, the equilibium levels of ω and a will lie on the latte line.

13 Altenative models of owth and distibution 79 = s ω B Fiue 6.5 A classical-maxian model with an endoenous wae Now conside the effects of a fall in the owth of labo supply, n. he cuve shift down in the uppe iht quadant, implyin an incease in equilibium a,, and and a eduction in ω. he ates of owth of output and the eal wae incease, and that of employment falls. he fall in the ate of labo supply owth inceases labo maket pessue and induces a hihe ate of technoloical chane, which educes the wae shae as waes fail to keep up with poductivity owth, which inceases the pofit ate and esults in a hihe ate of capital accumulation. In equilibium, labo demand ows at the lowe ate of owth of labo supply, but poductivity ows faste, as does the eal wae and output. his esult may be compaed to the implications of a fall in n in the classical-maxian model discussed in the pevious section and the neoclassical model also discussed in that section. In the classical-maxian model of the pevious section, as we saw ealie, a fall in n inceases poductivity owth, but with the wae shae exoenously iven, thee is no chane in the ate of capital accumulation. echnoloical chane has no effect on the ate of capital accumulation, unlike what happens in the model of this section. In the neoclassical model of Fiue 6.2 thee is also no effect on capital accumulation and output owth, althouh with labo supply owin moe slowly, thee is an incease in pe capita income. he ate of labo poductivity owth may have additional effects on the paametes of the model. One such effect is that on capital poductivity, iven by B. If the pice of hihe labo poductivity owth is a fall in capital poductivity, we may have a neative effect on B. But if hihe labo poductivity owth leads to a concomitant incease in capital poductivity, a will be positively elated to B. hese chanes will esult in additional chanes in the ate of capital accumulation. Rathe than analyse these effects, which is staihtfowad to do, we tun to a post- Keynesian model. Seveal analysts of owth models detemined by aeate demand, includin Kalecki (97), have emphasized the ole of technoloical chane in inceasin A n ω ω G a a

14 80 Amitava Dutt desied investment. o take this effect into account we may modify equation (6.23) and assume that = γ 0 + γ 2 u + γ 3 a. (6.28) Replacin equation (6.23) by (6.28) in the Kaleck-Steindl model, we find that it is no lone possible to daw the investment line in the uppe left quadant of Fiue 6.4, since its position depends on a. ω + z u s B Fiue 6.6 A post-keynesian model with investment dependin on technoloical chane o examine the implications of this amendment fo Kalecki-Steindl model with full employment owth we use equations (6.9), (6.22) and (6.28) to obtain 0 + 3a = ( z + ) zs 2 A n 0. (6.29) Given the assumptions about the elative slopes of the savin and investment cuves, the denominato of of the left-hand side is positive, so that the equation can be epesented by the staiht line AG with positive intecept and positive slope in the uppe-left quadant of Fiue 6.6. We also assume that γ 3 is small, so that the effect of technoloical chane on investment, while positive, is small. his line shows the equilibium level of the ate of capital accumulation which bins savin and investment to equality fo a iven a. his ensues that the AG line has a slope which is less than unity. We ae assumin also that autonomous investment, γ 0, is lae enouh compaed to n to make the vetical intecept of the AG line lae than that of the line. he intesection of this line with the line which shows how a hihe ate of capital accumulation inceases the ate of poductivity G a

15 Altenative models of owth and distibution 8 owth (fo instance, due to leanin by doin) detemines the equilibium ates of capital accumulation and technoloical chane. Conside, now, the effect of an incease in autonomous investment, γ 0. As in the post-keynesian model, which did not include the effect of technoloical chane on investment, this will incease investment spendin. While in the ealie model this is shown by an upwad shift in the I/K line in Fiue 6.4, in this model it is shown by an upwad movement in the AG line in Fiue 6.6. While in both models a inceases, in the pevious model thee is no feedback effect of this on investment. Howeve, in the pesent model, the ise in a has a multiplie effect on, induced by the hihe ate of technoloical chane. hus, thee is a stone effect on capital accumulation in this model, because it takes into account the intedependence of investment and technoloical chane which was absent in the pevious model (which only took into account the effect of investment on technoloical chane and not the evese causation). Note also, in this model, that a hihe γ 3, that is a eate esponse of investment to technoloical chane, esults in a hihe ate of capital accumulation, technoloical chane, output owth and eal wae owth, an effect which did not exist in the pevious model. he post-keynesian model can be futhe extended to take into account additional effects of technoloical chane, includin an effect on the makup and hence the distibution of income. his may eflect not only labo maket dynamics of the type discussed fo the classical-maxian model of this section, but also the effects of technoloical chane on industial concentation. hese extensions ae not pusued hee, since ou oal is only to illustate how the basic models can be extended to take into account additional effects of technoloical chane. Conclusion his chapte has developed a simple eneal famewok within which to examine and compae models of owth, distibution and technoloical chane fom altenative owth theoy taditions, includin what may be called the neoclassical (in which owth is constained by effective labo supply), classical-maxian (in which owth is constained by savin and capital accumulation) and post- Keynesian (in which owth is limited by aeate demand). In so doin, this chapte has extended ealie attempts to develop a eneal famewok in which altenative models can be seen as povidin altenative ways of closin the eneal famewok, but which inoed the ole of technoloical chane. he theoy of endoenous technoloical chane we have adopted is a simple one, but one which is elated to a numbe of influential and widely-used appoaches in the owth-theoy liteatue on technoloical chane. he main implications of ou analysis ae as follows. Ou extended eneal famewok is able to encompass a lae ane of models of owth and distibution than befoe, includin neoclassical new owth o endoenous owth theoies, and heteodox theoies with endoenous

16 82 Amitava Dutt technoloical chane. It is theeby able to make possible compaisons with a wide ane of theoies. 2 he extended famewok is found to naow down the diffeences between some of the altenative appoaches to owth and distibution. Fo instance, it is shown that we may have classical-maxian and post-keynesian models which behave like neoclassical models in the sense of havin full employment owth, but which have othe popeties that ae just like those of standad heteodox models. Fo instance, aeate demand has an effect on the lon un even with full employment owth, unlike what is sometimes suested in the owth liteatue which inoes aeate demand issues fom the stat (see Dutt, 986). 3 We ae also able to extend the simple famewok to conside effects of technoloical chane othe than those shown by simple chanes in input output coefficients. Fo instance, we have analysed the effects of technoloical chane on income distibution and investment, and shown how capital accumulation, technoloical chane and distibution can inteact with each othe in the lon un. If the analysis of this chapte is found to be useful, it can be extended to deal with additional complications. he implications of altenative theoies of technoloical chane may be examined, and the dynamics of the models outside lon-un equilibium can also be exploed, as has been done in Dutt (200b). he eneal famewok can also be modified to deal with additional issues, such as the ole of education and human capital fomation as a deteminant of technoloical chane (as in Dutt, 200a, and Dutt and Veneziani, 200). Such extensions can lead to a fulle appeciation of the ole of technoloical chane in the owth pocess and of how it inteacts with capital accumulation and income distibution. Notes Fo an ealy contibution usin this famewok to the analysis of theoies of distibution, see Sen (963). Fo applications to owth and distibution, the pioneein contibution is that of Malin (984), althouh a pecuso of the eneal method can be found in Hais (978). Subsequent contibutions, dawin on Malin s appoach usin altenative closues, include Dutt (987) and Dutt (990). 2 Additional neoclassical models may be obtained fom these models. Assumin that a is exoenously iven, the savin ate is fixed, and allowin fo facto substitution, poduces the Solow (956) model. Maintainin the fist and last assumption, but makin the savin ate depend on the ate of pofit poduces in effect the ovelappin eneations model (as a educed fom without optimization by economic aents). 3 Vaiants of the model assume that desied investment depend positively on both the ates of capacity utilization and pofits. his is the assumption made in the oiinal pesentations of this model by Rowthon (982) and Dutt (984). 4 he neo-keynesian one can be examined by assumin full capacity utilization and usin equation (6.9) fo the desied investment function. 5 his equies that s > γ 2 ( + z)/z, which ensues that vaiations in savin due to a chane in the ate of pofit (and the ate of capacity utilization) exceed vaiations in investment, a standad macoeconomic stability condition in models with quantity adjustment in oods makets.

17 Altenative models of owth and distibution 83 6 See Dutt (986) fo a Keynesian model which examines the dynamics of technoloical chane and capital accumulation to poduce a model of this type, inteatin the aeate demand and aeate supply sides of the economy. Refeences Aow, Kenneth J. (962). he Economic Implications of Leanin by Doin, Review of Economic Studies, 29(3), June, Dutt, Amitava K. (984). Stanation, income distibution and monopoly powe, Cambide Jounal of Economics, 8(), Mach, Dutt, Amitava K. (987). Altenative closues aain: a comment on Gowth, distibution and inflation, Cambide Jounal of Economics, (), Mach, Dutt, Amitava K. (986). Aeate demand, aeate supply and economic owth, Intenational Review of Applied Economics, 20(3), July, Dutt, Amitava K. (990). Gowth, distibution and uneven development, Cambide, UK: Cambide Univesity Pess. Dutt, Amitava K. (200a). Keynesian owth theoy in the 2 st centuy, in Philip Aestis and Malcolm Sawye (eds), wenty-fist Centuy Keynesian Economics Intenational Papes in Political Economy, Houndmills and New Yok: Macmillan Palave, fothcomin. Dutt, Amitava K. (200b). Altenative models of owth, distibution and technoloical chane, unpublished pape, Depatment of Political Science, Univesity of Note Dame, Note Dame, IN, USA. Dutt, Amitava K. and Robeto Veneziani (200). A classical-maxian model of education, owth and distibution, unpublished pape, Depatment of Political Science, Univesity of Note Dame, USA, Depatment of Economics, Queen May, Univesity of London, UK. Hais, Donald J. (978). Capital accumulation and income distibution, Stanfod, Stanfod Univesity Pess. Kaldo, Nicholas (957). A Model of Economic Gowth, Economic Jounal, 67, , epinted in Nicholas Kaldo, Essays on Economic Stability and Gowth, London: Duckwoth, 960. Kalecki, Michal (97). Selected essays on the dynamics of the capitalist economy, Cambide, UK: Cambide Univesity Pess. Malin, Stephen A. (984). Gowth, distibution and pices, Cambide, MA: Havad Univesity Pess. Max, Kal (867). Capital, Volume I, Vintae Books, New Yok, 976. Robinson, Joan (962). Essays in the theoy of economic owth, London: Macmillan. Rome, Paul M. (986). Inceasin etuns and lon-un owth, Jounal of Political Economy, 94, Rowthon, Bob (982). Demand, eal waes and economic owth, Studi Economici, 8. Sen, Amatya K. (963). Neo-Classical and Neo-Keynesian heoies of Distibution, Economic Recod, 39, pp Solow, Robet M. (956). A contibution to the theoy of economic owth, Quately Jounal of Economics, 70, Steindl, Josef (952). Matuity and Stanation in Ameican Capitalism, Oxfod: Basil Blackwell