2 The Bhaduri-Marglin model

Transcription

1 The Bhaduri-Marglin model n this chapter the basics o the Bhaduri-Marglin model ill be discussed. Doing so, attention ill be directed on hich eatures o the model ill hae to be altered hen endogeniing labor productiity and on hat this ill mean or other characteristics o the model. Changes in the real age rate hae dierent eects on the leel o employment and output. On the one hand, higher real ages increase demand, hich stimulates output. On the other hand, higher real ages increase the cost o production (Bhaduri/Marglin 990, 375). This reduces proits, hich has a negatie eect on inestment. The purpose o the Bhaduri- Marglin model is to sho ho moements in the real age rate aect the leel o employment (capacity utiliation) in the short run. (Bhaduri/Marglin 990, 375). This ork belongs to the group o the Kaleckian accumulation models. As such it assumes mark-up price setting (Hein 004,89). Bhaduri and Marglin do not comment on the ormation o the mark-up. According to Kalecki (97, 49.) the mark-up relects the degree o monopoly. The more oligopolistic the structure o the market, the higher ould be the mark-up. Additionally, m is inluenced by the strength o labor unions. proits are high as a consequence o a high mark-up, strong labor unions ould demand higher ages, hich ould push up costs. As the high m has a cost increasing eect, irms ould set loer markups. n this rameork, the authors abstract rom material costs. The representatie irm has to be seen as ertically integrated (Bhaduri/Marglin 990, 377), hich means that each step o production is carried out ithin the irm. This ay all costs or intermediate goods and ra materials chancel out (Bhaduri/Marglin 990, 377). These assumptions taken together, prices are set according to ( m) l p, (.) n here m is the mark-up, o inal output. Note that since n the nominal age rate and l the amount o labor needed per unit l L / Y, it ollos that / l Y / L, hich is equal to labor - 4 -

2 productiity (Bhaduri/Marglin 990, 377.). Labor productiity ill be denoted ith in this ork. As material costs do not enter the price equation, the only actors inluencing the price leel, apart rom the mark-up, are the nominal age rate and l. Equation () can be reormulated to yield m h n l m p, (.) here h denotes the proit share and the real age rate (Bhaduri/Marglin 990, 378). The real age rate and labor productiity are exogenous actors in this model. This is o course not a ery good approximation to reality. The real age rate, or example, could be treated as a decreasing unction o the unemployment rate. Labor productiity can also depend on a number o actors, or example on the alue o capacity utiliation (economies o scale) or the real age rate. This matter ill be discussed in detail in this ork. Treating as an exogenous ariable is, hoeer, necessary or the analysis and the purpose o this model, because in order to examine the connection beteen real age and employment it is necessary to perorm at least thought experiments based on exogenous ariation in the real age rate (Bhaduri/Marglin 990, 376). The assumption o exogenous labor productiity does not sere such a purpose, it only keeps the model simple, because ith held ixed, an increase in the real age rate alays leads to a decrease the proit share. This can also be seen by rearranging equation (): l n n ( m) ( h) p p Since labor productiity, the let side o the equation, is ixed, an increase in the real age rate has to decrease the proit margin m and the proit share h, otherise the equation ould not hold (Bhaduri/Marglin 990, 378). the assumption o constant labor productiity as dropped, a rise in ould only depress the proit margin i labor productiity rose less than. labor productiity and the real age Note that through this entire ork ill alays reer to the real age rate and not to the nominal age rate

3 rose by the same rate, the proit share ould remain at its initial leel. There ould be o course also the possibility that an increase in the real age leads to a decrease in proit share i it as accompanied by a rise in labor productiity that ould outeigh the initial rise in real ages. These additional aspects, brought about by a hich is subject to change, ill be, among others, the ocus o interest in this ork. Bhaduri and Marglin use the assumption that orkers do not sae. This means, on the one hand, that all age income goes into consumption and, on the other hand, that saings are only generated through proits. Thereore aggregate saing is S sπ, here Π stands or total proits. The aboe equation can be reritten as S Π Y sπ s Y Y * Y *, here Y is total output and Y* ull-capacity potential output. total income, i.e. the proit share, denoted by h. Y / Y * Π / Y is the share o proits in is the leel o capacity utiliation, denoted by (Bhaduri/Marglin 376.). the economy orks at ull capacity, hich means that it produces the maximum leel o output possible ith the existing means o production, then Y Y * and Y / Y*. Y* is set equal to, i.e. all actors are normalied as proportions o ull capacity output, the aboe equation can be ritten as S sh. (.3) t ollos rom here that, since a all in real ages increases h, any redistribution rom ages to proits ill increase saings and decrease consumption (Bhaduri/Marglin 377). Since saings depend on the allocation o income, endogenous labor productiity, by haing an inluence on the proit share, ould inluence the generation o saings. Setting Y* leaes potential output unable to change, hich does not correspond to the deelopment o human production acilities in the past centuries, oer hich potential output has in act increased a lot. Bhaduri and Marglin argue that, i not in the long run, ull

4 capacity output (Y*) can be treated as a constant in each short period (Bhaduri/Marglin 377). Their correct argument is that potential output does not change in the short run, hich makes their approach a short run model. t has to be said in this respectie, that since they abstract rom technical progress (remember that labor productiity is ixed), their model can theoretically also be considered alid or the long term, since in an economy ithout technical progress, potential output Y* ill een be constant in the long run. This can be seen rom the olloing deinition: Y * L * Bhaduri and Marglin do not comment on the issue hether there is ull employment at Y*. n Hein (004, 69), Y* is deined as the leel o output that is achieed at ull capacity utiliation o the gien capital stock, hich does not hae to mean ull employment. Thereore, L* is the leel o employment at ull capacity utiliation o the capital stock. Y* is the leel o output that can be achieed ith L* under gien labor productiity. L* is the leel o ull employment, an increase in Y* is possible i the labor orce increases. e do not speak o ull employment, an increase in Y* is only possible i increases. Since labor productiity can not change in this setup, Y* is een constant in the long run. We already discussed the demand or consumption in this model. What ollos next is the demand or inestment to complete the demand side. Typically or the post-keynesian theory, inestment decisions are independent o saing decisions in this model (Hein 004, 89). nestment depends positiely on the proit share and on the degree o capacity utiliation. The inestment unction is not made explicit: ( h, ) ; > 0, > 0 h (.4) The leel o proit share has a positie impact on inestment, as it orks as a predictor o uture proitability on ne inestment(bhaduri/marglin 990, 380.). A higher leel o proit share can also be thought o as making inestment easier or irms as they can use retained proits or inestment (Naastepad 006, 43). The degree o capacity utiliation orks as - 7 -

5 predictor o uture demand (Bhaduri/Marglin 990, 380). n this respectie, it has to thought about the consequences o a rate o labor productiity hich is subject to change or inestment behaior. t is obious, that endogenous labor productiity, by inluencing the proit share, ould indirectly inluence inestment decisions. Hoeer, it may een be necessary to go one step urther and think about adjustments in the inestment unction, since inestment criterias in an economy here labor productiity is not constant might be dierent. As it ill be seen later in this ork, some approaches assume that rises in labor productiity lead to increases in inestment. 3 Applying the equilibrium condition or the goods market, S gies ( h ) sh, (Bhaduri/Marglin 990, 380). (.5) The subject o interest or this model is ho a change in the real age rate, i.e. the proit share, inluences the degree o capacity utiliation in the short run. This means that e ant to get the expression d / dh. What makes this a little diicult is that the inestment unction is not made explicit. Bhaduri and Marglin sole this problem by applying total dierentiation to the aboe equation, hich yields. (.6) h ( s) dh ( sh) d dh d This can be put into the orm sh d sdh, h and some urther manipulation yields the inal result: The adantage o this inestment unction, compared to an inestment unction hich takes the orm (r), is that it goes behind the rate o proit to its indiidual constituents (Bhaduri/Marglin 990, 379.). The rate o proit r Π / K can be ritten as r Π / K ( Π / Y )( Y / Y *)( Y */ K) hk *, hich means h and ould also implicitly enter the inestment unction i it ould only depend on the rate o proit. The disadantage o (r) is that it is simply assumed that a gien rate o proit ill produce the same leel o inestment as results rom high capacity utiliation and a lo proit margin or rom lo capacity utiliation and a high proit margin. An inestment unction hich depends only on the rate o proit is insensitie to the existing degree o capacity utiliation, e.g. it neglects the possibility that, despite a high proit margin, inestors may not be inclined to inest in additional capacity i massie excessie capacity already exists (Bhaduri/Marglin 990, 379.). 3 See Cassetti (003) and Hein (004)

6 d dh s h (.7) sh This is the slope o the S-cure in the /h-space. Under the classic Keynesian stability condition that the response o saing to an increase in capacity utiliation is higher than the response o inestment, i.e. sh > /, the denominator is positie and the sign o the slope o the S-cure only depends on the numerator. The irst term in the numerator shos the response o saing to an increase in the proit share. this reaction is ery big, the numerator is positie and a higher proit share (a loer real age rate) has a positie impact on capacity utiliation. The second term shos the eect o an increase in the proit share on saing. Since orkers consume all their income, an increase in h decreases consumption and increases saings (because irms do sae a raction o their income). An increase in the proit share thereore has to eects on aggregate demand: it reduces it by loering consumption, but increases aggregate demand by increasing inestment. the irst eect outeighs the second one, i.e. s >, an increase in the proit share (a decrease in real ages) has a negatie eect on aggregate demand and the demand regime is called stagnationist. inestment is ery much stimulated by an increase in h (decrease in the real age rate), the eect on aggregate demand is positie. This is called the exhilarationist regime (Bhaduri/Marglin 990, 380.). n this rameork, cooperation beteen the to classes, orkers and capitalists, is possible. Firms may agree to higher real ages (and a loss in proit share) i it increases their total alue o normalied proits, hich is Π / Y * ( Π / Y )( Y / Y*) h. t can immediately be seen that since the proit share ould decrease in such a case, demand must increase suiciently to result in a net-gain in total proits. The crucial condition or the unctioning o cooperatie capitalism, as it is called by Bhaduri and Marglin, is d ( h) < 0 dh (.8) Reormulating yields - 9 -

7 d dh < (.9) h Substituting equation (.7) into (.9), rearranging and diiding both sides through inestment yields > h h (.0) Higher real ages beneit the capitalist class i the elasticity o inestment and capacity utiliation is bigger than the elasticity o inestment and the proit share (Bhaduri/Marglin 990, 38.). The other side o cooperatie capitalism relates to the orking class. Workers may agree to loer real ages (a loer age share) i it increases demand and employment by such an extent, that the total age bill rises. t becomes clear that such a scenario is only possible in the exhilarationist regime, since in the stagnationist regime loer real ages cannot lead to a rise in capacity utiliation. The crucial condition or cooperatie capitalism is d ( W / Y*) dh d [( W / Y )( Y / Y*) ] d[ ( h) ] dh dh > 0 (.) Rearranging yields the olloing condition: h d dh h > (.) h Real age restraint leads to a total rise in the orkers age bill i the elasticity o capacity utiliation and the proit share exceeds the ratio o proit share to age share (Bhaduri/Marglin 990, 384)

8 6 Endogenous productiity in the Bhaduri-Marglin model n this chapter, the knoledge attained until no ill be applied to the Bhaduri-Marglin model. First, only the inluence o labor productiity on the proit share ill be considered. This means that the only thing hich ill change at the beginning is that the constant labor productiity coeicient in equation (.) ill be replaced by a productiity regime. This productiity regime ill be incorporated in to steps: First only the inluence o economies o scale on labor productiity ill be considered. Then, also the impact o the real age rate on labor productiity ill be taken into account. Once the productiity regime is ully built in into the model, an additional aspect o changes in labor productiity ill be accounted or, namely the impact on inestment. 6. Economies o scale First, productiity is alloed to ary ith the degree o capacity utiliation: d ( ) > 0 d (6.) n the course o this ork e hae ound to ays o argumentation or this relationship: The irst one as discussed hen dealing ith the ork o Raghaendra (006). When the economy produces at high capacity, it creates economies o scale. n the ork o Raghaendra, this relationship as deried by diiding total labor in to parts, an operatie and a non-operatie part, rom hich only the operatie part aried ith actual output, hereas non-operaties aried only ith the leel o potential output. This led to the unctional relationship that labor productiity increased ith the leel o capacity utiliation (Raghaendra 006, 60.). The same argument can also be ound in Laoie (99, 6.). The second ay o argumentation as ound in the ork o Bhaduri (006), in hich it as assumed that irms try to keep orkers age-claims rom rising by keeping the rate o unemployment constant. By preenting unemployment rom decreasing through labor-saing innoation, they increased labor productiity (Bhaduri 006, 7). For the Bhaduri-Marglin model it is justiied to assume that employment ill be higher (unemployment ill be loer) at a higher rate o capacity utiliation. Supposing the behaior o irms just mentioned, labor productiity ill be higher in the Bhaduri-Marglin model hen capacity utiliation is higher, because irms put more eort in increasing labor productiity. Additionally it could be - 6 -

9 assumed that productiity increasing eects o learning by doing are higher hen the economy orks at a higher leel o capacity utiliation. As productiity ceases to be constant, the real age rate is not the only actor inluencing the proit share any more. t is no gien by h (6.) ( ) For later conenience it is useul to calculate the total dierential o h, hich is d dh d d d d d (6.3) Equilibrium in the goods market is still gien by ( h, ) sh (.5). and, like in the original Bhaduri-Marglin model, the total dierentiation o the equilibrium condition can be ritten in the orm (.6) h ( s) dh ( sh) d dh d nstead o dh e can substitute equation (6.3) into (.6). Rearranging yields s h d d sh d s d h Further manipulation leads to the olloing result: - 6 -

10 d d s h (6.4) d sh s h d Note that instead o d / dh e hae d / d no, hich makes it harder to compare the result gained here to the one in the original model. Thereore it ill be helpul to also express the original result in d / d, hich is just simple mathematics: 34 d d s h sh (6.5) No it can be seen that including the productiity regime did not lead to any change in the numerator. nstead, hat really changed is the denominator. The irst term in brackets in the denominator in equation (6.4) is equal to the denominator rom the result in the original model in (6.5). t is the dierence beteen the direct impact o a change in capacity utiliation on saing and inestment, hich must be positie according to the Keynesian stability condition. The second term in brackets is due to endogenous labor productiity. t turns negatie hen the response o inestment to a change in proit share is large. This might gie the impression that including the productiity regime created one additional possible outcome: the possibility or d / d > 0 ith s < as both parts o the raction no seem as they could turn negatie. Neertheless e ill immediately see that this scenario is ruled out by stability reasons: n this rameork, the reaction o saing to a rise in capacity utiliation must alays be greater than the reaction o inestment, i.e. the Keynesian stability condition must hold: ds d d d > 0 (6.6) 34 The total dierential o equilibrium condition (.5) can also be ritten in the orm d d h ( s) ( sh) d d Some manipulation yields equation (6.5)

11 Calculating the dierentials o saing and inestment ith respect to capacity utiliation and substituting into equation (6.6) yields, because o the additional inluence o capacity utiliation on the proit share, ds d d d sh s d d h d d > 0, (6.7) hich is equal to sh d s > 0 (6.8) h d n other ords, the denominator in equation (6.4) cannot turn negatie or stability reasons, since it is equal to the dierence beteen the total reaction o saing and inestment to a change in capacity utiliation. Thereore the introduction o the productiity regime did not change the act that the denominator has to be positie. For a better understanding o the denominator, equation (6.4) is reritten in the olloing ay: d d sh s s h d d h d d s h ds d d d (6.9) As already mentioned, the irst bracket in the denominator shos the total impact o a rise in on saing, i.e. the deriatie o total saing ith respect to. A rise in ill increase saings in a direct and in an indirect ay. Saing is gien by S sh, hich means it can be increased by a rise in the proit share and by a rise in capacity utiliation. The irst term in this bracket shos ho saing is directly increased by a rise in. As capacity utiliation also increases the proit share (through labor productiity), e get an additional eect on saing, since this rise in h also causes total saings to increase. The second bracket in the denominator shos ho an increase in capacity utiliation aects inestment. t is the total deriatie o inestment ith respect to. On the one hand, a rise in capacity utiliation increases inestment directly as it means higher demand. This is shon by the irst term in

12 this bracket. On the other hand, higher capacity utiliation causes productiity to go up, hich leads to an increase in the proit share. The rise in proit share additionally increases inestment, shon by the second term in this bracket. Concluding, the results or hether real age restraint can be beneicial or an economy gained by Bhaduri and Marglin (990) continue to be alid hen economies o scale are introduced. For real age restraint to hae a negatie impact on capacity utiliation, s > is the suicient condition as in the original model ith exogenous productiity. Endogenous labor productiity, by only inluencing the denominator, can neertheless inluence the sie o the eect, hich means that the closer the denominator gets to ero, the bigger the sie o the (positie and negatie) eect o real age restraint on capacity utiliation ill be. Returning to equation (6.4) again, e see that under s > 0, the denominator increases because the sign o the second bracket is positie. This means that in this case, the eect o real age restraint is smaller (because the denominator is bigger) than in the original model. The reason is that the all in capacity utiliation, due to a shit rom age income to proit income, causes a all in labor productiity, hich reerses some o the initial shit in income as it decreases the proit share. The larger the all in labor productiity, the bigger this reerse shit and the smaller the negatie impact o real age restraint on capacity utiliation under s >. s < 0, the sign o the second bracket in equation (6.4) is negatie, hich means endogenous labor productiity decreases the denominator and this ay increases the total eect o real age restraint on capacity utiliation. There is a reason or it: s < 0, loer real ages increase demand as additional inestment compensates or the loss in consumption. The rise in causes labor productiity to go up too, i.e. the proit share rises urther, hich means additional inestment and the oerall gain in capacity utiliation ill be higher. Thereore the larger the reaction o labor productiity is, the larger ill be the second (negatie) term in the denominator in (6.4) and the larger ill be the eect o a change in the real age rate on capacity utiliation (gien s < 0). We already kno that the denominator cannot turn negatie or stability reasons, hich means that changes in labor productiity can only bring the denominator close to ero but not urther don. This leads to the olloing question: What happens i an economy here d / d is ery large? n s >, a rise in the proit share (due to loer real ages) causes a

13 all in demand. d / d is ery large, a signiicant all in labor productiity ould be the consequence, leading to a all in proit share belo its initial leel beore the increase. As s >, the loer proit share ould cause a rise in demand and capacity utiliation ould go up, hich ould leae the total eect o a policy o real age restraint positie. But as e see rom equation (6.4), respectiely (6.9), the numerator is positie in this case and so must be the denominator, hich means that d / d negatie, in other ords, the impact o this policy under can get close to ero but cannot turn s > is predicted to hae a negatie impact on. So is there an error in our result? The anser is no, and the reason hy labor productiity cannot turn the result can be explained as ollos: n an economy here s > and d / d is ery large, loer real ages cause a all in demand and this leads to a all in labor productiity by such an amount that the proit share is suddenly loer than beore its initial rise. n such an economy, the loer proit share should cause a sharp rise in demand (because s > ) and leae the total eect o real age groth restraint on positie. Hoeer, by the same logic, the higher leel o capacity utiliation should lead to a large rise in labor productiity in turn, increasing the proit share again and causing a sharp all in demand and capacity utiliation. n other ords, in such an economy, here ery big and d / d s >, each rise in caused by the large response o productiity should be olloed by a all in caused by the same mechanism. Thereore the result gained in equation (6.4), respectiely (6.9), can be considered correct also or this special case. is This leaes Bhaduri s and Marglin s result alid that real age restraint ill only lead to a rise in output hen s < 0. ncluding economies o scale did not change that, as already mentioned. What they did change in act as the sie o the eect, since moements in labor productiity can either increase or decrease the total eect o a policy o real age restraint in this rameork. 6. The age eect As a next step a age eect ill be added to the productiity unction. There are three concepts behind this modiication: Higher real ages make labor more expensie and it may be assumed that more expensie labour induces irms to intensiy their search or and adoption o labour productiity-raising techniques (Naastepad 006, 40). This concept ound application in the models o Cassetti (003), Bhaduri (006) and Naastepad (006), hich hae already been discussed in this ork. A ery similar concept is called by Laoie

14 the Webb eect : Higher real ages lead to an increase in costs or the irms. As a consequence, those irms hich produce less eiciently ill be eliminated rom the market and demand ill shit to the more eicient irms, hich leads to a general rise in labor productiity (Laoie 99, 50). Hoeer, this modiication can also be justiied by the theory o eiciency ages, since higher ages are likely to create more motiated and better orking employees. 35 According to this, the labor productiity unction is no gien by (, ) (6.0) ith / > 0, hich makes the proit share h (6.) (, ) Total dierentiation o (6.) yields dh d d d d d (6.) Substituting (6.) into (.6) and rearranging gies the inal result: d d s h sh s h s ( ε, ) h sh s h (6.3) The age eect did not hae any impact on the denominator but instead changed the numerator, hich is no multiplied by ( ε ), hereε,, is the elasticity o labor productiity ith respect to the real age rate. As beore the modiication, a higher proit share leads to a decrease in consumption by s and an increase in inestment by. The dierence is that beore, a all in the real age rate as equal to a rise in the proit share. No loer ages lead to loer labor productiity. As labor productiity decreases, the proit 35 A urther application o the concept o real ages inluencing labor productiity can be ound in the ork o Laoie (99, 48.)

15 share decreases too. The result is that a all in the real age rate may no lead to an increase or a decrease in the proit share, depending on the elasticity o productiity and the real age rate. ε, a all in the real age rate is olloed by a all in productiity that is large, > enough to lead to an actual decrease in the proit share. ε, a all in the real age rate, < leads, as beore the consideration o a age eect, to a rise in the proit share, ith the eect o loer real ages on the proit share being smaller than beore. The reason is that the all in productiity reallocates some income share back to orkers. ε, a change in the real, age rate does not hae an impact on capacity utiliation because a all in leads to a proportional all in productiity to keep distribution beteen orkers and capitalists unchanged. 36 We kno rom beore that, or stability, the denominator in equation (6.3) has to be positie, hich means that the sign o d / d is only determined by the numerator. ε, the, < second term in brackets in the numerator is positie and e get the same result as beore, ith the dierence that the eect o real age restraint becomes smaller, because loer real ages also lead to loer labor productiity, hich makes the rise in the proit share smaller. n this case, as beore, real age restraint ill lead to a all in capacity utiliation i s > and to a rise in capacity utiliation i s <. Fig.. Since, <, real age restraint leads to a rise in the proit share (irst graph). As s > / h, this rise in h decreases capacity utiliation (second graph). Thereore real age restraint has a negatie impact on capacity utiliation (third graph). 36 Remember that Naastepad (006, 47.) receied similar results or her model

16 Fig.. Since, <, real age restraint leads to a rise in the proit share (irst graph). As s < / h, this rise in h increases capacity utiliation (second graph). Thereore real age restraint has a positie impact on capacity utiliation (third graph). Under the ne productiity regime, to additional outcomes become possible. When real ages ell and the reaction o inestment to a rise in the proit share as lo ( s > ), this led to a all in capacity utiliation beore. ε, the consequence o real age, > restraint is a all in labor productiity large enough to cause a drop in the proit share (despite higher real ages). n this case, the impact o loer real ages is positie despite eak responsieness o inestment. This can be seen in equation (6.3): The irst bracket in the numerator is positie. As the second bracket is negatie, d / d means that capacity utiliation goes up hen real ages go don. is also negatie, hich Fig. 3. Since, >, real age restraint leads to a all in the proit share (irst graph). As s > / h, this decrease in h increases capacity utiliation (second graph). Thereore real age restraint has a positie impact on capacity utiliation (third graph). The second additional possible outcome is that inestment reacts ery strongly to an increase in the proit share ( s < ), but since ε, real age restraint leads to a sharp all in, >

17 productiity, hich causes the proit share to all ater a decline in. The result is a all in capacity utiliation because loer real ages lead to a reallocation rom proit income to age income. This can also be seen in the numerator o equation (6.3): The irst bracket is negatie, as ell as the second bracket, hich results in capacity utiliation goes don hen real ages go don. d / d being positie. Thereore Fig. 4. Since, >, real age restraint leads to a all in the proit share (irst graph). As s < / h, this decrease in h decreases capacity utiliation (second graph). Thereore real age restraint has a negatie impact on capacity utiliation (third graph). The discussed outcomes are summaried in table. n accordance ith Bhaduri and Marglin (990, 39.), a demand regime is called stagnationist hen a reallocation toards proit income (a rise in the proit share) reduces demand (hich is the case hen s > in this model) and exhilarationist hen it increases demand (hich happens in this model hen s < ). Table. Summary o the possible outcomes Nature o the demand regime Stagnationist s > Exhilarationist s < ε, < d / d > 0 d / d < 0 ε, > d / d < 0 d / d >

18 We hae seen that, against the intuition, a all in the real age rate can theoretically lead to a reallocation rom proit income toards age income, in other ords, loer real ages may increase the age share hen ε, is larger than one. 37 Neertheless, een i this elasticity as generally smaller than one, these indings ould sho that the (positie and negatie) eect o real age restraint on capacity utiliation is smaller hen the impact o real ages on labor productiity is considered. 6.3 The inestment eect Folloing the orks o Cassetti (003) and Hein (004) already discussed, the eect o labor productiity on inestment ill be no considered. When irms try to gain adantage oer each other by increasing labor productiity in the production process, this increases the aggregate leel o productiity in the economy, as ne methods o production and more technically adanced types o capital emerge. The eect o the existence o more technically adanced capital is a rise in the aggregate leel o labor productiity. other irms ant to apply the ne techniques in the production process, they hae to inest in ne capital. Thereore an increase in the leel o labor productiity has a positie eect on inestment. 38 The inestment unction becomes ( h,, ) ith / > 0 (6.4) Substituting equation (6.4) into the equilibrium condition and applying total dierentiation yields h d. (6.5) ( s) dh ( sh) d dh d The total dierential o the labor productiity unction is d d d. (6.6) 37 Naastepad estimated ε, or the Netherlands and receied as a result ε, 0,5. This means that a decline in real age by one percentage point leads to a decline in labor productiity by 0,5 percentage points (Naastepad 006, 43). 38 The positie impact o labor productiity on inestment has been emphasied in the orks o Kalecki (97, 50.), Rothorn (98, 3.) and Dutt (003, 87)

19 Substituting (6.) and (6.6) into (6.5) gies, ater some manipulation, the inluence o a change in the real age rate on capacity utiliation again: d d s ( ε, ) h sh s h (6.7) ntroducing the inestment eect o labor productiity adds an additional positie term to the numerator and an additional negatie term to the denominator. We already kno that the denominator has to be positie or stability reasons. Thereore the additional negatie term can only bring the alue o the denominator closer to ero, but not urther don. Due to the additional negatie term, the denominator is no smaller, hich means that the oerall eect o a change in the real age rate becomes larger in general. This can be interpreted in the olloing ay: Any change in the real age rate that has a negatie (positie) eect on demand, no has an additional negatie (positie) impact on inestment because it exhibits a negatie (positie) inluence on labor productiity. This causes general. d / d to be larger in Taking account o the eect o labor productiity on inestment creates additional possible scenarios. This can be seen in the numerator in equation (6.7). The additional positie term makes d / d > 0 more likely, i.e. the consequences o real age restraint are no generally orse. The reason is that loer real ages hae a negatie inluence on labor productiity, hich decreases inestment. ε, < and the responsieness o inestment to a higher proit share is small ( s > ), real age restraint ill hae a negatie inluence on capacity utiliation. The additional negatie eect through smaller labor productiity only increases this all. This can be seen in equation (6.7): The irst to brackets in the numerator are positie. The ne term is alays positie, hich leaes no doubt about d / d being positie

20 Fig. 5. Since, <, loer real ages lead to a rise in the proit share (irst graph). As s > / h, this rise in h decreases capacity utiliation (second graph). Thereore real age restraint has a negatie impact on capacity utiliation (third graph)., hoeer, inestment reacts rather strongly to a rise in the proit share, i.e. s < (still gien that ε ), the result is less clear. Real age restraint can hae a positie or a, < negatie impact. On the one hand, the higher proit share increases inestment, but on the other hand, loer real ages hae a negatie impact on labor productiity, hich decreases inestment. The consequence o loer real ages on capacity utiliation depends on the sum o these eects. This can again be seen in equation (6.7): The irst bracket in the numerator is negatie hereas the second bracket is positie, making the product o these to negatie. the third (positie) term is suiciently large, d / d ill neertheless turn positie. Fig. 6. Since, <, loer real ages lead to a rise in the proit share (irst graph). As s < / h, this rise in h ould increase capacity utiliation (second graph). Neertheless, the oerall eect o real age restraint on capacity utiliation can be positie or negatie (third graph), depending on the negatie eect o loer labor productiity on inestment

21 ε, i.e. loer real ages lead to a all in the proit share (due to the large decrease in, > labor productiity) and s >, the oerall eect on capacity utiliation is also ambiguous. The reason is that reduced inestment, due to loer labor productiity, can outeigh the additional consumption demand due to the loer proit share. Looking at equation (6.7): The irst bracket in the numerator is positie, the second bracket is negatie, hich makes the product negatie. the third term is suiciently large, positie, i.e. capacity utiliation ill go don hen real ages go don. d / d ill be Fig. 7. Since, >, loer real ages lead to a all in the proit share (irst graph). As s > / h, this all in h ould increase capacity utiliation (second graph). Neertheless, the oerall eect o real age restraint on capacity utiliation can be positie or negatie (third graph), depending on the negatie eect o loer labor productiity on inestment. Finally, loer real ages alays lead to a all in capacity utiliation hen ε, > and s <. Real age restraint decreases productiity and the proit share hich causes inestment to go don. The result cannot be turned around, since loer labor productiity (induced by loer real ages) has a negatie impact on inestment and ould thereore only increase the negatie eect on demand. Looking at the numerator in equation (6.7): Both brackets are negatie hich makes the product positie. The third term is also positie hich means that d / d > 0 (real age restraint leads to loer capacity utiliation)

22 Fig. 8. Since, >, loer real ages lead to a all in the proit share (irst graph). As s < / h, this all in h decreases capacity utiliation (second graph). Thereore real age restraint has a negatie impact on capacity utiliation (third graph). n this section it as shon, ho considering the inluence o labor productiity on inestment can alter the results o the model in a ay that the policy o real age restraint ill lead to a all in capacity utiliation more oten. Like in the preious section, the possible scenarios are summaried in table :

23 Table. Summary o the possible outcomes Nature o the demand regime Stagnationist s > Exhilarationist s < ε, < d / d > 0 d / d > 0 or d / d < 0 ε, > d / d > 0 or d / d < 0 d / d > 0 > s h ( ) ε, and ε d / d > 0 d / d > 0, < and ε d / d > 0 d / d > 0, > < s h ( ) ε, and ε - d / d < 0, < and ε d / d < 0 -, > 6.4 Micro-oundations n this section the implicit labor productiity unction ill be replaced ith an explicit unction. Doing so it builds on the ork by Laoie (99). t can be stated in adance, that this ill not yield any ne results. The conclusions rom beore ill all remain alid. This

24 section purely seres the purpose to illustrate ho the implicit productiity unction could be substituted ith an explicit unction and that orking ith an implicit unction, like it has been done so ar, does not hae any negatie inluence or the quality o the results Economies o scale The productiity regime in equation (6.), ( ) ith d / d > 0, can be deried the olloing ay: Total labor must be thought o consisting o to kind o employees. On the one hand there are blue-collar orkers, hich belong to the ariable actors o production. They are directly linked to the production process, hich means their number aries ith actual output. They ill be denoted as L. On the other hand there are hite-collar orkers, hich are part o the oerhead costs. Administratie oicers, permanent sta, layers and so on belong to this group. Their number depends on the leel o ull capacity output and ill be denoted as L. Total labor can thereore be ritten as L L L (6.8) The number o blue-collar orkers is gien by the leel o actual output diided by the output produced by each o the blue-collar orkers, i.e. their leel o productiity (denoted by ): L Y (6.9) The number o hite-collar orkers is gien by the leel o potential output diided by potential output handled by each hite collar orker, i.e. their leel o productiity at ull capacity (denoted by ): L Y * (6.0) Equation (6.0) can be ritten in the olloing orm: L Y * Y Y Y * * Y Y (6.)

25 Substituting (6.9) and (6.) into (6.8) and diiding through Y yields Y L Further rearranging yields the labor productiity unction: ( ) L Y / / (6.) The irst deriatie o (6.) conirms that labor productiity is an increasing unction o capacity utiliation: ( ) 0 > d d (Laoie 99, 6.) (6.3) Taking equation (6.) instead o the implicit labor productiity unction (6.) yields the olloing result or the model: ( ) ( ) ( ) h s sh h s h s sh h s d d (6.4) The implications o this result are the same as the ones o the results or the implicit productiity unction in equation (6.4) respectiely (6.9). 6.5 The age-eect Next it is assumed that the productiity o blue-collar orkers is positiely aected by the real age rate. Higher real ages increase the pressure on the irm sector to make human

26 labor more productie, hich increases labor productiity o the orkers employed directly in the production process. Furthermore, higher real ages increase the orkers motiation, hich also leads to an increase o their leel o productiity. Using a linear ormulation, this can be ritten as ν ν 0 (Laoie 99, 5) (6.5) The labor productiity unction no becomes ( ) [ ] / / 0 0 ν ν ν ν (6.6) Dierentiation ith respect to the real age rate yields ( ) [ ] 0 / / > ν (6.7) A higher real age rate has a productiity increasing eect in this model. With the productiity regime in (6.6), the result or the model changes to ( ) [ ] ( ) ( ) / / h s sh h s d d ν, (6.8) ithout challenging the implications o the general results in equation (6.3). Finally, under the inestment unction ),, ( h, equation (6.8) becomes ( ) [ ] ( ) [ ] ( ) ( ) ( ) / / / / h s sh h s d d ν ν (6.9)

27 Again the implications o the result in (6.9) are the same as those or the result under the implicit productiity regime in equation (6.7). 6.6 A brie summary o results and implications or policies and the original model The incorporation o endogenous labor productiity in the Bhaduri-Marglin model as carried out in three steps. First, the impact o economies o scale on labor productiity as considered. Labor productiity inluenced the results o the model through its impact on the proit share. This, in principle, did not change the result gained by Bhaduri and Marglin on hether real age restraint leads to a decline in capacity utiliation or not: Loer real ages lead to a rise in output i the impact o a higher proit share on inestment is suiciently large, i.e. s <, and they lead to a decline in output i s >. Hoeer, considering productiity inluences the sie o the eect o real age restraint. this policy leads to a rise in demand ( s < ), the positie eect on output is larger (compared to the eect in original model) because higher demand leads to a rise in productiity hich causes the proit share to rise urther (leading to an additional increase in inestment). real age restraint reduces demand ( s > ), the negatie eect on demand is smaller. Again the reason is the change in labor productiity: As demand decreases, productiity declines, leading to a all in the proit share. This ay, income share is moed back to orkers, hich reduces the negatie impact on demand. The next step o the analysis as to include a age eect in the productiity regime. Three ays ere mentioned ho a policy o real age restraint may lead to loer labor productiity: First, loer real ages may decrease the irm s eort to raise labor productiity, as labor is rather cheap and there is less necessity to inest into ne capital making human labor more eicient. Second, loer real ages may preent a process that ould drie less eicient irms out o the market (hich ould lead to a rise in labor productiity). Additionally, badly paid orkers may be less motiated, hich makes them ork less eicient. Taking account o that in the productiity unction urther changed the results: On the one hand it shoed that a policy o real age restraint does not beneit the irms as much as it may seem, since loer real ages also lead to a decline in productiity, hich has a negatie inluence on the proit share. On the other hand it also shoed the possibility that loer real ages can lead to a decline in proit share i the drop in productiity is large

28 enough. This illustrated that, despite a large responsieness o inestment to changes in the proit share ( s < ), real age restraint leads to a all in output i the percentage decline in productiity exceeds the percentage decline in the real age rate ( ε ). n other ords,, > the policy o real age restraint could cause a all in output in the exhilarationist demand regime i it suiciently decreases the irms incentie to look or ne ays to make production more eicient. The last step o the analysis as to account or the positie inluence o labor productiity on inestment. t as argued that irms try to gain adantage oer each other by inesting in more technically adanced capital hich allos them to produce more eicient. This increases aggregate labor productiity and puts pressure on other irms to acquire ne capital. The modiication o the inestment unction changed the results in a ay that it became more likely or real age restraint to hae a negatie inluence on output. Finally, the implicit productiity regime as substituted by an explicit one. This did not change the results gained rom the implicit unction, hich shoed that using an implicit unction did not aect the quality o the results in any negatie ay. Concluding, in this chapter a ersion o the Bhaduri-Marglin model as deeloped hich does not rely on the simpliying assumption o constant labor productiity. Moreoer, this chapter shoed that real age restraint and productiity inluence the economy in dierent ays not recognied in the original model, hich is the reason hy Bhaduri and Marglin ere too simplistic