THE DYNAMICS OF DIFFERENT REGIMES OF DEMAND-LED EXPANSION. Any redistribution of income between profits and wages would have contradictory

Transcription

1 THE DYNAMC OF DFFERENT REGME OF DEMAND-LED EXPANON. by Amit Baduri Profeor, Deartment of Economic, Univerity of Pavia 7100 Pavia, taly Any reditribution of income between rofit and wage would ave contradictory effect in term of aggregate demand, o long a te roenitie to conume are different for te two clae. For intance, te lowering of te real wage rate would tend to dere total conumtion exenditure by reditributing income againt te wage earner wit a iger roenity to conume. At te ame time, it migt alo encourage invetment by increaing te margin of rofit er unit of ale. Deending on wic effect dominate quantitatively, two alternative regime or at bot led by demand emerge: te conumtion- or wage-led at wic a alo been called tagnationit,and te invetment- or rofit-led at called exilarationit (Baduri and Marglin, 1990; Marglin and Baduri, 1990). Te eential formalim i imle. Wit full caacity (otential) outut normalied at unity, te aving of te economy i written a, (1) =.., were i te aving roenity out of rofit, and all wage i aumed to be conumed for exoitional imlicity; ( P ) = Y = are of rofit in outut; and

2 = Y * Y = degree of caacity utiliation, wit Y * = 1, i.e. te normalied level of full caacity outut, 1, 0. We aume invetment deend oitively on bot caacity utiliation () and rofit margin (m) or rofit are () are by definition oitively related a, = m/(1+m). Auming for exoitional imlicity, tatic exectation, te invetment function i written a () = (, ),. >0, >0. From (1) and (), te loe of te locu of aving invetment equality, te - locu, i derived troug total differentiation a, (3) d /d = ( -) / (- ) Te oitive loe of (3) indicate tat a iger rofit are () reult in iger caacity utiliation (), lacing te economy in te exilarationit regime. n ti cae te timulating effect of te iger rofit are on invetment exenditure outweig it dereing effect on conumtion exenditure. Wen te loe (3) i negative, te economy i aid to be in te tagnationit regime te ooite reaon. However, te two regime ave normally been ditinguied by auming a valid te tability condition of te one-variable income adjutment roce troug te Keyneian multilier mecanim. Ti require aving to be more reonive tan invetment to cange in income, making te denominator of te rigt and ide of exreion (3) oitive. (4) Tu, auming ( )> 0, 1

3 (5) ( -)> 0, imlie tat invetment i more reonive tan aving to rofit are, etting te economy on an rofit-led exilarationit at; if, on te oter and, (6) ( )< 0, te economy i on a wage led tagnationit at for te ooite reaon. However, ti analyi remain valid only o long a te ditribution of income () i treated a an exogenou variable. n effect, ti make te underlying dynamical ytem correond to te uual ingle variable income adjutment roce of Keyneian teory wit income ditribution given, but caacity utiliation () adjuting to exce demand or uly in te roduct market. Wit caacity utiliation () a te only endogenou variable in te ytem, te dynamic adjutment equation, in view of (1) and () become, (7) d /dt = [ (,) - ], were >0 i ome arbitrary oitive of adjutment. However, te above argument could be revered by making income ditribution () te endogenou variable adjuting to exce demand or uly in te roduct market, wile te degree of caacity utiliation i aumed exogenouly fixed, ay at te full emloyment or full caacity level. n ti cae an exce of demand in te roduct market, would raie te rice level; and, if te money wage rate fail to kee ace in ercentage term, te real wage rate would fall, te margin and are of rofit would rie. Ti would tend to cloe te ga between invetment and aving at te exogenouly given full emloyment or full caacity level of outut. Ti teory of ditribution, ketced originally by Keyne (1930; ee alo 1936,.vii), wa develoed later a te Keyneian teory of ditribution (Kaldor, 1956; Painetti, 196; Robinon, 196, Marglin, 1984). Te teory reume not only full emloyment, but alo forced aving by te worker even in a ituation of full emloyment. On te oter and, if ti latter aumtion i abandoned, te oibility of

4 a rofit queee, rater tan forced aving by te worker, a to accommodated in te analyi. n ti cae te money wage rate would rie fater tan te rice level, and te are of rofit would fall rater tan rie in reone to exce demand in te roduct market. Tu, a more general verion of te dynamic adjutment equation for te Keyneian teory of ditribution migt be written a, (8) d/dt= β [ (,) - ], were te eed of adjutment β >0 in cae of forced aving by te worker, but β <0 in cae of rofit queee. Note te central difference between adjutment equation (7) and (8).n te former, te rofit margin a well a rofit are are given wic make te real wage inflexible o tat te entire burden of adjutment fall on caacity utiliation (Kalecki, 1971). n te latter cae, te margin i flexible but caacity utiliation i fixed by aumtion, making adjutment work excluively troug te real wage rate, i.e. income ditribution. Conequently in a more general cae in wic neiter te rofit margin and are () nor te degree of caacity utiliation() i treated a exogenou, and bot are endogenou variable reacting imultaneouly to an exce demand or uly in te roduct market, we ave a couled dynamical ytem coniting of (7) and (8). Te roduct market clearing, equilibrium at of te ytem deicted by te -curve wit it loe given in (3) till remain te ame. However, te tability roerty of ti two variable dynamical ytem need no longer correond to te one- variable tability condition (4) of te uual Keyneian ytem. Moreover, ince bot and are aumed to be endogenou, a oitive relation between and lacing te economy on te rofit- led exilarationit at mut old, if bot and β are oitive. Ti mean tat forced aving by te worker necearily imlie tat te economy i necearily on an exilarationit at, wen bot and are endogenou. Obverely, wit >0, but β<0 in te rofit queee cae te economy i necearily laced on a wage-led 3

5 tagnationit at. Ti can een eaily from dividing (7) by (8) to obtain te integral curve determining te ign of te loe of te locu a, (9) d /d= / β, were >0 but β can be oitive or negative.. Te tability of te dynamical ytem (7) and (8) may be examined by conidering te function, (10) 1 V() t = [ (, ) ] Te function V i a Liaunov function wit all te deirable roertie for tability in te large, i.e. oitive definitene and unboundne a (-) tend to infinity, rovided alo dv/dt <0 (e.g. Laalle and Lefcet, 1961; Minorky, 196; Gondolfo,1995),. Ti lat condition can be cecked by differentiating (1) and () wit reect to time, and ubtituting from (7) and (8) to obtain, dv dt (11) [ ] β ( ) ( ) = < 0 Terefore, global tability require, (1) ( ) < ( ) β. Uing (3) and (1), a comlete claification of te variou cae of rofit-led or exilarationit a well a wage-led or tagnationit ub-regime according to teir tability roerty become oible. Note owever tat ti claification i done in two ucceive te to igligt te difference between a ingle endogenou variable tability analyi given by condition (3) to (6), and te tability analyi in te cae of 4

6 te dynamical ytem (7) to (9) wen bot te variable, and are endogenou.claification ( > 0; β 0) Cae ign of d / d from (3) Nature of Regime tability Proerty from (11) for β > 0 for β < 0 A.1 ( ) > 0 and ( ) > 0 A. ( ) > 0 and ( ) < 0 B.1 ( ) < 0 and ( ) > 0 B. ( ) < 0 and ( ) < 0 Poitive Profit-led tability ambiguou, and more likely te larger i β Negative Wage-led Unambiguouly table, but not oible from (9),ince and are endogenou. Negative Wage-led Unambiguouly untable, but not oible from (9),ince and are endogenou. Poitive Profit-led tability ambiguou, and le likely te larger i ( β ).. Unambiguouly table, but not oible from (9),ince and are endogenou tability ambiguou; more likely to be table larger β tability ambiguou. tability le likely, te larger β Unambiguouly untable, but not oible from (9),ince and are endogenou. 5

7 n te cae of te general dynamical ytem wit bot variable endogenou, it emerge a a general reult tat te tability of te neiter te rofit-led nor te wageled at of exanion i unambiguouly table. Te tability deend critically on te relative magnitude of te eed of adjutment, i.e. te abolute value of te ratio ( / β). Tu, wen β>o i.e. te cae of forced aving by te worker, only te rofitled at i relevant, and te uual one variable Keyneian tability condition (4) may or may not matter in determining te tability of ti rofit- led regime deending on te ratio of te relative eed of adjutment. Te iger (lower) i te ratio, imlying fater (lower) eed of adjutment of caacity utiliation relative to tat of income ditribution, te more (le) likely i te tability of te rofit led regime, deending on weter te enitivity of aving i more (le) tan tat of invetment to cange in income (i.e.condition 4 atified or not). n a imilar manner, in te cae of rofit queee i.e.β < 0, leading to wage- led exanion, again te Keyneian tability condition may or not be relevant deending on te (abolute) value of te relative eed of adjutment. t follow te Keyneian tability condition i neiter neceary nor ufficient witout conidering imultaneouly te relative eed of adjutment of caacity utiliation and, of income ditribution. Te critical role layed by te relative eed of adjutment oint toward an intereting oibility of extending ti analyi. t i often argued tat Keyneian analyi neglect te uly ide. One way of reckoning wit te uly ide would be to incororate into te analyi te fact tat te eed of adjutment of caacity utiliation tend to decreae a te degree of utiliation increae, and variou bottleneck begin to aear on te uly ide. Ti mean can be treated a a decreaing function of to incororate artly conideration on te uly ide. Ti 6

8 would lead non-linearitie wic we ave avoided dealing wit in ti aer, and mut remain a matter of future reearc. AMT BHADUR Deartment of Economic Univerity of Pavia, taly abaduri40@otmail.com 7

9 Reference Baduri, A. and Marglin, Unemloyment and te real wage: te economic bai for eonteting olitical ideologie, Cambridge Journal of Economic, 14: Kaldor, N Alternative teorie of ditribution, Review of Economic tudie, 3: Kalecki, M elected Eay in te Dynamic of te Caitalit Economy, Cambridge, Cambridge Univerity Pre. Keyne, J. M Te General Teory of Emloyment, nteret and Money, London, Macmillan. Marglin,. A Growt, Ditribution and Price, Cambridge, Ma; Harvard Univerity Pre. Painetti, L. L Te rate of rofit and income ditribution in relation to te rate of economic growt, Review of Economic tudie, 9:

10 Te Profit queee Cae (Aendix) ( ) [ ] =, ; ( ) [ ] =, () ( ) 1 t V = dt dv ( )[ ] + = ( )( ) ( ) [ ] + = ( )( ) ( ) [ ] ( ) ( ) { } + = ( ) ( ) ( ) [ ] 0 < + = For 0 < dt dv ( ) ( ) 0 < + ( ) ( ) < or ( ) ( ) < (11A) i.e. intead of (11) ( ) ( ) > ; 0 > = β. Cae A.1 H..>0; R.H..<0 unambiguouly table A. H..>0; R.H..>0 tability ambiguou; larger more likely tability B.1 H..<0; R.H..<0 tability ambiguou, larger tability le likely B. H..<0; R.H..>0 unambiguouly untable 9