Keynes Business Cycle Theory: A New Formulation *

Transcription

1 eyne Buine Cycle Theory: A New Formulaion Jumpei Tanaka The Univeriy of iakyuyu Abrac The purpoe of hi paper i o formulae eyne view regarding he buine cycle by uing a imple macro-dynamic model baed on he ineremporal opimizaion behavior of firm invemen deciion under oupu conrained according o demand. We demonrae ha under cerain aumpion regarding a firm expecaion modificaion behavior eyne inigh wih repec o he buine cycle may be properly formulaed, i.e., he heory ha economic flucuaion are caued by opimiic oar in he marginal efficiency of capial and heir ineviable collape. We alo how ha he long-run eady ae of our model when he labor marke clear baically correpond o he eady ae of he andard neoclaical growh model, bu ha inroducing wage flexibiliy ino our model deabilize he economy by worening unemploymen. JEL Claificaion:D50, D90, E12, E30 eyword:eyneian Economic, Buine Cycle, Wage Flexibiliy, Ineremporal Opimizaion of Invemen Deciion I hank he many paricipan a he workhop a obe Univeriy and he Japanee Sociey for Po eyneian Economic for helpful commen. Of coure, any error remaining are my own. j-anaka@kiakyu-u.ac.jp 1

2 1. Inroducion The objecive of hi paper i o formulae he heory of he buine cycle ha wa propoed by eyne in The General Theory [eyne (1936)]. In Chaper 22 of The General Theory ( Noe on he Trade Cycle ) eyne ummarize hi own view regarding he phenomenon of he buine cycle a follow: 1 The mo imporan facor ha generae he buine cycle i flucuaion in he marginal efficiency of capial. 2 A boom i mainly caued by exceive invemen driven by an opimiic oar in he marginal efficiency of capial. Here, exceive invemen i inerpreed according o eyne own word a a ype of invemen ha i made in condiion which are unable and can no endure becaue i i promped by expecaion which are deined o diappoinmen. 3 The main reaon why he economy recover regularly from receion i ha capial ock over-accumulaed during a boom naurally depreciae and reurn o i normal level wihin everal year 1. Thi convincing view regarding he phenomenon of he buine cycle ill eem o be imporan 2. However, hi view of eyne ha no necearily been properly formulaed in he conex of po-eyneian buine cycle heorie. There are well-known claical model of eyneian buine cycle heory uch a he muliplier-acceleraor model of Samuelon (1939) and Hick (1950), an endogenou buine cycle model by aldor (1940), a non-linear acceleraor model by Goodwin (1951), a imple growh cycle model 1 eyne alo poined ou he exience of invenory co a a reaon for regular recoverie from receion. 2 For example, Yohikawa (1995) demonraed boh heoreically and empirically ha hi view i ill ufficienly convincing when aemping o underand he experience of he Japanee economy afer World WarⅡ. 2

3 by Goodwin (1967) 3, and o on. However, hee model may no be regarded a appropriaely formulaing eyne own viion, becaue ad-hoc hypohee regarding invemen deciion uch a he acceleraor principle or paricular invemen funcion are ued o formulae firm invemen behavior in hee model in pie of he fac ha eyne reed he forward-looking apec of firm invemen deciion and he role of long-erm expecaion 4 5.Similarly, here eem o be no reearch ha aemp o conruc a heory of buine cycle expreing eyne viion faihfully alo in o-called New eyneian economic repreened by Mankiw e al. (1991), becaue in hi line of udy i i hough ha economic flucuaion are mainly caued by change in nominal aggregae demand under he rigidiy of nominal wage and price, which i quie differen from eyne own view. In hi paper we herefore aemp o conruc a eyneian macro-dynamic model in which an opimiic oar in he marginal efficiency of capial and i ineviable collape generae he flucuaion of he economy. The main characeriic of our model are he following wo poin. Fir, our model i baed on andard dynamic invemen heory wih an invemen adjumen co. Thi i becaue he concep of he marginal efficiency of capial defined by eyne can 3 In Goodwin (1967) model, buine cycle are led by a cerain income diribuion rucure beween employee and capiali, o hi model hould baically be inerpreed a a kind of Marxian buine cycle heory. Bu hi model wa ubequenly exended o he eyneian framework where he oupu level i deermined by he principle of effecive demand by Wolfeer (1982), Aada (1984), and o on. 4 Thi hold rue for more ophiicaed Po eyneian macroeconomic model uch a Flachel e al. (1997), Chiarella e al. (2000) and Chiarella e al. (2005). 5 One excepion i Adachi (1982), who conruced, baed on Roe (1967) employmen cycle model, a macro-dynamic model where firm expeced growh rae play an imporan role. Thi model i cloer o eyne own view of he buine cycle relaive o oher Po-eyneian buine cycle model in ha firm long-erm expecaion are conidered more eriouly. However, he fac ha he formulaion of he expeced growh rae i raher ad-hoc i a weak poin of hi model. 3

4 be well formulaed uing hi framework a Nagaani (1981, Ch6) clearly demonraed. Second, in our model boh firm and houehold are aumed o behave under demand conrain. Such a non-walraian aumpion i indipenable when modeling an economy naurally, where he equilibrium oupu i deermined hrough he principle of effecive demand. By conrucing a model aifying uch properie, we demonrae he following poin. Fir, we how ha eyne inigh regarding he buine cycle can be properly modeled by auming ha a firm behavior obey a paricular expecaion correcion. In our model firm derive he opimal pah for invemen expendiure under ubjecive expecaion regarding preen and fuure oupu demand, and he invemen expendiure hu derived deermine he equilibrium level of oupu hrough he principle of effecive demand. In general however, here i no guaranee ha a firm ubjecive expecaion regarding oupu demand will coincide wih i realized value in equilibrium. In hi paper, we herefore aume ha firm correc heir expecaion in he direcion of he acual value when hee value are no equal in he eady ae 6. Under hi aumpion i i demonraed ha eyne view a aed above can be formulaed effecively. Secondly, we clarify he relaion beween he long-run eady ae of our model and he andard neoclaical growh model. In our model, he long-run eady ae i defined a a ae where real wage are flexibly adjued in order o clear he labor marke. We how ha he eady ae of our model baically coincide wih ha of he neoclaical growh model if acual wage are given by he level a which he labor marke clear. However, hi doe no mean ha our model i a mere pecial cae of he 6 In oher word, i i aumed ha while he economy ay in a raniion proce, firm do no modify heir expecaion even if hey are no equal o heir acual value. 4

5 neoclaical growh model, for we can demonrae ha inroducing wage flexibiliy deabilize he economy by enlarging he gap beween upply and demand in he labor marke. Thi mean ha wage flexibiliy deabilize he economy a wa reed by eyne himelf in Chaper 19 of The General Theory. The remainder of hi paper i organized a follow. In he nex ecion we model he invemen problem faced by firm and examine he properie of opimal invemen plan. In ecion 3 we inveigae he hor-run macro-behavior of he economy, and in ecion 4 we formulae eyne heory of he buine cycle a a deviaion from he medium-run eady ae. In ecion 5 we inroduce wage flexibiliy ino he model and dicu he properie of he long-run eady ae. The paper i hen concluded in he ecion Firm invemen deciion Before conrucing a macro-dynamic model, in hi ecion we dicu firm invemen deciion 7. Conider an economy where only one ype of final produc which can be ued for boh conumpion and capial formaion i creaed. We aume ha here are many homogeneou firm in he producion ecor and normalize heir number o one wihou lo of generaliy. I i alo aumed ha, ince he ize of each firm i ufficienly mall, he repreenaive firm doe no imagine ha i own invemen demand are capable of affecing he aggregae demand for he final produc. A ime he repreenaive firm face he following problem: r( ) (1) Max [ F(, L ) w L c( I )] e d 7 We mainly follow Nagaani (1981, Ch6) regarding he argumen in hi ecion. See alo Groman (1972) on he formulaion of firm invemen behavior. 5

6 .. d / d = I -δ ( :given), Y = F, L ) ( [, ] ) ( where i he capial inpu, L he labor inpu, F, L ) he producion funcion, ( w he real wage (meaured in erm of he final produc), I he invemen expendiure, c( I ) he invemen co funcion8, r he real inere rae (meaured in erm of he final produc), and δ he depreciaion rae. We aume ha he producion funcion F, L ) ( aifie he uual neoclaical properie and ha he invemen co funcion c ( I ) i ricly convex (i.e., boh c and c are ricly poiive) aking ino accoun he exience of he inernal invemen adjumen co. Problem (1) i an ineremporal opimizaion problem according o which he firm maximize he preen dicoun value of he ne cah flow ream, bu i differ from he andard eing in ha he firm in our model ha a ubjecive expecaion regarding preen and fuure oupu demand { Y } and aim o maximize he objecive funcion = under he demand conrain: Y = F, L ) for any 9. Thi conrain mean ha ( he firm produce a quaniy of he final produc which i equal o he effecive demand. Furhermore, in order o implify he analyi, we aume hroughou he paper ha boh { Y } and he exogenou ream of he real wage {w } are = = conan over ime: (2) Y =Y, w = w Under hee aumpion, he firm opimizaion problem can be rewrien a: 8 The invemen co include no only he paymen for he purchae of he final produc for invemen bu alo he inernal invemen adjumen co. 9 Noe ha he expeced demand i ubjecive o here i no guaranee ha he firm ubjecive expecaion regarding he oupu demand coincide exacly wih he value realized in macroeconomic equilibrium. Regarding he formulaion of he firm expecaion correcion behavior, ee ecion 4. 6

7 (3) Max r( ) [ Y wg(, Y ) c( I )] e d.. d / d = I -δ ( :given) where he funcion L G(, Y ) can be derived from he demand conrain Y = = F, L ) ( and aifie he following properie: (4) G <0, lim G =-, lim G =0, G >0, G >0, G >0, G <0. 0 The fir order condiion (FOC) of he problem (3) are (5) c ( I ) = q, dq / d = ( r + δ ) q wg (, Y ), + d / d = I -δ (wih he TVC) Y YY Y where q i he hadow price of capial and TVC mean he ranveraliy condiion. From hee FOC he dynamic yem of he opimal invemen plan choen by he firm can be derived a ( r + δ ) c ( I ) + wg (6) di / d = c ( I ) (, Y ), d / d = I -δ (wih he TVC). Figure 1 how a phae diagram of he yem (6). The figure clearly how ha hi yem ha a unique opimal invemen pah and ha hi pah aifie addle-poin abiliy. (Figure 1 around here: The opimal invemen pah) How can he marginal efficiency of capial (hereafer MEC), defined by eyne (1936) a he pecial dicoun rae which equae he preen dicoun value of he ne cah flow ream from an addiional invemen wih i invemen co, be formulaed wihin hi framework? I i well known ha in our framework he marginal benefi from new invemen i repreened by he hadow price of capial q in (5), becaue by inegraing he econd equaion in (5) he following can be derived: 7

8 (7) q = ( r+ δ )( ) [ wg ] e d = nc ( r+ δ )( ) e d where nc Y wg, Y ) c( I ) i he ne cah flow a ime. Thi q i known ( a Tobin marginal q, which can be inerpreed roughly a a firm ock price10. I can be verified ha he funcion q decreae wih he capial ock and he inere rae, and increae wih he ubjecive expeced demand and he real wage: (8) q = q (, r, Y, w) + + On he oher hand, ince he invemen co (or more preciely, he marginal co of he fir uni invemen) i given by c (0), he MEC a ime can be derived a he R pecial dicoun rae ( ) which aifie he following equaion (9): (9) c (0) = q (, R, Y, w) I can eaily be confirmed from (8) ha he MEC hu derived i increaing in Y and w and decreaing in (i.e., R ( Y, w, ) ). Therefore, according o our framework + + he iuaion in which he MEC i flucuaing i idenical o he iuaion in which exogenou variable uch a Y or w are changing11. Laly, he effec of change in exogenou variable on he firm opimal invemen plan are ummarized. An increae in he ubjecive demand expecaion Y hif he di / d =0 line in Figure 1 upward, cauing inananeou upward jump in he MEC q 10 Sricly peaking, he hadow price i no equal o he firm ock price in our framework. A Hayahi (1982) demonraed, hey become equal if and only if (i) he firm behave compeiively, and (ii) he invemen co funcion i linearly homogenou in I and. In our framework, neiher of hee condiion hold. 11 Naganai (1981) furher clarified he difference beween he chedule of he MEC (i.e., he relaionhip beween R and which aifie (9)) and he chedule of he marginal efficiency of invemen (i.e., he relaionhip beween r and I which aifie he fir equaion in (5)), and reed ha he chedule which deermine he curren rae of invemen i no he former bu he laer. 8

9 ( R ), he ock price ( q ) and he invemen level ( I ) a ime, and hen raie he capial ock in he eady ae. An increae in he real wage w alo hif he di / d =0 line upward and yield he ame change a an increae in Y. The reaon why an increae in w imulae capial accumulaion i ha uch a change lower he relaive price of capial and encourage facor ubiuion from labor o capial. Finally, an increae in he inere rae r hif he di / d =0 line downward, leading o an inananeou drop in ock price and in he invemen rae a ime, ubequenly reducing he capial ock in he eady ae. Thi i becaue an increae in he inere rae hrink he preen dicoun value of he ne cah flow ream and dicourage he firm invemen aciviy. 3. Shor-run macro-dynamic In hi ecion we conruc a eyneian macro-dynamic model and explore he properie of i hor-run behavior. Here, he erm eyneian mean ha he equilibrium oupu a any ime i deermined by he principle of effecive demand. The erm hor-run will be defined laer. Le u inveigae macroeconomic equilibrium. Regarding he behavior of he firm, we add he following wo aumpion. Fir, alhough he firm deermine he level of invemen ( I ) according o he opimizaion problem (3) in he previou ecion, we aume ha he firm acually finance I no from i reained earning bu inead from houehold aving hrough he exernal financial marke 12. Since he choice 12 In fac, if we ake he firm invemen problem (3) lierally, he invemen projec i financed only by he firm reained earning and herefore houehold do no need o ave. In uch a cae he equilibrium oupu canno be deermined hrough he principle of effecive demand. 9

10 beween inernal and exernal finance doe no have any impac on he invemen plan ielf in an economy wih perfec financial marke, hi aumpion eem juifiable. Second, he firm i aumed o diribue all ale o he houehold ecor in he form of eiher wage income wl or profi π Y wl 13. Thi implie ha he houehold ecor alway receive a oal income which i equal o he firm oupu level. Regarding he houehold ecor on he oher hand, i i aumed ha here are many homogenou houehold in he economy, and heir number i normalized o one a in he cae of he producion ecor. Thi repreenaive houehold i endowed wih conan uni of labor L a each momen in ime, bu we aume ha he houehold upplie labor a a level which i equal o he firm labor demand L due o he exience of he demand conrain. Since he houehold i alo an owner of he firm, i receive no only he wage income wl a ime a an employee, bu alo he firm profi π a a ockholder. Under hi eing he houehold receive a oal income equal o he firm oupu level, and he following hold a a conequence: (10) AS = Y where AS mean he aggregae producion level (or he aggregae upply level) of he final produc and Y i he oal income received by he houehold. For deciion regarding he houehold conumpion, we aume he following mo imple eyneian conumpion funcion: (11) C = cy ( 0 < c < 1) where c i he conan marginal (average) propeniy o conume. The reaon for avoiding opimizing he houehold conumpion deciion i merely becaue by doing 13 According o hi definiion of profi, he inernal adjumen co of invemen (given by c( I ) I ) i alo included a profi, alhough i hould acually be recognized a a co like he wage paymen wl. 10

11 o he model may be kep a concie a poible. I i well known ha uch a implificaion can be a eriou defec when analyzing macroeconomic policie implemened by he governmen (ee Luca (1976) regarding hi poin), bu ince in hi paper we do no conider policy iue, bu raher examine only he macro-dynamic behavior of he privae ecor, hi implificaion doe no eem o be a eriou problem. Under hee aumpion he produc marke equilibrium can be inveigaed. The aggregae upply ( AS ) of he produc i already given by (10). On he oher hand, ince he governmen and foreign ecor are negleced in our model, he aggregae demand ( AD ) of he produc i (12) AD =C + I = cy + I where he invemen demand I i derived from he firm invemen problem (3) in he previou ecion. Therefore, from (10) and (12) he equilibrium oupu Y a ime can be derived a follow: (13) Y = I / ( 1 c ) where i he marginal (average) propeniy o ave. Noe ha under he macroeconomic equilibrium derived in (13) he economy i generally in a ae of diequilibrium in he following wo ene: fir, he firm deermine he invemen level I according o he ubjecive demand expecaion Y, bu here i no guaranee ha under macroeconomic equilibrium he firm expecaion i conien wih i realizaion value Y. Second, under macroeconomic equilibrium he firm labor demand, which i expreed by G( Y, ), generally deviae from he poenial labor upply L of he houehold. In hi paper we define he hor-run a 11

12 he period during which uch diequilibrium remain. In oher word, he hor-run mean he iuaion in which he following wo properie are aified a he ame ime 14 : (Ⅰ)Even if he firm ubjecive demand expecaion i differen from i realizaion value, he firm doe no correc he expecaion. (Ⅱ)Even if he firm labor demand i no equal o he houehold poenial labor upply, he real wage i no adjued flexibly o clear he labor marke. In hi ecion, he hor-run macro-dynamic behavior of he economy i analyzed according o hi definiion of hor-run. Since in he hor-run boh he firm expecaion and he real wage remain fixed, he opimal invemen plan derived in (6) become equal o he acual invemen pah. So he hor-run macro-dynamic of he economy can be derived by ubiuing (13) ino (6): ( r + δ ) c ( Y ) + wg (14) dy / d = c ( Y ) (, Y ), d / d = Y -δ ( dy / d =0) ( r + δ ) c ( Y ) + wg (, Y ) =0, ( d / d =0) Y =δ / The phae diagram of hi yem i imilar o Figure 1 in he previou ecion, and accordingly here exi a unique hor-run equilibrium pah aifying addle-poin abiliy. Finally, he effec of change in exogenou variable on he hor-run macro-dynamic are ummarized. Fir, an increae in he ubjecive demand expecaion Y or he real wage w, which imulae he MEC, he ock price and he 14 Noe ha he concep hor-run ued in hi paper i no equivalen o he uual meaning of he erm. The concep of medium-run and long-run defined laer alo differ from heir uual meaning. 12

13 invemen level a hown in he previou ecion, hif he dy / d =0 line upward in he phae diagram and raie he equilibrium oupu and capial ock in he eady ae. Second, an increae in he inere rae ock price and he invemen level, hif he r 15, which dicourage he MEC, he dy / d =0 line downward and lower he equilibrium oupu and capial ock in he eady ae. Finally, an increae in he aving rae, which doe no have any direc impac on he firm invemen deciion hif boh he dy / d =0 and d / d =0 line downward. Such a change lower he equilibrium oupu in he eady ae by dicouraging he muliplier effec while keeping he eady-ae capial ock conan. 4. The buine cycle a a deviaion from he medium-run eady ae In hi ecion we focu on he medium-run behavior of he economy. In hi paper he medium-run i defined a he iuaion in which a firm demand expecaion coincide wih i realizaion value (in oher word, he expecaion i elf-fulfilling) hrough i expecaion modificaion behavior alhough diequilibrium ill remain in he labor marke. When he firm demand expecaion (Y ) differ from i realizaion value ( Y ) in he hor-run eady ae characerized by (14), he expecaion will coninue o be berayed permanenly. In uch a iuaion any firm which i no irraional will correc i miaken expecaion. In hi paper we adop he following aumpion regarding he 15 Noe ha in our macro-model he inere rae i an exogenou variable. Thi i becaue in he eyneian framework he inere rae i deermined by he money marke, which i omied in hi paper. In oher word, we implicily aume ha he equilibrium inere rae i deermined by he money marke, which i ouide our model and aken for graned by he firm. 13

14 firm expecaion reviion behavior: Aumpion: When he firm demand expecaion Y deviae from i realizaion value Y in he hor-run eady ae, he firm modifie he expecaion oward i realizaion value. In oher word, hi aumpion ae ha when he economy ay on he hor-run raniion proce he firm doe no modify i expecaion even if i i no equal o i realizaion value. The reaon for impoing hi aumpion i ha i eem more difficul o deermine an accurae expecaion regarding fuure ae in he proce of raniion han in eady ae, and ha in uch a iuaion he firm would no change i expecaion recklely. Thi aumpion may be unrealiic when we analyze he economy aying on a raniion proce for a fairly long period, bu when he cae in which he economy mainly ay in he neighborhood of a medium-run eady ae i analyzed, hi aumpion i no o unrealiic. In fac he iuaion conidered in hi ecion i one in which he economy baically ay in a medium-run eady ae, omeime deviaing from i for a while due o exogenou hock o he economy. When a firm revie i expecaion according o he aumpion above, doe an arbirarily choen expecaion ably converge o a elf-fulfilling one? From (14) he relaion beween he expecaion Y and i realizaion value Y in he hor-run eady ae i (15) ( r + δ ) c ( Y ) + wg ( Y / δ, Y ) =0. From (15) i can be verified ha dy / dy >0, and i can alo be demonraed ha he unique equilibrium oupu (or equivalenly, he unique elf-fulfilling expecaion) in he 14

15 medium-run eady ae can be calculaed a (16) m Y = wg c 1 r + δ (where G = G ( / δ,1) ). However, i i difficul o examine he abiliy of he expecaion modificaion proce wihou adding furher aumpion regarding he hape of he producion funcion and he invemen co funcion. A hi poin we herefore examine he abiliy of he expecaion modificaion proce by pecifying boh funcion a follow: α (17) F(, L ) = 1 α 2 L, c( I ) = I + ψi / 2 Under hi pecificaion equaion (15) can be rewrien a (18) Y = ) 1 α Θ ( 1+ ψy Y (where ( r + Θ = δ δ )(1 α ) wα 1 α ). Figure 2 depic he relaionhip aed in equaion (18). A i obviou from hi figure, he expecaion modificaion proce according o he above aumpion i globally able under he andard pecificaion of he funcional form in (17), o any hor-run eady ae converge o he unique medium-run eady ae even if he iniial ubjecive demand expecaion i choen arbirarily. (Figure 2 around here: Relaion beween Y and Y in he hor-run eady ae) Nex, le u examine he mechanim of buine cycle uing hi framework. Conider he iuaion in which he economy iniially ay in a medium-run eady ae ( E Y 0, ) in Figure 3 below) where he expecaion i elf-fulfilling bu ome 0 ( 0 exogenou hock caue he firm expecaion o deviae from elf-fulfillmen. How doe he economy repond o uch an exogenou hock? Figure 3 depic a erie of behavior enaced by he economy when he firm undergoing he hock adop a new expecaion 15

16 Y 1 which i larger han he elf-fulfilling expecaion ae. m Y in he medium-run eady (Figure 3: Buine cycle a a deviaion from he medium-run eady ae) Fir of all, when he firm adop he new expecaion, he dy / d =0 line in Figure 3 hif upward (change 1 in Figure 3), and he economy move from he iniial medium-run eady ae E o he new hor-run eady ae E ( Y, ). A i obviou from he argumen in he previou ecion, during hi proce he economy experience a boom when he MEC, he ock price, he invemen level and he equilibrium oupu inananeouly jump, and he equilibrium oupu and capial ock in he eady ae alo rie 16. However, he economy canno coninue o ay in E 1, becaue i can be confirmed from Figure 2 ha he firm expecaion Y exceed i realizaion value in E. 1 Y1 1 Accordingly, he firm correc he expecaion downward and adop a new expecaion, for example, Y 2 which i maller han Y 1. Thi change hif he dy / d =0 line downward (change 2 in Figure 3), and he economy move from E 1 o he nex hor-run eady ae E Y 2, ). During hi raniion he economy experience a 2 ( 2 lump when he MEC, he ock price, he invemen level and he equilibrium oupu inananeouly fall, and he equilibrium oupu and capial ock in he new eady ae alo decline relaive o hoe in E1 17. I can alo be een ha during hi proce he level of capial depreciaion ( δ ) exceed he poiive gro invemen level ( I ) and he level of capial ock decline coninuouly. Therefore, when he capial depreciaion rae become larger, he over-accumulaed capial induced by he 16 During hi proce he capial-oupu raio drop. 17 During hi proce he capial-oupu raio rie. 16

17 firm opimiic expecaion depreciae more rapidly, and a a reul he period of lump ha he economy experience become horer. In he cae where Y2 > Y m hold he firm mu ill revie i expecaion downward becaue i i ill higher han i realizaion value in he eady ae, and he economy will evenually converge o he iniial medium-run eady ae E 0. On he oher hand, if he firm modifie he expecaion o an exceively low level uch ha Y < Y m, he 2 exen of he downward hif of he dy / d =0 line become fairly large (change 3 in Figure 3), and he economy experience a more evere lump (i.e., a depreion ) E1 3 during he raniion from o E. Such a deep lump i alo ofen called a negaive bubble, becaue in uch a iuaion he firm revied expecaion i oo peimiic and i lower even han he elf-fulfilling expecaion in he iniial eady ae E 0, cauing an exceive drop in he ock price. However, he economy recover from hi evere lump ooner or laer, reurning o he iniial medium-run eady ae E 0, becaue he firm expecaion i lower han i realizaion value in E 3 and he firm accordingly revie he expecaion upward. I i clear ha he heory of he buine cycle formulaed in hi manner correpond exacly o he following view of eyne aed in Chaper 22 of The General Theory: 1 The mo imporan facor ha generae he buine cycle i flucuaion of he marginal efficiency of capial. 2 A boom i mainly caued by exceive invemen driven by an opimiic oar in he marginal efficiency of capial. Here, exceive invemen mean, in eyne own word, a ype of invemen ha i made in condiion which are unable and can no endure becaue i i promped by expecaion which are deined o 17

18 diappoinmen. 3 The main reaon why he economy recover regularly from receion i ha capial ock over-accumulaed during a boom naurally depreciae and reurn o i normal level wihin everal year. I i remarkable ha hi view of eyne regarding he buine cycle canno be formulaed if we aume he perfec foreigh of he firm. In fac, if uch an aumpion i impoed, he economy alway ay in he medium-run eady ae and a a conequence he buine cycle canno be decribed a being governed by opimiic and peimiic urge in expecaion. In hi ene our model i fundamenally differen from aemp uch a, for example, Farmer (1999), which aemp o formulae eyne animal piri uing he concep of unpo equilibria under he raional expecaion hypohei. Noice alo ha a buine cycle phenomenon heorized in hi manner can be inerpreed a a deviaion from he neoclaical (i.e., Walraian) equilibrium ae becaue i i formulaed under he aumpion of wage rigidiy 18. Such a view ha he acual buine cycle hould be inerpreed a a diequilibrium phenomenon wa hough o be more plauible and promiing by Solow (1988), who placed a doub on he viion of he real buine cycle heory according o which he flucuaion of he economy are mainly caued by ochaic echnological hock (ee for example Cooley (1995) for hi line of buine cycle reearch). Tobin (1993) alo uppored hi ype of view regarding he buine cycle. Our formulaion of he buine cycle phenomenon can hu be regarded a an aemp along he line uggeed by Solow and Tobin. 18 In fac i will be demonraed in he nex ecion ha if he real wage i given by he level a which he labor marke clear he eady ae, hen our model correpond exacly o ha of he andard neoclaical growh model. 18

19 Finally, we briefly menion he relaion beween our model and he exbook eyneian income-expendiure model. Our model can be regarded a a direc exenion of he exbook eyneian income-expendiure model in ha firm dynamic invemen deciion are explicily inroduced in our framework. By exending he exbook model in uch a way we can obain he new implicaion regarding he effec of macroeconomic policy. In he exbook model an increae in invemen alway raie he equilibrium oupu, which implie ha during a receion he governmen hould encourage he invemen aciviy even if he rue rae of reurn from he invemen projec i low. In our model, however, uch a policy implicaion canno be juified, becaue even if he governmen imulae he economy by inducing exce invemen which rae of reurn are low uch a emporary boom doe no coninue and he economy afer all reurn o he iniial medium-run eady ae. Thi reul reveal ha a macroeconomic policy during a lump ha encourage bad invemen projec by eaily imulaing firm fuure expecaion doe no necearily conribue o an improvemen of economic welfare even from he purely eyneian poin of view. 5. Wage flexibiliy and he properie of he long-run eady ae Thi ecion inveigae he properie of he long-run eady ae. Here, he erm long-run i defined a he iuaion in which he firm expecaion i elf-fulfilling and in addiion, he labor marke clear. The long-run eady ae i herefore equivalen o he medium-run eady ae when he labor marke clear. m The firm labor demand in he medium-run eady ae ( L ) i derived a m (19) L = G( m, Y m ) m m = G( Y / δ, Y ) (by he relaion m m = in (14)) Y /δ 19

20 =Y m G (by linear homogeneiy of he funcion G ) where m i he capial ock in he medium-run eady ae and G G ( / δ,1) i a conan. Since he labor wih which he houehold i endowed a any ime i aumed o be L, he following equaliy mu be aified in he long-run eady ae. (20) L m = L From hi, he equilibrium oupu in he long-run eady ae ( Y l ) can be obained a (21) l Y = L / G. Inereingly, i can eaily be hown ha l Y derived in hi manner i exacly equal o he equilibrium oupu in he eady ae of he following andard neoclaical growh model (he Solow-Swan ype growh model): (22) d / d = F (, L ) δ Thi reul mean ha he long-run eady ae in our model i baically idenical o he eady ae of he Solow-Swan neoclaical growh model wih he ame economic rucure (he producion funcion, he labor endowmen, he aving rae and he capial depreciaion rae) 19. The hor-run and medium-run macroeconomic behavior dicued in he previou ecion can hu be inerpreed a deviaion from neoclaical marke-clearing equilibrium due o real wage rigidiy. Nex, he repone of he economy in he medium-run eady ae when he real wage i differen from he equilibrium real wage i examined. In order o conider hi queion, he uual wage adjumen rule according o which he real wage increae (rep. decreae) when here i an exce demand (rep. exce upply) in he labor 19 Noe however, ha he equilibrium real wage in he long-run eady ae of our model i no equal o ha in he eady ae of he neoclaical growh model which i deermined by he marginal produc of labor. The long-run eady ae of our model i herefore no perfecly idenical o ha of he neoclaical growh model. 20

21 marke i aumed. Doe he economy hen converge ably o he long-run eady ae? The anwer o hi queion i no, becaue from (16) and (19) he following can be hown: (23) L m w GG = >0 ( r + δ ) c Thi reveal ha when he real wage in he medium-run eady ae decreae, he firm labor demand alo fall. Thi i becaue in our model a lower real wage dicourage he firm incenive o accumulae more expenive capial, and herefore reduce he aggregae demand and he firm labor demand. A a conequence, if here i involunary unemploymen (i.e., a iuaion where L m < L ) in he medium-run eady ae, he exce upply in he labor marke furher lower he real wage, which furher woren unemploymen becaue he decline of he real wage reduce he firm labor demand. Thi reul mean ha inroducing real wage flexibiliy deabilize he economy 20. I can herefore be concluded ha alhough he long-run eady ae of our model i baically equal o ha of he neoclaical growh model, our model neverhele canno be regarded a a pecial cae of he neoclaical growh model becaue he effec of wage flexibiliy i fundamenally differen from he neoclaical model 21. Thi conequence of wage flexibiliy i omewha imilar o eyne view, a aed in Chaper 19 of The General Theory. I i well known ha eyne rongly criicized he 20 I i known ha omewha imilar reul alo hold in he non-walraian fixed price model developed by Clower (1965), Barro and Groman (1971), Malinvaud (1977), and o on. Since our model i in a ene a implified verion of hi non-walraian model, he ame concluion regarding he non-walraian model alo hold in our model. 21 A omewha imilar poin o hi ha been dicued alo in he conex of po-eyneian or po-aleckian economic. In hi conex he economy i called wage-led (rep. profi-led ) if rediribuion oward labor income (rep. capial income) imulae he equilibrium oupu. See Taylor (2004, Ch4) for hi argumen. 21

22 neoclaical view concerning he labor marke ha involunary unemploymen diappear ooner or laer hrough mooh wage adjumen, and ha he reed he poibiliy ha wage flexibiliy deabilize he economy. Noe however, ha eyne argumen differ from our in ha he conidered he flexibiliy of he money wage and alo in ha he hough wage flexibiliy deabilize he economy mainly becaue i end o renghen firm deflaionary expecaion. A a conequence, furher exenion of our model may be needed o appropriaely formulae eyne view concerning hi poin, bu our model can neverhele be regarded a being cloe o wha eyne mean o propoe, in ha he inigh ha wage flexibiliy canno olve involunary unemploymen and may even woren i i well repreened heoreically. 6. Concluion In hi paper we conruced a eyneian macro-dynamic model and mainly inveigaed he mechanim of buine cycle. Our model i radiional in ha he equilibrium oupu a any ime i deermined hrough he principle of effecive demand, bu he main difference from radiional eyneian buine cycle model i o explicily inroduce firm ineremporal invemen deciion under he demand conrain. Uing hi framework we demonraed ha eyne own view regarding he buine cycle aed in Chaper 22 of The General Theory can be properly formulaed under a cerain aumpion regarding firm expecaion modificaion behavior. I wa alo hown ha uch a buine cycle phenomenon can be regarded a a deviaion from he neoclaical (Walraian) equilibrium ae due o wage rigidiy, bu ha inroducing wage flexibiliy deabilize he economy becaue i enlarge he gap beween upply and demand in he labor marke. A far a we know hi i he fir explici model in 22

23 which eyne view regarding buine cycle and he conequence of wage flexibiliy have been formulaed yemaically in a unified heoreical framework. In hi paper we did no conider he opimizaion of houehold behavior for he ake of analyical impliciy. However, i i neceary o conider hi explicily in order o rigorouly inveigae he effec of houehold expecaion and governmenal macroeconomic policie on he behavior of macro-dynamic in our eyneian framework. Therefore, providing a more olid microeconomic foundaion for our model i one of he imporan focue of fuure reearch. Anoher problem which remain o be inveigaed furher i he refinemen of firm expecaion modificaion behavior. In our model, firm are aumed o revie heir ubjecive expecaion only in eady ae, bu hi aumpion i no necearily aifacory. I may be imporan o explore he impac of more ophiicaed expecaion modificaion behavior on he equilibrium of he economy and i abiliy. Reference in Englih Barro, R. and H. Groman (1971) A General Diequilibrium Model of Income and Employmen, American Economic Review, Vol.51, pp82-93 Beaudry, P. and F. Porier (2004) An Explanaion ino Pigou Theory of Cycle, Journal of Moneary Economic, Vol.51, pp Chiarella, C., Flachel, P. and R. Franke (2005) Foundaion for a Diequilibrium Theory of he Buine Cycle, Cambridge Univeriy Pre Chiarella, C. and P. Flachel (2000) The Dynamic of eyneian Moneary Growh, Cambridge Univeriy Pre 23

24 Clower, R. (1965) The eyneian Couner-Revoluion: A Theoreical Appraial, in F. Hahn and F. Brechling(ed.), The Theory of Inere Rae, London, Macmillan Farmer, R. (1999) The Macroeconomic of Self-Fulfilling Prophecie, MIT Pre Flachel, P., Franke, R. and W. Semmler (1997) Dynamic Macroeconomic, The MIT Pre Goodwin, R. (1951) The Nonlinear Acceleraor and he Perience of Buine Cycle, Economerica, Goodwin, R. (1967) A Growh Cycle, In Socialim, Capialim and Economic Growh, edied by C. H. Feinein, Cambridge Univeriy Pre Groman, H. (1972) A Choice-Theoreic Model of an Income-Invemen Acceleraor, American Economic Review, Vol.62(4), pp Hayahi, F. (1982) Tobin Marginal q and Average q: A Neoclaical Inerpreaion, Economerica, Vol.50, pp Hick, J.R. (1951) A Conribuion o he Theory of he Trade Cycle, Oxford Univeriy Pre aldor, N. (1940) A Model of he Trade Cycle, Economic Journal, Vol.50, pp78-92 eyne, J.M. (1936) The General Theory of Employmen, Inere Rae and Money, London, Macmillan Luca, R. (1976) Economeric Policy Evaluaion: A Criique, Journal of Moneary Economic, Supplemen, pp19-46 Mankiw, G and D. Romer (ed.) (1991) New eyneian Economic, The MIT Pre Malinvaud, E. (1977) The Theory of Unemploymen Reconidered, Oxford, Bail Blackwell Nagaani,. (1981) Macroeconomic Dynamic, Cambridge Univeriy Pre 24

25 Roe, H. (1967) On he Non-Linear Theory of he Employmen Cycle, Review of Economic Sudie, Vol.34 Samuelon, P.A. (1939) Ineracion beween he Muliplier Analyi and he Principle of Acceleraion, Review of Economic Sudie, Vol.21, pp75-78 Solow, R. (1988) Growh Theory and Afer, American Economic Review, Taylor, L. (2004) Reconrucing Macroeconomic, Harvard Univeriy Pre Tobin, J. (1993) Price Flexibiliy and Oupu Sabiliy: An Old eyneian View, Journal of Economic Perpecive, Vol.7(1), pp45-65 Yohikawa, H. (1995) Macroeconomic and he Japanee Economy, Oxford Univeriy Pre Wolfeer, E. (1982) Fical Policy and he Claical Growh Cycle, Journal of Economic, Vol.39, pp Reference in Japanee Adachi, H (1982) Theory of Economic Flucuaion, Nihon eizai Shinbunha Aada, T (1984) Moneary Sabilizaion Policie in a eyne-goodwin Growh Cycle Model, Hioubahi Rono, Vol.91(3) 25

26 I d / d =0 Saddle Pah di / d =0 (Figure 1) Y 45 degree line Y 1 m Y Y 1 Y 26

27 (Figure 2) Y d / d =0 E 1 Saddle Pah E 2 2 E 3 E dy / d =0 (Figure 3) 27