Discussion Papers in Economics

Transcription

1 Discussion Papers in Economics No 2/62 No 999/4 Dynamics of Oupu Growh, Consumpion and Physical Capial ulipliers in and Two-Secor Capial: Wha odels is he of role Endogenous of Imperfec Growh Compeiion? by Luis Farhad F Cosa Nili Deparmen of Economics and Relaed Sudies Universiy of York Heslingon York, YO 5DD

2 ULTIPLIERS AND CAPITAL: WHAT IS THE ROLE OF IPERFECT COPETITION? Luís F Cosa ABSTRACT In saic general equilibrium models considering imperfecly compeiive goods markes, he effeciveness of fiscal policy o sir oupu is shown o be greaer han in he walrasian case However, labour is he only inpu in hese models Here, I develop a simple ineremporal model allowing us o sudy he seady-sae role of opimal capial sock in he fiscal policy ransmission mechanism I demonsrae he resuls depend srongly on he se of parameer values chosen and on he oupu definiion Using plausible calibraions he muliplier is larger in he walrasian case for small iniial governmen purchases, and smaller for inermediae values JEL Classificaion: D5, E, E3, H6 Keywords: uliplier, Fiscal Policy, Imperfec Compeiion Deparmen of Economics and Relaed Sudies Universiy of York Heslingon York YO 5DD Unied Kingdom E-ail: lfpc@yorkacuk Insiuo Superior de Economia e Gesão Universidade Técnica de Lisboa Rua do Quelhas, 6 2 Lisboa Porugal E-ail: lukosa@isegulp hp://wwwisegulp/~lukosa/lcosa2hml Work in progress Commens and suggesions are welcome Revision: 22 June 999

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4 ULTIPLIERS AND CAPITAL: WHAT IS THE ROLE OF IPERFECT COPETITION? Luís F Cosa In saic general equilibrium models considering imperfecly compeiive goods markes, he effeciveness of fiscal policy o sir oupu is shown o be greaer han in he walrasian case However, labour he only inpu in hese models Here, I develop a simple ineremporal model allowing us o sudy he seady-sae role of opimal capial sock in he fiscal policy ransmission mechanism I demonsrae he resuls depend srongly on he se of parameer values chosen and on he oupu definiion Using plausible calibraions he muliplier is larger in he walrasian case for small iniial governmen purchases, and smaller for inermediae values INTRODUCTION IN STATIC GENERAL EQUILIBRIU ODELS considering imperfecly compeiive goods markes, he effeciveness of fiscal policy o sir oupu is shown o be greaer han in he walrasian case This line of research begins wih he seminal papers of Dixon (987), ankiw (988), and Sarz (989) (henceforh DS), and includes more recen aricles such as Dixon and Lawler (996) and Reinhorn (998) However, labour is considered o be he only inpu in hese models, ignoring he implicaions of he exisence of invesmen Here, I develop a simple ineremporal model allowing us o sudy he seady-sae role of opimal capial sock in he fiscal policy ransmission mechanism This can be seen as a dynamic exension of he models in he Blanchard and Kiyoaki (987) radiion In secion 2, he opimal ineremporal behaviour for agens is derived The microeconomic equaions are pu ogeher, he model is closed, and he long-run equilibrium is derived in Secion 3 In secion 4, I derive he saic fiscal oupu muliplier and analyse i under several assumpions abou he iniial seady sae Economic inerpreaion and comparison wih he DS framework are done in secion 5, using some numerical simulaions Secion 6 analyses he ne oupu muliplier Secion 7 concludes I demonsrae resuls depend srongly boh on he se of parameer values chosen and on he oupu definiion Using plausible calibraions he muliplier is larger in he I would like o hank Huw Dixon for all his commens, suggesions, and who encouraged me o ransform a simple noe ino his aricle I am also indebed o he paricipans a he Young Economiss eeing 999 in Amserdam, and a he 4h SPiE Conference in Évora for heir commens Fauls remain my own Financial suppor from NATO fellowship is graefully acknowledge

5 2 LUÍS F COSTA walrasian case for small iniial governmen purchases, and smaller for inermediae values 2 THE ODEL This model represens an arificial closed economy composed of hree groups of agens: one represenaive household, n Dixi and Sigliz (977) monopolisic producers, and he governmen I assume here is no uncerainy, agens are infiniely living, and money does no exis I use very sandard assumpions and specific funcional forms, so I will no be exhausive in he model descripion 2 The represenaive household This agen maximises an addiively separable ineremporal uiliy funcion, depending on an aggregae consumpion index and labour supply: C N () max β ξ C, N γ µ = L N γ µ O Q P, where C is he aggregae consumpion index, N he labour supply, <β< is he discoun facor, /(-γ) wih γ gives us he elasiciy of ineremporal subsiuion in consumpion (EIS C ), and /(µ-) wih µ gives us he elasiciy of ineremporal subsiuion in labour supply (EIS L ) The consumpion index is a CES funcion of he quaniies consumed for n goods, and here is no love for variey: σ (2) C n C σ, F = H G n j= j σ I KJ σ σ C j, is he consumpion of good j and σ> is he reciprocal of he elasiciy of subsiuion beween goods The appropriae cos-of-living index, P, is also a CES funcion of all he p j,, he individual prices, and i is normalised o uniy The budge consrain expressed in erms of aggregae consumpion good is given by: n (3) b + r g B + w N + π = B + pj, Cj, + T, where B is a governmen real bond designaed in aggregae consumpion held by he household a he end of period, r is he real ineres rae paid on bonds held unil he end of period, w is he real wage rae, π τ oal real profi income, and T is a real lump-sum ax For similar models in open economy see, iner alia, Cosa (998b) and Obsfeld and Rogoff (995) Behavioural equaions (consumpion Euler equaion, j= 2

6 ULTIPLIERS AND CAPITAL 3 demand for goods, and labour supply) are exacly he same as in he above-menioned aricles Since I am ineresed in he seady sae analysis, I presen hem in appendix A 22 Governmen Governmen purchases a baske of he n goods, represened by G, wih idenical preferences o he household Since he household is infiniely living ricardian equivalence holds, he only source o finance governmen spending is he lump-sum ax on he household, balancing he budge overime: G =T 23 Firms Firm j (j=,, n) maximises a sream of discouned cash flows: (4) max a π j, π = p q w N I qj,, N j,, Ij, =, j, j, j, j, j,, where π j, represens is cash flow, q j, is oupu, N j, is labour demand, and I j, is gross invesmen in he aggregae capial good I assume he echnology o produce he capial good uses no labour and i is idenical o he household s sub-uiliy funcion given by (2) The firm s discoun facor given by a = /( + r ) Firm j uses Πs= s ψ ψ j, = j, j, he following Cobb-Douglas echnology o produce is good: q A N K where A is oal facor produciviy, K j, is he capial sock owned by his firm a he end of period, and <ψ Capial is accumulaed according o: b g, where δ is a consan depreciaion rae K = δ K + I j, j, j, The number of firms, n, is assumed o be sufficienly big o avoid he exisence of Ford effecs as i happens in d'aspremon e al (989), Cosa (998a), and Cosa (998b) Therefore, he objecive demand funcion faced by his firm is given by:, σ j, j, (5) D = p Q n, n where Q =C +I +G is he aggregae demand, and I = Σ j= Ij, Assuming he equilibrium is symmeric, p j, =P =, and we obain a Lerner index given by m=/σ, represening he marke power of he individual firm Again, see appendix A for equaions giving us he supply of good j, and he demands for labour and invesmen, in is dynamic forms I also assume p j, is he opporuniy cos of no selling a uni of good j, herefore he aggregae price index for he capial sock is he same as he consumpion cos-of-living index, ie, is equal o uniy 3

7 4 LUÍS F COSTA 3 LONG-RUN GENERAL EQUILIBRIU To close he model, an aggregae oupu definiion is needed: n j, j, j= (6) Y = p q This definiion corresponds o gross oupu, ie, GDP In secion 6 his assumpion is relaxed I follows from (6) and from he marke clearing condiion in all markes, q j, =D j, for all j=,, n, ha aggregae demand equals aggregae oupu: Q =Y We n also need an aggregae capial sock definiion given by: K Σ K, 3 Seady sae = j= Assuming he economy can reach a zero-growh seady sae, he condiions defining i are given by he hree dynamic equaions in he model: he consumpion Euler equaion, he capial accumulaion equaion, and he opimal capialisic inensiy (k =K /N + ) Therefore, hese equaions can be wrien as follow, where variables wih aserisks represen heir seady-sae equilibrium values: (7) r = β ; β (8) I = δ K ; w (9) k = ψ ψ r + δ Equaion (7) represens he condiion equalising he real ineres rae o he household s discoun rae, imposing zero growh in consumpion The zero neinvesmen condiion necessary for a saionary capial sock is given by (8) Finally, he opimal inpu allocaion is represened by (9) Reducing he seady-sae sysem o hree equaions in Y (or Q ), C and I, we obain: j a2 = a () (a) Y = C + I + G, (b) Y a z C b2 = b, (c) I b z C, where z=/(-m) is an alernaive marke power measure, 2 a =+b <, b =-µ[ψ(µ )]<, a 2 =b 2 =-(-γ)/(µ )<, and a,b > are funcions of he fundamenal parameers 2 This measure is equal o he raio of price o he marginal cos 4

8 ULTIPLIERS AND CAPITAL 5 4 STATIC FISCAL ULTIPLIER The muliplier can be derived using a firs-order Taylor approximaion around he iniial seady sae Since here is no closed-form soluion o (), 3 he implici funcion heorem is used o derive he muliplier: h=+c G +I G, where X R =dx /dr, X=C, I, Y and R=G, z The reduced forms for hese expressions are given by: () (a) C = G s + F + γ µ e HG I K J <, (b) I G = s e >, s + e γ b g µ γ where e=c /Y (,] is he consumpion share, and s=e+i /G (,] is he privae expendiure share in aggregae demand Using hese resuls, he following reduced form for he muliplier is obained: (2) h = > s + e γ b g µ γ We can noice his muliplier is sricly posiive for finie values of EIS C Furhermore, i decreases wih boh shares e and s 4 The governmen shu-down fallacy Firs, le us assume G = (or s=) in he iniial seady sae Considering governmen expendiure is pure wase, his is he governmen expendiure level maximising household s uiliy 4 In his case, we may sae: PROPOSITION : If governmen expendiure is zero (governmen shu down) in he iniial seady sae, hen he saic fiscal muliplier is larger under perfec compeiion han in he monopolisic case PROOF: Firs, le us express consumpion share as a funcion of governmen purchases and he mark-up, e=e(g,z) I is easy o demonsrae ha (de/dz) s= =(- e)/z>, ie, he consumpion share in aggregae demand increases wih he mark-up Consequenly, a bias owards consumpion exiss in he monopolisic equilibrium (z>), when compared wih he walrasian case (z=), ie, e(,z)>e(,), for all z> Since s= in he iniial seady sae, we obain: 3 A closed-form soluion exiss in he special case where G = 4 For a recen aricle analysing he relaionship beween opimal fiscal policy and he muliplier, wihin he DS framework, see Reinhorn (998) 5

9 6 LUÍS F COSTA γ γ h z = > h z > e, µ γ e, z µ γ b gb g b gb g, provided EIS C and EIS L are finie QED This resul conradics he findings of he DS aricles, and also oher models considering labour o be he only inpu used in producion as i happens in Cosa (998a) and Cosa (998b), iner alia Thus, is he absence of capial in he producion funcion a necessary condiion o observe a larger fiscal muliplier under imperfec compeiion han in he walrasian case? 42 The general case In general, we canno ignore he role of he governmen share in aggregae demand (-s), in he muliplier Therefore, imperfec compeiion affecs he muliplier o he exen i affecs e(g,z) and -s(g,z) Considering Y z, I z and C z (under cerain condiions) are negaive, ie, he oupu, invesmen and consumpion levels decrease wih he mark-up, 5 i is easy o see ha: db sg = b sg Y > dz Yz Hence, if we could prove de/dz> holds for all s [,), he muliplier would be sricly decreasing in he mark-up However, a higher monopoly degree reduces boh consumpion and oupu, and he way i affecs he consumpion share depends on he relaive weigh of hese wo changes: de dz ehx =, x = s e ψ µ γ s µ ψ + ψ ψ z b γg b g b g b g b g When s=, i is easy o see ha x > However, for s (,), x implies G /I < [ψ(µ γ)]/[µ( ψ)+ψ] mus hold Since I canno guaranee his condiion holds even for plausible ses of parameers, furher invesigaion has o be done Considering de/dz does no have an unambiguous sign holding for all he range of he parameers, a simplifying assumpion as o be made Firs, le us wrie his expression as: de/dz=ec (C z -ey z ) ASSUPTION : There exiss a unique finie number G, such ha, for a given value for z and for G =G, de/dz=, ie, C z /Y z =e 5 See appendix B for reduced forms and necessary condiion 6

10 ULTIPLIERS AND CAPITAL 7 Hence, if assumpion holds, hen de/dz is posiive in he firs inerval 6 and negaive in he second When his analysis is ransposed o he muliplier iself, we noice ha: (3) dh dz L N b g O QP 2 µ γ de d s = h + γ dz dz Thus, hree cases have o be considered: Case I Case II Case III de dz de dz de dz dh > < ; dz de d s < < γ dz dz dh < dz µ γ b g ; de d s < > γ dz dz dh > dz µ γ b g For G [,G ), we are clearly in case I However, I canno demonsrae wha happens for G >G wihou furher informaion Thus, anoher assumpion is needed: ASSUPTION 2: There exis wo finie numbers, G A,G B and G A G B, such ha hey are he only exising feasible soluions for he equaion h/ z= If assumpion 2 holds, hree inervals for G ha generae differen signs for dh/dz can be found: (i) for G [,G A ), dh/dz is negaive since [,G ) [,G A ) and i is negaive in he firs of hese inervals; (ii) for G (G A,G B ), dh/dz is posiive; (iii) for G (G B,+ ), dh/dz is negaive In nex secion I ry o assess he how realisic he wo assumpions are and how imporan he swiching poins G A and G B can be o explain he role of imperfec compeiion in he muliplier mechanism 5 SIULATION AND INTERPRETATION 5 Simulaion Se A in Table I, a plausible se of parameer values, is used o generae numerical values for he muliplier and is componens The value for β yields a 5% per period discoun rae (and seady sae real ineres rae), γ implies EIS C =75, and σ deermines a Lerner index of 7 All hese values were aken from Suherland (996) The value for δ assumes a fory-period maximum lifeime for he capial 6 Remember I demonsraed i was posiive for s= 7

11 8 LUÍS F COSTA sock This value was aken from Hairaul and Porier (993) The value for ψ produces a 625% labour share in oal income, which is lower han he 7% proposed in Hairaul and Porier (993), bu is consisen wih mos values used in he real business cycles lieraure 7 The value for µ generaes EIS L =67< EIS C, which is generally acceped as a sylised fac The value for ξ gives rise o an employmen level equal o 33, given all he oher values and a governmen consumpion share equal o 2 This las value was aken from Baxer (995) [Inser Table I here] Funcions de/dz (lef-hand side) and dh/dz (righ-hand side) are ploed in Figure, using se A 8 For his simulaion G A corresponds o -s=22, and G B corresponds o -s=87 According o OECD ( ), he average share of governmen expendiure in goods and services in he GDP for he period , a proxy for -s, varied beween 98 (Japan) and 27 (Sweden), in a sample of 25 counries Given his fac, mos ineresing cases can be found wihin an inerval for wich G A sis, roughly, in he middle Hence, given he simulaions made, assumpions and 2 are likely o hold for plausible ses of parameer values [Inser Figure here] 52 Economic inerpreaion for he swiching poins 52 Very small values of G For G [,G ), case I is he relevan one Figure 2 illusraes he iniial general equilibrium for he special case G =, for which fiscal policy maximises household s welfare The household s maximisaion problem is presened he (N,C ) space (a), and U are he indifference curves, w he wage raes, BC he budge consrains, and refers o he monopolisic equilibrium and W o he walrasian one The figure in he (I,C ) space (b) represens he macroeconomic equilibrium for his special case where Y =C +I There are wo explanaions for he exisence of a bias owards consumpion in he monopolisic equilibrium (e >e W ), in his case: (i) due o he exisence of pure profis in he monopolisic case, ie, π > r K, he household has an exra source of permanen income and, consequenly, i can afford fuure consumpion wihou saving such a big proporion of is income; (ii) he oher effec comes from a lower 7 See, iner alia, Baxer (995), 58%, and Kydland and Presco (982), 64% 8 Similar picures were obained for oher plausible ses of parameer values 8

12 ULTIPLIERS AND CAPITAL 9 real wage under imperfec compeiion 9 ha makes labour cheaper relaively o capial, lowering he opimal capial level in he monopolisic case when compared wih he compeiive one Thus, he crowding-ou effec of public expendiure in consumpion is proporionally larger under imperfec compeiion, and he posiive effecs on oupu and invesmen are smaller [Inser Figure 2 here] 522 Small values for G For G (G,G A ), more governmen expendiure reduces e However, his change is very small and e is sill very high Also, -s, governmen s share in aggregae demand, is sill oo small o off-se he consumpion crowding ou effec Here, case II is he relevan one 523 Inermediae values for G Le Figure 3 be used o represen wha happens when G (G A,G B ) Here, -s is more imporan now Neverheless, consumpion crowding ou is sill he main mechanism o explain he differences in he mulipliers under differen mark-up levels We can see, on (b), ha e/s is now larger in he walrasian case, ie, OW is seeper han O Furhermore, due o efficien allocaion, -s is smaller in he walrasian case Thus, e=(se)/s is larger in he compeiive case Consequenly, given he bias owards invesmen in he monopolisic case, a permanen increase in lumpsum axes as a proporionally smaller negaive impac han in he walrasian case 2 This corresponds o case III [Inser Figure 3 here] 524 Large values for G For G >G B we are in case II again, bu for differen economic reasons Now, e is small, due o increasing shares of boh governmen consumpion and invesmen, 3 9 Inefficiency under imperfec compeiion implies a lower consumpion level, expanding labour supply, and a reducion in labour demand, when compared wih he walrasian case Remember he ineres rae was assumed o be fixed in order o have a zero growh seady sae Noice i is parial for finie elasiciies of ineremporal subsiuion, as we can see in () (a) 2 A similar consumpion-led mechanism, due o he exisence of disorionary axaion on labour income, can be observed in Torregrosa (998) There, despie he fac ha labour is he only inpu, he muliplier may be negaive 3 Privae expendiure may even be crowded in by governmen purchases because: 9

13 LUÍS F COSTA and hese las wo componens dominae wha happens o aggregae demand (and oupu) Considering exra unis of capial are used more efficienly in he compeiive case, he muliplier is larger here han under monopolisic compeiion Of course here is a value for G such ha N equals he ime endowmen, and no more capaciy can be added Bu even before ha poin, we expec he muliplier o decrease wih G, if consumpion of goods and leisure is so low ha he opimal response o higher axes is o reduce labour supply Considering he esimaes for G B already imply such a high value for -s, 4 we will concenrae in he range G [,G B ) 53 Comparing wih he DS framework As i can be seen in Dixon (987), referring o he DS framework: () he governmen expendiure muliplier is in a very precise sense «Walrasian» in his model By his we mean ha he mechanisms underlying he Walrasian muliplier are he same wih imperfec compeiion There will be crowding ou, and he muliplier has he Walrasian value as is lower bound, is sricly less han uniy, and sricly increasing in he degree of monopoly 5 The model here presened shares he crowding-ou feaure for consumpion, even if he same does no apply for invesmen The second characerisic, being less han uniy, does no hold in general, bu I expec i o hold for plausible calibraions 6 Finally, my invesigaion clearly conradics he possibiliy of exending he hird propery - a muliplier sricly increasing in he degree of monopoly - o a model where labour is no he sole inpu In order o evaluae how robus hese resuls are, numerical values for G A and G B were generaed, modifying he values for key parameers in he benchmark se (se A) The oucomes are shown in Table 2 [Inser Table 2 here] c h b g C + I G F HG EISC I = he γ, EIS C L I KJ and assuming EIS C >EIS L, I canno guaranee C >I, a sufficien condiion for crowding ou o exis For large values of I and small values of C, he expression may well be posiive Obviously, I do no advocae his o be a realisic assumpion 4 I was no able o generae values inferior o 8, for plausible feaures of he iniial seady sae 5 Op ci pp 35 6 For se A, -s=87 would be needed in order o generae a muliplier bigger han uniy

14 ULTIPLIERS AND CAPITAL The changes in γ were made o produce values for EIS C equal o (γ=), and 25 (γ=/5) When ψ=55 he labour share in oal income is 46, and for ψ=95 is equal o 79 The parameer σ deermines he mark-up level, z, equal o (σ=+, ie, perfec compeiion), or equal o 4 (σ=35) Finally, for µ=233 EIS L =EIS C =75, and for µ=22 EIS L =83>EIS C =75 We can noice all he values for G A generae governmen shares in aggregae demand (-s) very similar o hose observed in he OECD counries Only for ψ=55 he model generaes a value of G A low enough o generae a larger muliplier under imperfec compeiion for all he counries in he sample We can observe -s(g A ) is highly sensiive o changes in he parameers, especially γ, ψ and σ A larger value for one of hese parameers generaes a lower value for G A In he limi, he DS framework can be seen as a special case of his model where ψ=, ie, labour is he only inpu, and γ=, ie, presen and fuure consumpion are perfec subsiues Also, i seems plausible ha he efficiency gains from reducing he mark-up increase wih he degree of imperfec compeiion in he iniial seady sae 7 Apparenly, he elasiciy of ineremporal subsiuion in labour supply, and is relaionship wih is homologous in consumpion, does no play an essenial role deermining he posiion of G A Thus, a second se of parameers was used, se B in Table I, keeping he main feaures of he benchmark iniial seady sae The main differences are an elasiciy of ineremporal subsiuion in consumpion equal o uniy, a larger mark-up level (z=4), 8 and a slighly larger labour share in oal income (643) Se B, generaed - s(g A )=9, hence including all he counries in he 992 sample in he inerval (G A,G B ), compared wih only five counries meeing he same crierion in se A Finally, he proporional difference beween he monopolisic and he walrasian mulipliers, η(g,z)=h(g,z)/h(g,)- was ploed in Figure 4, using he wo ses Three main characerisics can be observed: (i) he smaller value of G for which η= (approximaely equal o G A ) is 6 imes larger for se A; (ii) he maximum value for he η() funcion is 34 bigger in se B; (iii) he value for η is always larger for se B Therefore, any conclusion drawn abou he imporance of imperfec compeiion for he long-run effeciveness of fiscal policy depends decisively upon he parameer values chosen for he arificial economy If we inend o simulae he feaures of a specific real economy, special aenion has o be paid o he esimaes for he elasiciy of ineremporal subsiuion in consumpion, labour elasiciy in he 7 A similar effec for he free-enry mulipliers was noiced in Cosa (998a) and Cosa (998b) 8 See Hairaul and Porier (993) for a discussion abou esimaes for z in he US economy

15 2 LUÍS F COSTA producion funcion (ie, z imes he labour share in oal income), he mark-up level in he economy, and he share of governmen purchases in aggregae demand Consequenly, he DS conclusion ha fiscal policy is more effecive on oupu under imperfec compeiion does no hold in general when he model is exended inroducing capial as an inpu 6 NET OUTPUT Le us use now a differen definiion for oupu, ne of capial depreciaion, insead of (6): 9 (4) y = Y δ K In his case, he seady-sae equilibrium is given by y =C +G The ne-oupu muliplier is hus given by: (5) h N dy = = + CG = dg µ + e γ N C >, en = y PROPOSITION 2: Under he normal assumpions, he ne oupu muliplier is sricly increasing in he monopoly degree PROOF: Firs, we know ha e N (G,z)=-G /y(g,z) For a given level of governmen consumpion G, e N varies wih he mark-up in he same direcion ha y does i Using he equilibrium equaion, we recognise ha y z =C z Thus, as long as C decreases wih he mark-up level, so does y and consequenly e N Since h N is sricly decreasing in e N for finie values of EIS C and EIS L, and e N is decreasing in z, he ne oupu muliplier increases wih z QED Hence, if we use his oupu definiion, our findings corroborae he DS conclusions abou he monooniciy of he muliplier 7 CONCLUSIONS In his aricle I presen a zero-growh seady-sae model for a closed economy, considering capial accumulaion This model can be considered as an ineremporally founded exension of he saic framework in he Dixon (987), ankiw (988), and Sarz (989) (DS) radiion 9 This definiion corresponds o NNP 2

16 ULTIPLIERS AND CAPITAL 3 The role of imperfec compeiion in he size of he saic fiscal (oupu) muliplier of governmen purchases was analysed The opimal fiscal policy, ie, he one ha maximises he represenaive household s uiliy, corresponds o zero governmen purchases In his case, i can be unambiguously shown ha imperfec compeiion produces a smaller muliplier since i inroduces a bias owards consumpion ha amplifies he crowding ou effec of governmen expendiure This is exacly he opposie o he DS conclusions However, I canno demonsrae his proposiion (or he opposie) holds in general For plausible parameer values I found wo swiching poins for he muliplier s derivaive wih respec o mark-up For small values of governmen consumpion he muliplier is larger in he walrasian case, and for inermediae values he opposie happens Consumpion crowding ou is he main mechanism explaining he differences For (implausibly) large values of governmen expendiure he walrasian case overakes he monopolisic one due o more efficien usage of invesmen Also, I showed he firs swiching poin is very sensiive o changes in he key parameers, namely labour elasiciy in he producion funcion, elasiciy of ineremporal subsiuion in consumpion, and he degree of marke power We concluded i is no possible o defend a priori neiher he DS resuls nor he opposie for his exended model Finally, i was demonsraed ha he muliplier is sricly increasing in he monopoly degree when we use ne insead of gross oupu In his case, he DS resuls hold Universiy of York and ISEG, Universidade Técnica de Lisboa APPENDIX A The behavioural equaions are: (A) C = β + r γ C b + L = N γ bg O Q P (A2) N C w ξ j, j, (A3) C = p (A4) G = T d i σ g C n µ 3

17 4 LUÍS F COSTA j, j, (A5) G = p d i σ G n (A6) k w ψ = r + δ ψ + j, w (A7) N j z A ψ i (A8) I = p ψ = L N O Q P K, j, c h σ j, i, i I n n σ i σ j, j, i= σ (A9) I n I = F H G (A) N = N n j, j= I KJ σ σ Equaion (A) is he consumpion Euler equaion, (A2) is he labour supply and (A3) is he household s demand for good j (A4) represens he governmen budge consrain and (A5) is demand for good j Equaion (A6) sands for firm j s he opimal capialisic inensiy, (A7) is demand for labour, (A8) is demand for good i, and (A9) is gross invesmen Equaion (A) is he marke demand for labour APPENDIX B The derivaives of consumpion, invesmen and oupu wih respec o he mark-up measure are given by he following expressions: hc Cz = µ s+ e ψ µ γ ψ z b g b g b g, which is negaive if oal consumpion share in aggregae demand, -s+e, is larger han ψµ/(µ ) This condiion held for all he simulaions made; hi Iz = µ e + ψ γ < γ b g b g ; L b g g N b g hc µ ψ + ψ Yz = 2 s e + e P < 2 γ ψ ez γ ψ b g O Q 4

18 ULTIPLIERS AND CAPITAL 5 REFERENCES Baxer, : "Inernaional Trade and Business Cycles," NBER Working Papers Series, 525 (995) Blanchard O J, and N Kiyoaki: "onopolisic Compeiion and he Effecs of Aggregae Demand," American Economic Review, 77 (987), Cosa, L: "Can Fiscal Policy Improve Welfare in a Small Open Economy?," ISEG/UTL Working Papers Dep Economia, 8/98 (998a) : "Produc Differeniaion, Fiscal Policy, and Free Enry," Universiy of York Discussion Papers in Economics, 98/2 (998b) d'aspremon C, R Sanos Ferreira, and L-A Gérard-Vare: "Unemploymen in a Courno Oligopoly odel wih Ford Effecs," Recherches Economiques de Louvain, 55 (989), 33-6 Dixi A, and J Sigliz: "onopolisic Compeiion and Opimum Produc Diversiy," American Economic Review, 67 (977), Dixon H: "A Simple odel of Imperfec Compeiion wih Walrasian Feaures," Oxford Economic Papers, 39 (987), 34-6 Dixon H, and P Lawler: "Imperfec Compeiion and he Fiscal uliplier," Scandinavian Journal of Economics, 98 (996), Hairaul J-O, and F Porier: "oney, New-Keynesian acroeconomics and he Business Cycle," European Economic Review, 37 (993), Kydland F, and E Presco: "Time o Build and Aggregae Flucuaions," Economerica, 6 (982), ankiw N G: "Imperfec Compeiion and he Keynesian Cross," Economic Leers, 26 (988), 7-4 Obsfeld, and K Rogoff: "Exchange Rae Dynamics Redux," Journal of Poliical Economy, 3 (995), OECD: Economic Surveys Paris: OECD,

19 6 LUÍS F COSTA Reinhorn L: "Imperfec Compeiion, he Keynesian Cross, and opimal fiscal policy," Economics Leers, 58 (998), Sarz R: "onopolisic Compeiion as a Foundaion for Keynesian acroeconomic odels," Quarerly Journal of Economics, 4 (989), Suherland A: "Financial arke Inegraion and acroeconomic Volailiy," Scandinavian Journal of Economics, 98 (996), Torregrosa R: "On he onooniciy of Balanced Budge uliplier under Imperfec Compeiion," Economics Leers, 59 (998),

20 TABLES TABLE I NUERICAL VALUES FOR THE PARAETERS Se β γ δ ψ µ σ ξ A n A /5 -/ B / TABLE II CHANGES IN THE PARAETER VALUES AND THE SWITCHING POINTS Se -s(g A,z) -s(g B,z) A γ /5 ψ σ + 35 µ

21 e z h z G G G A G 5 B 5 2 G -5 (a) (b) FIGURE - Consumpion Share, uliplier, and Imperfec Compeiion C C UW > U w > w W Y W U W U BC W Y π W BC W π W α Μ (a) N Y N (b) Y W I= δ K= S FIGURE 2 - General Equilibrium wih Governmen Shu Down

22 C C U w W W > U > w U W BC W G Y W W U G Y W π BC π W α Μ (a) N Y N (b) Y W I= δ K= S FIGURE 3 - General Equilibrium wih Inermediae Governmen Procuremen F HG η G, z I K J Se B Se A 5 5 G FIGURE 4 - Walrasian and onopolisic ulipliers for Two Parameer Ses