Discussion Papers in Economics

Transcription

1 Discussion Papers in Economics No. 2000/62 No. 998/20 Dynamics of Oupu Growh, Consumpion and Physical Capial Produc in wo-secor Differeniaion, Models Fiscal of Endogenous Policy, and Free Growh Enry by Luis Farhad F Cosa Nili Deparmen of Economics and Relaed Sudies Universiy of York Heslingon York, YO0 5DD

2 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY Luís F. Cosa ABSRAC Enry is recognized o be an imporan issue in macro models considering imperfecly compeiive markes. However, wo lines of research have been kep apar: he homogeneous-produc oligopoly approach, where enry means more firms in he indusry, and he monopolisic compeiion approach, where i means more brands. Our model ries o go beyond hese limiaions, considering a small open economy wihin a moneary union (characerised by a fixed exchange rae and perfec financial capial mobiliy). In his economy each indusry produces a differeniaed non-radable good and is composed several Courno compeiors. Compeiion works a boh he inraindusry and secor level. Decisions on boh axes and governmen expendiure are aken by he economy s governmen, i.e., fiscal policy is decenralised wihin he moneary union. Since he model generaes muliple equilibria, hree ypes of enry are considered: more firms (I), more indusries (II), and a combinaion of boh (III). Fiscal policy is shown o be effecive on aggregae oupu under he hree cases. Is effec on welfare is mainly walrasian in case II, bu i can be keynesian when marke power is high in cases I or III. JEL Classificaion: E32, E62, D43, F4, L3 Keywords: Produc Differeniaion, Fiscal Policy, Free Enry, Small Economy Deparmen of Economics and Relaed Sudies Universiy of York Heslingon York YO 5DD Unied Kingdom lfpc00@york.ac.uk Insiuo Superior de Economia e Gesão Universidade écnica de Lisboa Rua do Quelhas, Lisboa Porugal lukosa@iseg.ul.p Work in progress. Commens and suggesions are welcome. Revision: 25 June 998

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4 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY Luís F. Cosa In his aricle we exend he ineremporal general equilibrium wo-secor model for a small open economy, previously developed in Cosa (988). Produc differeniaion is inroduced in he non-radable good secor, where large firms compee over quaniies. he exchange rae is fixed and financial capial is perfecly mobile. We sudy he macroeconomic effecs of fiscal policy considering hree differen ypes of enry: new firms per indusry, new indusries, and a combinaion of boh. A welfare analysis is also produced.. IRODUCION ERY is recognised o be an imporan issue in macro models considering imperfecly compeiive markes. However, wo lines of research have been kep apar. he homogeneous-produc oligopoly approach, where enry means more firms in he indusry, can be found in Cosa (988), and in he Cournoian Monopolisic Compeiion model of Snower (983). he monopolisic compeiion approach, where i means more brands, can be found in monopolisic compeiion models like Blanchard and Kiyoaki (987), Dixon and Lawler (996), Dixon and Sanoni (995), Heijdra and van der Ploeg (996), Roemberg and Woodford (995), Sarz (989), and Weizman (982), and in he oligopoly wih differeniaed producs model of Pereo (996). For surveys see Dixon and Rankin (994) and Dixon (994). Our model ries o go beyond hese limiaions, considering a small open economy wihin a moneary union (characerised by a fixed exchange rae and perfec financial capial mobiliy). In his economy each indusry produces a differeniaed non-radable good and is composed several Courno compeiors. Compeiion works a boh he inra-indusry and secor level. he size of non-radable goods producers is assumed o be large also a he economy level and Ford effecs are considered as in d'aspremon e al. (989). In addiion, fiscal policy is decenralised wihin he moneary union, i.e., decisions on axes and governmen expendiure are aken a he economy s level, and labour markes are compeiive. Since he model generaes muliple equilibria, hree ypes of enry are considered: more firms (I), more indusries (II), and a combinaion of boh (III). In case I, we A NAO fellowship is graefully acknowledged. I would like o hank Huw Dixon, whose idea and challenge led o his aricle. I am also indebed o Karim Abadir, Giovanni Lombardo, Marcus Miller, Alan Suherland, Gabriel almain and Michael Wickens for heir simulaing and challenging commens, and o he paricipans a a seminar a he Universiy of Ken, a he Workshop on he EMU and he EU (Universiy of York), and a he Spring Meeing of Young Economiss (Humbold Universiy, Berlin), for heir commens and suggesions. Errors remain unerringly my own. he laer is closer o spaial models han o pure monopolisic compeiion ones.

5 2 LUÍS F. COSA sudy he effecs of fiscal policy when enry implies more firms per indusry and a consan number of indusries, as in he homogeneous-produc oligopoly approach. In case II, enry means a change in he number of non-radable goods, bu no in he number of firms per indusry, as in he monopolisic compeiion approach. Finally, in case III, we assume a special case of a simulaneous change of boh numbers. In secion 2, we derive he microeconomic foundaions of he model. In secion 3, we generae a benchmark iniial seady sae and we do a comparaive saics analysis of small deviaions in iniial condiions for he hree cases considered. In secion 4, we briefly sudy he shor-run feaures of he model. In secion 5, we invesigae he longrun effecs of eiher emporary and permanen fiscal shocks, under he hree ypes of enry. Finally, in secion 6, we assess fiscal policy hrough household s ineremporal uiliy. Fiscal policy is shown o be effecive on aggregae oupu under he hree cases. Is effec on welfare is mainly walrasian in case II, bu i can be keynesian when marke power is high in cases I or III. herefore, pure wase governmen spending can be used o increase households welfare when he economy is in one considerably inefficien seady sae and profis are likely o induce he enry of more firms in he exising nonradable goods indusries. 2. MICROECONOMIC FOUNDAIONS here are wo ypes of goods produced: a homogeneous radable and n brands of non-radable good. he economy is small, so ha he price of he radable good is se in he inernaional marke. Labour is he only inpu and is secor specific. We refer o each ype as radable and non-radable labour. Boh labour markes are compeiive. Governmen expendiure is pure wase, and is made in a baske of boh ypes of goods. Lump sum axes and seignorage are used o finance i. here is only an inernaional bond, he exchange rae follows a fla shock-free pah over ime, financial capial is perfecly mobile, and labour inernaionally immobile. 2.. Household behaviour he represenaive household maximises an addiive ineremporal uiliy funcion over an infinie lifeime horizon R bc g ξ µ µ χ F M max β. S. cn h + cn h +. G γ µ ε H P C, N, N, M/ P = 0 γ ε I U J V K W (.) where 0 < β < is he discoun facor, C is an aggregae consumpion index, N s he quaniy of ype e = ( radable ), ( non-radable ) labour supplied, and M /P he 2

6 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY 3 real money balances a he end of period. 2 Also we suppose ε > 0, γ 0, 3 χ, ξ 0, and µ >. he consumpion index, C, is Cobb-Douglas and homogenous of degree one (HoDO) C = C. C α c h c h α (2.) where C is he consumpion of radable good, and C is a CES baske of n nonradable goods consumpion, where here is no love for variey σ σ C = n dc i (3.) n L. M j, j = N σ O P Q σ σ c j, (j =,..., n) is he consumpion of ype j non-radable good, and he σ > is he reciprocal of he elasiciy of subsiuion 4. he budge consrain is given by b + i g. B + M + w. N + w. N + Π = = B + M + p. C + p. c + P. τ n j= j, j, h (4.) where i is he nominal ineres rae paid on bonds held unil he end of period, F he real domesic ne foreign asses holdings, M he money holdings, w e (e =, ) he wage raes for ype s labour, Π he profi income, p is he price of he radable good h in domesic currency, p j, (j =,..., n) is he price of ype j non-radable good, and τ a real lump-sum ax. he appropriae cos of living index, P, is given by n P = ι. p. p, p = L. p M, n α α σ j j = c h c h c h N O P Q σ a,b (5.) where ι = α α.( α) α and p is he appropriae non-radable good price index. he household opimal decision in erms of consumpion is made in hree sages. Firs, i decides he consumpion levels of aggregae consumpion good, leisure and real money balances. Second, i decides he opimal composiion of aggregae consumpion beween radable and non-radable good. Finally, i deermines he 2 All socks are measured a he end of he period denoed. 3 We exclude he range (0,] from he domain of γ. his implies an elasiciy of ineremporal subsiuion smaller or equal han one. Since empirical evidence suggess his elasiciy o be small, and numerical experimens for posiive values of γ do no generae significan differences, we use his simplified version. For more deails see Cosa (988). 4 We can see Cosa (988) as a special case of his model when σ =. 3

7 4 LUÍS F. COSA opimal composiion of he non-radable good index. he household is a price aker in labour and financial markes, and has no influence on he firm s decisions. We can summarise is behaviour wih he following se of equaions C + L N γ P = M. β. + i P. C P + O b g (6.) Q C F H p = α. G J. C P I K (7.) C F H p = a αf. G J. C (8.) P I K e µ e γ w (e =, ) N. C. P a,b (9.) ξ P = L N M O Q (j =,..., n) c M P j, = L M N ε γ i. C. P (0.) χ + i F pj, = H G I p J K σ C. n O Q (.) Equaion (6.) is he aggregae consumpion Euler equaion. Equaions (7.) and (8.) are he radable and non-radable good demands. (9.)represens he labour supplies. Equaion (0.) represens real money balances demand. Finally, (.) gives us he demand for each brand of non-radable good. Addiionally, we have o consider he ransversaliy condiion for non-human wealh he radable good secor he represenaive firm in his secor maximises he presen value of is real profis max a. q = 0 L M N p. q w. N P O P Q (2.) where a = / ( + r s = 0 s) for, and a 0 =, is he discoun facor, r = ( + i). P / P + is he real ineres rae, and q sands for he firm s oupu. We assume a Cobb-Douglas echnology q =. cn h φ (3.) 4

8 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY 5 where 0 < φ implies non-increasing reurns o scale. Considering he firm is a price aker in he radable good, radable labour, and financial markes, we have a saic opimisaion problem wih he following firs order condiions q N = L M N = L M N w O φ. P (4.) φ p Q φ w O φ. P (5.) φ p Q Equaion (4.) gives us he domesic supply for radable good. Equaion (5.) is he radable labour demand he governmen Governmen purchases boh ypes of goods wih he same preferences as he household. Is aggregae consumpion, G gives no uiliy o he household, and does no affec firms produciviy. Governmen expendiure is financed levying a real lump sum ax on he household, τ h, and a lump-sum corporae ax on each firm in he nonradable good secor, τ. Since we have m firms in each one of he n non-radable good indusries, oal real ax revenues are given by τ = τ h + m.n.τ. Also, seignorage is a source of income. Considering we have a represenaive infinie living household, ricardian equivalence holds in his model. herefore, here is no los in ignoring governmen borrowing. Also, we assume he governmen/cenral bank is responsible for keeping he exchange rae level, and commis iself o a ime-invarian ne foreign asses sock. hus, he budge consrain is G = τ + M /P, and demand funcions are similar o (7.) and (8.) he non-radable good secor In his secor, firms o m produce he brand, firms m+ o 2.m produce he brand 2 and so forh. Hence, firms (j-).m+ o j.m are he producers of good j (j =,..., n). Firm i j ={(j-).m+,..., j.m} 5 maximises is presen discouned value of real profis j =,..., n i j max a. qi, = 0 L M N p. q w. N j, i, i, P τ O P Q (6.) 5 We use j o represen non-radable good indusry j=,..., n. 5

9 6 LUÍS F. COSA where q i, is is oupu, and N i, is non-radable labour inpu. he firm is a price aker in he relevan labour marke. he lump-sum corporae ax is he source of a fixed cos as we can find eiher in Cosa (988) and Snower (983) 6. We assume he following echnology j =,..., n i j q =. N (7.) i, i, Firm i compees over quaniies assuming oher firms acions (producions), wihin he indusry, are given o iself. However, since each ype of non-radable good is an imperfec subsiue of he ohers, compeiion goes beyond he inra-indusry level and exiss a he iner-indusry level as well. We assume firm i akes prices in oher indusries as given. Consequenly, we presuppose a marke srucure ha does no correspond o he radiional Courno oligopoly. We will call i Cournoian Oligopolisic Compeiion. Each firm compees for he residual demand exising for is ype of good, a he indusry level, and, simulaneously, for he residual demand for all non-radable goods, a he secor level. If we consider he limi of his srucure when n ends o infiniy, we have Cournoian Monopolisic Compeiion, using he classificaion of he general equilibrium conceps under imperfec compeiion in d'aspremon e al. (997). In able we presen some special cases of marke srucures for he non-radable good secor, arising from he framework we described. Using our framework, he model shown in Cosa (988) can be viewed as a special case of he presen one when we consider n, he number of indusries in he secor, o be equal o one. In he same way, models considering monopolisic compeiion in he non-radable good secor can be considered a limi case of his model when m, he number of firms per indusry, is one and n is large. he walrasian case is also a limi case when we consider m o be large, whaever he number of indusries in he secor 7. [INSER able HERE] Looking a anoher dimension of he problem, he size of he non-radable good secor in he economy is an imporan issue o define firms behaviour. If -α, which is a measure of he secor s imporance in he economy, is significanly differen from zero, boh he aggregae consumpion and price index canno be seen as exogenous variables by he individual producer. As in Cosa (988), we follow d'aspremon e al. (989) when we assume here are Ford effecs on hese wo aggregae variables o be considered a he microeconomic level. Le us analyse he behaviour of firm i in 6 We discuss he reason for his choice in deail in he firs of hese papers. 7 In his case, we have o consider he fixed cos o be zero. 6

10 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY 7 indusry j. he objecive marke demand clearing he marke for non-radable good j, given equaions (8.), (.) and heir homologous for governmen, corresponds o he following pair of equaions j =,..., n i j q i, F σ pj, D p =. q D Q k,,.. H G I F I p J = α G J n P K k j \{} i a f a,b (8.) H K where Dj cj g, =, + j, is he oal demand for non-radable good of ype j, g j, is governmen demand for he same ype, D = C + G is oal demand for composie non-radable good, G is he governmen non-radable good consumpion index, and Q = C + G is oal domesic demand for aggregae consumpion good. We now assume a symmeric equilibrium o hold in each marke for a non-radable good ype. herefore, in marke j every firm mus produce he same quaniy and, consequenly, poss he same price q = q i h. Given idenical echnologies i, h,, and demands, i is easy o see symmery holds across non-radable goods markes as well. Firm i s maximisaion program is consiued by equaions (2.) and (3.), and heir corresponden definiions for governmen, giving us he Ford effecs via aggregae consumpion; (5.) which ake ino accoun he Ford effecs hrough he aggregae price level; (6.), defining he objecive funcion; (7.), he producion funcion; (8.)he marke demand for his ype of good; and he symmery condiions due o idenical preferences beween he household and governmen c / C = g / G and j j, j, C / C = G / G. Assuming he firm akes he real ineres rae as given, he ineremporal maximisaion problem coincides wih a saic one, and he corresponding firs order condiions under a symmeric equilibrium, are given by equaions (9.) and (20.). We supposed he pure non-co-operaive equilibrium o be he one o hold, since we face a muliple equilibria problem arising from he Folk heorem. he price seing condiion is given by j =,..., n i j p j, ηi, = + ν η i, i,. w. m = α + σ. w σ. m α (9.) where ν i, is he reciprocal of demand elasiciy faced by his firm. Likewise, η i, is he elasiciy giving us he proporional change in he aggregae price level when firm i increases is producion by one percen, assuming he oher firms o mainain he same producion level, i.e., ηi, = c P / qi, hc. qi, / P h. Under he symmeric equilibrium assumpion, ν i, = -/(σ.m) and η i, = -(-α)/(σ.m). Firs, we can easily see he limi of price-wage raio when σ ends o one, i.e., when non-radable goods end o be perfec subsiues, corresponds o he raio obained in Cosa (988). Second, since he price- 7

11 8 LUÍS F. COSA wage raio depends negaively on σ, for he same values of α and m, produc differeniaion reduces he marke power of he individual firm. he economic inuiion lies on he compeiion wih firms in oher indusries and no only wihin he same indusry 8. he oher firs order condiion gives us firm i s labour demand driven by he need o clear demand in is marke for he price i ses j =,..., n i j N =. q (20.) i, i, We assume he number of firms per indusry, m, and he number of indusries in he secor, n, canno change immediaely, due o he exisence of a one-period lag o seup or close down an exising firm. However, when we impose a zero profi condiion in he seady sae, we face anoher muliple equilibria problem. he parial equilibrium in he marke for good j implies a reduced form for firm i s real (saic) profis which is of ype π i, = c mnd,,, p, w, τ, α, σ h, and D = C + G. Firm i s profi funcion is decreasing on boh n and m, as we would expec. Given he values for he parameers and he exogenous variables, and for he same n, an increase in m decreases boh he marke power and, under a symmeric equilibrium, he average marke demand for his ype of good. We can observe his relaionship hrough he following parial derivaive α π i, aa. f gm a,. f =. m n m. a α + σ. m 2 2 f L α. a α. 2. σ. m M σ. m α N fo < P where a(.) = ι ( α)/α.p. D. w α /n > 0, g(m,.) is he price-wage raio and m 2. Considering he same m, an increase in n, under a symmeric equilibrium, decreases he average demand for each indusry and, herefore, he profis of each firm, as we can see using Q 0 π i, aa. f gm a,. f = 2. 2 n n m. gam,. f α < 0 Le us imagine we deparure from a zero profi siuaion. hen an unanicipaed shock his firm i, generaing posiive profis for he iniial values of n and m. he siuaion before he shock is represened by poin A in Fig.. Any poin on he BCD schedule is a zero profi equilibrium. We are going o consider hree cases: (i) in case I, 8 If we consider he Lerner index, µ L i,, as a more appropriae measure of marke power, we reach he same conclusion as we observe ha µ σ. m α L m α = < lim µ i = α σ α L i,, j =,..., n i j 8

12 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY 9 he number of indusries is fixed and enry means more firms in each indusry. his corresponds o he shif from A o D. Noice he model in Cosa (988) uses he expression free enry in his sense and for he special case when n = ; (ii) in case II, he number of firms per indusry is fixed and enry means more brands in he nonradable good secor. his corresponds o he shif from A o B. A model of monopolisic compeiion would be a special case when m = ; (iii) in case III, we assume n = k.m and, consequenly, enry means more firms per indusry and more indusries as well. Of course here would be much more cases o deal wih, including he consideraion of he limi case of monopoly, he upper limi for profis and represened by poin M, bu we hink hese hree cases are sufficien o give us an exensive cover of he mos ineresing cases occurring in real economies. [INSER Fig. HERE] Equilibrium in he non-radable labour marke is given by he marke clearing condiion equalising supply, which is described by (9.)b, and is demand given by N n j. m i j = i= aj f. m+ = N, (2.) 3. A BENCHMARK INIIAL SEADY SAE 3.. Finding a closed form soluion o he model A he macroeconomic level, we can define an aggregae oupu concep as Y n p P q j, =. + M. pp j = L NM F H G j. m qi, i= j. m+ a f IO K J QP (22.) We suppose he res of he world supplies or purchases any quaniy of he radable good a he curren price level. Ne expors, X, are he difference beween domesic supply and demand for he radable good X = q D, and an aggregae budge consrain for domesic agens, adding up individual consrains is given by C + G = Y + r. F F (23.) 9 where F =B /P represens real ne foreign asses held by he household. In he seady sae we rule ou unlimied Ponzi borrowing schemes considering he ineremporal budge consrain which follows from (23.) 9 For sake of simpliciy, we assume he represenaive household s share on foreign firms o be zero. 9

13 0 LUÍS F. COSA C + G = Y + r. F (24.) where variables wih aserisks represen heir seady sae equilibrium values. We assume he necessary condiion for a zero growh seady sae in a small open economy wih perfec capial mobiliy holds, i =r =( β)/β, where he ineres rae as o be equal o domesic household rae of ime preference. As in Obsfeld and Rogoff (995), Suherland (996), and Cosa (988), we assume G = F = 0, in order o obain a closed form soluion o he seady sae model. he corresponden seady sae pah will be our benchmark 0. When we consider eiher n o be exogenous or o be proporional o m, we can reduce he seady sae sysem o a wo-equaion sysem wih wo variables o be deermined, C and m, for convenience. In boh cases (I and III), we canno obain a closed form soluion for he whole sysem and, consequenly, we have o obain m hrough numerical mehods. When we consider m o be an exogenous variable (case II), we obain a closed form soluion for he reduced model deermining C and, in his case, n. For he benchmark seady sae we derive a soluion for C given m and n which, in any of he hree cases considered, will be deermined joinly by his equaion and he zero profi condiion. Seady sae real aggregae consumpion is hus given by C = L b NM a f g α f m. ξ. F H G αφ. ξ I K J α. φ O QP ρ (25.) where f(m) = (-α+σ.m)/[(-α).(σ.m-α)] and ρ = µ γ.[-α.( φ)] > 0. he aggregae consumpion (and oupu) level in his equilibrium is greaer han when we consider a single homogeneous non-radable good, given he same value for m. he reason lies on he effec of produc differeniaion on he marke power of he individual firm, reducing i and, herefore, reducing he imperfec compeiion inefficiency level in he economy. We can easily demonsrae ha considering C f m,. a α. C f = a f a ρ. f m,. f a < 0 and f m,. m = σ σ. m α f a f 2 < 0 Finally, using (25.) in he zero profi condiion 0 he balance budge consrain and our assumpion of an exogenous fiscal policy imply he posiive ax revenue from he non-radable good secor has o be offse by benefis graned o he household so ha n.m.τ = τ h. 0

14 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY j =,..., n i j π i γ µ µ ξ. C. an. mf. qi = 0 aσ. m αf = τ (26.) Le us compare he benchmark seady sae levels for some of he variables (e.g. aggregae consumpion) wih he one in Cosa (988). In ha case, we use he same se of parameer values, excep for σ, which has o be greaer han one wih produc differeniaion. he difference beween he wo siuaions lies in he value for f(.). Since C is decreasing in f(.), and f(.) is decreasing in σ.m, i is easy o see ha: (i) if σ < m H /m, where m H is he number of non-radable good firms considering a homogeneous non-radable good 2, he benchmark seady sae level for aggregae consumpion would be lower under imperfec subsiuabiliy; (ii) if σ = m H /m he benchmark seady sae level for aggregae consumpion would be he same in boh models; (iii) if σ > m H /m he benchmark seady sae level for aggregae consumpion would be higher under imperfec subsiuabiliy. Noice ha m H /m >, given he slope of he isoprofi schedule in he (m, n) space, and m can be endogenous (cases I and III) or exogenous (case II), in he model wih produc differeniaion. herefore, none of hese cases can be ruled ou a priori Comparing differen iniial seady saes he firs sep in he analysis of he general equilibrium in his economy consiss on a comparaive saics invesigaion of a log-linear version of he model. We look upon he effecs of slighly differen iniial condiions on he general equilibrium se. We use he values obained for he benchmark seady sae and he relevan behavioural equaions, o derive a log-linearised version of he sysem around ha paricular equilibrium poin. However, as we demonsraed before, general equilibrium depends on he assumpions we make abou enry in he non-radable good secor. herefore, we have o consider hree differen log-linearised models corresponding o he cases we proposed o sudy. Variables wih has represen is long-run percenage deviaion from he benchmark seady sae and can be defined as $ H = dh / H. An excepion has o be made for G $ and F $ because is equilibrium values in he benchmark seady sae were se o zero. herefore, we define is permanen log-deviaions wih respec o he consumpion of composie good $ G = dg / C and $ F = df / C. he sysem of equaions we obain is he following, assuming p$ = 0 Q = β F + Y β $. $ $ (27.) he value for q i can easily be obained using C. 2 he number is given by he limi of m when σ ends o uniy.

15 2 LUÍS F. COSA P$ = α.. Q $ +. C $ b. m$ aµ f a γ f 2 (28.) αµ. $ $ $ C = Q G (29.) b = d i case I R $. $ m Q n$ b. b 2. $ $ b b2 Sn Q. m$ = case II b k = case III k. b $. $ m Q 2 α αφ.. b $ $ Y =. Q + b. m$. P $ a γ f d 2 i µ µ φ µ. aµ φ 3. $ f C (30.) (3.) he values for he new parameers, considering m 2, are given by b = (σ.mα)/(2.σ.m- α), /3 b /2, b 2 = σ.m/[(σ.m- α).(+σ.m- α)], 0 < b 2, k = b /(+b ) and b 3 = µ.[ α.( φ)] ( α).φ > 0. We can compare hese parameers wih heir homologous from Cosa (988), for he same values of m and α, which are given by he limi when σ ends o uniy a = lim b > b σ and a = lim b < b 2 σ 2 2 (m = m H ) 3. o obain he previous seady-sae sysem, firs we subsiue all he indusry and secor variables, exceping m and n, leaving only he macroeconomic relevan variables. Equaion (27.) is he log-linear form of (24.). Equaion (28.), arises from (5.) and from he reduced form for p$. We obain (30.) using he zero profi condiion in (26.), and (3.) is he log-linear version of (22.). We use he following noaion for saic mulipliers σ H, h = H$ h $ G$ = 0 F$ = 0 H$, σ H, G F $ G R $ = = 0 n$ = 0 case I Sm$ = 0 case II n$ = m$ case III and σ H, F H $ G F $ = = 0 $ R n$ = 0 case I Sm$ = 0 case II n$ = m$ case III for h = n (case I), m (case II). able 2 show us he saic mulipliers for H = Y, C, m and P, and where v b. b case I R 2 = s S 0 case II k. b case III 2 and s b s g a f s case I = v. ρ α. v = ρ case II R S 3 case III [INSER able 2 HERE] 3 If we wan o generae benchmark iniial seady saes where he number of firms per indusry is he same, we have o allow for differen fixed coss. 2

16 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY 3 he deerminan of he sysem, s, is posiive, and i is easy o observe ha ρ > 3 > > = lim. 4 σ Case I: n is exogenous Here we consider enry affecs he number of firms per indusry, bu no he number of non-radable good indusries, which we assume o be exogenously deermined. his version of equaion (30.) deermines m $ given n $. Firs, le us sudy he effecs of considering a larger number of non-radable good ypes in he economy. he obvious effec of a greaer value for n is he consequen reducion in he value for m under a zero profi equilibrium. he saic muliplier is σ m,n = ρ.b / <0. he immediae consequence of he smaller m is a higher marke power for each firm. hus, he aggregae producion of (composie) non-radable good is smaller and is sold a a higher price, inducing a higher aggregae price index, i.e., σ P,n =( α).(µ γ.φ).b.b 2 /(µ. ) 0. Even considering effec on he radable good equilibrium producion is posiive, we obain a negaive effec on aggregae oupu and consumpion arising from he larger inefficiency level in he economy: σ Y,n =σ C,n = ( α).b.b 2 / 0. Second, le us now analyse he effec on he iniial seady sae values of marginally differen level of governmen expendiure. Considering anoher iniial seady sae where he non-radable good is homogeneous, i.e., σ ends o one, and he fixed cos, τ H, is such ha m H, he number of firms in he secor, is equal o m.σ, he values from he benchmark seady sae wih differeniaed producs. In his special case, he pricewage raio is he same in boh models and, consequenly, all variables presen he same iniial values. Furhermore, he parameer values in he log-linearised seady sae model are he same since a = b and a 2 = b 2. herefore, he model wih a single homogeneous non-radable good produces exacly he same oucome as he one we presen here. However, we also wan o compare he saic mulipliers in his model wih he one in Cosa (988) when he se of parameer values is he same, of course exceping σ and n. We know a smaller value for m is generaed, i.e., m<m H and σ>. Unforunaely, b and b 2 depend on σ.m which can be smaller, equal or greaer han m H. herefore, anyhing is possible in erms of ranking he saic mulipliers in boh 4 I is easy o demonsrae ha is greaer han, for m=m H, he deerminan of he sysem marix in Cosa (988). he main sep o consider is o recognise ha ( ) b. b m. 2. σ. m + α. ( α) 2 2 = 2 σ ( 2. σ. m α). ( α + σ. m) 2 2 < 0 and, herefore, b.b 2 < a.a 2. We showed in he above-menioned aricle i is impossible for o be non-posiive, given γ 0. 3

17 4 LUÍS F. COSA cases. A larger governmen expendiure level would have a posiive impac on he profis in he non-radable good secor and, herefore, would generae a larger iniial m. Considering he effec on aggregae consumpion is σ C,G = σ Y,G -, i is no possible o rule ou eiher crowding ou or crowding in of privae consumpion due o a larger iniial governmen consumpion level. Given he effec on oupu and marke power, and he paricular srucure of he labour marke, he negaive muliplier for aggregae prices is replicaed in his model. hird, we have o analyse he effec of a differen iniial endowmen of ne foreign asses. A posiive iniial level of ne foreign asses, of one per cen of aggregae consumpion, is an exra source of income for he household. herefore, considering he elasiciy of ineremporal subsiuion is less han uniy, he household is willing o supply less labour of boh ypes and aggregae oupu is lower. his is due o he effec on aggregae consumpion 5. A higher level of wealh induces a bigger consumpion level and, consequenly, a negaive effec on labour supplies. he effec on m and on he aggregae price index is posiive Case II: m is exogenous In his case we assume enry affecs he number of non-radable goods in he economy, and herefore he number of indusries in he Courno secor, bu no he number of firms exising in each indusry, which we assume o be deermined exogenously. he seady sae log-linearised sysem remains he same, bu equaion (30.) has now a differen inerpreaion, when we ake ino accoun n $ is he endogenous variable in he zero profi condiion and m $, enering (28.) as well, is no deermined in he sysem. Firs, le us sudy he effec of a larger m in he iniial seady sae. he consequence of his change in iniial condiions on n is given by σ n,m = [ρ.( b.b 2 )+α.b.b 2 ]/(ρ.b )<0. he saic muliplier is differen from -/b since m influences marke power and, herefore, price and oupu in he non-radable good secor. Given he lower marke power, aggregae oupu and consumpion are higher as he mulipliers show σ Y,m =σ C,m =( α).b 2 ]/ρ 0. he aggregae price index is lower due o he indirec effec hrough price-wage raio: σ P,m = ( α).(µ γ.φ).b 2 /(µ.ρ) 0. Second, we sudy he effecs of a differen iniial fiscal policy in he iniial seady sae. A higher value for G simulaes profis and, herefore, induces enry in he nonradable good secor. Enry means, in his case, a larger n: σ n,g =( γ).[ α.( 5 We expec his muliplier o be non-posiive for γ 0 and for a plausible se of values for he oher parameers. he relevan consrain implies ha he increase in he household s seady sae aggregae consumpion canno exceed he (new) real ineres income. Noice ha his resricion is somehow equivalen o impose a marginal propensiy o consume less or equal han uniy. For more deails, see Cosa (988). 4

18 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY 5 φ)]/ρ 0. However, since he price-wage raio is no affeced by changes in n, deviaions from he benchmark iniial seady sae aribuable o a disinc fiscal policy, are no affeced by produc differeniaion and is relevan saic mulipliers correspond o heir homologous in he homogeneous good model, when we rule ou enry. hird, a higher iniial level of ne foreign asses would induce more firms o be in he secor, which would mean more ypes of non-radable good: σ n,f =( β).(µ φ)]/(β.ρ) 0. Again, he oher saic mulipliers remain indifferen o he inroducion of non-radable good brands Case III: n/m is exogenous When we analyse he las of he hree cases considered, enry in he non-radable good secor means, simulaneously, a change in he number of firms per indusry and in he number of indusries. We assume boh numbers move ogeher according o a proporional relaion where n = k.m, k > 0. herefore, we add an exra independen equaion o he seady sae sysem, allowing us o deermine boh numbers as endogenous variables. his fac alers he form of equaion (30.) in he log-linearised sysem. Firs, when we consider he iniial seady sae changes arising from a differen iniial fiscal policy. he saic mulipliers are similar o hose presened in case I, even if hey show differen values. Noice, in his case, he enry incenive has o be shared beween firms and indusries. Second, a higher iniial level of ne foreign asses sill has posiive effecs on m, aggregae consumpion and prices. Again, he effec on aggregae oupu is negaive Comparing he hree cases Finally, le us compare he values for he saic mulipliers amongs he hree cases considered and wih he findings in Cosa (988). A differen iniial fiscal policy as differeniaed impacs on he key endogenous variables. Mulipliers are sored in able 3. We obain a clear paern for he effecs of a larger governmen expendiure on hese variables, where we can conclude he sensiiviy of hese saic mulipliers decreases when he imporance of he number of indusries in he free enry process increases (and he imporance of he number of firm per indusry decreases). he same paern is observed for he saic ne foreign asses mulipliers for he aggregae consumpion, aggregae price index and he number of firms per indusry. his also applies unambiguously o aggregae oupu. [INSER able 3 HERE] 5

19 6 LUÍS F. COSA 4. SHOR-RUN ANALYSIS If an unexpeced shock occurs, boh n and m remain unchanged during ha period, i.e., enry can only happen in he following one. Log-linearising he shor-run sysem around he benchmark seady sae pah we obain a se of equaions very similar o (27.) o (3.). Assuming boh he nominal ineres rae and he price of he radable good remain a heir benchmark seady-sae values, we obain F = F + Y Q β $. $ $ $ (32.) α αµ. aµ f a γ f (33.) P$.. Q $. C $ b. m$ = + 2 Q = G + C (34.) $ $ $ $ $ C C. P$ P$ + = + (35.) γ d i b = d i case I R m$. Q$ n$ b. b 2 b. b $ $ 2 Sn Q. m$ b = case II k = case III m$. $ k. b Q b $ $ Y = α αφ. Q + b. m$. P $ a γ f d 2 i µ µ φ µ. aµ φ 3. C $ f (36.) (37.) where variables wih has represen is shor-run percenage deviaion from he benchmark seady sae pah, and are defined as $ H = dh / H. Again, G $ and F $ are defined respecively as dg / C and df C. Equaion (32.) is he log-linear version / of (23.), and highlighs he fac ha F is an endogenous variable in he shor-run sysem. Equaion (34.) is idenical o (29.), bu defines Q, he domesic aggregae demand, insead of C, which is now given by (35.), he log-linear version of (6.), he Euler equaion. Equaions (33.) and (37.) are similar o (28.) and (3.). Finally, equaion (36.), reflecs he dynamic paern of enry. As in Cosa (988), Obsfeld and Rogoff (995) and Suherland (996), iner alia, he presence of a uni roo in his ype of models is ineviable. However, we resric our analysis o eiher unanicipaed oneperiod emporary or permanen fiscal shocks, i.e., log-deviaions from he benchmark seady sae pah for G are of ype G $ = for =, G $ = 0 for 2 and he shock is 6

20 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY 7 emporary (emp), and $ G =, for and he shock is permanen (Perm). Furhermore, $n = 0 in case I, $m = 0 in case II, and n$ = m$ in case III. Assuming he economy is on is benchmark seady sae in = 0, we can concenrae he dynamic feaures of he model in =, and a new seady sae is reached no laer han = 2. herefore, we can ignore ime subscrips for he shor-run variables. he soluion o ne foreign asses log-deviaion is given by $ F = F $ = Y $ C $ G $. We can compue a closed form soluion o his value, given our assumpions abou he shocks, equaions (27.) o (3.), (32.) o (37.), and he ransversaliy condiion for he household wealh F$ = R + R. G $ 0 (38.) where R 0 and R are boh non-negaive. We presen he expressions for hese parameers in Appendix A. he following feaures can be observed: (i) F $ Case II F $ Case III F $ Case I 0 for a emporary shock ( G $ = 0 ), (ii) F $ Case I F $ Case III F $ Case II = 0 for a permanen shock ( G $ = ), and, since R is nonnegaive, F $ Case I for a permanen shock is always greaer or equal han is value for a emporary shock. See Appendix B for proof. 5. LONG-RUN ANALYSIS 5.. A emporary fiscal shock From he soluion of he shor-run model we know an unexpeced one per cen increase in governmen consumpion generaes a permanen foreign deb siuaion, i.e., $ F = F$ = R0 0. Since we assume no furher shocks will happen in period = 2, he long-run effec on he endogenous variable H $ is due only o he surprise effec and, consequenly, we have $,. $ H =σ H F F. hus, a emporary posiive fiscal shock increases oupu, decreases consumpion and prices in period = 2, for he hree cases considered. When we allow m o change, he negaive wealh effec implies negaive profis in he Courno secor and he zero profi condiion induces a decrease in m and, as a resul, an increase in her marke power. he new long-run equilibrium is Pareodominaed by he iniial one A permanen fiscal shock A permanen fiscal shock has differeniaed effecs on he value of he sae variable, ne foreign asses, in he hree cases considered. In case II, R 0 = R and, herefore, $F = 0. Moreover, he macroeconomic variables jump o heir new long-run equilibrium in period =. 6 When we consider γ = 0, we also obain F $ = 0, in all he hree cases. 6 he non-radable good indusry variables are affeced in period = 2 by he new value of n. 7

21 8 LUÍS F. COSA he paricular value assumed for he elasiciy of ineremporal subsiuion (one) equals he elasiciy of inraemporal subsiuion beween radables and non-radables, which implies addiional effor in period =, in order o smooh he consumpion pah 7. he effec of a one per cen permanen increase in governmen consumpion on m is given by $. $ m = σ + σ F. However, since boh mulipliers are posiive, we face mg, mf, wo opposie effecs on m: (i) he permanen fiscal expansion has a direc effec increasing profis and inducing new firms o ener each marke, and (ii) he permanen reducion on he ne foreign asses level reduces profis and induces firms o leave. We can compue he reduced form for he seady-sae change in m = Rb s I $. $ m = us d C i where u s S0 s = II k s= III 3 Even if we canno demonsrae C $ > holds in general, we expec i o hold for plausible values of he parameers 8. hus, under his assumpion, fiscal policy has a posiive impac on m in cases I and III and, no impac in case II. Furhermore, i is clear-cu ha m$ Case I > m$ Case III > m$ Case II = 0. Now, i is easy o analyse he impac of fiscal policy on he oher variables since we can separae he effec of enry from he no-enry effec. herefore, he impac of a permanen fiscal shock on he aggregae oupu is given by $. $ Y = σ + σ F which is equivalen o Y, G Y, F γ. α. φ... z + β γ α φ φ α. $ ρ β ρ ρ a f a f a f $ a f s =. F +. m$ Y where z s = b 2 in cases I and III, and z s = 0 in case II. Since he firs erm in he righhand side of he equaion does no depend on he ype of enry considered, we can concenrae on he second and hird erms. hus, in case II, he effec of a permanen one per cen increase in governmen expendiure is given by he firs erm alone. he rank for he second erm is case I, case III and case II (zero), according o he order of he change in ne foreign asses. In cases I and III, (-α).b 2 /ρ is he same, bu more firms per indusry ener he non-radable goods markes in he firs one. herefore, we can conclude ha, given he assumpions made, $ $ $ Y Case I > Y Case III > Y Case II 0. 7 See Cosa (988) and Obsfeld and Rogoff (996) pp for more deails. 8 Numerical experimens, even considering exreme values for he parameers, where no able o generae an equilibrium where C. 8

22 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY 9 he hird variable o sudy is aggregae consumpion. Using equaion (27.), we can observe he effec of a one per cen permanen increase in governmen consumpion. When we allow m o vary (cases I and III), we have o consider wo effecs: (i) oupu is bigger and, as a consequence, consumpion ends o be higher; (ii) ne deb is also larger, opposing he previous effec. herefore, we canno unambiguously rank his variable for he hree cases 9. Finally, we analyse he effec on he aggregae price index. As we did for he aggregae oupu, we can obain a reduced form for his effec, given by γ. α. φ.. + β α µ φ µ γ ρ β αµρ.. $ b g b g b g b g b g b g.. $ = F P α. µ γ. φ. z b g b g µρ. s. m$ Even if enry means more indusries and no more firms per indusry in he nonradable goods secor (case II), a permanen fiscal shock reduces permanenly he aggregae price level. When we allow m o vary, he marke power decreases and so does he level of ne foreign asses, inroducing exra sources of price reducion. herefore, we noice ha $ $ $ P Case I < P Case III < P Case II WELFARE ANALYSIS 6.. Uiliy flows We know, from Cosa (988), uiliy decreases in he shor run due o he decrease in consumpion and in boh ypes of leisure. Also, we know a emporary fiscal shock reduces he household s seady sae uiliy flow due o he permanen reducion in he ne foreign asse level, which induces a seady sae aggregae consumpion and boh ypes of leisure decrease. Considering enry of firms in each non-radable good indusry, worsens he siuaion since firms end o leave heir marke in his siuaion (cases I and III). When we consider a permanen fiscal shock, he seady sae uiliy level may improve if wo condiions hold: he aggregae oupu saic fiscal muliplier is bigger han one, i.e., we observe crowding-in in consumpion, and he increase in uiliy due o a consumpion (and real money balances) increase is large enough o compensae he reducion generaed by he increase in working ime. he change in he seady sae uiliy level is given by 9 Also, we canno guaranee he effec will be non-negaive. 9

23 20 LUÍS F. COSA du = e L β. e. F $ e. z. m$ M ρ β N O P Q (39.) where e = u. µ + α. φ + γ. u + u > 0 C N N e = u. µα.. a φf+ u. ϕ u. γ. α. aµ φf> 0 2 a f a f d i C N N e3 =. a α f. d uc γ. u + u. µ γ. α. φ > 0 N i a f N µ he expressions for u C = C γ +χ.( γ)/ξ.(m /P ), u N = ξ.ν Τ and u N = ξ.ν ΝΤ, are all posiive. When enry does no affec m, case II, is easy o see he effec of a permanen fiscal shock on he uiliy is unambiguously negaive. However, in cases I and III, he reducion on he price-wage raio, creaed by enry of new firms in each indusry, produces a posiive impac on uiliy which may increase he seady sae uiliy flow Ineremporal uiliy When we consider he sream of discouned uiliy flows, we know he difference beween he hree cases considered lies on he seady sae uiliy level. herefore, he rank for welfare is he same as for he seady sae uiliy flows, i.e., only cases I and III can generae a posiive change. A hird necessary condiion for fiscal policy o improve welfare is needed: he discouned gains in he seady sae flow have o overrun he shor-run los of uiliy. his condiion is, like Cosa (988), equivalen o du >-(-β)/β.du, where du is he change in he uiliy in period =. 7. CONCLUSIONS In his work we presen a dynamic general equilibrium wo-secor model for a small open economy considering produc differeniaion in he non-radable good secor. Considering imperfec subsiuion beween he several ypes of non-radable good allow us o nes in a single framework he models of monopolisic compeiion in he Blanchard and Kiyoaki (987) radiion, and hose involving homogeneous producs oligopolies following d'aspremon e al. (989), as in he case of Cosa (988). We noiced ha enry is a much more complex issue when i may mean changes in he number of indusries (n), changes in he number of firms per indusry (m) or a combinaion of boh. he presence of produc differeniaion implies a muliple equilibria problem due o he rade-off beween he wo above-menioned numbers in he zero profi condiion. In he long-run, we sudy he effecs of fiscal policy considering hree cases of enry: case I where n is fixed, case II where m is fixed, and case III where n/m is fixed. 20

24 PRODUC DIFFEREIAION, FISCAL POLICY, AND FREE ERY 2 he oucomes of case I are similar o hose of Cosa (988) when here is enry. Case II is also similar o he above-menioned model, bu considering enry is absen. he hird case lies in beween. his resul depends srongly on he assumpion ha he household has no love for variey. herefore, fiscal policy is more effecive, under plausible assumpions, when enry means more firms per indusry han when i means more brands. his applies for aggregae oupu and price index and, under paricular assumpions, for household consumpion and welfare as well. I is possible for he governmen o improve welfare using fiscal policy in cases I and III, bu no in case II. Once again he assumpion abou love for variey is crucial. he subse of he parameers space for which a welfare improvemen happens when here is a differen fiscal policy is more resriced in case III since par of he enry simulus is direced o change he number of non-radable good indusries. Universiy of York and Universidade écnica de Lisboa REFERENCES Blanchard, O. J. and Kiyoaki, N. (987). 'Monopolisic Compeiion and he Effecs of Aggregae Demand.' American Economic Review, vol. 77, no. 4, pp Cosa, L. (988). 'Can Fiscal Policy Improve Welfare in a Small Open Economy?' Working Papers do Deparameno de Economia do ISEG - Universidade écnica de Lisboa, forhcoming. d'aspremon, C., Sanos Ferreira, R., and Gérard-Vare, L.-A. (989). 'Unemploymen in a Courno Oligopoly Model wih Ford Effecs.' Recherches Economiques de Louvain, vol. 55, no., pp (997). 'General Equilibrium Conceps under Imperfec Compeiion: a Cournoian Approach.' Journal of Economic heory, vol. 73, no., pp Dixon, H. (994). 'Imperfec Compeiion and Open Economy Macroeconomics.' In he Handbook of Inernaional Macroeconomics (ed. van der Ploeg, F.), pp Oxford: Basil Blackwell. Dixon, H. and Lawler, P. (996). 'Imperfec Compeiion and he Fiscal Muliplier.' Scandinavian Journal of Economics, vol. 98, no. 2, pp Dixon, H. and Rankin, N. (994). 'Imperfec Compeiion and Macroeconomics: a Survey.' Oxford Economic Papers, vol. 46, no. 2, pp

25 22 LUÍS F. COSA Dixon, H. and Sanoni, M. (995). 'An Imperfecly Compeiive Open Economy wih Sequenial Bargaining in he Labour Marke.' Annales d'economie e de Saisique, vol , no. 0, pp Heijdra, B. and van der Ploeg, F. (996). 'Keynesian Mulipliers and he Cos of Public Funds under Monopolisic Compeiion.' Economic Journal, vol. 06, no. 438, pp Obsfeld, M. and Rogoff, K. (995). 'Exchange Rae Dynamics Redux.' Journal of Poliical Economy, vol. 03, no. 3, pp Obsfeld, M. and Rogoff, K. (996). Foundaions of Inernaional Macroeconomics. Cambridge: MI Press. Pereo, P. (996). 'Sunk Coss, Marke Srucure, and Growh.' Inernaional Economic Review, vol. 37, no. 4, pp Roemberg, J. and Woodford, M. (995). 'Dynamic General Equilibrium Models wih Imperfecly Compeiive Produc Markes.' In Froniers of Business Cycles Research (ed. Cooley,.), pp Princeon: Princeon Universiy Press. Snower, D. (983). 'Imperfec Compeiion, Underemploymen and Crowding-ou.' Oxford Economic Papers, vol. 35, no. S, pp Sarz, R. (989). 'Monopolisic Compeiion as a Foundaion for Keynesian Macroeconomic Models.' Quarerly Journal of Economics, vol. 04, no. 4, pp Suherland, A. (996). 'Financial Marke Inegraion and Macroeconomic Volailiy.' Scandinavian Journal of Economics, vol. 98, no. 4, pp Weizman, M. (982). 'Increasing Reurns and he Foundaions of Unemploymen heory.' Economic Journal, vol. 92, no. 368, pp APPENDIX A he reduced form for he parameers giving us $ F = F $ are R 0 R where D R 0 αµβ... a γ. = D s f s αβ.. a γ f. ρ. µ. b v v, sg a αf. R = D s s s = I, II, III = Θ. + S. v is assumed o be posiive. he new parameers are given by = ϕ. b v g a αf. v, ϕ = aµ γ f α. γ. aµ f> 0, S s = s s 2. v s = I, II, III s s s s s s Θ s s s s = aρ+ αf. ϕ+ a αf. γ. α. β. aµ φf, s 2 = aρ+ αf. aϕ + αf> 0 22

26 ILE OF ARICLE 23 he complexiy for he expression of D s does no allow us o demonsrae i is always posiive. However, numerical experimens for plausible values of he parameers did no generae an equilibrium able o produce D s 0. APPENDIX B For emporary fiscal shocks, we know $F 0, herefore: F$ F$ F$ F$ F$ F$ Case II Case I Case III Case I Case II Case III a αf. α. γ. aµ φf. a βf. b. b2 = F$ Case II F$ Case I ϕ. 2 2 a αf. α. γ. aµ φf. a βf. ρ. b. b2 = F$ Case III F$. D3. b + b. b2g a αf. α. γ. aµ φf. a βf. k. b2 = F$ Case II F$ ϕ. For permanen fiscal shocks, we know F$ Case II = 0, herefore: F$ F$ F$ F$ αβγ... a γ f. a αf. b. b2. α. a φf = D αβγ... γ. α. k. b2. α. φ = D 3 Case III 0 F$ F$ Case I Case I Case I Case II 0 F$ F$ a f a f a f Case III Case III Case II 3 Case I Case III 2 2 F z I, b. b2. nϕρ. + α. ρ γαβ... µ φ = +. + b F$ Case I F$ Case III G J z = H D b g K + b. b a f a f s

27 ABLES ABLE YPOLOGY OF MARKE SRUCURES FOR HE NON-RADABLE GOOD SECOR n One Few Many m One Monopoly a Berrand Oligopoly wih Monopolisic Differeniaed Goods a Compeiion Few Courno Oligopoly wih Cournoian Oligopolisic Cournoian Monopolisic One Homogeneous Good a Compeiion a Compeiion Many Perfec Compeiion Perfec Compeiion Perfec Compeiion a If he secor is large in he economy, here are Ford effecs which have o be considered. ABLE 2 SEADY SAE SAIC MULIPLIERS a Y$ σ ( s) Y, G $ G F$ γ =. α. φ. v s 0 $ C ( σ s ) ( s) C, G σ Y, G s ( s) β a f b g σ Y, F= b. oγ. c α. a φfh φ. b vsg a αf. vs< 0 β. s = P$ ( γ σ s ) P, G= a αf.. µ. a φf. b vsg+ φ. vs 0 µ. s m$ σ ( s) m, G γ =. α φ b v s.. a f 0. s 2 b σ σ ( s) P, F ( s) C, F σ β =. µ φ. v s 0 β. a f b g s β µ φ = a αf... aµ γ f. b vsg vs 0 β. µα. ( s) m, F s β =. µ φ β b v s. a.. s 2 f 0 c a For s = cases I, II and III. b Assuming he marginal propensiy o consume of ineres income is less han one. c Rigorously, hese muliplier have no meaning for s = case II.