Molana, Hassan

Montagna, Catia

English

Imperfectly competitive macroeconomic models typically assume a symmetric equilibrium with identical firms, despite the fact that most industries are characterised by substantial degrees of firm heterogeneity. We examine how inter-firm efficiency gaps affect fiscal policy effectiveness under monopolistic competition

University of Dundee Online Publications

                                                              University of DundeeMarket structure, cost asymmetries and fiscal policy effectivenessMolana, Hassan; Montagna, CatiaPublication date:1998Link to publication in Discovery Research PortalCitation for published version (APA):Molana, H., & Montagna, C. (1998). Market structure, cost asymmetries and fiscal policy effectiveness. (DundeeDiscussion Papers in Economics; No. 89). University of Dundee.General rightsCopyright and moral rights for the publications made accessible in Discovery Research Portal are retained by the authors and/or othercopyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated withthese rights. • Users may download and print one copy of any publication from Discovery Research Portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain. • You may freely distribute the URL identifying the publication in the public portal.Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Download date: 19. Mar. 2016Department ofEconomic Studies,University of Dundee,Dundee.DD1 4HNDundee Discussion Papersin EconomicsMarket Structure, Cost Asymmetries andFiscal Policy EffectivenessHassan MolanaandCatia MontagnaWorking Paper No. 89October 1998ISSN: 1473 – 236XMarket Structure, Cost Asymmetries, andFiscal Policy EffectivenessHassan Molana     and    Catia MontagnaUniversity of DundeeAbstractImperfectly competitive macroeconomic models typically assume a symmetric equilibriumwith identical firms, despite the fact that most industries are characterised by substantialdegrees of firm heterogeneity. We examine how inter-firm efficiency gaps affect fiscal policyeffectiveness under monopolistic competition.Key Words: monopolistic competition, cost asymmetries, fiscal policy, market structureJEL Classification: L16, L13Corresponding Author:  Catia Montagna, Dept. of Economics, University of Dundee, Dundee DD1 4HN, UKTel: (00)44-(0)1382-344845; Fax: (00)44-(0)1382-344691;E-mail: c.montagna@dundee.ac.uk11.  IntroductionRecent developments in macroeconomics have formalised the market-power foundations ofmacroeconomic policy effectiveness1. All these studies assume a symmetric equilibrium withidentical firms. Inter-firm differences in performance and market shares, however, are adistinguishing feature of real world industries, as reported for example by Cubbin andGeroski (1987), Mueller (1990) and Oulton (1998).This paper shows how relaxing the special assumption of symmetry affects thestandard conclusions on fiscal policy effectiveness under monopolistic competition. Within asimple macromodel, where monopolistically competitive firms are characterised byheterogeneous costs2, we show that when incumbents are more efficient than entrants theefficiency gap between firms can be sufficiently large to reduce the fiscal multipliersignificantly, or even make it negative. Section 2 outlines the model, Section 3 derives theeffects of a balanced budget fiscal expansion and Section 4 concludes the paper.2. The modelThe basic structure of the model is similar to Dixon and Lawler (1996), with three types ofagents: households, firms and a government.2.1. HouseholdsThere are a large number of identical households each with (i) a homothetic utility over acomposite, horizontally differentiated good C and leisure (1–Ls), where Ls is labour supplyand the time endowment is normalised to unity; and (ii) a CES sub-utility over varieties.  Thefirst stage of utility maximisation consists of choosing C and Ls to maximiseαα )L1(C)L,C(u s1s −= −  subject to the budget constraint TWLPC s −+= Π , where P is theconsumer price index for the CES consumption quantity index C,  W is the nominal wage2rate,  Π  is nominal profit share, and T is a lump-sum tax.  The number of households isnormalised to unity, and the resulting labour supply and consumption demand functions aregiven by, −+−=WTW1Ls Πα ,                  (1)and −+−=PTW)1(C Πα .  (2)There is a continuum of potential varieties of the horizontally differentiated goodindexed by j∈[0, n].  The interval [0, n] represents the ‘mass’ of available varieties and forexpositional simplicity henceforth n shall be referred to as the ‘number’ of varieties producedin the industry.  The second stage of utility maximisation then is to choose cj  to maximise( ))]/1(1/[10)/1(1/)1(εεελ−=−−= ∫njj djcnC  subject to the constraint ( ) PCdjcPnjjj =∫=0, where cj  andjP  are consumption and price of a typical variety j, ε>1  is the elasticity of substitutionbetween varieties, and the price index P is defined as( ))1/(101)1(εελ−=−−= ∫njj djPnP ,  (3)where λ is a constant parameter that reflects the extent to which the CES quantity and priceindices explicitly incorporate the so-called ‘love of variety’.  0≤λ≤1, and  λ=0 and λ=1correspond to the two extreme cases of ‘no love’ and ‘maximum love’.  It is straightforward toshow that the resulting demand for variety j, is  ( )CnPPc 1jj−−=λε − see Benassy (1996) fordetails.32.2. GovernmentGovernment consumption, G, consists of a composite index of the differentiated varietiesproduced in the economy which is assumed to be financed by the lump-sum tax T paid byhouseholds3.  The government budget constraint is given by   ( ) TPGdjgPnjjj ==∫=0, wherewe assume that the government pays the same price as that paid by consumers.2.3. FirmsIt follows from the above that the demand function facing a typical firm is( )YnPPy 1jj−−=λε,            (4)where jy  is private and public demand for the brand produced by the firm, jjj gcy += , andY  is the aggregate demand for output, GCY += .Each firm uses an increasing returns to scale technology which gives rise to theincentive to specialise in the production of one single variety. Labour is assumed to be theonly factor of production, and to be perfectly mobile between firms, so all firms pay acommon wage rate, W. Setting W=1 (using leisure as the numeraire), the total cost function ofa representative firm j is given by its labour demand, φβ += jjdj yL , where βj and φ areconstants denoting the marginal and fixed labour requirements, respectively. Departing fromthe existing literature,  we assume that, whilst having identical fixed costs, firms differ intheir labour productivity. This is captured by βj being  a firm-specific parameter according towhich firms can be ranked.A function ρ(j) can be defined to capture this ranking.  In particular, we (i) impose astrictly monotonic ranking and let 0)j( >′ρ  for all j≥0; (ii) assume that successive entrantsare less efficient than incumbents; and (iii) use an efficiency distribution with only one firm4per efficiency level4.  The endogenous determination of the equilibrium mass of firms willentail the determination of the industry ‘efficiency cut-off point’, i.e. the efficiency of themarginal firm in the industry. Given the assumed distribution, a larger equilibrium number offirms will correspond to a higher marginal cost of the marginal firm in the industry and to alower average industry efficiency. The effects of entry in this model are consistent with someof the empirical evidence reported in the literature (see the studies in Mayes, 1996).Each firm j chooses its price jP  to maximise its profit Π j j j j jP y y= − +( )β φ ,subject to the demand function in (4).  This implies the following optimal price rulePj j=− εεβ1.  Normalising the marginal cost by letting )j(1j ρεεβ  −= , implies theoptimal pricing policy)j(Pj ρ=   (5)Clearly, this suggests that - for any given market structure - the industry is characterised by anasymmetric equilibrium spectrum of prices, quantities, market shares and profits distributedaccording to the value of  )j(ρ , with lower cost firms having larger market shares and higherprofits.3. General equilibrium and the effects of a balanced budget fiscal expansionMarket structure is determined endogenously.  Because in equilibrium there should be no newentry or exit, the last firm (j=n) will break even. Hence 0n =Π  and nρ  defines the costefficiency of the least efficient, or ‘marginal’, firm and thus represents the industry ‘efficiencycut-off point’.  Clearly, 0j >Π  for all j<n since all firms whose marginal cost is lower thann1 ρεε − will make positive profits.  Thus, contrary to the standard model, firm heterogeneity5implies that positive profits persist in equilibrium for the non-marginal firms.  Using (4) and(5), the marginal firm zero-profit condition implies,( ) φελε =−−PYnPPn 11.            (6)The total industry profit is ∫=Π=Πnjj dj0  which, using (5), implies Π = −PY nεφ .Also, in equilibrium both product and labour markets should clear.  We have alreadyincorporated the product market equilibrium condition. Labour market equilibrium requiresequating the labour supply given by (1) with total labour requirement, namely ∫==n0jdjs djLL .To obtain explicit solutions, we assume an explicit functional form for the efficiencyranking function, that is ρ(j)=jδ, with δ≥0, which satisfies our requirement; the size of δdetermines the degree of firms’ heterogeneity and the symmetric case is characterised by δ=0.The model can be reduced to the following three equations,1)1()1/(1 n)]1(1[P −−−−−−−=εεδλεεδ ,            (7)αφααεα−=−+− −− 1n)1(GPPY11 ,            (8)andφεεεδλ =−−− YPn 1)1( .            (9)Equations (7)-(9) correspond, respectively, to the price index in (3), the goods marketequilibrium condition Y = C + G, and the marginal firm’s zero profit condition in (6) intowhich we have substituted for the rest of the endogenous variables from the other equations.Note that we have used  ρ(j)=jδ and imposed the condition 1-δ(ε-1)>0.Let )G;P,n,Y(  denote the initial equilibrium5 and suppose that 10,YG <<= γγ .The effects of a balanced budget fiscal expansion are given by the following6  −−−−−−+−+=εεδααγεδλεαγα)1()1()1()1)(1(1dGdY,            (10)dGdYYn)1)(1(1dGdn −−+−=εδλε,            (11)anddGdYYP)1)(1()1(dGdP −−+−−−=εδλεδλ.            (12)Upon examination (10)-(12) imply that:  (1) dY/dG depends positively on λ and negatively onδ;  (2) dY/dG>0 as long as λ-δ(ε-1)≥0.  In this case, a fiscal expansion leads to entry sincedn/dG>0, and the price level falls.  P is affected by (i) the mass of varieties and (ii) theefficiency composition of the industry.  When λ>0, an increase in n directly reduces the priceindex.  Entry, however, reduces the average efficiency of the industry and results in ceterisparibus increases in P.  Thus, for λ-δ(ε-1)>0 the ‘love of variety’ effect dominates the ‘firms’heterogeneity’  effect and dP/dG<0 when dY/dG>0.  The sufficient condition for a negativemultiplier, 0dGdY< , can be derived from (10)6 and is given by)/11)(1()1/(111εααγεαγλδελ−−+−+<<−+ . Thus:Proposition 1: The balanced budget fiscal multiplier is more likely to be positive thelarger are ε  and λ and the smaller is δ.A high love of variety (large λ) and a low monopoly power of firms (large ε) will offset theincrease in P resulting from the entry induced deterioration of the cost efficiency compositionof the industry.  For sufficiently small values of ε and λ, the latter effect will dominate,leading to a negative multiplier7.7In the basic setting considered by the existing literature, where there is no “love ofvariety” (λ=0) and firms are homogeneous (δ=0),  (10)-(12) respectively reduce to  α=dGdY,dGdYYndGdn =  and 0dGdP=  which correspond to the long-run case explained in Startz (1989).The output multiplier is a positive constant below unity, it is solely determined byhouseholds’ preferences and is independent of the elasticity of substitution between varieties(ε) and the initial size of the government (γ).  With homogenous firms, entry does not affectthe cost efficiency composition of the industry. Thus, given the absence of love of variety, afiscal expansion  - whilst inducing entry - will not affect the price index,Instead, introducing love of variety and abandoning the assumption of identical firmsimplies that while the multiplier may remain positive, its size becomes dependent on α, ε, γand δ.  In particular,1dGdY ≥   as    εγαδεεαεδλ )1())(1)(1()1(−−−−≥−− , and <=>αααdGdYas −<−=−>θεδθεδθεδλ)1()1()1(,where 10,1)/11)(1(1 <<−−−−= θαγεαθ .Proposition 2: The output multiplier will exceed unity if the ‘love of variety’ effect morethan compensates the ‘inefficient entry’ effect.Otherwise, there will be some degree of crowding out and it is in fact possible for the outputmultiplier to fall even below that obtained in the basic case.4. Summary and ConclusionsThe effects of fiscal policy under monopolistic competition are not neutral to the inter-firmhomogeneity assumption which currently dominates the literature and relaxing thisassumption is likely to raise interesting theoretical issues. Within  a model which allows for8as direct a comparison as possible with the existing literature, we show that - whenincumbents are less efficient than entrants - the efficiency gap between firms significantlyreduces the effectiveness of fiscal policy.New avenues for research naturally suggest themselves. Inter-firm heterogeneityquestions the plausibility of assuming away strategic interactions between firms. Given thepersistence of supernormal profits in the long-run, interesting results may stem fromcomparing the short-run and the long-run effects of government policy.  Most importantly, themarket structure effects of fiscal policy points towards the need to investigate the interactionof macroeconomic and industrial policy.9ReferencesBenassy, J.P., 1996, Taste for Variety and Optimum Production Patterns in MonopolisticCompetition, Economics Letters 52, 41-47.Cubbin, J.  and P. Geroski, 1987,  The Convergence of Profits in the Long Run: Inter-firmand Intra-industry Comparisons, Journal of Industrial Economics 35, 427-442.Dixon, H. and P. Lawler, 1996, Imperfect Competition and the Fiscal Multiplier,Scandinavian Journal of Economics 98, 219-231.Heijdra, B.J., J.E. Ligthart, and F. Van der Ploeg, 1998, Fiscal Policy, Distortionary Taxation,and Direct Crowding Out under Monopolistic Competition, Oxford Economic Papers50, 79-88.Mankiw, N.G., 1988, Imperfect Competition and the Keynesian Cross, Economics Letters 26,7-13.D.G. Mayes, ed., 1996, Sources of Productivity Growth (Cambridge University Press,Cambridge).Molana, H. and T. Moutos, 1989, Useful Government Expenditure in a Simple Model ofImperfect Competition,  in: U. Reider, P. Gessner, A. Peyerimoff and F.J. Radermacher,eds.,  Methods of Operations Research 63, (Verlag Anton Hain, Frankfurt). PP??Molana, H. and T. Moutos, 1992, A Note on Taxation, Imperfect Competition, and theBalanced-Budget Multiplier, Oxford Economic Papers 44, 737-52.Montagna, C. 1995, Monopolistic Competition with Firm-Specific Costs, Oxford EconomicPapers 47, 318-328.Mueller, D.C., 1990, The Dynamics of Company Profits: An International Comparison(Cambridge University Press, Cambridge).Oulton, N.,  1998, Competition and the Dispersion of Labour Productivity amongst UKCompanies, Oxford Economic Papers 50, 23-38.10Reinhorn, L.J., 1998, Imperfect Competition, the Keynesian Cross, and Optimal FiscalPolicy, Economics Letters 58, 331-337.Startz, R.,  1989, Monopolistic Competition as a Foundation for Keynesian MacroeconomicModels, Quarterly Journal of Economics 104, 737-52.Torregrosa, R.J., 1998,  On the Monotonicity of Balanced Budget Multiplier Under ImperfectCompetition, Economics Letters 59, 331-335.11Notes                                                1 See for instance  Mankiw (1988),   Startz (1989),   Molana and Moutos (1989, 1992), Dixonand Lawler (1996) and Torregrosa (1998).2 See Montagna (1995) for the market structure effects of firm heterogeneity undermonopolistic competition.3 Proportional income taxation is analysed in Molana and Moutos (1992) and Heijdra et al.(1998). We follow the standard textbook convention and do not consider agents’ benefit fromG. See Molana and Moutos (1989),  Startz (1989), Reinhorn (1998) and Heijdra et al. (1998)for alternatives which allow for ‘useful’ government expenditure.4 One could easily extend this to allow for a ‘mass’ of firms to exist per type but this wouldnot affect the qualitative nature of the results.5 It can be easily shown that (7)-(9) yield a unique solution.6 From (10), the necessary, but not sufficient, condition for dY/dG<0 is λ+(1-δ)(ε-1)<0.Thus, we need λ, ε and δ to satisfy: 0<λ≤1; ε>1; and  1+λ/(ε-1)<δ<1/(ε-1) which requires1<ε<2-λ.7 Clearly, the likelihood of the multiplier being negative will be ceteris paribus higher whenλ=0.

Imperfect Competition and the Fiscal Multiplier,

Imperfect Competition and the Keynesian Cross,

Imperfect Competition, the Keynesian Cross,

Monopolistic Competition as a Foundation for Keynesian Macroeconomic Models,

Monopolistic Competition with Firm-Specific Costs,

Taste for Variety and Optimum Production Patterns in Monopolistic Competition,

The Convergence of Profits in the Long Run: Inter-firm and Intra-industry Comparisons,

The Dynamics of Company Profits:

Useful Government Expenditure in a Simple Model of Imperfect Competition,

Dundee Discussion Papers in Economics 089:Market structure, cost asymmetries and fiscal policy effectiveness

                                                                    University of DundeeDundee Discussion Papers in Economics 089Molana, Hassan; Montagna, CatiaPublication date:1998Link to publication in Discovery Research PortalCitation for published version (APA):Molana, H., & Montagna, C. (1998). Dundee Discussion Papers in Economics 089: Market structure, costasymmetries and fiscal policy effectiveness. (Dundee Discussion Papers in Economics; No. 89). University ofDundee.General rightsCopyright and moral rights for the publications made accessible in Discovery Research Portal are retained by the authors and/or othercopyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated withthese rights. • Users may download and print one copy of any publication from Discovery Research Portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain. • You may freely distribute the URL identifying the publication in the public portal.Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Download date: 03. Sep. 2023Department ofEconomic Studies,University of Dundee,Dundee.DD1 4HNDundee Discussion Papersin EconomicsMarket Structure, Cost Asymmetries andFiscal Policy EffectivenessHassan MolanaandCatia MontagnaWorking Paper No. 89October 1998ISSN: 1473 – 236XMarket Structure, Cost Asymmetries, andFiscal Policy EffectivenessHassan Molana     and    Catia MontagnaUniversity of DundeeAbstractImperfectly competitive macroeconomic models typically assume a symmetric equilibriumwith identical firms, despite the fact that most industries are characterised by substantialdegrees of firm heterogeneity. We examine how inter-firm efficiency gaps affect fiscal policyeffectiveness under monopolistic competition.Key Words: monopolistic competition, cost asymmetries, fiscal policy, market structureJEL Classification: L16, L13Corresponding Author:  Catia Montagna, Dept. of Economics, University of Dundee, Dundee DD1 4HN, UKTel: (00)44-(0)1382-344845; Fax: (00)44-(0)1382-344691;E-mail: c.montagna@dundee.ac.uk11.  IntroductionRecent developments in macroeconomics have formalised the market-power foundations ofmacroeconomic policy effectiveness1. All these studies assume a symmetric equilibrium withidentical firms. Inter-firm differences in performance and market shares, however, are adistinguishing feature of real world industries, as reported for example by Cubbin andGeroski (1987), Mueller (1990) and Oulton (1998).This paper shows how relaxing the special assumption of symmetry affects thestandard conclusions on fiscal policy effectiveness under monopolistic competition. Within asimple macromodel, where monopolistically competitive firms are characterised byheterogeneous costs2, we show that when incumbents are more efficient than entrants theefficiency gap between firms can be sufficiently large to reduce the fiscal multipliersignificantly, or even make it negative. Section 2 outlines the model, Section 3 derives theeffects of a balanced budget fiscal expansion and Section 4 concludes the paper.2. The modelThe basic structure of the model is similar to Dixon and Lawler (1996), with three types ofagents: households, firms and a government.2.1. HouseholdsThere are a large number of identical households each with (i) a homothetic utility over acomposite, horizontally differentiated good C and leisure (1–Ls), where Ls is labour supplyand the time endowment is normalised to unity; and (ii) a CES sub-utility over varieties.  Thefirst stage of utility maximisation consists of choosing C and Ls to maximiseαα )L1(C)L,C(u s1s −= −  subject to the budget constraint TWLPC s −+= Π , where P is theconsumer price index for the CES consumption quantity index C,  W is the nominal wage2rate,  Π  is nominal profit share, and T is a lump-sum tax.  The number of households isnormalised to unity, and the resulting labour supply and consumption demand functions aregiven by, −+−=WTW1LsΠα ,                  (1)and −+−=PTW)1(CΠα .  (2)There is a continuum of potential varieties of the horizontally differentiated goodindexed by j∈[0, n].  The interval [0, n] represents the ‘mass’ of available varieties and forexpositional simplicity henceforth n shall be referred to as the ‘number’ of varieties producedin the industry.  The second stage of utility maximisation then is to choose cj  to maximise( ))]/1(1/[10)/1(1/)1(εεελ−=−−= ∫njj djcnC  subject to the constraint ( ) PCdjcPnjjj =∫=0, where cj  andjP  are consumption and price of a typical variety j, ε>1  is the elasticity of substitutionbetween varieties, and the price index P is defined as( ))1/(101)1(εελ−=−−= ∫njj djPnP ,  (3)where λ is a constant parameter that reflects the extent to which the CES quantity and priceindices explicitly incorporate the so-called ‘love of variety’.  0≤λ≤1, and  λ=0 and λ=1correspond to the two extreme cases of ‘no love’ and ‘maximum love’.  It is straightforward toshow that the resulting demand for variety j, is  ( )CnPPc 1jj−−= λε − see Benassy (1996) fordetails.32.2. GovernmentGovernment consumption, G, consists of a composite index of the differentiated varietiesproduced in the economy which is assumed to be financed by the lump-sum tax T paid byhouseholds3.  The government budget constraint is given by   ( ) TPGdjgPnjjj ==∫=0, wherewe assume that the government pays the same price as that paid by consumers.2.3. FirmsIt follows from the above that the demand function facing a typical firm is( )YnPPy 1jj−−= λε,            (4)where jy  is private and public demand for the brand produced by the firm, jjj gcy += , andY  is the aggregate demand for output, GCY += .Each firm uses an increasing returns to scale technology which gives rise to theincentive to specialise in the production of one single variety. Labour is assumed to be theonly factor of production, and to be perfectly mobile between firms, so all firms pay acommon wage rate, W. Setting W=1 (using leisure as the numeraire), the total cost function ofa representative firm j is given by its labour demand, φβ += jjdj yL , where βj and φ areconstants denoting the marginal and fixed labour requirements, respectively. Departing fromthe existing literature,  we assume that, whilst having identical fixed costs, firms differ intheir labour productivity. This is captured by βj being  a firm-specific parameter according towhich firms can be ranked.A function ρ(j) can be defined to capture this ranking.  In particular, we (i) impose astrictly monotonic ranking and let 0)j( >′ρ  for all j≥0; (ii) assume that successive entrantsare less efficient than incumbents; and (iii) use an efficiency distribution with only one firm4per efficiency level4.  The endogenous determination of the equilibrium mass of firms willentail the determination of the industry ‘efficiency cut-off point’, i.e. the efficiency of themarginal firm in the industry. Given the assumed distribution, a larger equilibrium number offirms will correspond to a higher marginal cost of the marginal firm in the industry and to alower average industry efficiency. The effects of entry in this model are consistent with someof the empirical evidence reported in the literature (see the studies in Mayes, 1996).Each firm j chooses its price jP  to maximise its profit Π j j j j jP y y= − +( )β φ ,subject to the demand function in (4).  This implies the following optimal price rulePj j= −εεβ1.  Normalising the marginal cost by letting )j(1j ρεεβ  −= , implies theoptimal pricing policy)j(Pj ρ=   (5)Clearly, this suggests that - for any given market structure - the industry is characterised by anasymmetric equilibrium spectrum of prices, quantities, market shares and profits distributedaccording to the value of  )j(ρ , with lower cost firms having larger market shares and higherprofits.3. General equilibrium and the effects of a balanced budget fiscal expansionMarket structure is determined endogenously.  Because in equilibrium there should be no newentry or exit, the last firm (j=n) will break even. Hence 0n =Π  and nρ  defines the costefficiency of the least efficient, or ‘marginal’, firm and thus represents the industry ‘efficiencycut-off point’.  Clearly, 0j >Π  for all j<n since all firms whose marginal cost is lower thann1 ρεε − will make positive profits.  Thus, contrary to the standard model, firm heterogeneity5implies that positive profits persist in equilibrium for the non-marginal firms.  Using (4) and(5), the marginal firm zero-profit condition implies,( ) φελε= −−PYnPPn 11.            (6)The total industry profit is ∫=Π=Πnjj dj0  which, using (5), implies Π = −PY nεφ .Also, in equilibrium both product and labour markets should clear.  We have alreadyincorporated the product market equilibrium condition. Labour market equilibrium requiresequating the labour supply given by (1) with total labour requirement, namely ∫==n0jdjs djLL .To obtain explicit solutions, we assume an explicit functional form for the efficiencyranking function, that is ρ(j)=jδ, with δ≥0, which satisfies our requirement; the size of δdetermines the degree of firms’ heterogeneity and the symmetric case is characterised by δ=0.The model can be reduced to the following three equations,1)1()1/(1 n)]1(1[P −−−−−−−= εεδλεεδ ,            (7)αφααεα −=−+− −− 1n)1(GPPY11 ,            (8)andφεεεδλ =−−− YPn 1)1( .            (9)Equations (7)-(9) correspond, respectively, to the price index in (3), the goods marketequilibrium condition Y = C + G, and the marginal firm’s zero profit condition in (6) intowhich we have substituted for the rest of the endogenous variables from the other equations.Note that we have used  ρ(j)=jδ and imposed the condition 1-δ(ε-1)>0.Let )G;P,n,Y(  denote the initial equilibrium5 and suppose that 10,YG <<= γγ .The effects of a balanced budget fiscal expansion are given by the following6 −−−−−−+−+=εεδααγεδλεαγα)1()1()1()1)(1(1dGdY,            (10)dGdYYn)1)(1(1dGdn−−+−=εδλε,            (11)anddGdYYP)1)(1()1(dGdP−−+−−−=εδλεδλ.            (12)Upon examination (10)-(12) imply that:  (1) dY/dG depends positively on λ and negatively onδ;  (2) dY/dG>0 as long as λ-δ(ε-1)≥0.  In this case, a fiscal expansion leads to entry sincedn/dG>0, and the price level falls.  P is affected by (i) the mass of varieties and (ii) theefficiency composition of the industry.  When λ>0, an increase in n directly reduces the priceindex.  Entry, however, reduces the average efficiency of the industry and results in ceterisparibus increases in P.  Thus, for λ-δ(ε-1)>0 the ‘love of variety’ effect dominates the ‘firms’heterogeneity’  effect and dP/dG<0 when dY/dG>0.  The sufficient condition for a negativemultiplier, 0dGdY < , can be derived from (10)6 and is given by)/11)(1()1/(111εααγεαγλδελ−−+−+<<−+ . Thus:Proposition 1: The balanced budget fiscal multiplier is more likely to be positive thelarger are ε  and λ and the smaller is δ.A high love of variety (large λ) and a low monopoly power of firms (large ε) will offset theincrease in P resulting from the entry induced deterioration of the cost efficiency compositionof the industry.  For sufficiently small values of ε and λ, the latter effect will dominate,leading to a negative multiplier7.7In the basic setting considered by the existing literature, where there is no “love ofvariety” (λ=0) and firms are homogeneous (δ=0),  (10)-(12) respectively reduce to  α=dGdY,dGdYYndGdn=  and 0dGdP =  which correspond to the long-run case explained in Startz (1989).The output multiplier is a positive constant below unity, it is solely determined byhouseholds’ preferences and is independent of the elasticity of substitution between varieties(ε) and the initial size of the government (γ).  With homogenous firms, entry does not affectthe cost efficiency composition of the industry. Thus, given the absence of love of variety, afiscal expansion  - whilst inducing entry - will not affect the price index,Instead, introducing love of variety and abandoning the assumption of identical firmsimplies that while the multiplier may remain positive, its size becomes dependent on α, ε, γand δ.  In particular,1dGdY ≥   as    εγαδεεαεδλ)1())(1)(1()1(−−−−≥−− , and <=>αααdGdYas −<−=−>θεδθεδθεδλ)1()1()1(,where 10,1)/11)(1(1 <<−−−−= θαγεαθ .Proposition 2: The output multiplier will exceed unity if the ‘love of variety’ effect morethan compensates the ‘inefficient entry’ effect.Otherwise, there will be some degree of crowding out and it is in fact possible for the outputmultiplier to fall even below that obtained in the basic case.4. Summary and ConclusionsThe effects of fiscal policy under monopolistic competition are not neutral to the inter-firmhomogeneity assumption which currently dominates the literature and relaxing thisassumption is likely to raise interesting theoretical issues. Within  a model which allows for8as direct a comparison as possible with the existing literature, we show that - whenincumbents are less efficient than entrants - the efficiency gap between firms significantlyreduces the effectiveness of fiscal policy.New avenues for research naturally suggest themselves. Inter-firm heterogeneityquestions the plausibility of assuming away strategic interactions between firms. Given thepersistence of supernormal profits in the long-run, interesting results may stem fromcomparing the short-run and the long-run effects of government policy.  Most importantly, themarket structure effects of fiscal policy points towards the need to investigate the interactionof macroeconomic and industrial policy.9ReferencesBenassy, J.P., 1996, Taste for Variety and Optimum Production Patterns in MonopolisticCompetition, Economics Letters 52, 41-47.Cubbin, J.  and P. Geroski, 1987,  The Convergence of Profits in the Long Run: Inter-firmand Intra-industry Comparisons, Journal of Industrial Economics 35, 427-442.Dixon, H. and P. Lawler, 1996, Imperfect Competition and the Fiscal Multiplier,Scandinavian Journal of Economics 98, 219-231.Heijdra, B.J., J.E. Ligthart, and F. Van der Ploeg, 1998, Fiscal Policy, Distortionary Taxation,and Direct Crowding Out under Monopolistic Competition, Oxford Economic Papers50, 79-88.Mankiw, N.G., 1988, Imperfect Competition and the Keynesian Cross, Economics Letters 26,7-13.D.G. Mayes, ed., 1996, Sources of Productivity Growth (Cambridge University Press,Cambridge).Molana, H. and T. Moutos, 1989, Useful Government Expenditure in a Simple Model ofImperfect Competition,  in: U. Reider, P. Gessner, A. Peyerimoff and F.J. Radermacher,eds.,  Methods of Operations Research 63, (Verlag Anton Hain, Frankfurt). PP??Molana, H. and T. Moutos, 1992, A Note on Taxation, Imperfect Competition, and theBalanced-Budget Multiplier, Oxford Economic Papers 44, 737-52.Montagna, C. 1995, Monopolistic Competition with Firm-Specific Costs, Oxford EconomicPapers 47, 318-328.Mueller, D.C., 1990, The Dynamics of Company Profits: An International Comparison(Cambridge University Press, Cambridge).Oulton, N.,  1998, Competition and the Dispersion of Labour Productivity amongst UKCompanies, Oxford Economic Papers 50, 23-38.10Reinhorn, L.J., 1998, Imperfect Competition, the Keynesian Cross, and Optimal FiscalPolicy, Economics Letters 58, 331-337.Startz, R.,  1989, Monopolistic Competition as a Foundation for Keynesian MacroeconomicModels, Quarterly Journal of Economics 104, 737-52.Torregrosa, R.J., 1998,  On the Monotonicity of Balanced Budget Multiplier Under ImperfectCompetition, Economics Letters 59, 331-335.11Notes                                                1 See for instance  Mankiw (1988),   Startz (1989),   Molana and Moutos (1989, 1992), Dixonand Lawler (1996) and Torregrosa (1998).2 See Montagna (1995) for the market structure effects of firm heterogeneity undermonopolistic competition.3 Proportional income taxation is analysed in Molana and Moutos (1992) and Heijdra et al.(1998). We follow the standard textbook convention and do not consider agents’ benefit fromG. See Molana and Moutos (1989),  Startz (1989), Reinhorn (1998) and Heijdra et al. (1998)for alternatives which allow for ‘useful’ government expenditure.4 One could easily extend this to allow for a ‘mass’ of firms to exist per type but this wouldnot affect the qualitative nature of the results.5 It can be easily shown that (7)-(9) yield a unique solution.6 From (10), the necessary, but not sufficient, condition for dY/dG<0 is λ+(1-δ)(ε-1)<0.Thus, we need λ, ε and δ to satisfy: 0<λ≤1; ε>1; and  1+λ/(ε-1)<δ<1/(ε-1) which requires1<ε<2-λ.7 Clearly, the likelihood of the multiplier being negative will be ceteris paribus higher whenλ=0.

http://discovery.dundee.ac.uk/ws/files/108476/DDPE_089.pdf

Dundee Discussion Papers in Economics 089:Market structure, cost asymmetries and fiscal policy effectiveness

Abstract

Similar works

Full text

Available Versions

University of Dundee Online Publications

University of Dundee Online Publications