У статті досліджується процес становлення української національної ідентичності в контексті сучасних теорій націоналізму.  The article studies the process of Ukrainian national identity development

Tyskyi, Mykhailo H.

Тиский, Михайло Григорович

Electronic Eastern European National University Institutional Repository

Stages of Ukrainian National Identity

藤原, 憲二

53951

50434882

Fujiwara, Kenji

53952

Kwansei Gakuin University Repository

Losses from competition policy in a generaloligopolistic equilibriumjournal orpublication titleThe journal of economics of Kwansei GakuinUniversityvolume 72number 4page range 31-39year 2019-03-20URL http://hdl.handle.net/10236/00027630　　Losses from competition policyin a general oligopolistic equilibrium¤Kenji Fujiwara 　We develop a general oligopolistic equilibrium model where freeentry industries and restricted entry industries coexist, and examine thewelfare e®ect of a competition policy, i.e. increasing the number of¯rms in the latter industries. We show an intriguing possibility thatthis policy can reduce welfare by raising the wage and promoting ¯rmexit in the free entry industries.Kenji Fujiwara　　 JEL：D43, L13, L41Keywords：general oligopolistic equilibrium, restricted entry, free entry,welfare1 IntroductionIt is one of the central questions in industrial organization whether acompetition policy increases welfare.1) When one supposes the simplestsituation in which identical ¯rms compete in a single oligopolistic indus-try, the above policy raises welfare by eliminating ine±ciency associatedwith market power. Is the same still valid even in more realistic situa-tions? While there is a large literature that addresses this question, Lahiriand Ono (1988) demonstrate a striking result that if two sets of ¯rms that* I gratefully acknowledge ¯nancial support from JSPS KAKENHI Grant Number25285087. Any remaining error is my own.1) We de¯ne a competition policy simply as increasing the number of ¯rms. Chapters14 and 16 in Belle°amme and Peitz (2015) provide a comprehensive account ofcompetition policies.| 31 |経済学論究第 72 巻第 4 号di®er in production cost are allowed, an increase in the number of inef-¯cient ¯rms can reduce welfare. More recently, Shimomura and Thisse(2012) construct a model in which oligopolistic and monopolistic compe-tition coexists, and prove that increasing the number of oligopolistic ¯rmsunambiguously enhance welfare although it decreases the number of mo-nopolistically competitive ¯rms.This paper also belongs to this strand of literature, but we reconsiderthe welfare e®ect of competition policy by applying a general oligopolisticequilibrium (GOLE) model ¯rst developed by Neary (2003, 2016).2) Weassume a continuum of oligopolistic industries in which entry is impossible(the number of ¯rms is exogenously given) in one set of industries andentry is free (the number of ¯rms is endogenously determined) in the otherset of industries. Then, we show that an increase in the number of ¯rmsin the former set of industries can worsen welfare.3)As noted earlier, Neary (2003, 2016) is the ¯rst to develop the GOLEmodel. In particular, Neary (2003) assumes that all oligopolistic indus-tries have the same number of ¯rms, and shows that increasing it raiseswelfare increases unless all industries are identical. Using a GOLE modelin which oligopolistic and perfectly competitive industries coexist, Cret-tez and Fagart (2009) ¯nd that the same is no longer valid because theoligopolistic industries may over-produce and the market distortion associ-ated with this over-production is accelerated by the competition policy. Inaddition, Kamei (2014) shows that the competition policy reduces welfare2) For the detailed account of the GOLE model, see Neary (2003, 2016) and Colacicco(2015).3) Supposing a single industry that consists of oligopolistic and monopolistically com-petitive ¯rms, Shimomura and Thisse (2012) ¯nd that welfare improves as theoligopolistic ¯rms increase. The main di®erence between their and our models iswhether the competition policy changes the factor price (wage). In Shimomura andThisse (2012), the wage is always unity from the pro¯t maximization condition ofthe perfectly competitive numeraire sector.| 32 |Fujiwara：Losses from competition policy in a general oligopolistic equilibriumby allowing for economies of scale in the original Neary (2003) model. Thisis because the competition policy prevents ¯rms from enjoying the gainsfrom economies of scale by decreasing output per-¯rm. We also show thatthe competition policy can be welfare-reducing, but the underlying reasonis quite di®erent. In our model, the competition policy raises the wageand leads to crowding out of the ¯rms in the free entry industries, therebybeing welfare-reducing.This paper is organized as follows. Section 2 presents a model, andSection 3 proves and discusses the main results. Section 4 concludes.2 ModelThis section presents the model. There is a continuum of oligopolisticindustries in a closed interval [0; 1] in which all goods are produced fromlabor only. We begin by considering the consumer behavior, and then turnto the ¯rm behavior. The utility maximization problem of a representativeconsumer is given bymaxfcigZ 10ln cidi subject toZ 10picidi = I; (1)where ci and pi is a consumption and price of good i, respectively, and I isnational income. Then, the ¯rst-order condition for utility maximization is1=ci = ¸pi, where ¸ is a Lagrangean multiplier which represents marginalutility of income.4) A crucial assumption commonly made in the GOLEmodel is that all ¯rms take ¸ as given in maximizing their pro¯t. Thatis, oligopolistic ¯rms are `large' in their product market, but `small' in thewhole economy including the factor (labor) market. Given this assumption,we set ¸ = 1 in what follows.The continuum of industries consists of a set of industries i 2h0;eii in4) Note that ¸ is an endogenous variable that is determined in the whole generalequilibrium system.| 33 |経済学論究第 72 巻第 4 号which entry is restricted (the number of ¯rms is exogenously given) anda set of industries j 2hei; 1i in which entry is free so that the numberof ¯rms is endogenously given by the zero-pro¯t condition. Denoting bym > 1 and nj > 1 the number of ¯rms in the former and latter industries,the inverse demand function is given by pi = 1= Pmk=1 xikand pj =1= Pnjl=1 xjl, where xik and xjl are the output of a representative ¯rmin each set of industries.5) The labor input coe±cient ®i di®ers acrossindustries, and ¯xed labor f > 0 must be employed in the free entryindustries. Summarizing these assumptions, the pro¯t of a representative¯rm in each set of industries is de¯ned as follows.¼i ´ pixik ¡ w®ixik; ¼j ´ pjxjl ¡ w®jxjl ¡ wf;where ¼i and ¼j are the pro¯t, and w is the wage. Assuming Cournotcompetition and a symmetry within each industry, the output per ¯rmand price in industry i are6)xi =m¡ 1m2w®i; pi =mw®im¡ 1 : (2)Similarly, the output per ¯rm and price in industry j arexj =nj ¡ 1n2jw®j; pj =njw®jnj ¡ 1 : (3)Substituting (3) into the zero-pro¯t condition ¼j = 0 and solving for nj ,the number of ¯rms in the free entry industries is computed asnj =1pwf; (4)which turns out to be common for all j 2hei; 1i.Thus far, we have assumed that the wage is given to all ¯rms. We nowendogenize it, and describe the full general equilibrium by introducing the5) We assume that the number of ¯rms m is common for all the restricted entryindustries since the analysis becomes too complicated if it is di®erent.6) Subscripts k and l are dropped hereafter because all ¯rms within each industryare identical.| 34 |Fujiwara：Losses from competition policy in a general oligopolistic equilibriumlabor market-clearing condition:L=Z ei0m®ixidi+Z 1ei n (®jxj + f) dj =m¡eimw;where L > 0 is the labor endowment, and the last equality uses Eqs. (2),(3) and (4). Solving this equation for w, the equilibrium wage is explicitlyobtained asw =m¡eimL: (5)Substituting (5) into (2), (3) and (4), the outputs, prices and the numberof ¯rms in the free entry industries are derived, and the model is closed.Eq. (5) immediately leads to:Lemma. A competition policy in the form of increasing m raises theequilibrium wage.In order to understand the intuition behind this result, let us note that anincrease inm has the following two impacts. An increase inm has a positivee®ect on aggregate labor demand, and hence the wage will increase. On theother hand, an increase in m leads some ¯rms in the free entry sectors toexit, which serves to decrease aggregate labor demand and put downwardpressure on the wage. As a result, the competition policy de¯ned abovehas both a positive and negative impact on the equilibrium wage, but itends up raising the wage because the former e®ect dominates the lattere®ect. This e®ect of the competition policy on the equilibrium wage willbe useful in the subsequent arguments.3 Welfare e®ectsBased on the model in the last section, we address the welfare e®ect ofthe competition policy. Substituting the demand functions ci = 1=pi andcj = 1=pj into the direct utility function in (1), indirect utility or welfare| 35 |経済学論究第 72 巻第 4 号W is expressed byW = ¡Z ei0ln pi ¡Z 1ei ln pjdj: (6)In order to ¯nd how m a®ects pi and pj in (6), we substitute (2), (3) and(4) into the inverse demand functions pi = 1=(mxi) and pj = 1=(njxj).Then, these prices become a function of m as follows.pi =m¡ei®i(m¡ 1)L ; pj =w®j1¡pwf ; (7)where w in pj is given by (5). Di®erentiation of these prices with respectto m leads todpidm= ¡1¡ei®i(m¡ 1)2L < 0;dpjdm=@pj@w¢ dwdm=ei®j 1¡ pwf2 m2L 1¡pwf2 > 0;that is, the competition policy lowers pi and raises pj . Relating this e®ecton prices to Eq. (6), it is generally ambiguous whether the competitionpolicy enhances welfare.To seek more, let us substitute (7) into (6), and di®erentiate the resultingexpression with respect to m. Then, the welfare e®ect of increasing m isderived as follows.dWdm=¡Z ei01pi¢ dpidmdi¡Z 1ei1pj¢ dpjdmdj=ei1¡ei(m¡ 1)m¡ei ¡ei1¡ei  2¡pwf2 1¡pwfmm¡ei=ei1¡ei¢2m(m¡ 1)m¡ei  1¡pwf ;where ¢´ 2¡ (m+ 1)pwf = 2¡vuut (m+ 1)2 m¡ei fmL:It follows from this result that the welfare e®ect of the competition policydepends on the sign of ¢. More speci¯cally, we establish:| 36 |Fujiwara：Losses from competition policy in a general oligopolistic equilibriumProposition. A competition policy in the form of increasing m reduceswelfare if(m+ 1)2m¡ei f ¡ 4mL > 0: (8)Proof. The competition policy is welfare-reducing (dW=dm < 0) if ¢ < 0,which is rewritten as2 <vuut (m+ 1)2 m¡ei fmL:Rearranging this inequality, we arrive at the proposition. jjIt is a little di±cult to know why the competition policy is detrimentalunder condition (8). To see this, it is helpful to rewrite (8) as a conditionon m. Noting that inequality (8) is rewritten asfm3 + f2¡eim2 + hf 1¡ 2ei¡ 4Lim¡eif > 0;we can say that the competition policy is welfare-reducing if m is su±-ciently large. This ¯nding is intuitively explained as follows. When m issu±ciently large, the pro-competitive e®ect of increasing m is small sincethe oligopolistic equilibrium is su±ciently close to the competitive equi-librium. Therefore, the marginal pro-competitive e®ect of increasing m isquite small. In contrast, the decrease in nj led by the competition pol-icy has a negative welfare e®ect, and plays a primary role in the overallwelfare e®ect. In other words, under condition (8), the negative welfaree®ect arising from crowding out in the free entry industries is overweighsthe positive welfare e®ect from the pro-competitive e®ect. Consequently,the competition policy decreases welfare.Remark. The above result rests on the assumption of logarithmic utility.If, instead, quadratic utility is used as in Neary (2003, 2016), nothing clear| 37 |経済学論究第 72 巻第 4 号is obtained.4 ConclusionApplying Neary's (2003, 2016) GOLE model to the situation where re-stricted entry industries and free entry industries coexist, we have showna possibility that a competition policy, i.e. an increase in the number of¯rms in the restricted entry sectors, raises the equilibrium wage and forcesthe ¯rms to exit in the free entry sectors, thereby reducing welfare.Despite that the above result may be useful in competition policy-making,it is admittedly based on many simplifying assumptions. First, we ignoreproduct di®erentiation by straightforwardly following Neary (2003, 2016).If products are di®erentiated within each industry and/or across industries,our results are expected to be modi¯ed. Second, it is interesting to endo-genize ei that divides the two sets of industries. In this extended model,a competition policy a®ects welfare not only through the wage but alsothrough this threshold of industries. It is our future research agenda toenrich the analysis by noting these limitations of this paper.References[1] Belle°amme, P. and M. Peitz (2015), Industrial organization: markets andstrategies 2nd edition, Cambridge: Cambridge University Press.[2] Colacicco, R. (2015), `Ten years of general oligopolistic equilibrium: asurvey,' Journal of Economic Surveys, 29(5), 965-992.[3] Crettez, B. and M. Fagart (2009), `Does entry improve welfare? A generalequilibrium approach to competition policy,' Journal of Economics, 98(2),97-118.[4] Kamei, K. (2014), `Pro-competitive e®ect, division of labor, and ¯rm pro-ductivity,' Economics Letters, 124(1), 132-135.| 38 |Fujiwara：Losses from competition policy in a general oligopolistic equilibrium[5] Lahiri, S. and Y. Ono (1988), `Helping minor ¯rms reduces welfare', Eco-nomic Journal, 98, 1199-1202.[6] Neary, P. (2003), `The road less travelled: oligopoly and competition policyin general equilibrium,' in Arnott, R., B. Greenwald, R. Kanbur, and B.Nabelu® (eds.) Imperfect Economics: Essays in Honor of Joseph Stiglitz,Mass: MIT Press, 485-500.[7] Neary, P. (2016), `International trade in general oligopolistic equilibrium,'Review of International Economics, forthcoming.[8] Shimomura, K. and J. Thisse (2012), `Competition among the big and thesmall,' RAND Journal of Economics, 43(2), 329-347.| 39 |

Losses from competition policy in a general oligopolistic equilibrium

Kenji, Fujiwara

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Stages of Ukrainian National Identity

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