Monopolistic Competition

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1 Welfare Ranking of A-valorem an Specific Tariffs in a Moel of Monopolistic Competition Esra Durceylan Bilkent University May 3, 2010 Abstract This paper compares the welfare implications of a-valorem an specific tariffs in a moel of monopolistic competition. We show that the welfare ranking result of Jørgensen an Schröer(2005) showing that specific tariff results in higher welfare than the a-valorem tariff is sensitive to the utility specification. In particular, when we use a utility function that yiels a variable mark-up as in Melitz an Ottaviano (2008), we reestablish results from non-monopolistic imperfect competition settings. Uner some parametric conitions an a-valorem tariff yiels higher welfare than an import equivalent specific tariff given that ifferentiate goos are not close substitutes among each other. 1 Introuction Although tariffs can be impose in a number of ways, the most common are a-valorem an specific. In a perfectly competitive market, whether the tariff is a-valorem or specific oes not matter. Since firms are price takers, only the cost-price increase generate by the tariff is relevant. Consequently, for every specific tariff rate there exists an equivalent a-valorem tariff level. However, in an imperfectly-competitive environment, this equivalence result breaks own: an a-valorem tariff generates higher welfare than a specific tariff. This has been shown for ifferent tariff equivalence efinitions such as revenue or import equivalence. 1 The result is riven by the fact that profit-maximizing firms increase their output when an a-valorem tariff is impose. Higher output reuces prices an ecreases the wege between the price consumers pay an the I woul like to thank Kala Krishna, Susanna Esteban, Refet Gürkaynak an Remzi Kaygusuz for their helpful comments. Department of Economics, Bilkent, Ankara. 1 See Helpman an Krugman (1989) for the non equivalence of these tariff regimes uner imperfectly competitive market structures. Also recently, it is reestablishe that a-valorem tariff generates higher welfare if a country faces a foreign monopoly (see Kowalczyk an Skeath (1994)) an this can be extene to a wier oligopolistic setting (see Skeath an Trenel (1994b)). 1

2 price proucers get. Thus, consumers are better off with more output an lower prices compare to specific tariff. So far, the focus of these papers has been on markets that are imperfectly competitive. Recently, Jørgensen an Schröer (2005) contribute to this literature by stuying welfare effects of two tariff regimes with a moel of monopolistic competition. Specifically, they buil a symmetric two country moel with homogenous firms an consumers who have CES utility functions, an show that a specific tariff yiels higher welfare than an import equivalent a-valorem tariff, which reverses the finings of the papers with imperfect competition. We show that this striking result is sensitive to the utility specification. If the utility function is quaratic, as in Melitz an Ottaviano (2008), an a-valorem tariff results in higher welfare than a specific tariff at lower levels of love for variety. 2 The trae literature has wiely use the CES utility function. However, it has its own rawbacks. It leas to constant mark-up of price over marginal cost. Hence, when firms face higher competition through e.g. opening up to trae, their prices on t change. Therefore, it fails to explain the pro-competitive effects of international trae. 3 Our paper not only eals with the issue of tariff comparison, it also brings the Melitz-Ottaviano utility function into play which allows for enogenous mark-up. Many of the results of Jørgensen an Schröer (2005) is replicate with the quaratic utility function that we use. First, a-valorem tariff generates higher tariff revenue, but lower consumer surplus than the import equivalent specific tariff. This is becuase uner a-valorem tariff regime prices increase less compare to specific tariff regime when firms move from free trae. Secon, number of varieties are higher, but firms are smaller uner specific tariff regime. Higher prices uner specific tariff regime enables more firms, as a result more varieties to survive at lower output levels. Hence, consumer surplus uner specific tariff is higher ue to higher variety generate. However, in contrast to Jørgensen an Schröer (2005) we fin that for a-valorem tariff regime, gain in welfare ue to higher tariff revenue is higher than the loss ue to lower consumer surplus at lower levels of love for variety. The question is how can a CES utility an quaratic utility generate ifferent results. When consumer eman is characterize by quaratic utility functions (linear eman), it enables for enogenous mark-up. As a result, when the consumers love for variety increases, ue to higher competitive pressure, firms ajust their mark-ups up an import equivalent a-valorem tariff rate becomes less restrictive compare to specific tariff level. Thus, tariff revenue generate uner a-valorem tariff eteriorates as love for variety increases. On the other han, higher variety is appreciate more uner specific tariff. Hence, an increase in love of variety results in a shift in the relative weight of tariff revenue 2 This utility function is introuce by Ottaviano, Tabuchi, an Thisse (2002), an has been wiely use in the Trae an Geography literature. 3 See Feenstra (2003) for an extensive comparison between CES utility functions an utility functions which allows enogenous mark-ups. 2

3 an consumer surplus in welfare. Taxation/tariff policy is not a policy tool that is only use in international trae settings. There is a substantial public economics literature that compares the market outcomes an welfare implications of a-valorem an specific tax policies. This literature s conclusion about welfare ranking of the a-valorem an specific taxes are in line with the international trae literature. Uner perfect competition, an equal yiel a-valorem tax is equivalent to specific tax. A-valorem tax is welfare superior to specific tax when the market structure is a monopoly an this superiority continues to hol for a wie range of market structures (see Suits an Musgrave (1953), Delipalla an Keen (1992) Skeath an Tranel (1994a), Hamilton (1999) an Schröeer (2004)). 4 In contrast to the preceing work that supports the superiority of a-valorem tax, Anerson, e Palma, an Kreier (2001b) showe that specific tariff may be welfare superior if either revenue requirements of the government, or the strength of tastes for variety relative to entry costs are large. 5 They use a iscrete choice framework for consumer eman, an Bertran-Nash characterizes the firms competition. Later, this parameter epenent result is challenge by Schröeer (2004) who applies Dixit an Stiglitz utility to moel consumers love of variety an monopolistic competition setting. He shows that an equal yiel a-valorem tax is still welfare superior uner monopolistic competition settings. Similar to the iscussion in this paper, the results of Schröeer (2004) an Anerson, e Palma an Kreier (2001b) show that the welfare implications of these tax policies epen on how one moels market structures an consumer eman. On the one han specific taxation caters consumers love for variety as it creates more entry. On the other han, a-valorem tax isplays a lower tax-overshift an therefore markets are less istorte. Which effect ominates the other epens how one moels the competition among firms an consumer s eman. One can also ask the following question: How woul the results of Schröeer (2004) change if the quaratic utility function were use to escribe consumer preferences in a moel of monopolistic competition? We can argue that unit tax generates higher welfare than a-valorem tax when love for variety increases. The results for this taxation case are exactly analogous to the tariff case analyze in this paper. 6 The paper is organize as follows. Section 2 buils a two country moel of homogenous firms in an open economy. Section 3 stuies the welfare effects of ifferent tariff regimes an iscusses the results an Section 4 conclues. 4 See Keen(1998) for a review of the literature. 5 I focuse only on the long-run equilibrium analysis of Anerson, e Palma an Kreier (2001b) because the anlaysis in this paper is also a long-run analysis. In their paper, they also show that in the short run the unit tax is more efficient than the a valorem tax uner Bertran competition in a linear city moel when marginal prouction costs iffer, an revenue requirements are sufficiently high. 6 However, that analysis is not presente for brevity. The results for the taxation analysis can be provie upon request. 3

4 2 Moel The moel is base on Melitz-Ottaviano (2008). As mentione earlier, the quaratic utility function enables enogenous mark-ups as it permits firms to respon to the competition by varying their markups. With the CES utility function, firms have constant mark-ups an pricing policy is not affecte by the competitiveness of the market. Although the moel is base on one of the new-trae theories that incorporates heterogeneity in firms prouctivities, the current version of this paper switches off that aspect of the new trae literature. We want to replicate Jørgensen an Schröer (2005) s moel features except the utility function an compare the results of this moel with that of Jørgensen an Schröer (2005) s who moels firms as ientical. 2.1 Preferences an Deman There are L ientical consumers in each country. Their preferences are efine over a continuum of ifferentiate proucts which can be either omestic or foreign an a numeraire goo. They choose ifferentiate proucts from the set of varieties, H F. H is the set of varieties prouce at home an F is the set of foreign varieties. Numeraire goo is inexe by 0 an ifferentiate goo is inexe by i. Then a consumer, c s utility function is U = q c 0 + α q c i i 1 2 γ where q c 0 is the numeraire goo consumption an q c i (qi c ) 2 i 1 2 η 2 qi c i, (1) is the ifferentiate goo consumption of variety i by each iniviual c. α, η an γ are positive eman parameters. α an η inex the substitution between the numeraire goo an the ifferentiate goo. If the parameter α increases an the parameter η ecreases, the eman for the ifferentiate goos relative to numeraire goo increases. The egree of prouct ifferentiation increases with γ. If γ=0, there is no ifferentiation an consumers only care about their total consumption which is Q c = qc i i. Consumers like variety as reflecte in iɛh F (q i) 2 i being low when expeniture is concentrate in more varieties. A consumer s inverse eman for each variety is given by p i = α γq c i ηq c, (2) where Q c is the total quantity consume by consumer c. When we aggregate over all consumers, we get the linear eman for variety i which is given by 4

5 q i = Lqi c αl = γ + η(n H + N F ) L γ p i + η(n H + N F ) L γ + η(n H + N F ) γ P. where N H is the mass of home varieties an N F is the mass of importe varieties. ( 1 P = N H +N F iɛh p ii + ) jɛf p jj is the average price over all prices. 2.2 Prouction an Firm Behavior In this economy, the worl consists of two symmetric countries which we ll refer as home an foreign. Each country consists of L consumers who are enowe with one unit of labor. Labor is inelastically supplie, there is no leisure in the utility function. Labor is the only factor of prouction. The numeraire goo is prouce uner constant returns to scale at a cost of a unit labor. Deman for numeraire goo in both countries is ensure to be positive with the assumption that income is high enough an it is freely trae in a perfectly competitive market. If the price of the numeraire goo is normalize to one an since workers get their revenue of marginal prouct; the wage is unity. Moreover, wages are ientical across countries. All firms which are proucing ifferentiate proucts have the same technology. They pay a one time fixe cost, f e, to enter the ifferentiate goo sector. Each goo is prouce at a constant marginal cost of c (equal to c unit labour requirement). Thus, the cost of prouction for a home firm entering the market is cq 7 i. There is free entry an exit. As a result, firms enter until an entering firm woul make zero expecte profits. New entrants always choose to prouce a goo that is not being prouce in the market since this allows them greater profits than sharing the market with an existing firm. Thus, each firm prouces a unique variety. There is no one time fixe cost to enter the foreign market; exporting firms only pay the tariff. All firms have the same technology an face the same problem. Thus, if it is profitable for one of the home firms to export, it is profitable for all the home firms to export. Countries are symmetric in terms of consumers, firms, an tariff restrictions. Therefore, the number of firms in the foreign country an the home country is equal in equilibrium,i.e N H = N F = N. So, the total number of varieties is twice the number of varieties prouce at home. Firms maximize their profit taking the total number of varieties an average price in the market as given. Since firms are homogenous an countries are symmetric, profit maximizing prices of home an foreign firms 7 The cost of prouction is actually cwq i an the fixe entry cost is wfe. Since the wage rate is unity, the w s will be roppe from this point on. 5

6 proucts at their own omestic market are equal,i.e qi = q i in both countries 8. The profit-maximizing price p an the output level of a home firm q satisfy q = L γ (p c). (3) 3 Analysis First, we analyze the market if the government restricts imports using an a-valorem tariff. Namely, the government collects a fraction, t, of the price per unit of importe goo. Therefore, importe goos are more expensive than their omestic competitor s price. By the symmetry assumptions, all home firms an foreign firms set the same price for their exporte goos in equilibrium, i.e. q x i = qx i in both home an foreign countries. Aitionally, markets are assume to be segmente; hence, firms maximize the profit earne in the foreign market an in the home market separately. The expecte profit of a firm with a marginal cost of prouction c is Π t (c) = Π t (c) + Π x t (c) = ( q t p t cq t ) + ((1 t)q x t p x t cq x t ) f e, (4) where superscript x an enote the export market an omestic market variables respectively an subscript t enotes a-valorem tariff variables. From the first orer conition of the firm s maximization problem, we obtain the price of the exporte goo in the estine market p x t an quantity prouce q x t satisfying; q x t = L γ ( p x t c ). (5) 1 t Firms enter the market until the ex-post profit of a firm, Π t (c), is riven to zero which is the free entry conition. Suppose now exporting firms face a specific tariff. Specifically, firms have to pay s for each unit exporte. The total profit mae by a firm in omestic an exporting markets is: Π s (c) = Π s(c) + Π x s (c) = ( q sp s cq s) + (q x s p x s cq x s sq x s ) f e, (6) where x enotes export, enotes omestic market variables, an s enotes specific tariff variables. The 8 Superscript enotes home market variables. 6

7 profit maximizing price in the foreign market, p x s, an the quantity supplie, q x s, satisfy q x s = L γ (px s (c + s)). (7) Firms price higher in foreign markets because specific tariff acts as if it is an increase in marginal cost. We have escribe the moel an two ifferent restrictions uner bilateral tariff imposition. Given that the two tariff regimes create the same level of imports, Q, we can compare the number of varieties, the levels of output prouce in both omestic an foreign markets (size of the firms) an welfare implications of ifferent implementation of import restrictions. Lemma 1 For a given specific tariff s an import equivalent a-valorem tariff t, omestic an foreign output levels of firms uner specific tariff is lower than that of the a-valorem tariff: q s < q t an q x s < q x t. Proof. In the appenix. Lemma 2 For a given specific tariff s an import equivalent a-valorem tariff t, total varieties uner specific tariff is higher than the a-valorem tariff: N s > N t Proof. In the appenix. Briefly, specific tariff creates smaller firms compare to a-valorem tariff. Firms facing a-valorem tariff restriction in the export market increase their output an ecrease their price. By oing so, firms ecrease the ifference between the price consumers pay an the price proucers get. This is a result of a-valorem tariff ecreasing the marginal revenue. On the other han, specific tariff acts like an increase in marginal cost. Therefore, firms ten to ecrease their output while they increase their prices. Hence, with higher operating surplus, smaller outputs are sufficient to offset the fixe entry cost to enter the market. This allows more firms to exist in the market uner specific tariff. The results for firm size an number of varieties are in line with Jørgensen an Schröer (2005). However, the paper eparts from theirs when we compare the welfare implications of the two tariff regimes. For high levels of love for variety, import equivalent specific tariff generates higher welfare as in Jørgensen an Schröer (2005). However, for low levels of love for variety we reestablish the non-competitive welfare ranking results: a-valorem tariff generates higher welfare than an import equivalent specific tariff. We emonstrate this result below using a numerical analysis 9. 9 The moel propose by Melitz an Ottaviano (2008) is simple enough to analyze an fin close form solutions not only for ientical firm case, but also for heterogenous firm case. However, the comparison in this moel requires to fin an import equivalent a-valorem an specific tariff. To be able to fin close form solution, one has to solve N tqt x = Nsqx s equation an solve for t, given s or vise versa. The terms on both sies of the equation are a quaratic function in t. an s respectively. Hence, the close form solutions requires teious algebra. Therefore, the results are presente with numerical analysis. 7

8 Figure 1: Welfare Comparison of Import Equivalent A-valorem an Specific Tariffs γ love for variety α relative eman for the ifferentiate proucts A valorem ominates Specific ominates Problem unefine The above figure shows the welfare ranking of a-valorem tariff an specific tariff. It is create as follows: take particular values for the eman parameters α, γ an η, specific tariff rate s, the cost parameters f e an c. 10 Using free entry conition (6), the first orer conition of profit maximization firms in omestic market (3), the first orer conition of profit maximization in the export market (7), an the inverse eman function (2) we fin qs x, qs an the number of home varieties in the market, N s. The total import is qs x N s. The a-valorem tariff rate t is set so that the import level is same uner both tariff regimes. Using the free entry conition (4), the first orer conition of profit maximization in omestic market (3), the first orer conition of foreign market profit maximization (5) an inverse eman function (2), we fin qt x, qt, the 10 The values chosen for the parameters are as follows: c=0.005 f e = 1000, α ranges from 4 to 20, γ ranges from 0.1 to 1, η is 100 an s is taken to be

9 number of home varieties in the market, N t, an the import equivalent a-valorem tariff rate, t. Note that the problem has to be well efine i.e., eman for numeraire goo has to be positive. The figure above illustrates that welfare ranking reverses with an increase in γ. The explanation for this observation requires an unerstaning of how consumer surplus an tariff revenue changes with love for variety uner two regimes. Specific tariff yiels in higher consumer surplus an the excess surplus increases with γ. On the other han, a-valorem tariff generates more tariff revenue. In aition, the excess tariff revenue ecreases with γ. As a result, as γ increases, a-valorem tariff loses its superiority to specific tariff. The following iscussion justifies these statements. In orer to better unerstan why the ifference between the tariff revenue uner a-valorem tariff an specific tariff eclines with γ, we make the following exercise: Assume that for a given level of γ 1 an s, import equivalent a-valorem tariff rate is t 1. Now consier γ 2 > γ 1 an keep t 1 unchange. At higher levels of love for variety, consumers ten to buy less from each firm (firms face lower resiual eman). Thus, output per firm ecreases. As one can see from figure (2), keeping a-valorem tariff rate constant at t 1 results in lower number of firms than the import equivalent a-valorem tariff rate t As a result, in the economy with γ 2 an t 1 total imports are going to be lower than the one with γ 1 an t 1 ) As a result, ecline in output per firms an number of firms below the import equivalent level t generate less total imports than the specific tariff rate s. Without loss of generality this allows us to make the following conclusion about how the import equivalent tariff rate changes with γ: for a given specific tariff rate as γ increases import equivalent tariff rate ecreases. Although prices increase ue to higher mark-up, the increase is curbe by ecrease tariff restriction together with lower resiual eman. In return, ecrease in tariff rate ominates the increase in prices. Hence, per unit tariff revenue eclines with γ. On the other han, per unit tariff revenue uner specific tariff regime(s) is kept exogenously constant. Therefore, tariff revenue collecte uner a-valorem tariff eclines faster than the tariff revenue collecte uner specific tariff. Now we iscuss why consumer surplus ecreases with γ. Consumer surplus is a function of total consumption (Q), an total number of varieties. As iscusse above, output per firm both in omestic an foreign markets uner a-valorem tariff is higher than that of the specific tariff for any given parameters. However, as γ increases, q t an qt x eclines faster than the specific tariff counterparts. One reason is the ecline in resiual eman ue to increase love for variety, which is common for both regimes. Moreover, ecline in t ecreases both q t an qt x even further because lower tax payments makes it possible to break even at lower output levels. Next, total consumption (or ientically total output of firms) eclines faster uner specific tariff. Using inverse eman function (eq (2)) an the supply curve of firms (eq.(3)), we can fin the total 11 The figure is generate with the same basic parameters of the numerical analysis. The line below is the number of firms that can survive if the a-valorem tariff rate is kept constant at the import equivalent rate t for γ = Then, number of varieties is calculate for every γ values at constant t. 9

10 Figure 2: Equilibrium Number of Firms by Love for Variety an A-valorem Tariff Rate 5 x number of firms γ love for variety Number of firms for import equivalent a valorem tariff Number of firms for a valorem tariff=0.98 consumption : Q r = (α c) 2γq r where r represents the regime type12. Since γ increases faster than the ecline in q r, total consumption eclines for both regimes. However, since we also know from the above iscussion that q t eclines faster than qs, the ecline in Q t is slower than the ecline in Q s. Finally, number of varieties ecline faster uner specific tariff. This can easily be conclue by the fact that per firm output eclines slower but total consumption eclines faster uner specific tariff. In this moel, the consumer surplus in a tariff regime r is 1 2 γn r((q r x) 2 + (q r )2 ) η(q r) With the given parametric configuration, our numerical calculations show that uner specific tariff regime the slower ecline in output per firm ominates the faster ecline in number of varieties an total consumption. As a result, consumer surplus uner specific tariff regime eclines faster than the one uner the a-valorem tariff regime. The above iscussion of how tariff revenue an consumer surplus behaves with γ allows us to conclue that the excess consumer surplus of specific tariff increases an the excess tariff revenue generate uner a- 12 This formula also shows that total consumption uner a-valorem tariff is less than the total consumption uner specific tariff for any given parameter level. 13 (see the erivation in the appenix) 10

11 valorem tariff regime eclines with γ. Moreover, a-valorem tariff inucing firms to exit might even further increase welfare by keeping the number of firms close to the efficient number of firms when consumers on t value variety much. This effect isappears as number of variety becomes a utility increasing factor with an increase in γ. In their paper Anerson, e Palma an Kreier (2001b) argue that the relative efficiency of the two tax forms epens on the government s revenue requirement an the strength of tastes for variety relative to entry costs. For either higher levels of revenue requirement (t being high in our analysis) or higher love for variety relative to entry costs, unit tax is welfare superior than the a-valorem tax. They analyze the moel using the iscrete choice moel with exponentially istribute match values uner Bertran competition with free entry. The intuition for their result is the following, for low levels of revenue requirement, a-valorem tariff is more efficient because it ecreases the number of firms to efficient level. However, when love for variety is higher or revenue requirement is high enough, a-valorem tax inuces excessive firm exit. Their iscussion is ientical to this paper s. For low levels of love for variety, consumers value total consumption more than consuming variety. Hence, a-valorem tariff generates more welfare. It happens, first by generating more tariff revenue an hence more income, secon, by keeping the number of firms close to efficient level. However, as love for variety increases, creating less variety or else inucing excessive exit ecreases welfare. This paper eparts from Jørgensen an Schröer (2005) by moeling consumer eman with a utility function that allows for enogenous mark-up. As a result, as we change love for variety parameter, the firms can not only ajust output, they can also ajust their price by changing their mark-up. We argue that more flexibility to ajust to more competitive environments (a higher love for variety immeiately increases competition) generates a relatively less restrictive a-valorem tariff given same level of specific tariff as love for variety increases. Thus, for some parameter values tariff revenue eclines faster uner a-valorem tariff an consumer surplus eclines less uner specific tariff. However, CES utility function is more restrictive than a utility function that allows enogenous mark-up. With constant mark-up import equivalent avalorem tariff oes not change in a way that alters the relative importance of tariff revenue an consumer surplus because firms can only respon by ajusting their outputs, price is alreay etermine as a constant multiple of their marginal cost. 4 Conclusion Although the effects of ifferent tariff regimes in imperfectly-competitive markets have been stuie in the literature, little attention is given to the welfare effects in monopolistically competitive markets. Jørgensen an Schröer (2005) show that specific tariff generates higher welfare in a symmetric two country setting 11

12 with monopolistic competition moel. In contrast to the general belief that a-valorem tariff is welfare superior than the specific tariff, they show that specific tariff always generates higher welfare than an import equivalent a-valorem tariff. This paper argues that Jørgensen an Schröer (2005) s result is sensitive to the functional form of the utility. When the utility function is change to the one that yiels variable mark-up as in use in Melitz-Ottaviano (2008), their welfare result oes not hol in general. Welfare uner a-valorem tariff is superior than the specific tariff when the love for variety is not high enough. This parametric result reestablishes the results from non-monopolistic imperfect competition settings for some parameter values. The main reason for the ifference in results are ue to the utility function use which gives a linear eman that allows enogenous mark-up. Besies its contribution to the literature on welfare comparisons of unit versus a-valorem tax/tariff, this paper also opens up a new research question: How will the welfare comparison results change if we incorporate the heterogeneity of firms as in the new trae literature? 14. Recently, Cole(2008) moels firms as heterogenous an allows for asymmetric trae restrictions. However, he only focuses on the effects of asymmetric trae restrictions on prouct variety. Hence, the question pose above is still open. When a government imposes specific tariff, the share of tariff in the price that consumers pay increases as prouctivity of a firm increases. This eteriorates the competitiveness of prouctive firms an allows relatively less prouctive firms to operate. Thus, we can observe more variety. On the other han, less competition brings higher average prices. Contrary to specific tariff, a-valorem tariff favors more prouctive firms. Maintaine competition makes it harer for less prouctive firms to survive. Hence, we observe less variety but lower prices compare to specific tariff. The aggregate effect of these two opposing forces on welfare may be parameter epenent. I leave this question as a future research topic. References [1] Dixit A., an J.Stiglitz (1977) Monopolistic competition an optimum prouct iversity, American Economic Review, (67), 1977, [2] Delipalla, S., an M. Keen. (1992) The comparison between a valorem an specific taxation uner imperfect competition, Journal of Public Economics, (49), [3] Cole M.,(2008) The Choice of Moeling Firm Heterogeneity an Trae Restrictions, Working Papers , School Of Economics, University College Dublin. 14 I woul like to thank the eitor an the referees for pointing out this question. 12

13 [4] Feenstra R.(2003), A homothetic utility function for monopolistic competition moels, without constant price elasticity, Economic Letters (78) [5] Jørgensen, J.G., an P.J.H.Schröer, (2005) Welfare-ranking a valorem an specific tariffs uner monopolistic competition, Canaian Journal of Economics 38(1), [6] Hamilton,S., (1999), Tax incience uner Oligopoly : A Comparison of Policy Approaches, Journal of Public Economics, (71), [7] Helpman,E. an P.Krugman, (1989) trae Policy an Marlet Structure, Cambrige MIT press. [8] Keen, M. (1998), The balance between Specific an A-valorem taxation, Fiscal Stuies, (19), 1-37 [9] Kowalczyk, C., an S.E. Skeath (1994) Pareto ranking optimal tariffs uner foreign monopoly, Economic Letters 45,, 3559 [10] Melitz M., an G. Ottaviano, (2008) Market Size, Trae, an Prouctivity, Review of Economic Stuies, (75), [11] Ottaviano, G. I. P. T. Tabuchi, an J.F.Thisse, (2002), Agglomeration an Trae Revisite, International Economic Review, (43), [12] Schröer,P.J.H (2004), The Comparison between a Valorem an unit taxes uner monopolistic competition, Journal of Economics (83), [13] Skeath, S. an R. Trenel, (1994a) A Pareto comparison of a valorem an unit taxes in noncompetitive environments, Journal of Public Economics 53(1), [14] Skeath, S.E., an G.A. Tranel (1994b) Paretosuperior trae policy, Journal of International Trae an Economic Development, 3, [15] Suits, D. B. an R.A. Musgrave (1953), A valorem an unit taxes compare, Quarterly Journal of Economics (67),

14 APPENDIX When firms ecie on the output level, both in omestic market an in foreign market, they optimize the level of prouction given the resiual eman in each market. I also argue that the two markets are segmente. Therefore, the optimal level of output in omestic market is not a function of the foreign market variables. However, the total profit level in both markets has to cover the fixe entry costs. Therefore, it is the free entry conition that escribes how the omestic market output level an foreign market output level are relate. In aition, using the pricing an inverse eman rules, one can escribe the ifference between omestic an foreign output levels. These two equation for two import restrictions are escribe below: Free entry conition for a-valorem tariff is ( q t ) 2 + (1 t) ( q t x ) 2 = fe L γ, (A-8) ifference between the quantity prouce in omestic an foreign market is q t q t x = L 2γ t c, (A-9) 1 t free entry conition for specific tariff is (q s ) 2 + (q s x) 2 = fe L γ, (A-10) an ifference between the quantity prouce q s q s x = L 2γ s. (A-11) Equations (A-10) an (A-11) is rawn on a omestic output versus foreign output graph. However, to be able to raw equations relevant for a-valorem tariff restriction, we nee to know the import equivalent tariff level compare to s, in other wors we nee to know how s compares to t 1 tc. The proposition below escribes the range of equivalent t compare to s. t H is efine as the a-valorem tariff restriction that creates the same level of foreign output as the specific tariff, i.e qx s = q t H x. Similarly, t L is the a-valorem tariff restriction that creates the same level of omestic output as the specific tariff, i.e. q s = qt L. Lemma: Given specific tariff rate s, import equivalent a-valorem tariff rate t is between t H an t L.Firms are larger uner a-valorem tariff: i.e q t > qs an qt x > q s x Proof: Lets assume an a-valorem tariff rate t L such that q s = qt L. From free entry conitions (6) an 14

15 q q s qs qs x = L 2γ s t L 45 t H F EC s F EC t q s x q x (4),we get q t L x > q s x. When we calculate the aggregate import levels; import level with specific rate s is Q s = N s qx s = L(α c) 2γqs η(q s+qs x ) qx. s Import level with a-valorem tariff rate with t L is Q tl = N tl q t L x = L(α c) 2γqtL η(q t L +q t L x ) q t L x. Q s Q tl = L(α c) 2γqs η(q s + qs x) = L(α c) ( qxq s t L qx s L(α c) 2γqt L η(q t L + q t L q t L x q s η (q s + qs x) ( q t L x ) q t L x ) 2γq t L q s (qs x q t L + q t L x ) = (qs x q t L x ) ( L(α c)q t L 2γq t L q s η (q s + qs x) ( q t L + q t ) < 0 L x Therefore, Q s < Q tl, which means that t L is not restrictive enough to generate equal import level for given s. In orer to ecrease imports uner a-valorem tariff, we have to increase the import restriction. So import equivalent t has to be less than t L. Thus, q t > qs = qt L. Lets assume an a-valorem tariff rate t H, st. q t H x q s < qt H. ) x ) = q s x. From free entry conitions (6) an (4), we know Q s Q th = L(α c) 2γqs η(q s + q qs x s 1 x) 2 = L(α ( c)qt H x q t H q s η (q s + qs x) ( q t H = ( q t H ) q s q t H x η (q s + qs x) ( q t H L(α c) 2γq t (q H t H + q t ) q t H H x x ) ( 2γq t H x qx s q s q t ) H + q t H x ) (L(α c) + 2γq t H x ) + q t ) > 0 H x Thus Q s > Q th, t H is too restrictive, an there are more imports than uner the a-valorem tariff regime. 15

16 So import equivalent t shoul be less than t H. Therefore, q t H x = q s x < q t x. tariff. Lemma: There are more varieties uner spesific tariff restriction. Proof: Ns = L(α c) 2γqs η(q s +qs x ) an N t = L(α c) 2γqt η(q t +qt x ). Since q s < qt an qs x < q t x, N s > N t. Lemma:Consumer surplus with specific tariff is greater than the consumer surplus with a-valorem Proof:Consumer surplus can be expresse as utility from consuming the goos minus the expeniture on them. CS = q0 c + α qi c i 1 2 γ (qi c ) 2 i 1 2 η = α qi c i 1 2 γ = 1 2 γ = 1 2 γ (qi c ) 2 i η (qi c ) 2 i 1 2 η (q c i ) 2 i η (Qc ) 2 qi c i 2 qi c i qi c i 2 2 qi c p i i q0 c qi c (α γqi c ηq c )i CS = 1 2 γn(q2 x + q 2 ) η(qc ) 2 anηq c = α c 2γq CS s CS t = 1 2 γn s((qx) s 2 + (q) s 2 ) η(qc s) γn t( ( qx t ) 2 ( ) + q t 2) 1 = 1 2 γn s (qx) s γn s (q) s γn ( ) t q t 2 1 x > 1 2 γn s (q s x) γn s (q s ) γn t ( q t x ) γn t 2 η(qc t) 2 2 γn ( ) t q t (ηqc s ηq c t)(q c s + Q c t) ( ) q t γ(qt q)(n s s q s + N t q) t ) = 1 (N 2 γ s (qx) s 2 ( ) N t q t 2 ( ) x + Nt q t 2 Ns (q) s 2 + 2N s qq s t 2N t qq t s = 1 (N 2 γ t qxq t x s N s qxq s x t ( ) ) + N t q t 2 Ns (q) s 2 + 2N s qq s t 2N t qq t s = 1 2 γ (( N s N t )(q s q t q t xq s x) + N t q t (q t q s ) + N s q s (q t q s )) > 0 tariff. Therefore, consumer surplus with specific tariff is greater than the consumer surplus with a-valorem 16

17 Figure 3: Tariff Revenue Ranking of Import Equivalent A-valorem an Specific Tariffs γ love for variety α relative eman for the ifferentiate proucts A valorem tariff ominates Specific tariff ominates Problem unefine 17