DEPARTMENT OF ECONOMICS DISCUSSION PAPER SERIES

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1 ISSN EPARTENT O ECONOICS ISCUSSION PAPER SERIES Optimal Trade Policy ith onopolitic Competition and eterogeneou irm Jan I. aaland, Anthony J. Venable Number 782 ebruary 206 anor Road Building, Oxford O 3UQ

2 5/2/6 Optimal trade policy with monopolitic competition and heterogeneou firm Jan I. aaland Norwegian School of Economic Anthony J. Venable Univerity of Oxford Abtract Thi paper derive optimal trade and dometic taxe for a mall open economy containing a monopolitically competitive C ector in which firm may have heterogeneou productivity level. Analyi encompae cae in which the dometic C ector i able to expand or contract flexibly, or i contrained to be of fixed ize. In the former cae dometic protection can bring gain by increaing the number of product varietie on offer; thee gain and the correponding rate of dometic ubidy or of import tariff are reduced by heterogeneity of foreign exporter ome of whom may withdraw from the market. In the latter cae gain from protection arie from term-of-trade effect; ince variou margin of ubtitution are witched off, only the relative value of dometic taxe, import tariff and export taxe matter. In general, policie work through both a term-oftrade and a variety effect, and the paper how how the relative importance of each depend on the tructure of the economy. Keyword: trade policy; monopolitic competition; heterogeneou firm; term of trade; variety; productivity. JEL claification: 2, 3 Acknowledgement: Thank to Swati hingra, Andre Rodriguez-Clare, referee, and participant in eminar in Bari, Bergen, ETSG and Oxford, for comment. Thi paper i a revied verion of CEPR icuion Paper no. 029, October 204 and N icuion Paper SA Author Addree: Correponding author J.I. aaland A.J. Venable epartment of Economic, epartment of Economic N anor Road 5045 Bergen, Norway Oxford O 3UQ UK Jan.haaland@nhh.no tony.venable@economic.ox.ac.uk

3 . Introduction hat combination of dometic and trade taxe maximie welfare in an open economy? The anwer to thi turn on two ort of reaon for intervention; one i to manipulate the term of trade and the other i to mitigate dometic ditortion. The optimal tax and tariff tructure depend on the extent to which policy can operate on each of thee margin. e reviit thi quetion in an economy in which ome activity take place in a ector with monopolitic competition and firm differing in their productivity. Our objective i to better undertand the welfare economic of model with thee feature by identifying ource of inefficiency in the market equilibrium and the tax policie that correct them. To achieve thi objective we work with a relatively general model tructure that encompae and extend a ubtantial part of the exiting literature. e derive explicit formulae for optimal and contrained optimal taxe on dometic ale, import, and export, both when the monopolitically competitive C ector contain ymmetric firm Krugman 980, and when firm have different productivity level elitz Thi ditinction matter for the repone of firm in the C ector to policy. Optimal policy alo depend on the general equilibrium repone of the economy, in particular the elaticity with which labour the only ectorally mobile factor can be hifted between the C ector and a perfectly competitive PC ector. e derive reult for intermediate value of thi elaticity a well a for the polar cae that are in the literature, i.e. perfectly elatic upply Krugman 980, Venable 982, lam and elpman 987, Baldwin and orlid 200, Campolmi, adinger and orlati 204, Oa 20, Bagwell and Staiger 205, or perfectly inelatic a in the one-ector economy of emidova and Rodriguez- Clare Our reult both encompa and extend part of the exiting literature. e how how many of the effect decribed in thi literature operate through different channel to manipulate the two ultimate ource of welfare gain the term of trade and dometic ditortion. By comparing cae C with and without heterogeneou firm, alternative pecification of the general equilibrium repone of the economy, and different combination of admiible policy intrument we gain coniderable inight into what drive reult and why they differ acro cae. Throughout the paper our focu i on unilateral policy action by a mall open economy. The mall open economy aumption mean that foreign wage, price indice, and number of firm are contant. owever, while dometic policy doe not influence the number of firm operating in foreign economie, it doe if firm are heterogeneou influence the number of thee firm that chooe to export to the dometic economy a in emidova and Rodriguez-Clare 2009.

4 Thi, we think, i quite a good characteriation of the policy margin faced by many countrie. Policy change the number of firm that engage in trade both the number of dometic firm that export, and the number of foreign firm that elect to upply the dometic market. or many countrie and many market thi eem to be a realitic approach; foreign activitie directly related to the country in quetion are affected by the country choice, while macro variable are not. hat are our finding? elfare gain from policy derive from two opportunitie that are not fully exploited by the market. One i the monopolitic competition C ditortion. In particular, the market under-upplie varietie becaue firm that are not perfectly dicriminating monopolit are unable to capture the entire conumer urplu aociated with a new variety. The other i the poibility of improving the term of trade ToT. Some relative price are fixed by the mall open economy aumption, and other uch a the price of firm export ale are et efficiently, maximiing the profit that can be extracted from foreign market. 2 owever, policy may, depending on the general equilibrium tructure of the economy, bring about a change in the dometic wage and thi create a ToT argument for policy intervention. Both thee mechanim generate a cae for ubidiing dometic ale to the dometic market and, in ome cae, for a poitive tariff on import. Thee policie have the effect of witching expenditure to the home C indutry leading, in general, to a price and quantity repone. The quantity repone increae the number of varietie that are offered, thereby reducing the C ditortion of under-upply of varietie. The price repone raie dometic wage relative to foreign and thereby improve the ToT. e provide a decompoition which enable u to attribute the impact of tariff to a precie combination of C and ToT effect. Thee argument apply both with ymmetric and with heterogeneou firm 3. The latter create no fundamentally new argument for policy ince thi pecification of technology i not itelf aociated with any market failure. owever, the combination of a fixed cot of exporting and heterogeneou productivity level mean that foreign firm repone to policy become more elatic. In particular, they may react to policy by changing the number of varietie old in the The C ditortion arie a price i greater than marginal cot and, for each variety, total benefit i greater than total cot. The ratio of benefit to cot are the ame at the margin and for the total, thi giving the CES property that the market upport an outcome that i efficient, conditional on the level of employment in the ector ixit and Stiglitz, 977. hingra and orrow 202 etablih that thi property alo hold with heterogeneou firm. 2 There i no trategic behaviour o trategic trade policy argument do not apply. 3 By ymmetric firm we mean firm that are identical, except in o far a their product are differentiated, a in ixit-stiglitz-krugman model. eterogeneou firm differ in their productivity, and hence in their endogenou choice to erve different market, a in elitz model. 2

5 dometic market. Thi reduce the value of uing policy to change the number of dometic varietie, ince more dometic varietie crowd-out ome imported foreign varietie. Related literature contain model which vary in at leat four repect. Some paper look at the effect of change in real trade barrier, other at tariff; ome look at unilateral change, other bilateral; model vary in their general equilibrium tructure; and they vary in whether they contain ymmetric or heterogeneou firm. Since the objective of the preent paper i to undertand the welfare economic of monopolitic competition and firm heterogeneity i.e. the inefficiencie preent in the market equilibrium we focu on tariff and other tax policy intrument that do not have a direct real cot effect, and look at a ingle open economy unilateral rather than multilateral policy. ith thi focu, we encompa everal general equilibrium tructure and both ymmetric and heterogeneou firm. An older literature from the 980 tudie tax and tariff policy under monopolitic competition, although without firm heterogeneity. Variety and a term-of-trade reaon for active policie are identified in work by Venable 982, 987, lam and elpman 987 and elpman and Krugman 989. The newer literature include paper by emidova and Rodriguez-Clare 2009 and elbermayr, Jung and Larch 203a. The former look at unilateral policy in a ingle ector economy and derive a policy reult taxing trade or ubidiing dometic production which we replicate and generalie. The latter extend the emidova and Rodriguez-Clare model to large countrie, and relate the optimal tariff to C ditortion and ToT effect. uch of the recent literature look at reduction in real trade barrier. Baldwin and orlid 200 tudy the effect of change in real trade barrier in a model with an C and a PC ector, and how that trade liberaliation will have an anti-variety effect, an effect that i preent in our work. owever, their finding that lower trade barrier raie welfare doe not generally hold with tariff rather than real barrier. The ubtantial new literature on the gain from trade alo focue on real, rather than revenue raiing, trade barrier. Arkolaki et al. 202 and following work point to the importance of trade elaticitie in determining the welfare effect of trade. Thi i developed further in elitz and Redding 204 who tudy gain from trade and from bilateral liberaliation in a ingle ector economy, looking at both ymmetric and heterogeneou firm. The two cae imply different trade elaticitie which hape the gain from liberaliation and in our work hape optimal tax and tariff policy. Our focu i on policy by a ingle country, maintaining the mall open economy aumption. The penultimate ection of the paper dicue how our reult would extend to a full multi- 3

6 country model, and hence to the work of Campolmi, adinger and orlati 204, Oa 20 and Bagwell and Staiger 205. The remainder of the paper i organied a follow. Section 2 et out the model in quite an extenive way, carrying a lot of variable and making few ubtitution. Reult are derived uing comparative tatic technique, lineariing the model and olving the enuing equation to derive firt order condition for tax rate. The appendix give the log-linearied ytem, and linear ubtitution of the full ytem are readily undertaken by athematica. They generate explicit optimal and contrained optimal tax formulae which are the core of our reult. Thi method enable u to derive optimal and econd bet taxe in a wide range of cae; it i conceptually imple, lending itelf to relatively eay interpretation and to application to other iue. Reult are preented and explained in ection 4 and 5. Section 4 look at the two polar cae, firt when the PC ector i uch that the upply of labour to the C ector i perfectly elatic, and then when the PC ector ha a fixed labour demand, a limiting cae of which i no PC ector at all emidova and Rodriguez-Clare Section 5 place thee in a general framework and how that reult are driven by a combination of C ditortion and ToT effect; we preent a decompoition that eparate thee force and etablihe that the former drive reult when labour upply i elatic o quantity effect are large and the latter when labour upply to the C ector i inelatic price effect dominate. Section 6 dicue the implication of relaxing the mall open economy aumption and relate our reult to literature with full two country model. Section 7 offer concluding comment. 2. The model e firt outline the ingredient of the monopolitically competitive C ector. e do thi in a uccinct manner ince many full expoition are in the literature e.g. elitz and Redding 205. Each firm in the ector produce a ditinct variety of differentiated product. Thee product generate utility according to a ub-utility function with contant elaticity of ubtitution σ. E denote total expenditure on C product in the dometic economy and P i the price index the unit expenditure function dual to the ub-utility function. The conumer price of a product i p, demand for the product i p EP, and the value of it ale i p EP. The marginal cot of a particular firm i / where i the price of labour, the only input, and i the firm productivity. irm mark-up price over marginal cot by factor σ/σ - o the producer price i / /. The conumer price deviate from thi according to ad 4

7 valorem tax factor τ, o p / /. The value, at conumer price, of a firm ale in one market i therefore EP revenue i EP. The firm capture fraction /τ of thi, o it. The remainder, fraction /τ, goe to government. 4 The firm operating profit, π, i fraction /σ of it revenue, o. EP where Entry deciion incur fixed cot that have to be weighed againt expected operating profit. In order to produce at all, each home firm pay a fixed cot from ditribution after incurring further fixed cot f E to draw a productivity parameter G. If thi exceed cut-off value the firm will ell in the dometic market f, o it expected profit on dometic ale are given by the firt term in equation below, where i the dometic tax rate. Similarly, exporting incur fixed cot price index f, i ubject to tax, and face foreign demand curve with fixed expenditure and E, P fixed by the mall open economy aumption. A firm will export if productivity exceed cut-off value. The firm expected profit on export ale are the econd term in, o the equation a a whole i the entry condition giving zero expected profit. EP f dg EP f dg fe 0. The urvival cut-off are the lowet level of productivity at which profit from an activity are non-negative. or dometic ale, atifie where EP f, and we define dg, 2 i an aggregate of the productivity of active firm according to their impact on ale. Similarly, the export cut-off i : EP f : dg. 3 In addition to home firm, there are foreign firm ome of which upply import to the dometic market. The foreign wage i fixed at unity, the number of foreign firm i exogenou, and thee 4 Our reult are qualitatively unchanged if, in addition to thee revenue raiing friction, there are real trade cot. 5

8 firm have productivity ditribution G poibly different from G. 5 They chooe whether or not to upply the dometic market. The fixed cot they incur in upplying import i f, o the importer cut-off i : EP f : dg. 4 It i convenient to have expreion for the total value of output old by dometic firm in the dometic market,, in the export market,, and by foreign firm in the dometic market, all at conumer price. The ma of dometic firm i denoted N and the ma of foreign firm N o, integrating over firm ale at conumer price and uing 2, 3, 4, N N N Notice that EP EP EP dg dg dg EP EP EP N N N E, and hence the uual definition of the price index follow from adding 5 and 7, 6 P e will call N and N N. 8 N the equivalent number of varietie upplied to the dometic market by home and foreign firm repectively. The term and adjut the number of firm that enter according to the proportion that upply the dometic market and their productivity ditribution. Government revenue, R, i earned from each of the tax intrument and, a noted above, i fraction /τ of ale at conumer price o: R / / /. 9 5 See emidova 2008 for further development of the implication of different productivity ditribution. 6 The number of active firm in each market depend on the ma of firm and the productivity cut-off,

9 Employment in the home C ector, L, i implicitly defined by the fact that, ince firm break even in expectation, the wage bill in the ector i equal to the value of ale at producer price, L / /. 0 Turning from the C ector to the general equilibrium of the economy a a whole, we aume that there i a fixed endowment of labour et at unity of which L i ued in the C ector and the remainder, L, i employed in the PC ector. The PC ector if it exit i freely traded with price unity and concave production function L. The value of national output at producer price,, i therefore L L. Labour i employed in the PC ector to the point where the wage equal the marginal value product, ' L. 2 The elaticity of labour upply from the PC ector with repect to the wage follow from thi, and i denoted ' / L' '. 7 Conumer income i the value of output plu government revenue, R. Utility i Cobb- ougla with expenditure hare on the C ector μ, giving utility U and C expenditure E, RP U, 3 E R. 4 Thi complete decription of the equilibrium; there are 4 equation in N, E, P,,,,,,, R,, L,, and U. The analyi of policy in our general cae require that both the C and the PC ector are active although the PC ector become inactive in one of the pecial cae we tudy. To enure thi, we aume that f E i mall enough for the expected profit of a dometic firm to be poitive if N = 0, implying that the C indutry i preent in the dometic economy; and large enough that expected profit are le than or equal to zero if the entire labour force i employed in the C ector. 8 e how in Appendix that expected profit are monotonically decreaing with N, thi 7 Thi elaticity i, in general, not contant. or example, if the PC production function i io-elatic, L L, then L / L. Strict concavity can be interpreted a dependence on a PC ector pecific factor of production, with factor hare -α. 8 Expected profit are the left hand ide of equation. The thought experiment here i to evaluate profit given 7

10 giving an interior equilibrium. Profit decline with N for two reaon. One i that the wage may increae a the PC ector contract equation 2. The other i dometic market crowding; entry of dometic firm increae upply to the dometic market and thereby reduce the price index equation 8 and EP import, occurring a lower value of, hence reducing profit. arket crowding i offet by diplacement of EP increae the importer cut-off, equation 4. owever, thi diplacement occur progreively becaue importer are heterogeneou, o increaing N i ure to reduce EP and hence the expected profit of dometic firm. 3. Comparative tatic Our primary tak i to invetigate the effect of change in tax intrument, and we do thi by log differentiation of the equilibrium. Expreion o derived contain proportionate change in the tax intrument and endogenou variable, together with ome further variable capturing relative value of endogenou variable. e define thee a follow. The hare of dometic firm ale in the dometic C market at conumer price, : E / /. 5 The hare of export ale in C production at producer price, : / L. 6 / Government revenue a a hare of total conumer income, r R/ R R / E. 7 inally, we define the hare of the C ector in total income,, L /. 8 Given the hare of C pending in income, μ, the hare 0, 4-8 the equation linking them i,,, are not independent. Uing r /. 9 or the remainder of the paper we aume that productivity i Pareto ditributed, i.e. G i k i k i j i, o that k / k for i =, j =, and for i =, j =. j i the number of dometic firm, N, and with other variable in equilibrium, i.e. atifying equation 2 4 8

11 e define the parameter i k i / and make the tandard aumption that k i o that i. The full log-linearied ytem i given in Appendix 2, with proportionate change denoted ^. There are exogenou change in three tax intrument, and 4 equation giving change in the endogenou variable correponding to equation 4 above 9. Our principal interet i to obtain the coefficient giving the effect of change in each of the tax rate,,,, on utility, U. Thee coefficient will in general contain parameter,,, ; endogenou variable r,,, ; and tax intrument,,,. Setting thee coefficient equal to zero give the firt order condition for optimal policy and, olving for tax rate, we obtain explicit olution for optimal policie. Thi i conceptually traightforward but i cumberome, even for the linearied ytem of proportional change; we ue athematica. One expreion containing total derivative i helpful for interpretation of reult. The welfare effect of change can be written a ee Appendix 3: ^ ^ ^ U R ^ R ^ ^ N R ^ R ^ ^. 20 R R In thi equation ^ denote a proportional change, and the term in curly bracket are proportional change in quantitie, i.e. change in the value,, deflated by their price. The equation i ueful a it how how change in the tax intrument and in endogenou variable determine the change in welfare. The firt term on the right-hand ide of 20 i the term-of-trade effect, capturing the welfare effect of an increae in the export price and remembering that the border price of import i contant by the mall open economy aumption. The export price i affected by an export tax and by any change in the dometic wage. The econd term we refer to a the C ditortion effect it capture the welfare effect of change in the number of varietie available to dometic conumer. Notice that the expreion i on change in the equivalent number of varietie, 9 The comparative-tatic equation are numbered to 4 and are found in Appendix 2. 9

12 N and N, o the effect of policy on firm election enter via change in and. The quare bracket in thi term i multiplied by factor / capturing the welfare gain from an increae in the number of varietie given total expenditure. 0 inally, the term in the econd row how the direct welfare effect of policy ditortion, generating welfare gain if policy expand an activity where the tax intrument create a poitive wedge between conumer and producer price. Optimal policie are found by etting U 0 in 20, either for one policy intrument at the time or jointly for all three taxe, and with change in endogenou variable coming from the loglinearied ytem given in Appendix 2. e derive reult both for heterogeneou firm, and for a cae which we term ymmetric firm. The difference i that in the ymmetric cae there are no firm election effect, i.e. the number of firm and varietie upplying each market varie only with N, the number of active dometic firm. The Krugman-ixit-Stiglitz model, in which all active firm upply all market, i an example of thi. In our etting, the parameter retriction equivalent to witching off election effect i, thi implying that i, i =,,, are contant ee appendix 2 equation 2 4. The point can be illutrated by inpection of the elaticity of the value of import with repect to a tariff which, uing 7 and 4, i d ln d ln. ollowing Chaney 2008, the firt element how the intenive margin the effect of a tariff on import from the exiting foreign firm and the econd element i the extenive margin, capturing the effect of changing cut-off level for the election into import. 2 ith ymmetric firm there i no election effect o the import elaticity i given by the intenive margin i.e. ha. ith heterogeneou firm, both intenive and extenive margin matter, and the combined elaticity i. Similar reaoning applie for export elaticitie. Since we allow for the poibility that, our etup i general enough for firm in one country to ymmetric and elewhere heterogeneou. In term of the welfare effect in 20, the ymmetric 0 Seen mot imply for a cloed economy with ymmetric firm where the price index i. Thi fall a N increae according to P N / p, ee alo Appendix 2 equation 8. P Np elitz and Redding 204 compare gain from trade with homogenou and heterogeneou firm in a imilar way, pointing out that the cae with ymmetric firm doe not require that all firm are identical. The key point i that there i no endogenou election effect. 2 ead and ayer 205 how how the extenive margin can be decompoed into a election effect and a compoition effect, and elbermayr et al 203b ue the ame framework to how how the effect of a tariff may differ from the effect of a real trade cot. Our expreion are conitent with elbermayr et al. 0

13 firm cae implie that the variety C ditortion effect only appear through change in the ma of dometic firm, a in tandard Krugman-ixit-Stiglitz model. 4. Optimal policie e tart by preenting reult for two pecial cae, firt with a perfectly elatic upply of labour from the PC ector to the C ector, ection 4. and then perfectly inelatic upply 0, ection 4.2. In both ection we look at policy with ymmetric firm cae A and heterogeneou firm cae B. e preent optimal tax formulae when all three tax intrument are optimied denoting value τ and where jut one intrument i optimied τ with other intrument not ued i.e. et at unity. e call the former firt-bet policie and the latter econd-bet. e omit expreion that are exceively complex. 3 In each ection we tabulate reult and draw out intuition, concentrating dicuion of intuition on the effect of an import tariff. In ection 4. we are able to develop intuition by ome imple argument which how how policy equate marginal benefit and cot. or other cae intuition i more complex and a crucial iue become undertanding the different role of C ditortion and ToT effect. Our dicuion of thi i contained in ection Perfectly elatic labour upply to the C ector A frequent aumption in the literature on trade under imperfect competition i that there i a PC ector that produce a good that ha fixed world price with contant return to labour alone 4. Thi fixe the wage in the economy, meaning that the C ector face a perfectly elatic labour upply curve. In term of the model,, 0, and L adjut freely. Table preent reult. The firt row of Table give optimal policy with ymmetric firm. The optimum i achieved by a ubidy on dometic ale of home firm, /, with the import tariff and export tax et at unity. The effect of the ubidy i to expand home C ector, bringing in new varietie thereby mitigating the C ditortion. The optimal import tariff i zero,, ince the economy i importing good at contant price. The optimal export tax i alo zero. The 3 E.g. reporting for the pecial cae in ection 4 but not the general cae in ection 5. Thee more complex expreion are available on requet from the author. 4 A tated in the introduction a number of contribution make thi aumption. In ection 6, below, we compare their reult to our and how how our decompoition of the effect help u improve the undertanding of the underlying welfare economic.

14 economy can vary it export term of trade, raiing their price by an export tax; however, dometic firm have already choen the price that maximie profit extracted from the foreign market, and any deviation from thi i welfare reducing. ith reference to equation 20, the optimal policie are determined from the trade-off between reducing the C ditortion through increaing the number of dometic varietie and increaing the policy ditortion from ubidiing dometic conumption. Turning to cae in which only one intrument i ued, the optimal value of i a above. If the tariff i the only intrument, then it hould be poitive,. In term of equation 20 thi ditort the dometic price of import away from the marginal cot at which they are upplied to the economy, but i a econd bet policy to expand the dometic C ector, bringing in dometic varietie and mitigating the C ditortion. 5 The economic intuition underlying thi can be developed by etablihing the marginal benefit and cot of the quantity change, and noting that optimal policy equate the ratio of marginal benefit to marginal cot acro affected quantitie. The firt quantity change from an import tariff i a reduction in import of C product. Their marginal cot to the economy i their price, and their marginal benefit i price time the factor, a the tariff raie the marginal value. 6 The econd quantity change i that, a the tariff hrink import of C product, o it expand dometic production. A uual in a ixit-stiglitz model ale per firm are unchanged, o the quantity change i met entirely by a change in the ma of dometic firm, N. Entry of a new variety bring conumer urplu, and the ratio of utility to expenditure i /. Since firm break even expenditure on each product equal expected cot, o the ratio of benefit to cot for a marginal change in the number of varietie i /. Equating thee marginal benefit-tocot ratio for the change in import and the change in dometic production give the tariff formula /. Continuing in part A of table, the final row give the optimal export tax when other intrument are not ued; it hould be ued to ubidie export it maximum value i unity, occurring if. Thi i econd bet policy haped by the interaction of two force. The ubidy attract entry of dometic firm an increae in N which increae the number of varietie offered in the dometic market, partially correcting the C ditortion. But, ince thi policy involve ubidiing foreign conumer ToT lo it i an inefficient intrument, o the ubidy i 5 Notice from that E P 0, o 0 from 7 and N 0 from 5, creating the policy ditortion and variety effect repectively. 6 Equivalently, marginal benefit i price time, where the econd term i tariff revenue earned. 2

15 3 relatively mall going to zero if. In term of equation 20, it i a trade-off between three element the ToT lo, the C ditortion gain, and the direct policy ditortion from ubidiing export. Table : Optimal policy with perfectly elatic labour upply. A: Symmetric firm. All taxe optimally et: ixed taxe Optimied taxe - B: eterogeneou firm:, All taxe optimally et: ixed taxe Optimied taxe, x The lower panel of Table give policy with heterogeneou firm, cae B. The key difference i that expanding the dometic C ector now reduce the number of foreign firm that elect to

16 upply import i.e. raie the foreign import cut-off and reduce in equation 4 and 4 o welfare gain from drawing in dometic varietie are offet by lo of imported varietie. irt-bet optimal policy i therefore the dometic ubidy a before, combined with an import ubidy,. The ize of thi depend on the magnitude of the expenditure elaticitie with repect to tax rate, with the import ubidy le than the ubidy to dometic firm, and collaping down to the ymmetric cae when. Notice that the expreion for contain not o it i heterogeneity of foreign, not dometic firm that make the cae for the import ubidy. ith reference to equation 20 again, we now have two force affecting the number of varietie in the econd term of the equation: an increae in the equivalent number of dometic varietie N 0 and a reduction in imported varietie 0 ; optimal policy require two intrument, each et to balance variety gain againt the direct policy ditortion. If i the only intrument ued then it hould be a ubidy, although at a lower rate i.e. cloer to unity than in the ymmetric cae becaue of the lo of imported varietie; the optimal value depend on foreign election,, not on dometic firm election. The import tariff alone mirror that in the ymmetric cae, but with replaced by, implying a lower tariff. 7 The argument for policy i imply the C ditortion, but the number of C varietie on offer now change at two margin, N and. The final row of the table i the export tax with heterogeneou firm. A in the ymmetric cae, the export ubidy i determined by tenion between ToT lo and variety gain. It collape to the ymmetric cae if and i a maller ubidy if,. Thi i becaue change in both the import and export cut-off reduce the impact of the export ubidy on the number of varietie old in the dometic market; ome import varietie are crowded out, and ome of the quantity repone of the dometic indutry i more firm exporting rather than an increae in N. It i noteworthy that thi i the only reult reported Table in which appear, i.e. where heterogeneity of dometic firm ha any bearing on policy. The reaon can be een by inpection of - 4 ; the productivity cut-off and ee footnote 3, again, while both thee cut-off are affected by. are unaffected by either or 7 Intuition for thi come from extending the line of reaoning that we ued in the ymmetric cae, but where proportion / of the change in import come from the extenive margin, i.e. a change in the number of varietie upplied, and thi change carrie the premium /. 4

17 4.2 Inelatic labour upply to C ector e now look at ituation in which the general equilibrium tructure of the economy i uch that the upply of labour to the C ector i perfectly inelatic, thi including the one ector economy tudied by emidova and Rodriguez-Clare 2009, henceforth RC. hile tax formulae derived in thi cae are imilar in everal cae identical to thoe in the previou ection, they are driven by quite different mechanim. Eentially, when labour upply i elatic quantity change interact with the C ditortion, but when it i fixed quantity effect are abent and price effect the ToT drive reult. The ditinction i key to undertanding the role of policy and welfare economic more generally in thi cla of model. It turn out that there are two aumption involved in going from a general etting to the reult of RC. One i that 0 o that the upply of labour to the C ector i perfectly inelatic. The other i that, o dometic conumer only purchae the C good. Table 2 preent reult in three tage; firt, the infinitely elatic labour upply cae, 0,, repeating the firt row of each ection of Table ; econd, 0, 0, ; and finally 0,, the RC cae. The firt row of each block of Table 2 give reult for, 0, in which optimal policy require etting all three of the intrument at the value indicated. In the econd row the ize of the dometic C ector i fixed by inelatic labour upply. Thi ha the conequence that, ince dometic C production cannot change, the only margin i it ditribution between dometic and export ale. ence, policy i achieved by the ratio / taking the value indicated the eparate value of and being immaterial, together with in the cae of ymmetric firm. 8 ith firm heterogeneity, it i optimal to ubidie import a well a dometic conumption to counteract the crowding out of imported varietie due to the foreign election effect. In the third row of each block the conumer demand margin i alo removed, by auming that conumption conit olely of the C good,. Thi mean that the only tax intrument that matter i the combination /. Varying any one of,, ha the ame real effect, changing export and import together. Thi i a conequence of Lerner ymmetry in what i now a very imple economy. ith heterogeneou firm final row, thi give the reult derived by RC in a ingle ector economy. e note that it doe not require that the economy contain a ingle ector, or that trade in the C good be balanced the PC ector could till exit, imply 8 Table 2 doe not report cae where an intrument i contrained to equal unity. 5

18 taking a fixed amount of labour to produce and export a fixed amount of output. But it doe require that margin of ubtitution between the C ector and the PC ector on both the upply and demand ide are witched off. Table 2: Inelatic labour upply and Lerner ymmetry A: Symmetric firm., 0, : 0, 0, : 0, : B: eterogeneou firm., 0, : 0, 0, : 0, :, epite the imilaritie in the tax and tariff formulae in Table and 2, the mechanim driving policy are completely different in the two cae. Conider firt ymmetric firm with 0,. Policy cannot be operating through the dometic C ditortion a it doe in Table, ince the ize of the C ector, number of varietie offered, and output of each firm are completely fixed and invariant to policy. Intead, the dometic wage change, and it i thi that generate a ToT effect. Given thi ToT effect, the optimal value of the export tax or equivalently import tariff i imply the reciprocal of the foreign elaticity of demand for home export. 9 9 Thu, in the ymmetric firm cae /. e have alo derived reult with ditinct notation for home and dometic elaticitie of ubtitution,, ; and in Table 2A it i not in thee 6

19 Similarly, with heterogeneou firm and 0,, there i a ToT effect and the optimal tariff i the invere of the foreign upply elaticity, /. ith firm heterogeneity and 0, 0, the econd row in Table 2B there will be a combination of a ToT and a variety effect, due to the election mechanim for home and foreign firm. The reaon i a follow: even if the total production of C good i given from the inelatic labour upply, a dometic ubidy or an export tax will affect both the wage rate and upply and demand of C good to dometic conumer. On the upply ide, reduced profitability of export implie that the number of exporting firm goe down, while the number of firm elling in the dometic market increae 20. On the demand ide, conumer expenditure are witched from PC to C good, a the price index for C good goe down. inally, import are affected poitively by the wage effect but negatively from the direct effect of the dometic policy meaure; the import ubidy partly offet thi. ence, there will be a combination of ToT and variety effect in thi cae and the relative importance of each depend on the trength of the election mechanim. e dicu thi more fully in the context of the general cae next ection, uing our decompoition of the welfare effect of policy, equation The general cae: optimal policie and welfare decompoition Our focu up to thi point ha been on deriving optimal tariff and tax formulae for the pecial cae of perfectly elatic and fixed labour upply to the C ector. e now witch to the general cae and invetigate two iue. irt we derive optimal policie ection 5. and then, focuing on the import tariff, decompoe it effect on welfare into a ToT part and an effect through C ditortion ection Optimal policie in the general cae Table 3 give firt and econd bet optimal policie for the general cae [i.e. 0,, 0, ]. Several obervation tand out. irt, if all three tax intrument are et optimally, then tax and expreion. 20 Uing -4 it i eay to ee that with 0 we have 0 and 0, and ince the ma of firm, N, i given in the cae of inelatic labour upply, the equivalent number of firm erving export and dometic market follow directly from thee election effect. 2 Oa 20 dicue the importance of labour market flexibility for policy motive; however, in hi analyi he aume a perfectly elatic labour upply to the C ector. Crozet and Trionfetti 2008 analye the importance of concavity in the PC ector for the home-market effect. owever, they do not focu on policy iue. See ection 6 for further dicuion. 7

20 tariff rate are independent of η and μ and hence the ame in Table, 2, and Thi i true both with ymmetric and heterogeneou firm. owever, although the firt-bet policie are the ame, the underlying mechanim differ, a we dicu further below. Second, when only dometic ubidie are in ue their optimal level,, doe not depend on the elaticity of labour upply,, ee Table 3. The reaon i that all relative conumer price between dometic C good, import and PC good are affected by, not by and individually; hence, the elaticity of labour upply doe not have a eparate effect on the optimal dometic ubidy. ith ymmetric firm the ubidy take value /. ith heterogeneou firm depend on, and it i eay to ee that a increae, goe toward /. 23 Third, optimal value of each of the trade policy intrument depend on we report import tariff only, the export tax formula being complicated. Thi i becaue, in contrat to the dometic tax rate, trade taxe and the wage rate have different effect on relative price faced by conumer. or both the ymmetric and heterogeneou firm cae, the econd-bet optimal tariff i increaing in and approache the level in Table a. It i alo increaing in. In the general cae, an import tariff will have both a variety C ditortion and a ToT effect; their relative importance will be further analyed in ection 5.2. inally, firm heterogeneity affect the magnitude, but not the ign of econd-bet policie. The role of firm heterogeneity come through by comparing ection A and B of Table 3. Selection effect for importer lead to a lower optimal tariff or a lower dometic ubidy, ince dometic varietie crowd out imported one. Selection at home on the other hand, increae the optimal econd-bet tariff. The reaon i that with heterogeneou firm, the change in export following a tariff will in part come a a reduction in the hare of firm exporting the extenive margin. Thi dampen the wage effect and increae the variety effect of an import tariff. 22 Although in the one-ector economy, only relative taxe matter, a hown in ection See alo Table and 3. The cae of dometic ubidie alone i not reported in Table 2 although, ince only relative ubidie matter, it i implied by other expreion. 8

21 9 Table 3: Optimal policy in the general model A: Symmetric firm. All taxe optimally et: ixed taxe Optimied taxe,.,,. B: eterogeneou firm:, All taxe optimally et:,, ixed taxe Optimied taxe,,, 5.2 ecompoition of the tariff effect e uggeted in preceding ection that policy i determined by a combination of C and ToT effect, the former dominant if the elaticity of labour upply to the C ector i high, the latter if it i low. In thi ection we give the precie decompoition of thee effect, building on equation 20 and focuing on an import tariff, o and 0. rom 20, the condition for the optimal tariff then become ee alo Appendix 3 0 R R N R R U 2

22 The change, N,,, come from differentiation of the equilibrium with repect to, and follow from equation 4 of Appendix 2, aking the ubtitution yield a complex expreion which it i convenient to ummarie a U ToT C T 0, where ToT i the term-of-trade effect, C i the variety effect, and T i the effect of the tariff wedge. If the tariff i optimally choen the term in curly bracket i equal to zero, T {ToT C}, o ToT C U ToT C ToT C ToT C The firt two term in curly bracket give the relative contribution of the TOT and C effect. The expreion for the hare of the ToT and C effect in the general cae evaluated at the optimal econd-bet tariff rate, i.e. from the final row of Table 3B are ee Appendix 3, ΤοΤ ΤοΤ ΜC x, 23 ΜC ΤοΤ. 24 ΤοΤ ΜC ΤοΤ ΜC It i clear from 23 that a more elatic upply of labour to the C ector higher η reduce the contribution of the ToT effect. A o 23 goe to zero and 24 to unity, confirming that the reult of Table are driven entirely the C ditortion, not the ToT effect. The polar oppoite cae of Table 2 ha 0,, o 23 and 24 become ΤοΤ ΤοΤ ΜC, ΜC ΤοΤ ΜC. 25 If the ditribution of productivity are the ame in both countrie,, then welfare effect are entirely due to ToT argument. Although individual firm take into account the lope of foreign demand curve for their varietie they do not internalie the fact that change in output change the wage, and it i thi that create the ToT effect. owever, if then there i alo a poitive C ditortion effect. Eentially, the poitive repone of dometic varietie to a tariff i greater abolute value than the negative repone of foreign varietie, meaning that even in the one ector economy of ection 4, there i a variety gain from an import tariff. ence, for the ingle-ector economy, the main meage from thi decompoition i that, while ome C ditortion effect are preent if, the cae for the tariff i driven principally by 20

23 the fact that it improve the ToT. A the tariff cut import, o the wage ha to rie in order to cut export in line. ore generally, the hare of the ToT effect i trictly decreaing in both η and μ, a can be een from equation 23 24, Small veru large economy analyi In the analyi o far we have focued on a mall open economy. hat additional effect come into play if thid aumption i relaxed? ometic policy can then, in principle, change the foreign wage, ma of active firm, and price index. Thi will change equilibrium repone the derivative of Appendix 2, and add two new term to our expreion for dometic welfare change, equation 20. A change in the foreign wage change the price of dometic import, having a ToT effect, and a change in the ma of foreign firm change the number of varietie old in the dometic economy, o ha an C ditortion effect. ormally, equation 20 become U R ^ R / N N R ^ R R R ^. 26 R Subcript and are added to identify home and foreign variable a appropriate. Thee term combine into ToT and C effect, together with the policy ditortion, a before. owever, the ToT effect the firt quare bracket i now the weighted um of change in export and import price, both meaured at international border price, where the weight are the value of export and import, repectively, meaured at border price. Thu, an increae in foreign wage,, reduce dometic welfare. The C ditortion effect the econd quare bracket depend on the change in the ma of dometic firm N and the election of dometic and foreign firm into upplying the dometic market, change in the ma of foreign firm, N. a before, and now alo on the It i ueful to compare thi expreion to paper analying the large economy cae. or example, Campolmi, adinger and orlati 204 henceforth C tudy a large economy Krugman 24 Thee are the derivative holding the hare variable, x, contant. 25 Similar exercie done for the firt-bet policie in Table 2B reveal that with 0, 0, there i a combination of a ToT and a variety effect even if, while for 0, there i only a variety effect if, a in 25. 2

24 model with perfectly elatic labour upply, and dicu four poible effect of policy. The firt i the C ditortion, operating via N. The econd i a production relocation effect ometime known a a home market effect and referred to by C a a delocation motive. Thi occur a, in a full two country model, a hock will in general change both ymmetric firm, o election effect, N and N C ha are abent. Thi production relocation effect change welfare through it impact on the upply of varietie, i.e. interacting with the Cditortion and impacting welfare through the econd quare bracket in 26. It ha been extenively tudied in the two-country Krugman model for example Venable 987, C, Oa 20, Bagwell and Staiger 205. Thu, a home import tariff raie N and, in the full twocountry model, reduce N. Thi may raie dometic welfare, a can be een by noting that, in equation 26, a ymmetric change N = - N > 0 will have a poitive effect on welfare if dometic firm ale are a larger hare of expenditure than are import, / R / R. The third mechanim analyed by C i a ToT effect. In their framework wage are contant o a ToT effect arie only through a change in dometic export taxe a in the firt term of equation 26 or wage taxe not preent in our model. If labour upply to the C ector i le than perfectly elatic, a in the preent paper, a hock will alo impact the ToT via change in wage, and. Thu, a production relocation will impact the ToT a well a the Cditortion. A we have een the relative importance of ToT veru C-ditortion effect depend on the elaticity of labour upply to the C ector. Thi i clearly tated although not formally modelled by Oa 20. hile our approach i to endogenie the wage repone via diminihing return to cale or equivalently the preence of a fixed factor in the PC ector, Crozet and Trionfetti 2008, in a paper about the home market effect, achieve wage endogeneity by making an Armington aumption on the output of the PC ector. C fourth mechanim i called a fical-burden-hifting effect, and correpond to the policy induced ditortion in the final row of 26. It appear when more than one policy intrument i in ue. A an example, if there i an export ubidy in place and a wage tax alter the quantity exported, then the change in export ubidie hould be taken into account when determining the effect of the wage tax. Thi comparion illutrate the conitency of our analyi with the reult of thee paper, and alo make an important general point. Ultimate gain from policy in thi cla of model arie from C-ditortion and ToT effect, but thee can be driven by different policy intrument and occur via different channel. Thu, ToT effect occur through export ubidie or, if labour i 22

25 upplied inelatically, through a broader et of meaure that change demand for labour in the C ector and hence change wage. C-ditortion effect arie a the number of dometic firm change and alo a the number of foreign firm upplying the dometic market may be affected by dometic policy. Thi arie in large economy model production relocation, and alo in the preence of firm level heterogeneity when, a we have hown, dometic policy will influence the number of foreign firm chooing to upply the dometic market. e think it important that the numerou different effect and channel decribed in the literature are undertood in term of the ultimate mechanim through which they change welfare. inally, a large open economy model enable analyi of the repone of foreign policy intrument to dometic policy. Thi i beyond the cope of the preent paper, although we note the contribution of Oa 20 and Bagwell and Staiger 205 to thi quetion, illutrating how relocation and term-of-trade effect may play key role in international trade policy competition. A hould be clear from our dicuion of C above, the policy motive are the ame in our mall open economy model a for large economie; however, with active policie in everal countrie, non-cooperative policy olution will typically differ from the unilateral policie of our model. 7. Concluding comment The model of trade and ixit-stiglitz monopolitic competition, with or without heterogeneou firm, i the workhore model of trade theory. The tructure i imple enough to yield explicit formula for optimal policie, yet alo complicated enough for the algebra involved in deriving thee for the general cae to explode. Thi ha given rie to a literature of pecial cae and incomplete general undertanding. The preent paper ha derived the optimal tax and tariff formulae in a model that encompae thee pecial cae and thereby draw out the underlying argument for policy. The main meage are that there are potential gain from uing policy to upport the home C ector, either through a ubidy to firm dometic ale or through trade taxe. The gain are driven by a combination of two effect, one through quantitie, the other through price. The quantity effect arie from the interaction of trade policy with the C ditortion; upporting the dometic indutry increae the range of product on offer with beneficial variety effect. The price effect arie through the general equilibrium of the model; if labour upply to the C ector i inelatic then upporting the C ector raie wage and thi bring a ToT improvement. The preence of heterogeneou productivity temper reult ince the number of foreign varietie old in the dometic market i endogenou and foreign reaction become more 23