P1: GIU International Tax and Public Finance SJNW NO April 2, :54

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1 International Tax and Public Finance, 12, 1 19, 2005 c 2005 Springer Science + Business Media, Inc. Printed in the Netherlands Tax Principles, Product Differentiation and the Nature of Competition NIGAR HASHIMZADE HASSAN KHODAVAISI University of Exeter GARETH D. MYLES g.d.myles@ex.ac.uk School of Business and Economics, University of Exeter and Institute for Fiscal Studies, UK Abstract We analyze the choice between the origin and destination principles of taxation when there is product differentiation and Bertrand competition. If taxes are redistributed to consumers and demand is linear the origin principle dominates the destination principle whatever the degree of product differentiation and extent of economic integration. With nonlinear demand the origin principle dominates if there is sufficient economic integration. When the social value assigned to tax revenue is higher than the private value, the destination principle dominates for intermediate values of product differentiation and economic integration. The same results are also shown to hold with Cournot competition. Keywords: commodity taxation, imperfect competition, Bertrand competition, Cournot competition JEL Code: F12, H20 Au: Pl. provide complete aff. and Introduction Continuing economic integration at the regional level, such as within the European Union and also in North America, and recent attempts by World Trade Organization at the international level, has re-opened the debate on the proper scheme of taxing international trade. The increasing revenues from taxes on goods and services have made indirect taxes the most important source of tax revenue in the European Union. This increased dependence on value added taxation (VAT) and the deepening of international economic integration makes it important to study the international repercussions of national commodity taxes. In particular, the issue of whether commodity taxes should be based on the destination principle or on the origin principle has become central to the policy debate. At present, commodities which are internationally traded are generally subject to taxation according to the destination principle so they are taxed in the jurisdiction in which final consumption occurs. In practice problems are met in implementing and maintaining the destination principle. The main problem is that not all consumers will be taxed under the destination principle when borders are open. Those consumers who cross borders and

2 2 HASHIMZADE, KHODAVAISI AND MYLES purchase their commodities abroad pay the tax of the foreign country rather than the tax of the 33 country of residence. Therefore the destination regime provides an incentive for jurisdictions 34 to engage in a mutually-harmful process of commodity-tax competition in order to attract 35 cross-border shopping and other forms of direct consumer purchases (Sinn, 1990). Cross- 36 border shopping will be increased, and as a direct result tax competition may be intensified, 37 if the transaction costs for tax arbitrage in the form of cross-border shopping are reduced The other important problem which undermines the general applicability of the destination 39 principle is the growth of remote sales through mail ordering and electronic commerce, 40 which open new routes for consumers to engage in tax arbitrage With regard to the above discussion, it is clearly recognized that enforcing destination- 42 based taxes on these purchases entails large compliance costs. The implementation of the 43 destination principle requires border tax adjustments to ensure that imports are taxed and 44 exports are exempted. These adjustments need a mixture of physical border controls and 45 accounting checks which on their own violate the free-trade agreements between coun- 46 tries. Given these practical shortcomings, the case for the destination principle has been 47 reconsidered in recent years and it has been asked whether it is welfare-enhancing to shift 48 to the origin principle. Under the origin principle, commodities are subject to taxation by 49 the jurisdiction in which they are produced. Given that a pure destination principle is not 50 possible in the absence of border controls, a number of arguments have been made in favour 51 of a complete switch to the origin principle (Sinn, 1990). 52 The choice between the destination and origin principles has been extensively discussed 53 in the literature. The main result is that the destination and origin principles are equivalent 54 if either exchange rates or producer prices are fully flexible and if the commodity tax can be 55 levied on all commodities at the same rate (Lockwood, de Meza and Myles, 1994). Under 56 these conditions it has been argued that a switch from the destination to the origin principle 57 has no real effects. However, important sectors of the economy such as banking or insur- 58 ance are currently not included in the regular VAT base, so a switch from the destination 59 to the origin principle can be expected to have real effects. The literature on international 60 commodity taxation has also come to the conclusion that if countries cooperate with re- 61 spect to tax rates, then the destination principle is favoured because it is compatible with 62 international production efficiency which maintains bilateral trade based on comparative 63 advantage. However, if countries do not cooperate, the result is dependent on market struc- 64 ture. Under perfect competition the destination principle dominates the origin principle, 65 while under the imperfect competition the opposite may be true. 66 Keen and Lahiri (1998) use a model of international duopoly with an integrated market 67 to show that imperfect competition is likely to reverse the general presumption in favour of 68 the destination principle developed under the assumption of perfectly competitive markets. 69 Their main finding is that in a symmetric Cournot duopoly, the origin principle achieves the 70 first best, while the same result is not true under the destination principle when taxes are 71 set non-cooperatively. Hence an integrated linear Cournot duopoly model produces exactly 72 the opposite policy conclusion to the perfectly competitive model. The model of Keen and 73 Lahiri (1998) does not capture trade costs and it also does not allow measurement of the 74 trade liberalization process. Haufler, Schjelderup and Stahler (2005) consider transportation 75 costs to incorporate a measure of economic integration under Cournot competition in the 76

3 TAX PRINCIPLES, PRODUCT DIFFERENTIATION AND THE NATURE OF COMPETITION domestic and foreign markets when firms are immobile between countries. They prove that the welfare comparison between the two tax regimes becomes ambiguous in this case. For low levels of transportation costs the origin principle continues to dominate the destination principle, but this ranking is reversed in favour of the destination principle when transportation costs become sufficiently high. Lockwood (2001) constructs a different model of imperfect competition with imperfect substitutability of goods. Taxes levied under either the destination or the origin principle create international spillovers on the profits of foreign firms and a welfare comparison of the Nash equilibria under the two tax regimes yields ambiguous results. Therefore, the strong finding of Keen and Lahiri (1998) in favour of the origin principle is not confirmed in this framework. Haufler and Pfluger (2003) study non-cooperative commodity taxation under destination and origin principles in a framework of monopolistic competition and product differentiation. An important result of their analysis is that non-cooperative tax setting under the destination principle achieves the first best. The reason for this striking result is that the fiscal externalities associated with international capital and firm mobility exactly offset each other. An increase in the domestic tax forces firms to relocate to the foreign country and raises foreign welfare by reducing aggregate transport costs. At the same time, a tax rise also reduces the rents that accrue to foreign capital owners. They show that under the origin principle, these effects are also present but there are additional externalities on the foreign tax base and the foreign price level which induce taxes to depart from their Pareto-efficient levels. They find that the non-cooperative tax equilibrium under the destination regime strictly dominates the tax equilibrium under the origin principle. 3 Therefore, this result is in direct contrast to the results of Keen and Lahiri (1998). So far almost all of the literature has assumed Cournot competition. It is hence important to ask whether the conclusions drawn remain valid under Bertrand competition. In this paper we extend the analysis of Keen and Lahiri (1998) in two directions: first, by introducing product differentiation and, second, by including Bertrand competition. In this way, we analyze the process of economic integration and compare the results with other studies in this area such as Haufler, Schjelderup and Stahler (2005). They compared the welfare level under the origin principle with the welfare level under the destination principle for both convex and concave demand functions but with homogenous products and Cournot competition. We demonstrate that their conclusions are robust to the extension to differentiated products and to Bertrand competition. The present analysis will show that when demand is linear the origin principle always dominates the destination principle for any degree of product differentiation and transportation cost. When demand is nonlinear, there is a critical value of transportation cost below which the origin principle dominates and above which the destination principle dominates. When the marginal social value of revenue exceeds one, there are some parameter values for which the origin principle does not dominate and the size of this set increases the higher the value placed on revenue. All of these results are shown to hold for both Bertrand and Cournot competition. As a consequence, the policy conclusions are unaffected by the form of competition between firms. The paper is structured as follows. In Section 2 we describe the model used in this paper. Sections 3 and 4 contrast the tax principles for Bertrand competition. Section 5 shows briefly

4 4 HASHIMZADE, KHODAVAISI AND MYLES that the same results apply for Cournot competition. Section 6 concludes. All proofs are 121 given in the Appendix The Model 123 The basic structure of the model is adopted from Keen and Lahiri (1998) and Haufler, 124 Schjelderup and Stahler (2005). These papers analyze Cournot competition with homoge- 125 nous products. In contrast we focus upon Bertrand competition, but also consider Cournot, 126 and employ a model with differentiated products. 127 The economy consists of two countries, home and foreign, which are identical. There 128 are three goods, X, Y and Z. Goods X and Y are differentiated products which are produced 129 in different countries by an international duopolistic industry. Good Z is a homogenous good 130 which is produced in a perfectly competitive industry in both countries using a constant 131 returns to scale technology. This good is traded freely and costlessly between the two 132 countries and acts as the numeraire. In each country there is a representative consumer, who 133 works and buys the two goods produced by the two firms, and a government. 134 We consider a two-stage game. In the first stage, the governments simultaneously and 135 non-cooperatively set their taxes to maximize their welfare. In the second stage, given the 136 taxes chosen by the governments, the firms compete upon prices or quantities. Given the 137 optimal taxes and the equilibrium consumption levels, the level of social welfare can be 138 calculated and contrasted between the tax principles. 139 The consumer is endowed with a fixed amount of labour, L. Labour is the only factor 140 of production and is intersectorally mobile, but internationally immobile. Labour units are 141 measured such that one unit of labour produces one unit of commodity Z, implying that 142 the wage rate is equal to unity. In addition to wage income the representative consumer 143 receives all profits, π, earned by the domestic firm. Furthermore, following the standard 144 procedure in the trade literature, we assume that tax revenue T is returned to the consumer 145 as a lump-sum. 146 In what follows, without loss of generality, we normalize the labour cost of production 147 of goods X and Y to zero. Exports of either firm to the other market incur trade costs of s 148 per unit of the exported good. The value of s is treated as a proxy for economic integration; 149 we say integration is complete if s = 0 and incomplete otherwise. We denote by x the 150 quantity produced by the home firm for domestic consumption, and by y the quantity 151 produced by the foreign firm for domestic consumption. Aggregate consumption in the 152 home market is x + y. The corresponding values in the foreign market are x, y and 153 x + y. A commodity tax of value t (t for the foreign country) is levied on the good 154 produced by the duopolistic industry. The tax is selective in that the numeraire commodity 155 remains untaxed. 4 Therefore, a shift from destination-based to origin-based commodity 156 taxes has real effects. Also, taxation is specific rather than ad valorem Each country has a representative consumer. The home consumer chooses the quantities 158 x and y to maximize the quasi-linear utility function U(x, y ; γ ) + Z, 160

5 TAX PRINCIPLES, PRODUCT DIFFERENTIATION AND THE NATURE OF COMPETITION subject to the budget constraint p x x + p y y + Z = L + T + π. The parameter γ,0 γ 1, measures the degree of differentiation between the products. If γ = 1 consumers perceive the products as perfect substitutes, and so U(x, y ;1) u(x+y ). Conversely, if γ = 0 the products are perceived as independent with U(x, y ;0) u(x) + u(y ). The representative consumer in the foreign country chooses quantities y and x in order to maximize U(y, x ; γ ) + Z. Taxes levied under the destination principle fall on final consumption in the country that sets the tax. Hence the home tax t is levied on the domestic and foreign goods sold in the home market (x and y ), while the foreign tax t applies to all sales (x and y)inthe foreign market. The profit of the home firm with destination taxation is π D = (p x t)x + (p x t s) x, (1) and for the foreign firm π D = (p y t )y + (p y t s) y, (2) where the superscript D refers to the destination principle. Domestic welfare under the destination principle is W D = U(x, y ; γ ) p x x p y y + L + t(x + y ) + π D, (3) and foreign welfare is given by W D = U(y, x ; γ ) p x x p y y + L + t (y + x ) + π D. (4) With the origin principle taxes are levied in the country where production occurs rather than in the country of final consumption. Hence the home country s tax is levied on the domestic sales of the home firm and on its exports sold in the foreign market, while the foreign tax applies to all foreign firm sales in each of the two countries. The profits of the domestic and the foreign firm with origin taxation are π O = (p x t)x + (p x t s)x, (5) π O = (p y t )y + (p y t s)y, (6) where the superscript O refers to the origin principle. The welfare levels under the origin principle are W O = U(x, y ; γ ) p x x p y y + L + t(x + x) + π O, (7) W O = U(y, x ; γ ) p x x p y y + L + t (y + y ) + π O. (8) The specification of the welfare levels illustrates the difference in tax base between origin and destination taxation with the tax now levied on total output and not consumption. Coordinated welfare maximization provides a benchmark for the comparison of the two tax principles. In our symmetric setting, the optimal coordinated tax policy is the same for both the destination and the origin principle (since both countries levy the same tax). Hence, it does not matter whether we maximize joint welfare under the destination or the origin

6 6 HASHIMZADE, KHODAVAISI AND MYLES principle. Denoting all values that obtain under global welfare maximization by a tilde, the 193 objective function is given by 194 W = U(x, y ; γ ) p x x p y y + L + t(y + x) + π + U(y, x ; γ ) p x x p y y + L + t(y + x ) + π. (9) 3. Bertrand Competition 195 In this section we contrast the origin and destination principles with Bertrand competition. 196 This is first undertaken for linear demand and then for nonlinear Linear Demand 198 To generate a linear demand system assume that the utility function is quadratic. For the 199 home consumer this gives the form (adapted from Vives, 1984) 200 U(x, y ; γ ) = x + y 1 2 (x 2 + 2γ xy + y 2 ). (10) 201 It can be readily seen that when γ = 1 this becomes a function of x + y,sothe goods are 202 perfect substitutes, and when γ = 0 the two goods are independent. 203 Since the model is symmetric, there will be a Nash equilibrium of the two-stage game 204 where both governments levy identical taxes. Solving the first-order conditions for welfare 205 maximization, the optimal tax under the destination principle is 206 tb D = s(1 + γ ) 2(2 + γ ). (11) 207 The features of this tax can be summarized by observing that, for any value of γ less than 208 1, the optimal tax rate is zero if economic integration is complete (s = 0) and negative if 209 economic integration is not complete. For the origin principle the optimal tax is 210 tb O 2 = sγ (2 γ 2 ) + (4 7γ 2 + γ 3 + 2γ 4 ). (12) (12 5γ 2 γ 3 ) 211 From (12) it can be seen that under the origin principle with Bertrand competition, the 212 optimal tax is negative for all γ [0, 1]. This is demonstrated by observing that 4 7γ γ 3 + 2γ 4 > 0 and 2 γ 2 > 0 for 0 γ<1, hence the numerator is always positive. The 214 denominator satisfies 12 5γ 2 γ 3 > 0 for 0 γ<1. The optimal coordinated tax t is 215 given by 216 t = (1 γ )(2 s). (13) If γ<1 (13) shows that the optimal coordinated tax is negative for s < 2, zero for s = and positive for s > 2. We know that in the case of perfect substitutes (γ = 1) with a linear 219 demand curve and a constant marginal cost, Bertrand competition leads to equality of price 220

7 TAX PRINCIPLES, PRODUCT DIFFERENTIATION AND THE NATURE OF COMPETITION and marginal cost so there is no need for government intervention. As a result, the optimal 222 coordinated tax for γ = 1isequal to zero. 223 The first result provides a contrast between the origin, destination and coordinated taxes. 224 Part (i) of Lemma 1 shows that the taxes for the two alternative principles and for co- 225 ordinated optimization are equal along a one-dimensional locus in the two-dimensional 226 parameter space. Part (ii) shows that away from the locus of equality the tax under the 227 destination principle is always further from the optimal coordinated tax than that under the 228 origin principle. This result provides the basis for an intuitive understanding of the welfare 229 comparison that follows. 230 Lemma γ 2γ (i) When s =, t = t O 3 γ 2 B = t B D 2 = 1 γ 3 γ (ii) If tb O t then tb D < t B O and if t B O > t then tb D > t B O. 233 The implications for the welfare comparison of the two tax principles follow immediately. 234 Along the locus where the taxes are equal, they generate an identical level of welfare. Away 235 from this locus, the origin tax is closer than the destination tax to the coordinated level. 236 Welfare is monotonic in the taxes, so the origin tax, being closer to the optimum, must 237 generate a higher level of welfare than the destination tax. These observations are presented 238 formally in the next theorem. In stating this, we say one tax principle dominates another if 239 it produces no less welfare and strictly dominates if it generates strictly higher welfare Theorem 1. For γ [0, 1], the origin principle dominates the destination principle for 2 4 2γ 2γ any s 0.Ifs, the origin principle strictly dominates the destination principle. 3 γ 2 The theorem demonstrates that origin taxation strictly dominates destination taxation everywhere except on the one-dimensional locus along which the taxes are equal. Because the one-dimensional locus is an insignificant part of the two-dimensional parameter space, origin taxation strictly dominates destination taxation for almost all parameter configurations (formally, it strictly dominates except for a set of measure zero in the parameter space). This shows that the result of Keen and Lahiri (1998) extends to Bertrand competition and to product differentiation. These observations also suggest an intuitive explanation for the conclusion. The taxes diverge from the optimum because of the tax externalities between the two countries. Origin taxes appear to internalize some of the externality because their tax base is partly determined by the level of demand in the other country. This partial internalization, which is missing with destination taxes, ensures that they are always at least as good as destination taxes Nonlinear Demand The work of Haufler, Schjelderup and Stahler (2005) has shown the importance of nonlinear demand when there is Cournot competition with homogenous products. We now explore the consequences of nonlinear demand for Bertrand competition with differentiated products.

8 8 HASHIMZADE, KHODAVAISI AND MYLES Figure 1. Convex demand (c = 0.2, γ = 0.5). To extend to a nonlinear demand system we assume that the preferences for the home 258 consumer are 259 U(x, y ; γ ) = x + y 1 2 (x 2 + 2γ xy + y 2 ) + c 3 (x 3 + 3γ x 2 y + 3γ xy 2 + y 3 ), 260 with a similar expression for the foreign consumer. These preferences imply a quadratic 261 demand function which is strictly concave if c < 0 and strictly convex if c > 0. The property 262 is retained that γ = 1 implies prefect substitutability and γ = 0 implies independent 263 demand. With these preferences, the Bertrand equilibrium cannot be solved explicitly nor 264 can the Nash equilibrium in choice of taxes for the countries. As a consequence, we employ 265 numerical simulation to obtain results Figure 1 displays the results for convex demand. The left-hand panel shows the equi- 267 librium taxes for 0.6 s 1. For lower values of s the tax for the destination regime 268 remains above that for the origin regime. The upper limit of s (approximately s = 0.98 for 269 the parameters used to produce the figure) is determined as the point at which trade in the 270 differentiated product ceases. The behavior of the equilibrium taxes results in the welfare 271 levels graphed in the right-hand panel. This shows the main point of Haufler, Schjelderup 272 and Stahler (2005), that the destination regime dominates the origin regime for high val- 273 ues of s, applies not only for Cournot competition with homogenous products but also to 274 Bertrand competition with differentiated products. In fact, our simulation results show that 275 it holds for all γ [0, 1]. 276 A further point is worth noting. Simulations were conducted for a range of parameter 277 values and in every case the difference between origin and destination welfare levels remains 278 very small beyond the point at which the destination principle dominates. In contrast, 279 the welfare difference for low values of s, where the origin principle dominates, can be 280 significant. Consequently, although the origin principle does not always dominate when 281 there is nonlinearity in demand a good argument can still be made for expecting it to 282 generate higher welfare than the destination principle. This argument is especially strong 283 in closely integrated economic unions. 284

9 TAX PRINCIPLES, PRODUCT DIFFERENTIATION AND THE NATURE OF COMPETITION Figure 2. Concave demand (c = 0.2, γ = 0.3). Figure 2 presents a sample of the results for concave demand. The conclusion remains that the destination principle dominates the origin principle for values of s close to where trade ceases (approximately s = 1.08 for the parameters used to produce the figure). There is one minor difference between concave and convex demand: with convex demand both origin and destination taxes are higher than the coordinated tax but with concave demand the origin tax is lower than the coordinated tax for high s. Asaconsequence, with concavity there is a value of s before the crossing of destination and origin taxes at which the origin principle produces the same welfare level as coordinated optimization. This does not occur with convex demand Summary In the case of linear demand our analysis shows that the results of Keen and Lahiri (1998) extend to Bertrand competition with differentiated products. The origin principle always dominates the destination and strictly dominates except for a subset of parameter values. Extending to nonlinear demand the domination of the origin principle still applies except for values of s close to the point at which trade ceases. This finding shows that the results of Haufler et al. apply beyond their setting of Cournot competition with homogenous products. If the outcomes of the simulations are representative of the general picture, then the destination principle achieves at most a small welfare improvement over the origin principle. This suggests that a practical policy recommendation can be made in favour of the origin principle it is certainly preferable in a closely-integrated economic union Tax Revenue Our analysis has so far been confined to the case where all tax revenues are returned to the representative consumer as a lump-sum. In this section we extend the analysis to incorporate

10 10 HASHIMZADE, KHODAVAISI AND MYLES a revenue objective for the government. This is done in a simplified way, following Keen 308 and Lahiri (1998), by assigning an exogenous weight λ>1 to each dollar of tax revenue 309 collected. Given the fiscal importance of general commodity taxes, the assumption that the 310 excess burden of the tax system is exogenous to the model is clearly an oversimplification, 311 but this specification does capture the general point that subsidies are costly for governments 312 to employ. 313 Empirical studies have provided a range of estimates for λ generally in the range 1 2, 314 but sometimes above 2. It is worth mentioning that there is no consensus on the value for 315 λ butaskeen and Lahiri (1998) argue it is reasonable to view values below 1.25 as fairly 316 normal, and values above 1.5 as uncommonly high. 317 To simplify the analysis we return to the utility function specified in (10). The equilibrium 318 conditions from the second stage of the game remain unchanged. Hence, the extended 319 analysis only changes the equilibrium values in the first stage of the game. Domestic welfare 320 under the destination principle becomes 321 W D = U(x, y ) p x x p y y + L + λt(x + y ) + π D, (14) 322 with an equivalent expression for foreign welfare. The expression for the origin principle is 323 obtained by changing the tax base. In this welfare function the government places additional 324 value λ > 1 on tax revenue. The relationship between the optimal taxes for the three 325 scenarios is described in the next proposition. 326 Proposition 1. When 327 γ = 0 and s = 4λ 6λ 3, t B D = t B O = t = 1 2λ 3 3 2λ 1. The implication of this proposition is that for each value of λ there is a unique pair {s,γ} 328 for which the taxes, and the level of welfare they generate, are equal. Away from this point 329 it must therefore be the case that destination taxation strictly dominates for some values 330 of the parameters and origin taxation for others. The regions of parameter space for which 331 each dominates can be found by using the optimal taxes to compute the welfare difference 332 φ(s,γ,λ) W O (s,γ,λ) W D (s,γ,λ). (15) 333 Given a value of λ, the solution to φ(s,γ,λ) = 0 defines the locus of s and γ values 334 for which origin and destination principles generate the same level of welfare. Figure graphs the solution for three values of λ. Inside each locus, destination taxation dominates 336 origin taxation. The situation is the reverse outside. It can be seen that as the weight on tax 337 revenue increases, so does the area of domination of destination taxation. When λ = 1, 338 origin taxation always dominates. In other cases, origin taxation dominates destination 339 taxation for low values of s and γ and for high values of s. Destination taxation dominates 340 for intermediate values. The range of parameter values for which destination taxation is 341 dominant increases as λ increases. 342 The explanation for this result lies in the two distinct roles of the taxes. The first role 343 is to combat the inefficiency caused by the imperfect competition while at the same time 344 internalizing the fiscal externality to as great an extent as possible. The results of Section 3 345

11 TAX PRINCIPLES, PRODUCT DIFFERENTIATION AND THE NATURE OF COMPETITION Figure 3. Areas of domination. have shown that this task is best undertaken by origin taxation. Once revenue is valued in its own right, the taxes have the second role of raising revenue at least cost. The advantage here lies with destination taxation since that succeeds in bringing part of foreign production within the tax base. As the value placed upon revenue increases, this second effect is more significant for a larger part of the parameter space. 5. Cournot Competition In this section we briefly repeat the analysis for Cournot competition. A general comparison of the two tax principles for the linear demand case is given and the results of Haufler, Schjelderup and Stahler (2005) are shown to extend to differentiated products Linear Demand The optimal taxes at the symmetric equilibrium of the two-stage game are and t D C = s 2(2 γ ), (16) tc O = 2γ 2 s (4 γ 3 + γ 2 ), (17) (12 5γ 2 + γ 3 ) t = s 2 2(γ + 1). (18) These taxes are contrasted in the next lemma.

12 12 HASHIMZADE, KHODAVAISI AND MYLES Lemma (i) When γ = 1, t = tc O for any s (ii) When s = 2(2 γ ), t = t O 3 C = t C D = (iii) If tc O < t then tc D < t C O and if t C O > t then tc D > t C O. 363 For a nonlinear demand function, but with perfect substitute goods, Haufler, Schjelderup 364 and Stahler (2005) show that the non-cooperative tax under the origin principle coincides 365 with the optimal coordinated tax at s = 0. The first part of the lemma shows that for linear 366 demand the result holds for any s 0. This implies that origin taxation must be at least 367 as good as destination taxation when the goods are perfect substitutes. The second part of 368 the lemma shows that the taxes for the origin and destination principles coincide with the 369 optimal coordinated tax along a locus in {s,γ} space and so origin and destination taxation 370 generate equal levels of welfare. The third part of the lemma shows that away from this 371 locus the origin tax is closer than the destination tax to the cooperative value. The contrast 372 between welfare levels is formalized in the following general result. 373 Theorem 2. For γ [0, 1], the origin principle dominates the destination principle for 374 any s 0.Ifs 2(2 γ ) 3 the origin principle strictly dominates the destination principle. 375 Theorem 2 shows that the dominance of the origin principle holds for any degree of 376 substitution and any degree of economic integration. This extends the results of Keen and 377 Lahiri (1998) to differentiated products and shows that the findings of Haufler and Pfluger 378 (2003) are sensitive to assumptions on product differentiation Nonlinear Demand 380 With differentiated products it is again not possible to solve the model explicitly and nu- 381 merical simulation must be employed. 382 Figure 4 displays the outcome for convex demand. As for the Bertrand case, the destination 383 principle dominates the origin principle for values of s close to the no-trade point. This holds 384 for all values of γ,showing that the results of Haufler, Schjelderup and Stahler (2005) extend 385 from their case of homogenous goods to differentiated products. The difference in welfare 386 between the two principles, and the coordinated case, is very small for the range of values 387 of s beyond which the destination principle dominates. 388 The outcome for concave demand is illustrated in Figure 5. Once more this demonstrates 389 that the destination principle dominates the origin principle for high s. The additional feature 390 identified here is that the origin and coordinated principles are equivalent at a value of s 391 prior to destination overtaking the origin Revenue Objective 393 Assume that the governments place a value λ>1 on tax revenue and that demand is linear. 394 The three taxes for Cournot competition are related in the next proposition. 395

13 TAX PRINCIPLES, PRODUCT DIFFERENTIATION AND THE NATURE OF COMPETITION 13 Figure 4. Convex demand (c = 0.2, γ = 0.5). Figure 5. Concave demand (c = 0.3, γ = 0.5) Proposition 2. When γ = 0 and s = 4λ 6λ 3, t C D = t C O = t = 1 2λ 3 3 2λ 1. This result again shows that for each λ there is a single pair {s,γ} for which the taxes are equal and generate equal welfare levels. Away from this point, origin taxation will dominate for some parameter values and destination taxation for others. The locus of parameter values for which the welfare levels are equal is determined by taking a value of λ, and finding the solution to the equation for welfare difference φ(s,γ,λ) = 0. Figure 6 graphs the solution for three values of λ. When λ = 1, origin taxation always dominates. In other cases, origin

14 14 HASHIMZADE, KHODAVAISI AND MYLES Figure 6. Areas of domination. taxation dominates destination taxation for low values of s and γ and for high values of s. 403 Destination taxation dominates for intermediate values Summary 405 The conclusion of this section is that the origin principle dominates the destination prin- 406 ciple for almost all parameter values for linear demand. This extends previous results for 407 homogenous products. With nonlinear demand the results demonstrate that the Haufler, 408 Schjelderup and Stahler (2005) results extend to product differentiation. Furthermore, the 409 conclusions for Bertrand competition and Cournot competition are identical Conclusions 411 We have extended the work of Keen and Lahiri (1998) to Bertrand competition and product 412 differentiation. The results show that if revenue is redistributed as a lump-sum to consumers, 413 then with linear demand the origin principle dominates the destination principle whatever 414 the extent of product differentiation or degree of economic integration. This conclusion also 415 holds with Cournot competition between firms. The analysis of nonlinear demand shows 416 that the results of Haufler, Schjelderup and Stahler (2005) are robust to the introduction 417 of product differentiation and also apply to both Bertrand and Cournot competition. When 418 revenue is valued, there are regions in the parameter space where the destination principle 419 is dominant since it has the advantage in this respect. Consequently, the range of param- 420 eter values for which origin taxation dominates is reduced as the social value of revenue 421 increases. 422 Our findings add additional weight to the body of evidence that is developing in favour 423 of the origin principle over the destination principle. In the case of linear demand this 424

15 TAX PRINCIPLES, PRODUCT DIFFERENTIATION AND THE NATURE OF COMPETITION preference for the origin principle is very robust since it is independent of the degree of product differentiation, the extent of economic integration and the form of product market competition. Although there are limits to this argument when demand is nonlinear, the welfare advantage of the destination principle is small. Even in this case, sufficient economic integration gives a decisive advantage to the origin principle. Appendix Proof of Lemma (i) Equating tb D and t gives (2 s)(1 γ ) = s(1+γ ), from which can be obtained that 2 2(γ +2) γ 2γ s =. Substituting this back into t, t O 3 γ 2 B and t B D completes the proof. 434 (ii) Note that t, tb O and t B D are linear functions of s, and for γ [0, 1] 435 t s = 1 γ 0, 2 t O B s = γ 2 (2 γ 2 ) 12 5γ 2 γ 0, tb D 3 s = 1 + γ 2(γ + 2) < Hence, it suffices to show that tb D/ s < t B O/ s, or, equivalently, t B D/ s > t B O/ s, 437 for any γ [0, 1]. Observe that ϕ B (γ ) tb D / s is a strictly increasing function of γ on 438 [0, 1]: 439 ϕ B (γ ) = 1 > 0 γ [0, 1], 2(γ + 2) with ϕ B (0) = 1/4 and ϕ B (1) = 1/3. Next, observe that ψ B (γ ) tb O / s is non- 441 decreasing function of γ on [0, 1]: ψ B (γ ) = γ [4(1 γ 2 )(12 5γ 2 γ 3 ) + γ 2 (2 γ 2 )(10 3γ 2 )] (12 5γ 2 γ 3 ) 2 0 γ [0, 1], with ψ B (0) = 0 and ψ B (1) = 1/6. Hence, ϕ B (γ ) >ψ B (γ ) for all γ [0, 1] Proof of Theorem 1 Substitute the optimal taxes into the welfare functions and define φ(s,γ) W O (s,γ) W D (s,γ). This is given explicitly by φ(s,γ) A B, where A Es 2 + Fs + G with E = 3.5γ γ 6 22γ γ γ γ 2 9γ + 45 > 0, F = 14γ γ γ 5 109γ 4 205γ γ γ 120 < 0, G = 14γ 7 + γ 6 100γ γ γ 3 152γ 2 96γ + 80 > 0,

16 16 HASHIMZADE, KHODAVAISI AND MYLES and 448 [ B [γ + 2] 2 γ ] 2 [ [γ 2] 2 γ ] 2 [1 + γ ] It is clear that the denominator of φ(s,γ)isalways positive. To prove that φ(s,γ) 0, 450 we need to prove that the numerator, A, isalways positive or zero. Observe that = 451 F 2 4EG = 0. These imply that A has two repeated roots, 452 s 1 = s 2 = F ( 2E, i.e.a = E s + F ) 2 0, since E > 0. 2E Proof of Proposition The optimal taxes are given by 454 t D B (λ 1)(2γ + 4) + s(1 λ(γ + 2)) =. 2((γ + 2)(2λ 1)) t O B = A + sb λ(2γ 3 8γ + 4γ 4 24γ ) + 8γ 3γ γ γ where A = 19γ 2 + 8γ 4γ 4 3γ γλ+ 2λγ 3 12λγ 2 + 2λγ λ and 457 B = 2γ 4 + γ λγ 2 8γ 2 4γ + 4λγ λγ 4 8λ λγ 3, and 458 (2λ(γ 2) 4γ + 6) + s(λ(2 γ ) + 2γ 3) t =. 2(λ(2γ 4) 2γ + 3) The proof is completed by equating the locus obtained from solving tb D = t with that from 460 solving tb O = t Proof of Lemma The proof of part (i) follows by substitution of γ = 1 into the solutions for t and tc O.Part (ii) 463 is obtained by equating tc D and t. This gives s 2(2 γ ) = s 2, from which can be obtained 2(γ +1) 464 that s = 2(2 γ ). Substituting this solution for s into t, t O 3 C and t C D completes the proof. (iii) 465 Note that t, tc O and t C D are linear functions of s, and for γ [0, 1] 466 t s = 1 2(γ + 1) > 0, t O C s = 2γ γ 2 + γ 3 0, t D C s = 1 2(2 γ ) < Hence, it suffices to show that t/ s > tc O/ s for any γ [0, 1). Observe that ϕ C(γ ) 468 tc D / s is a strictly decreasing function of γ on [0, 1]: 469 ϕ C (γ ) = 1 2(γ + 1) 2 < 0 γ [0, 1], 470

17 TAX PRINCIPLES, PRODUCT DIFFERENTIATION AND THE NATURE OF COMPETITION with ϕ C (0) = 1/2 and ϕ C (1) = 1/4. Next, observe that ψ C (γ ) tc O / s is a non- 472 decreasing function of γ on [0, 1]: ψ C (γ ) = 2γ (24 γ 3 ) 0 γ [0, 1], (12 5γ 2 + γ 3 ) 2 with ψ C (0) = 0 and ψ C (1) = 1/4. Hence, ϕ C (γ ) >ψ C (γ ) for all γ [0, 1). Proof of Theorem 2 Substituting the equilibrium taxes into W D and W O generates two welfare levels that are functions of s and γ.now define ˆφ(s,γ) W O (s,γ) W D (s,γ). This can be written as where with and ˆφ(s,γ)  ˆB,  Hs 2 + Is + J, H 2.25γ γ γ γ γ + 45 > 0, I 3γ 6 9γ γ γ γ 2 36γ 120 < 0, J γ 7 γ γ 5 3γ 4 16γ 3 24γ 2 16γ + 80 > 0. [ ˆB [γ + 2] 2 γ ] 2 [ [γ 2] 2 γ ] It is clear that the denominator of ˆφ(s,γ)isalways positive. To prove that ˆφ(s,γ) 0, we need to prove that the numerator, Â, isalways positive or zero. Observe that = I 2 4HJ = 0. These imply that  has two repeated roots, s 1 = s 2 = I (, i.e.  =H s + I ) 2 0, since H > 0. 2H 2H Proof of Proposition 2 The optimal taxes are t D C λ)(4 2γ ) + s(λ(2 γ ) + γ 1) = (1, 2(2 γ )(2λ 1) t O C = λa + B + sc λ(2γ 3 8γ γ 2 ) γ 3 + 3γ 2 + 8γ 20,

18 18 HASHIMZADE, KHODAVAISI AND MYLES where A = 2γ 3 4γ 2 8γ + 16 > 0, B = 3γ 2 γ 3 + 8γ 20 < 0 and C = 490 4λγ 4γ λγ 2 + γ 3 λγ 3 8λ, and 491 t = 2γ (1 λ) 4λ s(λ(γ + 2) (γ + 3)). 2γ + 6 4λ(γ + 2) Equate t D C and t to find the locus of equality, and then equate t O C = t. The two loci intersect 493 at the values of γ and s given in the statement. 494 Acknowledgment 495 Thanks are due to Jay Wilson, Andreas Haufler, two anonymous referees, and seminar 496 audiences in Athens (June 2003), Durham (November 2003) and Leicester (February 2004). 497 Notes Keen and Lahiri (1998, p. 323) mention several specific cases in which cross-border shopping results in low-tax 499 rates. They argue that... in Canada, for instance, cross-border shopping into the US has induced a dramatic 500 fall in the level of cigarette taxes Empirical evidence for the United States shows that residents of states with high sales taxes are significantly 502 more likely to buy in the internet (Goolsbee, 2000) It is probably fair to say that Krugman s (1979, 1980) monopolistic competition model has become the most 504 popular model used to study the effects of economic integration in the presence of product differentiation. The 505 wide applicability of Krugman s model is due to the fact that the assumption of the CES utility function allows 506 for a closed-form solution of a trading equilibrium in the presence of scale economies. A counterintuitive 507 feature of the CES taste for variety specification, however, is that an economy s move from autarky to free 508 trade has no effect on the prices and the output levels of the goods. Specifically, economic integration increases 509 the number of products available to consumers, but it has no effect on a firm s market power (as measured by 510 the price-cost margin) or its production level. This unsatisfactory result in Krugman s own words (1980, p ) comes from the CES utility specification. In our model, a move toward an integrated economy affects 512 both prices and output of each firm If the numeraire good is also taxed at the same rate, then the two regimes are equivalent under rather general 514 conditions, including the case of imperfect competition. (Lockwood, de Meza and Myles, 1994) This is done for analytical simplicity and in order to facilitate comparison with the modelling of specific tariffs 516 in most of the trade literature. Note that in the competitive case, specific and advalorem taxes or tariffs lead 517 to the same outcomes, while under imperfect competition they lead to different outcomes Since the utility function is quasi-linear, there will be no income effect We are happy to supply details of the supporting calculations and the Matlab routines on request Au: Pls. cite Brander (1984) and (1985) in the text. References 521 Brander, J. A. and B. Spencer. (1984). Tariff Protection and Imperfect Competition. In H. Kierzkowski (ed.), 522 Monopolistic Competition and International Trade. Oxford: Oxford University Press, pp Brander, J. A. and B. Spencer. (1985). Export Subsidies and International Market Share Rivalry, Journal of 524 International Economics 18, Goolsbee, A. (2000). In a World Without Borders: The Impact of Taxes on Internet Commerce, Quarterly 526 Journal of Economics 115,

19 TAX PRINCIPLES, PRODUCT DIFFERENTIATION AND THE NATURE OF COMPETITION Haufler, A. and M. Pfluger. (2003). International Commodity Taxation Under Monopolistic Competition, CESifo Working Paper 529, University of Munich. Haufler, A., G. Schjelderup and F. Stahler. (2005). Economic Integration and the Choice of Commodity Tax Base Under Imperfect Competition, International Tax and Public Finance (forthcoming). Keen, M. and S. Lahiri. (1998). The Comparison Between Destination and Origin Principles Under Imperfect Competition, Journal of International Economics 45, Krugman, P. R. (1979). Increasing Returns, Monopolistic Competition, and International Trade, Journal of International Economics 9, Krugman, P. R. (1980). Scale Economies, Product Differentiation, and The Pattern of Trade, American Economic Review 70, Lockwood, B. (2001). Tax Competition and Tax Co-Ordination Under Destination and Origin Principles: A Synthesis, Journal of Public Economics 81, Lockwood, B., D. de Meza and G. D. Myles. (1994). When are Origin and Destination Regimes Equivalent?, International Tax and Public Finance 1, Sinn, H. W. (1990). Tax Harmonization and Tax Competition in Europe, European Economic Review 34, Vives, X. (1984). Duopoly Information Equilibrium: Cournot and Bertrand, Journal of Economic Theory 34,