CROSS-BORDER SHOPPING FROM SMALL TO LARGE COUNTRIES

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1 Copenhagen Business School Solbjerg Plas 3 DK-2000 Freeriksberg LEFIC WORKING PAPER CROSS-BORDER SHOPPING FROM SMALL TO LARGE COUNTRIES Søren Bo Nielsen

2 Cross-borer shopping from small to large countries S ren Bo Nielsen Copenhagen Business School an EPRU May 2002 Abstract Contrary to preictions of theoretical moels, there are many examples in the real worl of cross-borer shopping from small to large countries. We emonstrate that a su±cient wege between marginal costs of public funs in small an large countries can explain this phenomenon. JEL classi cation: H87, H20 Keywors: cross-borer shopping, commoity taxation, MCPFs Forthcoming, Economics Letters. The activities of Economic Policy Research Unit are nance by a grant from The Danish National Research Founation. Aress of author: Department of Economics, Copenhagen Business School, Solbjerg Plas 3, DK-2000 Freeriksberg, Denmark; tel.: (+45) , fax: (+45) , sbn.eco@cbs.k.

3 1 Introuction The international e ects of taxation as well as the external constraints on tax policy in iniviual countries have come to the fore over the last ecae or so. In particular, there has been great interest in tax competition, i.e. national governments competing for capital, labor or sales of goos via their capital income, labor income an consumption tax policies. By now, the literature is well establishe an unerstoo, but sometimes the preictions of the literature are not quite borne out in practice. One example of this is foun in the literature on commoity tax competition an cross-borer shopping. In the famous moel by Kanbur an Keen (1993) as well as in subsequent work by Tranel (1994), Wang (1999) an Nielsen (2001), cross-borer shopping is moelle in a two-country framework with some size asymmetry between the two countries. 1 In Kanbur an Keen's moel as well as those of Tranel an Wang one country has a bigger population ensity; in Nielsen's moel, one country is larger than the other in geographical extent. Either way, one country has more inhabitants than the other, an cross-borer shopping is preicte as running from the large country to the small. The reason for this is that at given taxes in the two countries, potential crossborer shopping consumers make up a greater percentage of inhabitants in the small country than in the large country. Thus, the smaller country is le to attach a greater weight to luring borer crossers than the large country an therefore ens up setting the lower commoity tax rate. In the real worl, there are many examples of smaller countries setting relatively low value ae an excise taxes, thus attracting borer shoppers from bigger neighboring countries. For instance, Germans shopping in Belgium an the Netherlans are inuce to o so because of low excise taxes in the smaller 'low' countries. Such examples conform well to the preictions of the theory. However, there are also many examples of crossborer shopping running in the 'wrong' irection, that is from small to large countries. Cross-borer shopping from Canaa to the US an from Denmark to Germany are a few examples. This paper extens previous work in the area of commoity taxation an cross-borer shopping by proviing one possible explanation for the puzzle of cross-borer shopping from small to large countries. We emonstrate that provie smaller countries feature su±ciently larger marginal costs of public funs, their governments will select commo- 1 In Hau er (1996) there is no size asymmetry, but countries i er in their preferences for public vs. private goos. 1

4 ity taxes so that cross-borer shopping from small to large countries ensues. Greater marginal costs of public funs may erive from citizens in the smaller countries valuing public goos more than citizens in larger countries, or from other available taxes being more istortionary in the small countries. Whatever the reason, it may be enough to reverse the irection of cross-borer shopping. Section 2 sets up a simple moel of commoity taxation an cross-borer shopping, while section 3 establishes the central claim of the paper. 2 The moel Our moel, builing on that in Nielsen (2001), has two countries, together represente by the interval [ 1; 1]. Population is evenly sprea out with a ensity of unity in both countries. The larger of the two extens from 1 to some borer parameter b>0, while the smaller one extens from b to 1. Hence, population sizes are 1 + b an 1 b, respectively. This way of moelling the location of population implies variation in the istance to the borer, an this has the consequence, as we shall see below, that some iniviuals engage in cross-borer shopping, while others shop at home. There is one (composite) goo in the moel. Each iniviual purchases one unit of the goo, when his reservation price excees the price of the goo. Reservation prices in the large an the small country are enote by V an v, respectively. We shall assume that these reservation prices are high enough that for relevant tax-inclusive commoity prices in the two countries, all iniviuals will inee wish to purchase the commoity. With a constant number of iniviuals an with the guarantee that all iniviuals will purchase one unit of the goo, we may as well ignore the prouction cost of the goo an set it equal to zero. Commoity taxes are speci c taxes, an they are levie at the rates T in the large an t in the small country. Goos prices are then simply the relevant tax rates. For an iniviual to travel to the borer to purchase the goo abroa, a transportation cost of per unit istance travelle 2 is incurre. While some iniviuals may choose this option, the rest purchase the goo in the place of resience. An iniviual in the large country will purchase the goo at the borer, if the surplus obtaine by oing so, V t S, wheres stans for the necessary istance travelle, excees the surplus from buying at home, V T. Hence, those with a istance S S =(T t)= will opt for cross-borer shopping (for T>t;ifT t, no-one will o so). Similarly, citizens in 2 The cost inclues the return part of the trip as well. 2

5 the small country for whom the istance to the borer s ful ls s s =(t T )= will choose to shop abroa (again, if t T, no-one will). With an open borer, the two countries will have an incentive to unercut each other in orer to capture tax revenue from foreigners who are le to shop across the borer. Incorporating cross-borer shopping, the number of resients of the large country shopping abroa is (T t)=, ift>t.ifonthecontraryt<t,(t T )= small country iniviuals shop in the large country. Hence, tax revenues in the large an small countries amount to, respectively, R(T;t)=T[1 + b + t T ]; r(t; T)=t[1 b + T t ] (1) We now imagine that the two countries choose their taxes in a noncooperative manner so as to maximize national welfare. The tax system in either country (which isposes of other taxes than the commoity taxes uner consieration) is characterize by a given marginal cost of public funs (MCPF), ½ in the large country an ½ in the small. Below, these MCPFs will be allowe to i er. A welfare measure can now be constructe as the sum of tax revenue, weighte by the MCPF, an private surplus. The latter measures, as a sum over the population, the i erence between the value of the goo to consumers an their total cost of acquiring it. Two situations can be istinguishe: one, where cross-borer shopping runs from the large to the small country; an one, where the irection is reverse. In the former case, we may write welfare in the large country, W, asfollows: W =(V T)[1 + b T t Z (T ]+ t)= (V t s)s + ½R(T;t) (2) 0 Here, the rst term represents private surplus on the part of those iniviuals who o not engage in cross-borer trae. The secon term yiels private surplus for those that o. Finally, the thir term is tax revenue weighte by the MCPF (R(T;t) is given in (1) above). For the small country w =(V t)(1 b)+½ r(t; T ) (3) i.e. a simpler sum of private surplus an weighte tax revenue. Again, r(t; T ) is given in (1). 3

6 If instea cross-borer shopping runs in the opposite irection from the small to the large country, welfare expressions become w =(V t)[1 b t T Z (t T ]+ )= (V T s)s + ½ r(t; T ) (4) 0 an W =(V T )(1 + b)+½r(t;t) for the small an large countries, respectively. 3 MCPFs an the irection of cross-borer shopping We now wish to erive a conition on the MCPFs in the two countries which enables crossborer trae in the unexpecte irection from the small to the large country. Observe rst that the choice of commoity tax in one country impacts national welfare in the other. Hence, we shall assume commoity taxes to be set strategically an suppose that the resulting commoity tax equilibrium is a Nash equilibrium. 3 Rewrite the expression for w in (4) as w =(V +(½ 1)t)[1 b t T ]+t T [V t + T 2 ] (4 0 ) Using this an the expression for W in (5) we get the following reaction functions from welfare maximization, T = t 2 + (½ 1)(1 + b) 2½ (6) an t = (½ 1)T 2½ 1 + (½ 1)(1 b) 2½ 1 (7) From the reaction functions we can obtain Nash equilibrium taxes T = (3½ 1)½ [(1 b)½(½ 1) + (1 + b)(½ 1)(2½ 1)] (8) an t = (3½ 1)½ [(1 b)2½(½ 1) + (1 + b)(½ 1)(½ 1)] (9) 3 The commoity tax equilibria in Kanbur an Keen (1993), Tranel (1994), Hau er (1996) an Nielsen (2001) are Nash equilibria, while Wang (1999) an Hvit an Nielsen (2001) stuy Stackelberg equilibria. 4

7 If cross-borer trae is to run from the small to the large country as posite, then thelargecountrymusthavethesmallertax,t<t, implying from (8) an (9) that (½ 1)½ (½ 1)½ > 1+b 1 b (10) This requirement will be ful lle, if for given b>0the MCPF in the small country excees that in the large country by a su±cient margin. For example, let b =0:2 anthe MCPF of the the large country be equal to 1:2. Then if the MCPF of the small country excees 4/3, cross-borer shopping will run from the small to the large country. The reaer may, by the way, convince herself that if the inequality (10) hols with the inequality sign reverse, then the moel generates a Nash equilibrium with the higher tax in the large country an hence cross-borer trae from the large to the small country, just as in previous moels in the literature. So if the MCPF in the small country lies below that in the large country, or excees it by only little, then cross-borer trae will runintheusualirection. 4 Conclusions As empirical contraictions to previous results in the literature on commoity taxation an cross-borer shopping there are many examples aroun the worl of cross-borer shopping from a small to a large country. We have emonstrate that it is possible to generate cross-borer shopping from small to large countries in a simple moel of crossborer trae, where the marginal cost of public funs in the small country excees that inthelargecountrybyasu±cientamount. 5

8 References Hau er, A., 1996, Tax coorination with i erent preferences for public goos: Con ict or harmony of interest? International Tax an Public Finance 3, Hvit, M. an S. B. Nielsen, 2001, Non-cooperative vs. taxation, German Economic Review 2, minimum-rate commoity Kanbur, R. an M. Keen, 1993, Jeux sans frontiµeres: Tax competition an tax coorination when countries i er in size, American Economic Review 83, Nielsen, Soren Bo, 2001, A simple moel of commoity taxation an cross-borer shopping, Scaninavian Journal of Economics 103, Tranel, G.A., 1994, Interstate commoity tax i erentials an the istribution of resients, Journal of Public Economics 53, Wang, Y-Q., 1999, Commoity taxes uner scal competition: Stackelberg equilibrium an optimality, American Economic Review 89,