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Journal of Economic Integration15(2), June 2000; 294– 313 F i rm Location when Countries Dif fer in
I n f r a s t ru c t u res or Incomes
Ana M. Martín-Arroyuelos and José M. Usategui
Universidad del País Vasco (UPV-EHU) Abstract
This paper analyzes, in a linear market with two adjacent countries, how f i rm location and optimal plant size depend on diff e rences in the quality of infrastructures and income levels between countries. The study considers also how a free trade agreement may change, in this context where geography is made explicit, the country where a firm locates and discusses when variations in infrastru c t u res or incomes provide incentives for firm delocation. Among the results we obtain that an increase in income in the country with lower income may induce a firm to locate in the other country and that an increase in the diff e rence in qualities of infrastru c t u res between countries or a fre e trade agreement may move the optimal location of a firm from the country with worst infrastructure to the country with better infrastructure. (JEL Clas-
s i f i c a t i o n s: R30, F23) <Key Wo rd s: f i rm location, infrastru c t u re, income
* Correspondence Address: Dep. Economía Aplicada III (Martín-Arroyuelos)-Dep. Fun- damentos del Análisis Económico (Usategui). Universidad del País Vasco. Avda.
Lehendakari Agirre, 83. 48015 Bilbao. Spain. (Tel) +34-94-6013771, (Fax) +34-94-6013774. (E-mail) [email protected] (Martín-Arroyuelos), [email protected](Usategui). Research support from the Ministry of Education of Spain (DGES PB97-0603) andfrom the Basque Government (project PI-1998-86) is gratefully acknowledged. Wethank an anonymous referee for helpful suggestion.
2 0 0 0 – Center for International Economics, Sejong Institution. All rights reserved.
differences, linear market, economic integration.> I. Introduction
This work focuses on the effects on firm location and optimal plant size of d i f e rences in the quality of infrastru c t u res and in income levels between countries. The effects of the quality of infrastru c t u res and of the levels of income have not been analyzed previously in a context where geography is made explicit within each country. We show in this work the relevance of considering these factors to study firm location (and firm delocation), opti- mal plant size and the consequences of a free trade agreement. We are interested first in knowing how firm location and optimal plant size depend on diff e rences in the quality of infrastru c t u res or incomes.
Moreover, we want to learn how changes in these variables affect firm loca- tion and optimal plant size. This latter analysis is important to evaluate the impact of policies that affect infrastru c t u res or incomes. If the firm is a l ready installed when the variations in the quality of infrastru c t u res or incomes occur we want to know when there are incentives for firm deloca- tion from one country to the other. Although there are other factors re l e- vant for these decisions the factors emphasized in this paper deserve atten- tion as their impact may be important and is non trivial We also want to analyze the effect on firm location and optimal plant size of a Free Trade Agreement between the two countries. Free trade agre e- ments are becoming an increasingly extended reality: the European Union, the North-America Free Trade Agreement (US-Canada-Mexico), Mercosur in South-America and ASEAN in the Asia-Pacific area are well known exam- ples of this reality. The consequences of these agreements for firm location and for firm delocation within the same free trade area, however, have not been fully analyzed. In this paper we study the effects of a free trade agree- ment when there are diff e rences in incomes or geographical accessibility (quality of infrastructures) between countries The analysis in this paper may serve to study what effect a policy that i m p roves infrastru c t u re in a country will have on industrial location or to design income convergence policies to attract firms into the countr y with lower income. Our work may also be used to predict the effects of a fre e Trade Effects of Minimum Quality Standards with and Without Deterred Entry trade agreement on firm location or firm delocation We consider a firm that is the only producer of a good, may be because it has a patent on the good. This firm wants to install a unique plant and has to choose location within one of the two countries where the good produced by the firm may be sold. The firm may belong to one of these two countries or to a third countr y. Management and coordination costs between different plants may be the reason for the decision to install a unique plant In the analysis we assume a linear market in which the two countries are adjacent. Countries are not dimensionless points as it is costly to transport one unit of the good from any location to any other location within the same country or between countries. Hence, geography is made explicit as coun- tries have a spatial representation with a location, a size and a cost to trans- port the good along the space (see Krugman [1991a]) The quality of infrastru c t u res in a country affects costs of trade within this country and between countries. In our model these costs take the form of transport costs related to distance. Geography and past investments may explain differences in the quality of infrastructures between countries.1 On the other hand, income differences may be due to distinct degrees of economic development in the two countries. In this work, diff e rences in incomes will be re p resented by diff e rences in willingness to pay for the We consider the production cost independent of the location of the firm and, hence, assume away explanations of the firm location based on factor prices and factor availability. More o v e r, we do not discuss public policies t o w a rds business and, there f o re, suppose that these policies do not aff e c t 1. Bougheas, Demetriades and Morgenroth [1999] contains an analysis, in a different context, of the relationship between investment in infrastructures, transport costsand the volume of trade.
2. As an improvement in the quality of infrastructure in a country facilitates trade with- in this country and between countries its impact will be through demand as it occurswith an increase in the income level.
3. See Holmes [1998] and Haufler and Wooton [1999] for recent analysis on this direc- tion. The case of environmental dumping, that has been used to explain firm deloca-tion (see Motta and Thisse [1994]) is, therefore, also assumed away.
When we analyze how firm location and optimal plant size depend on dif- ferences in the quality of infrastructures or incomes between countries and how changes in these variables affect firm location and optimal plant size we consider a context where there are not tariffs on exports from one country to the other. This is the relevant context when we desire to study income or infrastructure policies within a free trade area, as it is the case of policies for income convergence or infrastructure convergence between countries with- in the European Union.4 H o w e v e r, the analysis of the case with tariffs is immediate from the developments presented and we use it to study the We obtain first how firm location and market coverage depend on trans- port costs and incomes (Propositions 1 and 2). As we expected when coun- tries differ only in transport costs (incomes) the optimal location of the firm may be in the country with higher transport cost (lower income). Hence, the firm may not locate in the country with higher income or with better i n f r a s t ru c t u re. However, this is contrar y to the results obtained in other analysis of industrial location based on different models.5 When transport costs differ between countries we obtain how the effects of changes in transport costs depend on the quantity of these changes, on the income level and on the initial relative transport costs of the two coun- tries. For instance, we obtain that an increase in the difference of transport costs between countries may move the optimal location of the firm from the country with lower transport cost to the country with higher transport cost.
In particular, the effects of variations in transport costs may be different if, as a consequence of these variations, the country with higher transport cost becomes the country with lower transport cost. This analysis can be used to study what effect a policy that improves infrastructure in a country will have When incomes dif fer between countries we prove that policies that 4. The Structural Funds and the Cohesion Funds in the European Union are policies oriented to promote infrastructure convergence and, more indirectly, income conver-gence among countries in this free trade area.
5. For instance, Martin and Rogers [1995] obtain that a policy of financing domestic infrastructure in a country will bring industrial location to this country.
Trade Effects of Minimum Quality Standards with and Without Deterred Entry increase incomes in both countries or in the country with lower income may change the optimal location of the firm from the country with lower income to the country with higher income and, hence, these policies will not neces- sarily attract firms into the countr y with lower income. This result is obtained in a context where the country with lower income remains as the country with lower income after the increase in its income. We show how the effect of a change in income within a country depend on the quantity of this change, the transport cost, the initial relative incomes of both countries and any variation in income in the other countr y. If the aim of a policy is to foster industrial convergence between a rich and a poor country these We also study the implications of transport cost or income convergence for firm location. If the transport costs converge, the optimal location of the firm may move only from the country with lower transport cost to the coun- try with higher transport cost. However, if incomes converge there are situ- ations where the optimal location of the firm changes from the country with lower income to the countr y with higher income.
F i n a l l y, considering that the countries have diff e rent qualities of infra- s t ru c t u res, we derive (Proposition 3) when a free trade agreement may induce a change in the optimal location of the firm from one country to the other. This analysis can be reproduced for the case where the countries dif- The paper is organized as follows: Section II presents the basic model.
Section III analyzes the decisions of the firm on location and price (hence, on market coverage) when the countries differ in transport costs. The firm decisions when the countries differ in incomes are studied in Section IV.
Section V centers on the implications for firm location and firm delocation of changes in transport costs or incomes. The effects of a Free Trade Agree- ment on the location of the firm are considered in Section VI. The last sec- 6. See Venables [1995] and Krugman [1991b] for other aspects relevant to the relation- ship between economic integration and the location of firms.
II. Model
Consider a linear market of length 1 which extends over two countries A and B. Country A takes up from 0 to 12 and country B occupies from 12 to 1.
Hence, 12 is the frontier between the two countries and they have equal size Consumers are uniformly distributed between 0 and 1 with unit density.
Each consumer buys one unit of the good if the sum of the price and the transport cost is lower than or equal to the reservation value of the good for the consumer, and zero units otherwise. We consider that consumers within each country are identical and that consumers in diff e rent countries may differ only in their reservation values. Let us denote by M the reservation value of each consumer in country I with I ∈ {A, B}. We assume that prefer-ences are such that M < M if and only if country I has higher income or is It is costly to transport the good along the market. It costs t per unit of distance to transport one unit of good in country I with I ∈ {A, B}. Weassume linear transport costs A firm, which is the only producer of a homogeneous good, may locate in this linear market at any s such that s ∈ {0, 1}. It produces the good withconstant marginal cost which is assumed independent of location and, with- out loss of generality, equal to 0. This firm decides first on location and after- wards it selects a nondiscriminatory (f.o.b.) selling price, p, to maximize its p rofits, . The decisions on location and price determine if the market is covered or not. The firm is completely informed about consumers’ reserva- III. Decisions When Transport Costs Differ
Consider that t < t and M = M = M with I, J ∈ {A, B} and I ≠ J. In this sit- uation there are five possible results in terms of market coverage and loca- tion of the firm: 1) the firm covers only part of country I, 2) the firm covers completely country I and it does not supply to consumers in country J, 3) the firm covers countr y I and part of countr y J with location in countr y I, 4) the firm covers country I and part of country J with location in country J and 5) the firm covers the whole market with location in country J.
Trade Effects of Minimum Quality Standards with and Without Deterred Entry Proposition 1 : For I, J
{A, B} and I J, when transportation costs dif - t the results in terms of market coverage and i) when M < tI the firm will locate in I and will cover completely country I I ≤ M ≤ tI tJ the firm will locate in I and will cover completely countr y I but it will not supply to consumers in country J (case 2), iii) when tI +tJ < M ≤ 3tI +tJ the firm will locate in country I and will cover completely this country and part of country J (case 3), < M < 3tJ I the firm will locate in country J and will cover part of this country and completely country J (case 4), and < M the firm will locate in J and will cover the whole mar- Proof: See the Appendix.
From Proposition 1 it is immediate to obtain: C o ro l l a ry : For I, J
J, when transportation costs diff e r t the firm will locate in country I if and only if F i g u re 1 illustrates Proposition 1 showing the zones where each case occurs. We have denoted by 1 to 5 the cases for t < t and by 1' to 5' the (symmetric) cases for t < t . The dashed zone corresponds to the pairs (t , t ) implying that the firm will locate in J. In the rest of situations the firm will IV. Decisions When Incomes Differ
Conside that M < M and t = t = t with I, J {A, B} and I ≠ J. The possi- ble results in terms of market coverage and location of the firm that we may obtain are the same ones than in the context of diff e rences in transport costs and we use the same notation for the five cases: 1, 2, 3, 4 and 5.
Proposition 2 : For I, J
{A, B} and I J, when incomes differ between M the results in terms of market coverage and firm loca - i) when M < t2 the firm will locate in I and will cover only part of country ii) when either t ≤ M < 5 t and M ≤ − M + 4tM − t2 or M M ≤ MI + t the firm will locate in I and will cover completely country I but it will not supply to consumers in countr y J (case 2), iii) when − M + 4tM − t2 ≤ M and 3M − M ≥ 2t the firm will locate in countr y I and will cover completely this country and part of countr y J iv) when − M + 4tM − t2 ≤ M , M firm will locate in countr y J and will cover part of this country and complete- ly country country I (case 4), and v) when M + M ≥ 2t and MI + t ≤ M the firm will locate in J and will Proof: See the Appendix.
From Proposition 2 it is immediate to obtain: Corollary: For I, J
{A, B} and I J, when incomes differ between coun - M the firm will locate in country I if and only if at least one of the following conditions occurs: i) M ≤ − M + 4tM − t2 ii) 3M − M ≤ 2t, and F i g u re 2 illustrates Proposition 2 showing the zones where each case occurs. We have denoted by 1 to 5 the cases for M < M and by 1' to 5' the (symmetric) cases for M < M . The dashed zone corresponds to the pairs (M , M ) implying that the firm will locate in J. In the rest of situations the Zones 3 and 4 in Figure 2 (and the symmetric zones 3’ and 4’) deserve particular attention. From the proof of Proposition 2 we have that in zones 3 Trade Effects of Minimum Quality Standards with and Without Deterred Entry and 4 market coverage and price increase with M but location moves to the left when M increases. This is a remarkable result that implies that in these zones an increase in the income of the poorest country may induce the firm to locate in the other country. This possibility will be important in the analy- V. Changes in Transport Costs or Incomes and Their Implications
In this section we discuss how variations in transport costs or incomes may imply that the optimal location of the firm changes from one country to the other. We may consider a situation where the firm has not decided yet its location and each country is interested in knowing if policies that modify transport costs or incomes may change the country of location of the firm.
Alternatively, we could consider that the firm is located according to the results in Propositions 1 or 2. This firm may have been producing the good during several periods at that location. However, there is a variation in trans- port costs or incomes that, from Propositions 1 and 2, changes the optimal location. This variation was unexpected when the original location was decided or it was uncertain and far in the future (heavily discounted) at that moment. After the variation in transport costs or incomes the firm will change its location if the costs of relocation are lower than the present value of the increase in expected profits (assuming risk neutrality) in the future. If this relocation implies that the firm translates its location to the other coun- t ry there will be firm delocation. To know if there are incentives for firm delocation we study when the variation in transport costs or incomes implies a change in the optimal location of the firm from one country to the A. Analysis When Transport Costs Differ
Consider that t < t and M = M = M with I, J {A, B} and I ≠ J. In this case, we know from Coro l l a r y 1 that the optimal location of the firm < t ). If this fraction decreases the optimal location of the firm may change from countr y I to countr y J and if this fraction i n c reases the optimal location of the firm may change from country J t o decreases if M increases and there is no varia- tion in transpor t costs, and if t and/or t d e c rease and M re m a i n s may also decrease if a decrease in M is accompanied by a higher decrease in 3t + t , if an increase in 3t + t is accompanied by a higher increase in M or if t and t move in opposite directions but 3t + t F rom Proposition 1 we shoud notice, however, that a decrease in the t r a n s p o rt cost within the countr y with higher transpor t cost will attract firms into this country or will expel firms away from this country depending on the quantity of this decrease, on M and on the initial relative transport costs of both countries. The reason is that changes in transport costs may be such that the country that initially had higher transport cost becomes the country with lower transport cost. Consider that initially t < t . Fro m Figure 1 we have that if t decreases, with t and M unchanged, and if coun- try J becomes the country with lower transport cost, the optimal location of the firm may change from country J (zones 4 and 5) to country I (zone 5’).
On the contrary, we know from the previous paragraph that a decrease in any transport cost, with M unchanged and such that after the change in transport costs t < t , could only cause a change in the optimal location of the firm from countr y I to countr y J (a decrease in t could only change the optimal location from country I, zone 3, to country J, zones 4 and 5).
Moreover there are situations (zones 1, 2 and 3) where an increase in tI induces a change in optimal location from country I to countr y J. Consider in Figure 1 that t increases, with t and M unchanged, and that country I becomes the country with higher transport cost. In this situation the new optimal location of the firm will be in countr y J, except in the case where the market was initially covered (zone 5) as in this case the new optimal loca- In Figure 1 we can track the changes in optimal location of the firm (and in market coverage) as transportation costs evolve from any initial situation.
7. From Proposition 1 we know how the decisions on firm location and on market cov- erage are related. The effect of the variations in M, t and t on firm location derives from the changes in market coverage opportunities.
Trade Effects of Minimum Quality Standards with and Without Deterred Entry B. Analysis When Incomes Differ
Consider that M < M and t = t = t with I, J {A, B} and I ≠ J. In this case, if t, M and M change in the same pro p o rtion the optimal location of the f i rm will not be affected. However, a variation in t with both incomes unchanged may cause a change of the optimal location from one country to the other as a variation in t implies a move in Figure 2 along the ray that goes through the origin and through the point representing the initial situa- F rom Coro l l a ry 2 and Figure 2 it is clear that if the countries become richer (M and M i n c rease) the optimal location of the firm may change 8. A decrease in t implies a move away from the origin and, hence, may change the optimal location of the firm from country I to country J as we expected.
from the country with higher income to the country with lower income (for instance, a move from zone 2 to zones 4 or 5 implying an increase in market coverage). However, the opposite result is also feasible as we may move in Figure 2 from zones 4 and 5 to zone 2 if M increases more than M (the firm prefers to cover only market I where income has increased more and the price charged may be higher). More o v e r, we see in Figure 2 that an increase in M may change the optimal location of the firm to country J (a move from zone 2 to zones 4 or 5). Nevertheless, there are other possibili- ties: Consider that M = 0.95t and M is such that we are in zone 4. As M increases we may move into zone 3 implying an optimal location in country I. Hence, policies that increase incomes in both countries or in the country with lower income will not necessarily attract firms into this country. These policies may induce the firm to locate in the country with higher income.
The effects of increases in M and M or of an increase in M depend on the quantities of these increases, on t and on the initial relative incomes of both countries, as a consequence of Proposition 2 Changes in income may be such that the country that initially had lower Trade Effects of Minimum Quality Standards with and Without Deterred Entry income becomes the country with higher income. Consider that initially MI> M . From the proof of Proposition 2 and Figure 2 we have that if initially the firm is located in I, M > 0 . 7 1 2t and M i n c reases, with M and t unchanged, in such a way that countr y J becomes the country with higher income the optimal location of the firm may remain in I. The rest of possibil- ities corresponding to the situation where the countr y with lower income becomes the country with higher income follow immediately from Proposi- In Figure 2 we can track the changes in optimal location of the firm (and in market coverage) as countries incomes evolve from any initial situation T h e re f o re, we have shown when variations in transport costs or in incomes may change the optimal location of the firm from one country to the other. If the firm is already located when the variations in transport cost or incomes happen there may be firm delocation. The occurrence of firm delocation will depend on relocation costs and on expected future variations in transport costs and incomes. If transport costs converge (t approaches t ) the optimal location of the firm may move from country I (zone 3 in Figur e 1) to countr y J (zones 4 or 5) but not from country J to countr y I. If incomes c o n v e rge (M a p p roaches M ) the optimal location of the firm may move from country I (zone 2 in Figure 2) to country J (zones 4 or 5% ) but also from country J (zone 4 in Figure 2 with 0.904t < M < t) to countr y I (zone 3) VI. Effects of a Free Trade Agreement
When two countries decide to start a process of integration a usual first step is a mutual tariff reduction. Consider an initial situation where country A has established a fixed- quantity tariff f on imports from country B and c o u n t r y B has established a per unit tariff f on imports from country A.
With tariffs there are two additional results in terms of market coverage and optimal location of the firm, besides 1 to 5. In this context we may also have: 3*) the firm covers countr y I and part of country J with location on the I- side of the frontier between the two countries and 4*) the firm covers coun- try I and part of country J with location on the J-side of the frontier. In this section we analyze when a free trade agreement may induce a change in the optimal location of the firm from one country to the other. We consider that the countries have different transport costs (the study would be analogous if the countries differ in incomes). In this context we can prove: Proposition 3 : For I, J
{A, B} and I J, consider that f and f are the per unit tariffs set, respectively, by countries I and J, respectively, and that t < t M. A free trade agreement may change the optimal location of i) from country J to country I only if f > f + fI , ii) from countr y I to country J in the rest of situations.
Proof: See the Appendix
As it is shown in the proof of Proposition 3 result ii) corresponds to a situ- ation where we have case 4* with tariffs and case 3 without tariffs. On the other hand result i) cor responds to a situation where we have case 2 or case 3* with tariffs and case 4 without tariffs. From Proposition 3 we know when a free trade agreement may change the optimal location of the firm from the country with lower transport cost to the other country or viceversa.
VII. Conclusion
In this paper we have analyzed how firm location and optimal plant size depend on diff e rences in the quality of infrastru c t u res and income levels between countries and how changes in these variables affect firm location and optimal plant size. From this analysis we have extended the study to consider how a free trade agreement may change the country where a firm locates when quality of infrastructures or incomes differ between countries and to discuss when variations in infrastructures or incomes provide incen- We have assumed a linear market where there are two adjacent countries.
Geography has been made explicit as countries have a spatial re p re s e n t a- tion with a location, a size and a cost to transport the good within each coun- Among other results obtained, we have shown in this work how a firm may not locate in the country with higher income or with better infrastruc- t u re, how an increase in income in the countr y with lower income (or in Trade Effects of Minimum Quality Standards with and Without Deterred Entry both countries) may induce a firm to locate in the other countr y, how an increase in the difference in the qualities of infrastructures between coun- tries may move the optimal location of a firm from the country with worst infrastructure to the country with better infrastructure or when a free trade agreement may induce a change in the optimal location of the firm from the country with lower transport cost to the country with higher transport cost or viceversa. Our study has stressed the importance of the initial conditions to analyze the effects on firm location and market coverage in each country of a free trade agreement or of variations in the qualities of infrastructures This analysis may serve to study what effect a policy that improves infra- structure in a country will have on industrial location or to design income c o n v e rgence policies to attract firms into the country with lower income.
The results obtained may also be relevant for countries that have decided to integrate by forming a free trade area. We can emphasize the importance of considering the foreseeable evolution of countries incomes and infrastruc- tures after integration as this evolution will have consequences in terms of The effects of the quality of infrastru c t u res and of the levels of income have not been analyzed previously in a context where geography is made explicit within each country. We have shown in this work the relevance of considering these factors to study firm location (and firm delocation), opti- mal plant size and the consequences of a free trade agreement.
References
Bougheas, S., Demetriades, P.O. and E.L.W. Morg e n roth [1999], “Infras- t ru c t u re, Tr a n s p o rt Costs and Trade,” J o u rnal of International Eco - H a u f l e r, A. and I. Wooton [1999], “Country Size and Tax Competition for F o reign Direct Investment,” J o u rnal of Public Economics 71; pp. 121- Holmes, T. J. [1998], “The Effect of State Policies on the Location of Manu- facturing: Evidence from State Borders,” Journal of Political Economy Krugman, P. [1991a], Geography and Trade, Leuven University Press, Leu- Krugman, P. [1991b], “Increasing Returns and Economic Geography,” Jour - nal of Political Economy 99(3); pp. 483-499.
M a rtin, P. and C.A. Rogers. [1995], “Industrial Location and Public In f r a- Structure,” Journal of International Economics 39; pp. 335-351.
Motta, M. and Thisse, J.F. [1994], “Does Environmental Dumping Lead to Delocation?,” European Economic Review 38; pp. 563-576.
Venables, A. [1995], “Economic Integration and the Location of Firm s , ” American Economic Review 85(2); pp. 296-300.
Appendix
A.1 Proof of Proposition 1
We derive the proof for the case t t with I, J ∈ {A, B}. In case 1 the firm will be indiff e rent between an inter val of locations.
The extremes of this inter val are those locations such that, at the corre- sponding optimum price, the consumer located at 0 (for the left extreme of the interval) and the consumer located at 12 (for the right extreme of thei n t e r val) get no surplus. Taking the left extreme of this interval we have p =M − t .s and = p. 2s. From profit maximization we obtain for this left extre m e = M . Hence, the inter val of locations will be 2t , i.e., when tI > M .
In case 2 it will be s = 1, p = M − tI . This alternative will ≤ M ≤ tI J . When M < tI we were in case 1 and when < M the good will be supplied to consumers in country J. In case 3 the consumer z in J that will be indifferent between buying and not buying the good will be such that M = p + t ( 1 − s) + t (z − 1 ). A s p = M − t s (the consumer at 0 gets no surplus in the solution that maxi- mizes the firm’s profits), we obtain from profit maximization ( = p.z) that . This alternative requires 1 < s = M − t t condition will also imply z > 1 ). Moreover, s in I implies s ≤ 1, i.e., M Trade Effects of Minimum Quality Standards with and Without Deterred Entry Hence, this solution will result when t + t J < M ≤ 3tI tJ .
In case 4 we proceed as in the previous case and, noting that the indiffer- J is z = tI + 2s − 1 = 2M+23 J I . As s in J requires t J ≤ M. More o v e r, in this case < 1, i . e ., M < 3tJ tI .
Hence, this solution will result when 3t + tJ ≤ M < 3tJ tI .
Finally, in case 5 the firm will locate in J. As profit maximization in a cov- ered market implies that the consumers located in the extremes of the mar- p = M − tI tJ . The market will be A.2 Proof of Proposition 2
We derive the proof for the case M < M with I, J ∈ {A, B}.
For case 1 we reason as in the proof of Proposition 1 and obtain s = M I , = M2I and s ∈ MI , 1 − MI In case 2 it will be s = 1, p = MI − t . This alternative is fea- sible only when M ≥ t. It is easy to show that the firm prefers situation 1 to situation 2 when t > M .
In case 3 consumer z indifferent in J will be such that M = p + t.(z − s). As p = M − t . s (the consumer at 0 gets no surplus in the solution that maxi- mizes the firm’s profits), we obtain from profit maximization ( = p.z) that = (MI MJ )2 . This alternative requires 1 < s ≤ 1 and 1 < z < , i.e., respectively, t < 3M − M ≤ 2t and t < M + M < 2t.
When the firm locates in country J we should distinguish between two possibilities: a) M ≥ M − 1 and b) M < M − t . With possibility a) it will always be optimal for the firm to decide price and location in such a way that the consumer located at 0 gets no surplus.9 However, under possibility b), at the optimal location such that the covered market is connected, the con- 9. Except in the case M = M − t2 there will be other locations that, with the same price, will be optimal for the firm.
sumer located at 0 will get a positive surplus. We consider first the case In case 4−a the problem to solve is the same one than in case 3 and, hence, the solution is the same: p = M − t . s, s = 3MI4t . However, the parameter values for case 4−a should imply loca- tion in J (not in I as in case 3). In par t i c u l a r, this alternative re q u i re s < 3M − M < 3t and t < M + M < In case 5−a we have p = M − ts = M − t(1 s) and profit maximization antees s ≤ 3. Moreover, this case requires p ≥ 0, i.e., t ≤ M + M .
Hence, each case is feasible in a particular zone in the space of parameter values. These zones do not intersect for cases 1, 3 and 4−a. On the other hand, the zones of cases 1 and 5−a do not intersect as in this latter case we re q u i re t ≤ M + M and this implies M ≥ t when M already know the result of the comparison between cases 1 and 2. Therefore it only remains to compare firm profits in case 2 with profits in cases 3, 4−a and 5−a and also firm profits in case 5−a with profits in cases 3 and 4−a.
The expression of in cases 3 and 4−a is the same. If we compare this expression with profits in case 2 we obtain that profits in this latter case are higher if and only if M ≤ − M + 4tM − t2 . On the other hand, if we com- pare the expression of in cases 3 and 4−a with profits in case 5−a, the lat-ter are always smaller. Finally, profits in case 5−a are higher than profits in case 2 if and only if M ≥ 3t .
Let us now consider that M < M − t . In this context case 1 is not feasi- ble. We study first case 4−b. Notice that profit maximization implies that for the optimal p the location s of the firm should be in an interval of locations with left extreme such that p = M − t(s − 1 ) and right extreme such that p = M − ts. As firm profits are the same for any location in this interval we pre- sent the algebra for the location in the left extreme of the interval. In case 4−b it is p = M − t. (s − 1 ) and we obtain from profit maximization . This alternative requires 1 < s < 3, i.e., t p r ofits in case 4−b a re always lower than profits in case 2 as ( + 1)< MJ + t < MI − t w h e re we have used Trade Effects of Minimum Quality Standards with and Without Deterred Entry the first inequality and M < M − t in the second inequality. So case 4−b In case 5−b it is s = 3 and p = M − t4. From profit maximization we obtain = p = M − t4 and re q u i re M ≥ t . From here it is clear that profits in case 5−b a re higher than profits in case 2 if and only if M > MI + t. More o v e r, the zone of intersection of cases 5−b and 3 is empty as M < M − t and 3M −M > A.3 Proof of Proposition 3
The analysis is analogous to the one developed in the proof of Proposition 1 and illustrated in Figure 1. However, notice that if the tariffs are very high some of the cases that imply exports from one country to the other may not be feasible (zones 3, 3*, 4 and 4* may not exist). On the other hand, when there is a tariff the profits of the firm in cases 1 and 2 do not vary as in these cases production and sales occur in country I. However, profits decre a s e with the tariff in cases 3, 4 and 5 as there are exports in any of these cases.
Hence, if case 1 or case 2 was selected without the tariff the same case (1 or 2 with location in I) will be chosen with the tariff It is immediate to obtain that zone 2 will be larger with tariffs as case 2 ≤ M ≤ tI J + fJ . However, zone 3 will be smaller with tariffs as case 3 will happen when t + t + fJ < M < 3tI J − fJ . On the other hand, all pairs (t , t ) that are in zone 4 when there are tariffs belong to zones 4 or 5 without tariffs as with tariffs case 4 is feasible if 3t t + 3 fI < M < tI J + fI.
Finally, zones 3* and 4*, if they exist, are located between zones 3 and 4, i.e., they occur for situations where 3t t − fJ ≤ M ≤ 3tI J + 3 fI .
It is not difficult to show that case 3* will happen when 3t +t ≤ (2 f + f )t +t t +2 f 2 and case 4* will occur when 3t +t − fJ ≤ M ≤ 3tI J + 3 fI .
Hence, to obtain results i) and ii) we have to compare the regions (2 f + f ) t + f t +2 f 2 = M and 3t + t = 4M (the limit from below of zone 3 with- and −1 , respectively. Hence, when f more horizontal than the second one and when f > f the first line is more vertical than the second one (the lines are parallel when f = f ). The point w h e re these lines cut each other in a Figure with axis t and t i s and t = −2 M − 6 fI . When f ≥ f the value of t correspond- ing to the cutting point is negative. When f < f the value of t at the cutting point will be lower than 4M if − 6 fI < 6M, i.e., if f + fI < f . Therefore, i)

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