Jean-Marc Callois

Carl Gaigné

ATTITUDES TOWARDS FOREIGN PRODUCTS AND WELFARE WITH CAPITAL MOBILITY January, 2009

Keywords: product of origin, capital location, consumer's surplus JEL Classification: F12, F21

We develop a model of trade with imperfect competition to study the welfare implications in developing and developed countries of the asymmetry in attitudes towards foreign products. In the developed country, consumers benefit from a better perception of foreign products while the rental rate of capital declines as long as the location of capital remains unchanged. However, when capital is mobile, the developing country hosts more and more capital at the expense of the developed country as the perception of varieties produced in the developed country improves and the surplus of consumers in the developed country can decrease.

Introduction

Different studies in marketing and economic psychology show consumers attach different values to products which are otherwise identical but produced in different countries. Although numerous studies reveal that country of origin matters, standard economic theory of trade and location does not consider this element in consumers and firms behaviour.

A large body of research is dedicated on country of origin effects on product evaluation such as perceived quality, attitudes and purchase intentions (see Peterson and Jolibert, 1995, for a survey). Product-country images contain not only cognitive and affective aspects but also normative aspects such as "buy domestic", "consumer ethnocentrism" and "customer voting" 1 . Numerous studies show that country of origin influences significantly product evaluation. From a metaanalysis of country-of-origin research, [START_REF] Verlegh | A review and meta-analysis of country-of-origin research[END_REF] show that the country' level of development matters in product evaluation. Products from Less Developed Countries (LDC) appear to be evaluated less positively than products from Developed Countries (DC). For example, US consumers (resp., Canadian) consumers are, ceteris paribus, more disposed to purchase Canadian (resp., US) products than Mexican products [START_REF] Lantz | Country of origin and ethnocentrism: an analysis of Canadian and American preferences using social identity theory[END_REF]. At the opposite, Indians, South African and Mexican consumers favour more foreign products (see Bara et al., 2000). Hence, firms producing in LDC have greater difficulties to penetrate the developed countries markets. This, in part, may explain why outward foreign direct investments in industrial sectors from developing countries (especially from Brazil, China, India, Malaysia, the republic of Korea, Singapore, and South Africa) to developed countries are becoming important (UNCTAD, 2004).

For example, the most important destination of for Indian and Chinese foreign direct investments 1 "customer voting" is related to the phenomenon where a consumer, by deciding to avoid or purchase a country's product, votes pro or contra the policies and practices of its government [START_REF] Smith | Morality and the market[END_REF]. This phenomenon include also ethical considerations [START_REF] Grolleau | Does ethical activism Lead to firm relocation?[END_REF].

has been the United-States between 2001 and 2003 while investment activities in Europe from

Korean and Taiwanese companies have grown over the last decade.

This paper aims at evaluating the effects of foreign products' perceptions on trade, capital location and welfare. To address this issue, we provide a two-country model with monopolistic competition and capital mobility. Countries are only distinguished from each other by differences in attitudes towards foreign products. This type of differentiation induced by the country of origin is not studied in existing models of trade and location. The model developed by [START_REF] Neven | Attitudes towards foreign products and international price competition[END_REF] is a notable exception because they consider that demand is subject to national product bias. However, they assume no capital mobility between countries, while in our model it is endogenous. We will see that some unsuspected results emerge when we take into account the mobility of capital.

Our first result is in line with standard analysis. Consumers living in the developed country always benefit from a rise in the knowledge of foreign products as long as the location of capital remains unchanged. In this case, they consume more varieties and prices decrease due to an increasing price competition between domestic firms and foreign firms. However, taking into account the mobility of capital reveals new results. First, the developing country hosts more and more firms (or capital) at the expense of the developed country as the perception of product improves. Second, and as a direct consequence of the previous result, the surplus of consumers in the developed country can decrease when perception of foreign products improves, whereas the surplus of developing country consumers increases. In other words, a better perception of foreign varieties produced in developing countries favours the convergence of economies. This result means that the international integration of product markets and that the international harmonisation of attitudes towards foreign products have opposite effects on the inequalities among nations since economic geography models show that a fall in trade costs fosters inequalities between countries (see [START_REF] Fujita | The spatial economy. Cities, countrys and international trade[END_REF]Fujita andThisse, 2002).

The remainder of the paper is organised as follows. In section 2, we present formally the main assumptions of the model. In section 3, we study the consequences of better perception about varieties produced in developing countries for the prices, rental rate of capital and consumer's surplus when the location of capital is exogenous. The impact of better perception of foreign products on the international allocation of capital is studied in section 4 while a welfare analysis is performed in section 5 by considering the equilibrium allocation of capital. Section 6 concludes and gives some suggestions for future theoretical investigations.

Model and some preliminary results

General assumption.

The economy is made up of two countries, labelled H (the home country or developed country) and F (the foreign or developing country). There are two sectors, a traditional sector (T) and a modern sector (M). The M-sector produces a continuum of varieties of a horizontally differentiated product, using capital as only input. The T-sector produces a homogenous good (the numéraire), using labour as only input. The economy is endowed with k units of capital and 2L consumers/workers. Workers supply their units of labour inelastically and are not internationally mobile. Consumers have a love for variety of differentiated product. Capital is perfectly mobile between countries and is owned by workers, who also supply inelastically their units of capital. In order to focus on effects of product knowledge on the international allocation of capital and welfare, we assume that technology, endowment in consumers and preferences are identical whatever the country.

Each consumer living in country H (resp., F) is willing to buy a share θ F (resp. θ H ) of varieties produced in country F (resp., H). There is no imports (θ F =0) when each consumer values very negatively a foreign country while all varieties produced in the foreign country are imported when consumers do not attach a negative value to foreign products (θ F =1). In addition, an increase in θ F from 0 to 1 means that the perception of varieties produced in country F improves and more products are imported from country F. 2One can show that, when θ F =θ H , full dispersion of capital is the only equilibrium spatial configuration, whatever the trade costs. A more interesting situation arises in the case where θ F <θ H . 3 Because our qualitative results depend only on the wedge between θ F and θ H , the representative consumer in country F is assumed to know all goods produced in country H (θ H =1), without loss of generality and let F θ θ ≡ . In other words, all varieties produced in country H benefit from a good perception of consumers living in country F and only prices determine the choice. Therefore, country F is the developing country, as it is more difficult for varieties produced in this country to reach the other country.

Notice finally that θ can also be interpreted differently. Indeed, 1 θ -can reflect the share varieties for which import to country F is prohibited by the government of country H. In different countries, governments, labour unions, industry groups sponsor campaign in order to establish of a "buy domestic" norm.

Consumption

Following [START_REF] Ottaviano | Agglomeration and Trade Revisited[END_REF], preferences are identical across workers located in the same country and are described by the following quasi-linear utility:

2 2 0 ( ) ( ) ( ) 2 2 n n n O O U q i di q i di q i di z β γ γ α   - = - - +     ∫ ∫ ∫ (1)
where α>0, β>γ>0 are exogenous parameters, q(i) is the quantity of variety i∈[0,n] and z the quantity of the numéraire. In this expression, α measures the intensity of preferences for the differentiated product with respect to the numéraire. The condition β>γ implies that workers have a preference for variety. Each worker is endowed with z'>0 units of the numéraire. The initial endowment is supposed to be large enough for the consumption of the numéraire to be strictly positive at the market outcome. His budget constraint can then be written as follows: 0 ( ) ( ) '

N p i q i di z w z + = + ∫
where w is the individual's income and p(i) is the consumer price of variety i.

The average number of products from country F that a representative consumer from country H is willing to buy is

F n θ .
Given the assumption of symmetry between varieties, solving the consumption problem yields the individual demand function for variety i produced in country j=H, F from a representative consumer located in country H:

' [ ' '( )] ' jH H F jH H q a b c n n p c P θ = -+ + + (2) with 1 ' ', ' and ' ' ( ) H F a b b c b n n γ α β γ γ θ β γ ≡ ≡ ≡ -+ + -
where jH p is the price of a variety prevailing in country H produced in country Given that consumers/workers in country F are willing to buy all varieties produced in country H, their individual demand function is the following:

[ ( )] jF H F jF F q a b c n n p cP = -+ + + (3)
where 1 , and ( )

H F a b b c b n n γ α β γ γ β γ ≡ ≡ ≡ -+ + - with F F FF H HF P n p n p = +
, FF p (resp., HF p ) being the price of each variety produced in country F (resp., H) and consumed in country F.

Production.

The traditional sector produces a homogeneous good under perfect competition and constant returns to scale. One unit of output requires one unit of labour. The T-good is costlessly traded between countries so that its price is the same everywhere (which is why that good is the natural choice for the numéraire). This implies that the price of the T-good and, at the equilibrium, the workers' wage is equal to one everywhere.

The modern sector supplies varieties under increasing returns to scale and monopolistic competition. The production of any variety requires one unit of capital. There exists a one-to-one correspondence between firms and varieties, so that n k = . We consider a market structure with monopolistic competition with free entry. Varieties of M-good are traded at a cost of t units of the numéraire per unit shipped between the two countries. In addition, we assume that markets are internationally segmented so that each firm chooses a delivered price, which is specific to the country in which its variety is sold. As firms bear trade costs and assuming one unit of capital per firm (n = k), and denoting H r (resp. F r ) the rental rate of capital in country H (resp. F), profits of a representative firm in country H are as follows:

( )

H HH HH HF HF H p q L p t q L r π = + - - (4)
and in country F are given by: ( )

F FF FF FH FH F p q L p t q L r π θ = + - - (5)
When producers maximise profits, they take price indices as given. Nevertheless, the market as a whole has a non-negligible impact on each firm's choice in that each firm must account for the distribution of all firms' prices through an aggregate statistics (the price index) in order to find its equilibrium price. Thus, the market solution is given by a Nash equilibrium with a continuum of players in which prices are interdependent. The profit-maximising prices are given by: 2 ( ) 2 ( ) 4( )

F HH H F t n p n n α β γ γθ γ θ β γ -+ = + + - (6a) 2 FH HH t p p = + (6b) 2 ( ) 2 ( ) 4( ) H FF H F t n p n n α β γ γ γ β γ -+ = + + - (7a) 2 HF FF t p p = + (7b)
As firms' prices net of trade costs are to be positive for any distribution of firms, we assume throughout this paper that

Λ - ≡ < ) ( 2 γ β α trade t t where ( ) 2( ) 0 H F n n γ β γ Λ ≡ + + ->
This condition also guarantees that it is always profitable for a firm to export to the other country.

Prices, rental rates of capital and consumer's surplus

In order to disentangle the different mechanisms at work, it is both relevant and convenient to distinguish between we call short-run equilibrium, in which capital is supposed to be immobile, i.e.

H n and F n are exogenous and, a long-run equilibrium when capital is internationally mobile, i.e.

H n and F n are endogenous. In this section, we study the impact of θ on (i) equilibrium prices; (ii) rental rate of capital and (iii) consumer's surplus, when the spatial distribution of firms is given.

Prices

It is easy to check that

[( 2( )] 2 ( )) 0 2( ( ) 2( ))² HH F H H F p n n t n n γ γ β γ α β γ θ γ θ β γ ∂ + - - - = ≤ ∂ + + - when t ≤ t trade and 0 FF p θ ∂ = ∂ .
In words, a better perception of varieties produced in the developing country (country F) decreases the prices prevailing in the developed country (country H). This means that better perception on varieties increases the price competition among producers serving market H since more varieties are imported from country F. Note that, because markets are segmented, prices in country F are not affected by attitudes towards foreign products of consumers living in country H.

Rental rate of capital

Due to free entry and exit, there are no profits in equilibrium. This implies that operating profits are equal to the fixed cost paid in terms of capital. In other words, the equilibrium rental rate is determined by a bidding process for capital, which ends when no firm can earn a strictly positive profit at the equilibrium market price. Hence, by introducing (2) (resp., (3)) into (6a) and (7b) (resp., (6b) and (7a)) and by using 0 H π = and 0 F π = , the equilibrium rental rate of capital located in countries H and F given by, respectively, 2 2

[( ) ( / 2) ] /( )

H HH FF r L p p t β γ = + - - (8) 2 2 [( ) ( / 2) ]/( ) F FF HH r L p p t θ β γ = + - - (9)
which increase with prices (given by (6a) to (7b)) whereas we have

F H F r n n β γ γ θ θ ∂   = -+ -   ∂  
As a consequence, we have / F r θ ∂ ∂ >0 as long as there are not more firms in country F than in country H (which, as we shall see, is always the case). In other words, without relocation of capital, an improve in the perception of varieties produced in the developing country increases rental rates of capital in this nation and decreases rental rates prevailing in the developed country.

Consumer's surplus

The expression of surplus for a consumer living in country H is given by: 4

( ) ( ) ( ) '2 2 2 2 ( ) ' 2 ' ' '( ) ' 2 2 H F H H HH F FH H F H HH F FH H HH F FH a n n S a n p n p b b c n n c n p n p n p n p θ θ θ θ θ + = - + + + + + - + (10)
while the consumer surplus of an individual residing in country F is expressed as follows:

( ) ( ) (
)

2
θ θ θ + - - ∂ ∂ ∂ = + > ∂ ∂ ∂
, and 0.

F S θ ∂ = ∂
Consequently, for a given spatial allocation of firms, better perception on varieties raises the surplus of consumers in country H since more varieties are consumed and because of decreasing 4 Due to the introduction of θ , the expression of the surplus differs from Ottaviano et al. (2002).

prices. In addition, for a given spatial allocation of firms, the surplus of consumers in country F is not directly affected by the change in the perception parameter, since we have / 0

FF p θ ∂ ∂ = .
To summarize, Proposition 1. Assume that the location of capital is fixed. When the perception of foreign products improves, the consumer's surplus only raises in the developed country whereas the rental rate of capital decreases in this country and increases in the developing country.

Asymmetry in perception of foreign products and capital location

We now analyse the role of the perception parameter θ on the location of capital. As there exists a one-to-one correspondence between firms and capital ( n k = ), we can write

(1 )

H F n n n n λ λ = = -
where λ is the share of capital or firms located in country H. The location of capital depends on the spatial differential of rental rates. A spatial equilibrium is such that, in each country, no firm has an incentive to change location, conditional upon the fact that the markets clear at the equilibrium prices. Formally, a spatial equilibrium arises at λ∈]0,1[ when ( , ) ( , ) ( , ) 0 [START_REF] Ginsburgh | On Existence and Stability of Spatial Equilibria and Steady-States[END_REF]. An interior equilibrium (λ∈(0,1)) is stable if and only if the slope of the profit differential is negative in a neighbourhood of the equilibrium ( ( , ) / 0 d r d λ θ λ ∆ < ,), whereas agglomerated equilibria (λ = 0,1) are always stable whenever they exist.

H F r r r λ θ λ θ λ θ ∆ = - = , or at λ=0 if ( , ) 0 r λ θ ∆ ≤ , or at λ=1 if ( , ) 0 r λ θ ∆ ≥ . Such equilibrium always exists because ( , ) r λ θ ∆ is a continuous function of λ (
Given ( 8) and ( 9), the difference in rental rates of capital between the developed country and the developing country is given by: 2 2

(1 ) ( , )

(1 ) 4

HH HH FF L t r p tp tp θ λ θ θ θ β γ   - ∆ = - + - +   -  (12). Observe that ( , ) / 0 d r d λ θ λ ∆ < for [0,1] λ ∈
because p HH is a decreasing function of λ while p FF an increasing function of λ. In other words, the slope of ∆r(λ,θ) is never positive or null.

This means that full agglomeration in the developing country is never an equilibrium spatial configuration. To summarize, Lemma 1. There exists a single spatial equilibrium for each combination of parameters (a positive share of firms in country F or full agglomeration in country H).

To determine the spatial equilibrium, we analyse three subcases:

1 θ = (case 1), 0 θ = (case 2) and 1 0 θ > > (case 3).

No negative perception of foreign products (

1 θ = ).
Because the purpose of the paper is the impact of attitudes towards of foreign products on location, it is important to establish as our benchmark how the spatial allocation of firms is characterised under the assumption for which the country of origin does not matter in consumption. Assuming θ =1 and introducing (6a) and (7a) in ( 12), the spatial differential of rents becomes ² ( 1/ 2) ( ,1) ( )

t nL r γ λ λ β γ - - ∆ = -Λ .
Clearly, the full dispersion of capital ( * 1/ 2 λ =

) is the single spatial equilibrium. When all consumers do not attach negative values to foreign products ( 1 θ = ), price competition discourages a higher concentration of firms in a single country. This result contrasts with a classical result of new economic geography literature, showing that the dispersion of activities is not a stable equilibrium when transport costs are low enough (see [START_REF] Fujita | The spatial economy. Cities, countrys and international trade[END_REF]Fujita andThisse, 2002) This proposition means that the agglomeration of the production is favoured when firms located in country F have no opportunity to serve country H. In this case, the location of production in country H allows firms to serve both markets. However, under certain conditions, it can be profitable to locate in country F even though firms do not export. Indeed, the spatial concentration of all capital does not occur when trade costs are high enough. This result requires some comments.

Remember that price competition works against agglomeration. Indeed, when trade costs are high enough, firms producing in country F can set high prices. Further, the share of local varieties consumption in total consumption in country F rises when trade barriers increases. This is due to a substitution effect between local varieties and varieties produced in country H. Note that this substitution effect is amplified when the degree of product differentiation is low. As a result, some units of capital are prompted to set up in country F in order to benefit from higher price and demand when trade costs are high enough or when products are weakly differentiated. However, when trade costs become sufficiently low, all firms set up in a single country.

4.3. The intermediate case (1 0 θ > > ).
Finally, suppose that 1 0 θ > > . We first determine the threshold value (θ ) below which full agglomeration remains a stable equilibrium. When all mobile firms are located in country H, the spatial differential of rental rates is expressed as follows:

[ ]

0 1 2 (1, ) (2 ( ) )² ² 4 ²( ) nL r t t t θ α β γ θ ρ ρ ρ β γ ∆ = - --Λ + + + Λ -
where ρ 0 , ρ 1 and ρ 2 are a combination of the exogenous parameters defined in Appendix A. We also know from this appendix that 0 This proposition confirms the intuitive implications of propositions 1 and 2. The more accessible the developed country is from country F, the more capital tends to settle in the developed country (country H). Moreover, 0 / < dt dθ implies that the higher the trade costs, the lower the perception threshold above which industry settles in country F (see figure 1). High trade costs thus implies a dispersion effect, as in most of economic geography models, but here stemming from a quite different mechanism. The previous results are summarised in the following proposition and illustrated in figure 1.

2 2 1 0 > + + t t ρ ρ ρ for 0<t<t*. Agglomeration remains a stable equilibrium when (1, ) 0 r θ ∆ > or, equivalently, when θ θ < where ² ² ² )² ) ( 2 ( ² 1 0 2 1 0 2 1 0 t t t t t t t Λ + + + + = Λ - - + + = ρ ρ ρ ρ ρ γ β α ρ ρ ρ θ
Proposition 5. When ) 1 , (θ θ ∈
or when t*<t<t trade , partial agglomeration of capital occurs in country H. Moreover, a better perception of varieties produced in countryF reduces gradually the international inequalities in terms of activity level.

To conclude this section, we have shown that the international convergence in the perception of foreign products and commodities prices have opposite effects on international allocation of capital.

Capital income, consumers' surplus and perception of foreign products

We now give some elements on the evolution of rental rates of capital and consumer's surplus when the perception of foreign products varies. In section 3, we have shown that, at location of firms given, the rental rate of capital located in country F depends positively on θ and the rental rate of capital in country H diminishes when θ increases while consumers' surplus only raises in country H.

However, the analysis is now more complex since the spatial distribution of capital is influenced by attitudes towards foreign goods. It is worth stressing that when full agglomeration of capital occurs (for example for very low values of trade costs), a better perception of varieties produced in country F does not affect the results obtained in section 3 because θ has no impact on the capital location. In what follows, we study the most interesting configuration where capital is located in both countries (θ θ > ).

Capital income.

Regardless of their location, the rental rate for each unit of capital reaches the same value at the equilibrium allocation of capital. Because we have

r λ .
However, it is straightforward to check that a rise in θ decreases the export revenue of firms in country H (given by (p FF -t/2) 2 /(β-γ)) and the local sales of firms located in country F (expressed as (p FF ) 2 /(β-γ)) since p FF declines. Those negative effects are higher when trade costs are high.

Numerical simulations are required in order to analyse how θ influences the rental rate of capital.

The outcome depends on the relative values of trade costs (see Appendix B.1). Numerical illustrations exhibit an inverted U-shape relationship between the knowledge of foreign products and rental rates of capital when trade costs take intermediate value. When t is relatively low (resp., high), the relationship is positive (resp., negative). Hence, simulations suggest that a better perception of varieties produced in the developing country increases the equilibrium rental rate of capital when trade costs are low enough.

In section 3, we have shown that rental rates of capital decrease when the perception of foreign products improves as long as the spatial organisation of production does not change.

However, when trade costs are low, better perception of foreign varieties raises the share of capital located in country F, increasing prices in country H, and thus the rental rate of capital. Conversely, returns of capital may decrease when trade costs are high enough because, under this condition, the relative intensity of price competition is high.

Consumer's surplus

We now analyse the consumer's surplus. The expressions of surplus for a consumer living in country H and country F are given by ( 10) and ( 11 The effect of a better perception of varieties produced in country F on the surplus of consumers living in country H is now ambiguous because they are two competing effects. On the one hand, more varieties are consumed by inhabitants of country H. On the other hand, when the perception of foreign products improves, more varieties are produced in the foreign country. This negative 'reallocation' effect on the surplus of consumers living in country H is higher when trade costs are low because price competition is fiercer. We have to resort to numerical simulations to derive the qualitative effect of a variation in θ, because of the very intricate nature of the relationship between θ and λ. We consider the same values of parameters used to analyse the rental rates of capital (see Appendix B.2.). Even though consumers have a love for variety, simulations reveal that consumer's surplus in country H can depend negatively on θ when trade costs are low enough. 5 In other words, Proposition 5. Assume that capital is internationally mobile. A better perception of varieties produced in the foreign country raises the surplus of consumers in the foreign country and, under some of condition, decreases the surplus of consumers in the home country.

λ θ θ θ λ θ + - - - - - > < ∂ ∂ ∂ ∂ ∂ ∂ = + + ∂ ∂ ∂ ∂ ∂ ∂ 144
Hence, the inhabitants of the developed countries are generally interested in keeping a low number of imported products in terms of consumer's surplus, contrary to the inhabitants of the developing countries. However, the improvement of perception of foreign products can raise the capital income when trade integration is sufficiently high. It finally should be noted that national welfare ( * * / 2 A S L r n + ) may decrease in the developed country, as suggested by numerical 5 Recall that the negative effect arising from the mobility of capital is higher when trade costs are low enough.

illustrations in Appendix B.3.6 Gains in revenue from capital can be lower than the losses in consumers' surplus when perception of foreign products improves.

Concluding remarks

Despite the stylised assumptions of this model, we were able to give some insights about the effects of perceptions of varieties produced in the developing countries. When capital is internationally mobile, we show that the developing country hosts more and more firms (or capital) at the expense of the developed country as perception of varieties produced in the developed country improves. As a direct consequence of this result, the surplus of consumers and the capital income in the developed country may decrease when the perception of foreign products improves whereas the surplus of developing country consumers increases.

Our framework is a first step to incorporate explicitly the effects of country of origin in models of trade and location. Our framework could be extended to take into account the diffusion of interest for foreign products among nationals due to word-to-mouth communication maintained by immigrants. Several empirical studies reveal the crucial role of social networks in international and interregional trade [START_REF] Head | Immigration and trade creation: Econometric evidence from Canada[END_REF].

Appendix A. Proof of proposition 2

We show that the full agglomeration is a stable equilibrium when * t t < . We know that d∆r(λ,θ)/dλ<0, so in order to prove that λ=1 is a spatial equilibrium, we must have that (1,0) 0 r ∆ > .

When λ=1, the spatial differential of rental rate of capital is given by: ( ) place. Indeed, we have (1/ 2,0) 0 r ∆ > . Since d∆r(λ,θ)/dλ<0, at the spatial equilibrium, we have

2

  of varieties produced in country F reduces the interval of trade costs in which full agglomeration is a spatial equilibrium.

Figure.

  Figure 1 about here

  a better perception in country H of foreign products leads to an increasing surplus of consumers living in country F since an increasing number of varieties are produced in country F, inducing lower local prices.

Figure

  Figure 1. Spatial configurations

  , so that the relationship between θ and rental rate of capital in the developed country (country H) is negative due to price competition when the spatial allocation of firms is exogenous. However, the impact on the rental rate of capital in country F is ambiguous. On the one hand, a rise in θ increasesAuthor-produced version of the article published in Open economies review, Volume 21, Issue 5, November 2010, Pages 751-770. Original publication available on http://www.springerlink.com, doi : 10.1007/s11079-009-9115-y the effective market potential in country H for a firm located in country F. But as it increases price competition in country H, it causes a fall of prices. However, a bit of algebra shows that

	sgn	{ sgn 2(	) (	} )
	H r θ ∂ < ∂	0

  . Our result arises from the absence of circular mechanisms leading to agglomeration such as input-output Author-produced version of the article published in Open economies review, Volume 21, Issue 5, November 2010, Pages 751-770.Original publication available on http://www.springerlink.com, doi : 10.1007/s11079-009-9115-y linkages. This feature of our model is not problematic, as is allows us to focus on the effects of perception of foreign products. To sum up, Suppose now that θ=0. In this case, a firm located in the developing country (country F) cannot export to the developed country. We obtain the following proposition: Proposition 3. Assume that θ=0. Full agglomeration occurs in country H when t<t* where

	Proposition 2. When the country of origin does not matter in consumption (	1 θ = ), dispersion of
	capital is favoured.
	4.2. No imports of varieties produced in the developing country (	0 θ = ).
	t	*	≡	n Λ -γ -+	2 2( γ β γ n Λ -	)	trade t	<	trade t

When t*<t<t trade , there is a unique stable equilibrium involving partial agglomeration in country H.

Proof. See Appendix A.

Note that θ does not measure the (dis)utility that consumers incur from buying the foreign good, as in[START_REF] Neven | Attitudes towards foreign products and international price competition[END_REF]. In our case, it measure the share of varieties produced in the foreign country that consumers are willing to buy.Author-produced version of the article published in Open economies review, Volume 21, Issue 5, November 2010, Pages 751-770. Original publication available on http://www.springerlink.com, doi : 10.1007/s11079-009-9115-y

The case θ F >θ H yields symmetrical results since countries are symmetric in endowment, preferences and technology.Author-produced version of the article published in Open economies review, Volume 21, Issue 5, November 2010, Pages 751-770. Original publication available on http://www.springerlink.com, doi : 10.1007/s11079-009-9115-y

Author-produced version of the article published in Open economies review, Volume 21, Issue 5, November 2010, Pages 751-770. Original publication available on http://www.springerlink.com, doi : 10.1007/s11079-009-9115-y

We assume here that workers own an equal share of capital. This result holds for all distributions of capital owners, even when all of them are located in the developed country.


A Banc

P Bauduin

O Diat

Tracking an ion complexing agent within bilayers

In this Letter, we show the benefit of using a lyotropic lamellar phase as a self assembled model system to investigate the distribution of a lipophilic molecule at a hydrophilic/hydrophobic interface. For complexing agents used for ion transfer in liquid/liquid extraction it is essential to determine their interfacial activity. Coupling scattering and spectrometry techniques, we show that it is possible to determine accurately the amount of this type of molecule at the interface.

INTRODUCTION

Investigation of localization, partitioning and orientation of molecules (small molecules [START_REF] Scheidt | The interaction of small molecules with phospholipid membranes studied by 1H NOESY NMR under magic-angle spinning1[END_REF], peptides [START_REF] Mcintosh | The 2004 Biophysical Society-Avanti Award in Lipids address: roles of bilayer structure and elastic properties in peptide localization in membranes[END_REF], membrane proteins [START_REF] Killian | Hydrophobic mismatch between proteins and lipids in membranes[END_REF]...) inserted into bilayers is ubiquitous in membrane related phenomena, especially for biological issues. Vesicles and lyotropic lamellar phases (L α ) are good model systems for membrane and are usually probed by various techniques such as NMR [START_REF] Scheidt | The interaction of small molecules with phospholipid membranes studied by 1H NOESY NMR under magic-angle spinning1[END_REF], fluorescence quenching [START_REF] Zucker | Localization of bilirubin in phospholipid bilayers by par-FIG. 5: µ-Raman spectroscopy performed on oriented lamellar phases. (a) Identification of oriented domains by polarized light microscopy. Spectra are performed on two kinds of configurations: (A) with the laser beam polarization oriented perpendicular to the bilayers, on planar domains and (B) with the laser beam polarization oriented parallel to the bilayers, on homeotropic domains. (b) Raman spectra of the C12E5/DMDBTDMA 80/20 oriented lamellar phase for configurations A (grey line) et B (black line). allax analysis of fluorescence quenching[END_REF], ATR-FTIR [START_REF] Martin | Attenuated total reflection ir spectroscopy as a tool to investigate the orientation and tertiary structure changes in fusion proteins[END_REF], X-ray scattering [START_REF] Ez Radlinska | Modification of the lamellar phase in C12E5/water system by a random hydrophilic-hydrophobic polyelectrolyte[END_REF], molecular dynamics [START_REF] Vijayan | A Steroid in a Lipid Bilayer: Localization, Orientation, and Energetics[END_REF] etc. The advantage of L α is the ability to confine host molecules into numerous stacked bilayers at the thermodynamic equilibrium and among which the interactions are very sensitive to weak effects [START_REF] Aroti | Effects of monovalent anions of the Hofmeister series on DPPC lipid bilayers part I: swelling and in-plane equations of state[END_REF]. Herein, we precisely characterize the insertion of a lipophilic complexing agent within a lamellar phase of surfactant using a simple combination of polarized light microscopy, X-ray scattering and µ-Raman spectroscopy experiments. This first study will allow later to track the complexing agent within the organic components as a function of interacting ions diluted in the aqueous phase. The host molecule here is N 1 , N 3 -dimethyl-N 1 , N 3 -dibutyl-2tetradecylmalonamide (DMDBTDMA), generally studied as extractant to separate minor actinides from high level radioactive liquid wastes by liquidliquid extraction processes in the nuclear industry [START_REF] Nash | Advanced Separation Techniques for Nuclear Fuel Reprocessing and Radioactive Waste Treatment[END_REF]. The lamellar phase is made with a non-ionic surfactant (to get a neutral host system for future studies with interacting ions) taken in the alkyl poly(ethylene oxide) series, pentaethyleneglycol dodecyl ether (C 12 E 5 ) (Fig. 1). C 12 E 5 is a well-known surfactant which forms a fluid lamellar phase at room temperature [START_REF] Mitchell | Phase behaviour of polyoxyethylene surfactants with water. Mesophase structures and partial miscibility (cloud points)[END_REF][START_REF] Strey | Dilute lamellar and L3 phases in the binary water-C12E5 system[END_REF]. This liquidcrystalline system was formulated with the aim to study the interfacial behavior of DMDBTDMA which is, at present, insufficiently known to develop precise predictive models of the solvent extraction process [START_REF] Szymanowski | Kinetics and interfacial phenomena[END_REF][START_REF] Erlinger | Effect of nitric acid extraction on phase behavior, microstructure and interactions between primary aggregates in the system dimethyldibutyltetradecylmalonamide (DMDBTDMA)/n-dodecane/water: a phase analysis and small angle x-ray scattering (SAXS) characterisation study[END_REF]. The evolution of the lamellar phase boundary within the phase diagram, as well as the lamellar structural parameters were analyzed and confirm the insertion of extractants into membranes. Then, for the first time, µ-Raman experiments were performed on oriented lamellar phase domains to probe the orientation of the confined host molecules. The whole result enables to identify and quantify equilibrium between extractants involved in the interfacial activity and those embedded within bilayers as an oily component.

EXPERIMENTAL SECTION

C 12 E 5 was obtained from NIKKO Ltd. (high purity grade > 99%) and used as received. DMDBTDMA was obtained from PANCHIM and was purified on an alumina column to eliminate traces of surface active impurities. LiNO 3 (1 M) solution was prepared using ultrapure water (resistivity 18.2 MΩ cm) and LiNO 3 salt (reagent grade) from Sigma. Samples were formulated adding the salted solution to a premix of C 12 E 5 and DMDBTDMA. Sample were homogenised with a succession of centrifugations and were left several days at 25 • C to reach equilibrium.

SAXS measurements using Mo-radiation (λ = 0.71 Å) were performed on a bench built by XENOCS. The scattered beam was recorded using a large online scanner detector (diameter: 345 mm, from MAR Research) located at 750 mm from the sample stage. A large Q range (2 × 10 -2 to 2.5 Å-1 ) was covered thanks to an off centre detection. The collimation is applied using a 12 : ∞ multilayer XENOCS mirror (for Mo-radiation) coupled to two sets of FORVIS scatterless slits [START_REF] Li | Scatterless hybrid metal-single-crystal slit for smallangle X-ray scattering and high-resolution X-ray diffraction[END_REF] providing a 0.8 × 0.8 mm 2 X-ray beam at the sample position. Pre-analysis of data was performed using FIT2D software, taking into account the electronic background of the detector (the flatfield is homogeneous) and the empty cell subtraction. The scattered intensities are expressed versus the magnitude of scattering vector Q = (4π/λ) sin(θ/2), where λ is the wavelength of incident radiation and θ the scattering angle. Experimental resolution was ∆Q/Q = 0.05.

Microscopic observations were performed on a ZEISS Axio Imager A1m microscope equipped with crossed polarisers. In order to establish the phase diagrams, temperature scan was realised with a stage temperature LINKAM controller.

Raman spectra were recorded at room temperature on a LabRAM Aramis confocal µ-spectrometer from Horiba Jobin Yvon, using a 532 nm laser. An Olympus BX41 microscope equipped with a 50× objective was used to focus the laser beam on oriented domains preliminary located by polarized light microscopy. We carried out a preliminary study of the anisotropy of the Raman tensors characteristic of our samples collecting polarized Raman spectra of the isotropic components of the sample: the 1 M LiNO 3 solution and the preliminary mixture of DMDBTDMA and C 12 E 5 (80/20). Bands associated with isotropic Raman tensors display the same intensity in parallel (VV) and crossed (VH) polarizations contrary to anisotropic ones. We have observed that elongation vibrations (µ) of CH 2 (2900 cm -1 ), OH (around 3400 cm -1 ), C=O (1647 cm -1 ), and CO (810 and 840 cm -1 ) are characterized by anisotropic Raman tensors when at 1300 cm -1 , a vibration mode associated to an isotropic Raman tensor is observed. This vibration mode was later used to normalize the intensity of all our spectra after their baseline correction with the spectrometer associated software.

For microscopic observations and acquisition of Raman spectra, flat capillaries (thickness 50 µm or 200 µm) were filled with the samples and sealed on glass slides with a UV curing adhesive (Norland Optical Adhesive 81).

RESULTS AND DISCUSSION

Scattering experiment

Mixtures of C 12 E 5 /DMDBTDMA (up to 70/30 M) were hydrated with a 1 M brine, to be in the ionic strength range applied in extraction systems [START_REF] Chan | Solvent extraction of metal ions from nitric acid solution using N, N-substituted malonamides. Experimental and crystallographic evidence for two mechanisms of extraction, metal complexation and ion-pair formation[END_REF]. In this work, LiNO 3 salt was chosen, being a commonly used anion, and Li + being a non complexant cation for the extractant. The monophasic lamellar domain for various mixtures was determined as function of C 12 E 5 /DMDBTDMA weight fraction (φ) and temperature, using polarized light microscopy. In Fig. 2a, the 80/20 system is compared with the one of the 100/0 also hydrated with 1 M LiNO 3 , which is similar to the pure C 12 E 5 /water system. It appears that the addition of DMDBTDMA shifts the lamellar domain to lower membrane fractions and lower temperatures. It is consistent with a modification of the spontaneous curvature of the aggregates towards water. It can be explained with the packing parameter (P) concept [START_REF] Israelachvili | Theory of self-assembly of hydrocarbon amphiphiles into micelles and bilayers[END_REF]. P, which character- izes the geometry of amphiphilic molecules, is related to the shape of the aggregates formed in water: P = 1 for zero curvature objects like bilayers, P < 1 or >1 for direct or reverse aggregates respectively. P value of C 12 E 5 is very sensitive to the hydration of polar heads and is modulated with temperature and concentration [START_REF] Mitchell | Phase behaviour of polyoxyethylene surfactants with water. Mesophase structures and partial miscibility (cloud points)[END_REF]. On the other hand, DMDBTDMA which is not soluble in water, and display a small polar head, is characterized by P > 1. Increasing the amount of extractant molecules, bilayers aggregates are formed at higher water content than for the reference, which is consistent with the localization of DMDBTDMA within the bilayers.

The lamellar phases were characterized by X-ray scattering. Spectra (Fig. 2b) display the first and second order Bragg peaks at q 0 and 2q 0 , characteristic of the lamellar phase. Moreover, a wide peak observed at large Qvector is analyzed using two GAUSSIAN signals roughly centered at q w = 19.8 nm -1 and q b = 14.4 nm -1 (see inset of Fig. 2b). Both contributions can be assigned to the correlation distances characteristic of the liquid order in the aqueous phase [START_REF] Hura | A high-quality x-ray scattering experiment on liquid water at ambient conditions[END_REF], and within the bilayers [START_REF] Mills | Liquid-liquid domains in bilayers detected by wide angle x-ray scattering[END_REF][START_REF] Mills | Order parameters and areas in fluid-phase oriented lipid membranes using wide angle x-ray scattering[END_REF], respectively. The former is constant whatever the dilution. Defining d the periodicity of the lamellar phase obtained with the position of Bragg peaks d = 2Π/q 0 , Φ HC the volume fraction of DMDBTDMA and alkyl chains of 12 E 5 into the sample, and δ HC the hydrocarbon thickness of bilayers, Fig. 3a displays the evolution of lamellar periodicities as a function of the inverse of Φ HC . As polyoxyethylene groups were considered to be in the aqueous region of the phase [START_REF] Funari | X-ray Studies on the C12EO2/Water System[END_REF], we fitted our data using the following dilution law:

d = δ HC Φ HC (1)
For calculations we used the following density values: [START_REF] Tanford | Micelle shape and size[END_REF], d C12E5 = 0.963 (from supplier) and d DM DBT DM A = 0.906 (measured). We can observe that the variation of lamellar periodicity d is not perfectly linear for the pure C 12 E 5 as a function of 1/Φ HC . This was previously observed [START_REF] Kurtisovski | Molecular origin of model membrane bending rigidity[END_REF] and was attributed to a change in the bilayer thickness with dilution [START_REF] Ruckenstein | On the stability of lyotropic lamellar liquid crystals and the thicknesses of their lamellae[END_REF]. This can have different origins (evolution of polyoxyethylene heads conformation [START_REF] Tonegawa | A Combined Raman and Deuterium NMR Spectroscopic Study on the Molecular and Phase Structure of a Nonionic Surfactant C12E5-Water System[END_REF], interpenetration of alkyl chains [START_REF] Kurtisovski | Molecular origin of model membrane bending rigidity[END_REF], defects [START_REF] Funari | Intermediate lyotropic liquid crystal phases in the C16EO6/water system[END_REF], ). For the C 12 E 5 /DMDBTDMA 80/20 system, the evolution of d appears more linear than for the 100/0 system. It attests to a more classical behavior of the dilution law characterizing a lamellar phase with a constant thickness of the bilayers and weak bilayer undulations. Slopes of the linear fits in Fig. 3 [START_REF] Rosen | Relationship of structure to properties in surfactants. 10. Surface and thermodynamic properties of 2-dodecyloxypoly (ethenoxyethanol) s, C12H25 (OC2H4) xOH, in aqueous solution[END_REF]. On Fig. 3b, the increase in the lamellar periodicity and in the averaged distance within the bilayers (∆ = 2Π/q b ) with the extractant molar fraction are displayed for Φ = 70 %. Both evolutions confirm the insertion of DMDBTDMA into the bilayers. The ∆ values range from that of pure surfactant (∆ S = 4.35 Å) towards that of pure extractant (∆ E = 4.58 Å) in their liquid state, respectively. Preliminary cryo-microscopic observations and temperature variation [START_REF] Dhez | Lamellar-tonematic phase transition in a lipid-surfactant mixture[END_REF][START_REF] Moreau | Dislocation-loop-mediated smectic melting[END_REF] studies confirming also that no topological defects have to be taken into account along a dilution of our lamellar phase, the lamellar periodicity values were directly converted into hydrocarbon bilayer thicknesses using the dilution law (see Equation .2). Assuming a constant polar area per molecule at the hydrophilic/hydrophobic interface and an ideal mixing of both amphiphilic species the bilayer thickness can be expressed as a function of the repartition of extractant molecules between the interface and the aliphatic part of the bilayer:

d C12 = 0.803
δ HC = V A = 2 (1 -x)V C12 + xV DM DBT DM A (1 -x)A C12E5 + xκA DM DBT DM A (2)
with V i molecular volumes determined from density values, A i polar head areas (A C12E5 = 50 Å2 /molecule, [START_REF] Erlinger | Effect of nitric acid extraction on phase behavior, microstructure and interactions between primary aggregates in the system dimethyldibutyltetradecylmalonamide (DMDBTDMA)/n-dodecane/water: a phase analysis and small angle x-ray scattering (SAXS) characterisation study[END_REF][START_REF] Bauduin | Relation between the hydrophile/hydrophobe ratio of malonamide extractants and the stability of the organic phase: investigation at high extractant concentrations[END_REF]), x the molar fraction of DMDBTDMA among the organic components and K the fraction of DMDBTDMA participating to the interfacial area. Two extreme cases are plotted on Fig. 4: (i) K = 0, the extractant molecules are considered as buried within the bilayer and a significant increase in the bilayer thickness is expected. (ii) K = 1, all extractant molecules participate to the interfacial area and a weak increase in the bilayer thickness should be observed. A good adjustment of our data requires K = 0.44 and A C12E5 = 48 Å2 /molecule. It validates our equilibrium model and indicates that 44% of extractant molecules are localized at interfaces whatever the ratio within the lamellar phase.

A DM DBT DM A = 100 Å2 /molecule

µ-Raman experiments

In order to reinforce the model described in Eq. 2, we performed polarized µ-Raman experiments on oriented domains of lamellar phases to qualitatively characterize the orientation of molecules. Planar and homeotrope oriented domains were localized by polarized light microscopy (see Fig. 5a) and their Raman spectra were obtained using the naturally polarized laser beam of the spectrometer (see Fig. 5). We simultaneously analyzed the stretching vibrations of OH groups between 3100 and 3700 cm -1 , the stretching modes of CH 2 and CH 3 around 2900 cm -1 , the characteristic bands of oxyethylene groups at 810 and 840 cm -1 [START_REF] Marinov | Raman Spectroscopic Study of Water Structure in Aqueous Nonionic Surfactant Solutions[END_REF], and the carbonyl stretching vibration at 1647 cm -1 [START_REF] Shashilov | Metal ion binding by a bicyclic diamide: Deep UV Raman spectroscopic characterization[END_REF]. Considering that the Raman signal is maximum for Raman tensors oriented parallel to the polarization of the incident laser beam [START_REF] Tanaka | Review Polarised Raman spectroscopy for the study of molecular orientation distributions in polymers[END_REF], we measured different intensities as a function of the orientation of the lamellar phase. We found out that the orientation of OH and oxyethylenes bonds is preferentially in the direction perpendicular to the bilayers whereas the CH 2 and CH 3 tensors are oriented in the plane of the membrane. These orientations are consistent with the normal orientation of the surfactant molecules within the bilayers as expected. However, the carbonyl band from the polar head of the extractant molecules has the same intensity whatever the orientation of the system. It indicates that the orientation distribution of the carbonyls bonds is isotropic into the system. This is in accordance with the model of equilibrium for which half part of extractant molecules behave as oil, without preferential orientation within the bilayers.

CONCLUSION

In summary, we identified and characterized a mixed lamellar phase which allows us to investigate interfacial properties of extractant molecules (weak amphiphiles by definition that can play the role of co-surfactants). Results indicate that the insertion of DMDBTDMA in a C 12 E 5 bilayer induces a decrease in the spontaneous curvature of the interface, by establishing equilibrium of extractant molecules within the bilayer: roughly, half of the extractant is buried within the organic part in the membrane, whereas the other half is adsorbed at the bilayer/water interface. As we demonstrate that this type of lyotropic lamellar phase is a good support system for tracking a complexing extractant molecule at a liquid/liquid interface, further works are currently in progress to study the effect of ion complexation reaction on the interfacial properties. Moreover, we think that the approach developed in this Letter is not only interesting in the extraction field but in a more general way to study partitioning of hydrophobic molecules (cholesterol, drugs, . . .) inserted into bilayers.

FIG. 1 :

 1 FIG. 1: Molecular structures of C12E5 (a) and DMDBTDMA (b).

FIG. 2 :

 2 FIG. 2: Comparison between C12E5/DMDBTDMA (80/20) and (100/0) lamellar phases. (a) Identification of the lamellar phase domains of the C12E5/DMDBTDMA 80/20 (black lines) and 100/0 (grey lines) systems. (b) X-ray scattering spectra of the 80/20 (full line) and the 100/0 (dashed line) lamellar phases at C12E5/DMDBTDMA weight fraction Φ = 70% (inset: decomposition of the wide angle scattering part).

FIG. 3 :

 3 FIG. 3: (a) Dilution laws of C12E5/DMDBTDMA 80/20 and 100/0 systems fitted according to Eq. (1). The range of ΦHC is fixed by the stability phase boundaries and shows that the lamellar phase containing the extractant molecule can be slightly more diluted. (b) Evolution of the lamellar periodicity (full dots) and the characteristic distance of the bilayer liquid order (empty crosses) versus the molar percentage of DMDBTDMA into the bilayers of a lamellar phase at Φ = 70%.

FIG. 4 :

 4 FIG. 4: (a) Evolution of the hydrocarbon bilayer thickness δH C versus the molar percentage of DMDBTDMA within the bilayers: the dotted and dashed lines display the models considering extractant molecules buried in the bilayer and at the interface of the bilayer, respectively. The experimental data (large dots), are fitted using Eq. 2. (b) Scheme of the equilibrium model proposed to adjust our data.

  indicate the average hydrocarbon bilayer thicknesses: δ HC = 14.0 Å for C 12 E 5 (100/0), and δ HC = 18.8 Å for C 12 E 5 /DMDBTDMA 80/20. The polar head area of C 12 E 5 deduced from the geometrical relationship A C12E5 = 2.V HC /δ HC is 50.1 Å2 /molecule, which is consistent with the data from the literature

ACKNOWLEDGEMENTS

We would like to thank Pr. T. Zemb for fruitful and stimulating discussions, Bruno CORSO for his assistance in SAXS experiments and Dr. R. Leparc for preliminary measurements in polarized Raman spectroscopy. This work was supported by the European ACSEPT network.