Market Access and Home Market Effect

Based on the standard Footloose Capital model developed by Martin and Rogers (1995), I consider an integrated model that consists of a system of two regions and a third external region, in order to study the impact of improved market access on the Home Market E ect within the system of the two regions. The concept of the HomeMarket E ect is well known in the literature, but once we extend the number of regions, many are unknown. The main nding of the model suggests that improved market access with respect to an external market enhances the Home Market E ect within the system of the two regions. Interestingly, I show that this nding comes from the fact that improved market access increases the Market Access E ect, while it has no impact on the Market Crowding E ect.


Introduction
In the current paper, I apply a model consisting of two symmetric regions and an external region, in order to study the impact of improved market access on Home Market E ect (HME) within the system of the two symmetric regions.
In their seminal work, Martin and Rogers (1995) develop the most tractable of all the economic geography models, which we refer to as the "Footloose Capital" (FC) model. They consider a framework with two-regions, two-sectors, and two-factors, introducing the HME, i.e., a given change in market size leads to a more than proportional change in the share of industry in the big region. The HME constitutes the central research issue in several other works, including the one of Krugman (1980). More speci cally, Krugman (1980) points out the HME in a model that di ers from the FC model by Martin and Rogers (1995), since he assumes a unique immobile production factor and location is driven by rms' creation/destruction instead of capital movement. Helpman (1990) speci es the demand conditions under which the HME materializes, while Davis (1998) shows that under the consideration of transportation costs on homogeneous goods, which are produced under perfect competition, the HME may disappear. Interestingly, Feenstra et al. (1998) nd that the consideration of monopolistic competition is not crucial per se as the HME can also be expected in homogeneous-good sectors with restricted entry. In a similar vein, Head et al. (2002) show that scarce immobile factor or preferences for goods from a speci c region (Armington, 1969) would work against the HME.
During the last two decades, economies have become more integrated, increasing their market access mainly due to institutional changes within countries and various trade agreements among countries (or groups of countries), which led to the abandonment of many trade barriers. Increased market access has indeed a ected the spatial distribution of economic activities within countries or regions in several ways, and hence it has become a major research issue for trade economists. Considering a framework with two symmetric countries, each consisting of two regions, Monfort and Nicolini (2000) show that trade openness to an external market favors regional agglomeration of economic activities. However, relaxing the assumption of identical interregional trade costs, Monfort and van Ypersele (2003) nd that both integration and agglomeration in one country make agglomeration within its parter country less likely. Extending the CP model of Krugman (1991) by considering 3 or more regions, Castro et al. (2012) conclude that additional regions favour agglomeration and discourage the dispersion of economic activity. There are several studies showing how the number of regions a ects the distribution of economic activity, including those of Gaspar et al. (2018) and Gaspar et al. (2019). Studying a Footloose Entrepreneur model with a nite number of equidistant regions, both studies show that as the number of regions increases, agglomeration becomes more likely. In their seminal work, Krugman and Livas-Elizondo (1996) relax the assumptions of "equidistant regions" (i.e., regions symmetric with respect to their access to the world market), assuming rent and commuting costs and show that trade openness to an external market leads to internal dispersion of the economic activity. Motivated by the latest EU enlargement, Brülhart et al. (2004) consider a version of the standard CP model, showing that improved external market access favors internal agglomeration of the mobile factor within the system of two symmetric regions. Generalizing the model of Brülhart et al. (2004) by taking into account regional productivity di erences and taste bias, Karavidas (2018) shows that pro-agglomeration e ects come from an external market being more important relative to the system of the two symmetric regions. Although there is a number of studies dealing with multiple regions, all of them do not really study the impact of market size difference on location patterns. In this line of research, Forslid and Okubo (2012) use a three-country trade and geography model with di erent market sizes, showing that the large country bene ts from globalization since both the intermediate and the small country lose industry when trade costs fall. Relaxing the assumption of constant wages assumed in the work of Forslid and Okubo (2012), Kato and Okubo (2018) conclude that the large country fosters industrial agglomeration in the early stage of globalization, but loses manufacturing in the later stage of globalization.
Despite their e ort on proving explanations about the spatial concentration of economic activities, only a few studies mentioned above investigate the impact of improved market access on HME. Thus, it is imperative to study further and shed light on the relationship between market access and HME. In this paper, based on the traditional FC model developed by Martin and Rogers (1995), I consider an integrated model consisting of a system of two symmetric regions and a third region (i.e., the rest of the world), in order to study the impact of improved market access on the HME within the system of the two symmetric regions. In particular, I explore a model with two countries named Foreign country and Domestic country, which is a union of two regions. I abstract from di erences in tastes, factor endowments, technology, and market structure, such as (i) changes in factor supplies through internal movements of workers and capital and (ii) improvements of internal transport systems that might lead to relocation of economic activities in peripheral regions. Therefore, I assume that both regions within Domestic country can access the foreign market at equal cost. Any location advantage will bias the results in favour of the region having the better market access (Behrens et al., 2006).
Providing many analytical solutions with respect to the investigation of HME, the results of this paper complement very well several existing ones. First of all, my results con rm the existence of HME in the current model, as introduced by Martin and Rogers (1995). However, my ndings enhance the existing literature by showing that improved market access with respect to Foreign country implies stronger HME within the two regions of Domestic country, all else equal. Intuitively, improvement of market access between Domestic and Foreign country intensi es the local price competition within Domestic country by rms located in Foreign country. Thus, agglomeration forces come from the foreign market dominate, since dispersion within Domestic country no longer weakens price competition. Finally, by studying the market forces analytically, I show that the main nding of the paper is driven by the fact that trade openness to an external market increases the Market Access E ect in Domestic country, but it has no impact on its Market Crowding E ect, which is the only dispersion force in the model.
The remainder of the paper is organized as follows. Section 2 presents the model and characterizes the location patterns of the market equilibrium. Section 3 describes the diagrammatic analysis of the results. Section 4 studies the market forces, introducing the Market Access E ect and the Market Crowding E ect for the current model. Finally, Section 5 concludes and summarizes the main ndings of the model; it also suggests avenues for future research.

The Model . Set up
The global economy consists of two countries named Domestic and Foreign. Domestic country constitutes a union, consisting of two regions labelled North and South. Following the standard assumptions of the FC model, in each country there are two production sectors: an agricultural and a manufacturing sector. Moreover, there exist two production factors: labor and capital. The FC model is marked by internationally mobile capital and immobile capital owners and workers. Thus, using the standard version of the FC model and based on previous works, such as those of Saito et al. (2011), Forslid andOkubo (2012), Kato and Okubo (2018), labor is assumed to be mobile between sectors, but immobile between regions. Capital, however, which is only used in the manufacturing sector (for xed input), is mobile between the two regions of Domestic country, but immobile between Domestic and Foreign country. In addition, capital owners in each region spend their income at their xed home location (repatriation). The assumption of capital immobility between countries can be justi ed by considering the case of Brexit. More speci cally, uncertainty over future trade arrangement between the UK and the EU will tend to dampen FDI (Dhingra et al., 2017). The UK might lose its ability to participate in the free movement of capital in the EU and thus, in terms of economic integration, leaving the EU will a ect the free movement of capital, including FDI (Busch and Matthes, 2016). Therefore, applying the current model in the real economy, Domestic country can be considered as the EU and Foreign country as the UK.
The agricultural sector produces a homogeneous good using labor as input under perfect competition and constant returns to scale. The homogeneous good is traded costless between regions and across countries; it also serves as the numeraire; the agricultural sector is su ciently large to guarantee positive output in all regions. The manufacturing sector produces a large variety of di erentiated products under increasing returns to scale in a Dixit-Stiglitz (Dixit and Stiglitz, 1977) monopolistic competition environment. Each variety is produced using both capital and labor. Labor is the variable input, and capital enters as a xed cost. Manufacturing goods are tradable with iceberg trade costs. The cost mark-up factor is denoted by τu > for trade within Domestic country, and by τ f > τu for trade between Domestic and Foreign country. Trade of manufacturing varieties within each region and within Foreign country is free.

. Households
Each household earns wage income or capital income. As in the standard version of the FC model, incomes Yn and Ys in North and South respectively are constant, independent of the distribution of capital used in the two regions of Domestic country. Let household preferences be a Cobb-Douglas utility function with CES sub-utility over manufacturing varieties with, where < µ < ; σ > and V = Vn ∪ Vs ∪ V f . C M is the consumption of the manufacturing aggregate, and C A denotes the consumption of the agricultural good. Per capita consumption of a household located in region i is denoted by l i . Vn, Vs and V f are the numbers of varieties that are produced in North, South and Foreign country, respectively. σ expresses the elasticity of substitution between any two manufacturing varieties. µ is the expenditure on manufacturing products.
In the upper nest, the household maximizes U with respect to C M and C A under the budget constraint This yields P M C M = µY and P A C A = ( − µ)Y. Inserting the optimal values of C M and C A into the utility function (1), the indirect utility is obtained as and after removing constants .

Market Equilibrium
Prices for the agricultural goods must be uniform and hence also wage rates and mill prices for the manufacturing goods, pn = ps = p f = p. In the long run capital is fully mobile between the regions of Domestic country. The long run equilibrium requires that capital migration stops. As in the standard FC model, there exist two types of long run equilibria, i.e., (i) the usual core-periphery outcomes where full agglomeration takes place either in North or in South, and (ii) interior outcomes where capital earns the same (reward) in both regions within Domestic country. Focusing on the interior solution, it yields that where πn and πs are the operating pro ts in North and South respectively. This implies where are parameters which are inversely related to trade costs. They capture the freeness of trade within Domestic country and between the regions of Domestic country and Foreign country. In addition, Pn, Ps and P f denotes the CES-price indices for the manufacturing varieties in North, South and Foreign country. Then, Pn is the perfect CES-price index for the manufacturing aggregate in North, and Ps is the perfect CES-price index in South, Similarly, the CES-price index for Foreign country is where pn, ps, and p f denote the producer prices for a variety that is produced in North, South and Foreign country, respectively. Dividing equation (7) by Yn + Ys and de ning Sr = Yr /(Yn + Ys), r = n, s, generates Sorting terms and dividing by ( − ϕu) yields or Sn P −σ s = Ss P −σ n (13) I normalize the total mass of varieties produced in Domestic country to be equal to one. Thus, a share λ is produced in North and the rest ( − λ) is produced in South. Moreover, δ varieties produced in Foreign country. After following the standard derivation, I obtain the CES-price indices for both regions within Domestic country as where pn = ps = p = σ σ− . Equations (13) and (14) imply Now, using Ss = − Sn yields Subtracting ( + ϕu)/ and solving for λ, equation (16) can be written as There is a linear relation between the distribution of expenditures in North (i.e., Sn) and the distribution of rms in North (i.e., λ), representing price equality for the mobile factor in both regions within Domestic country. Expression (17) is valid as long as it implies a λ that is economically relevant, i.e., ≥ λ ≥ . For values of ϕu, ϕ f and Sn that would imply a share below zero or above unity, all industry is concentrated in one region within Domestic country. More speci cally, expression (17)  > ; the distribution of rms reacts more than proportionally on the distribution of demand. This is the Home Market E ect (HME) in the current model.
In the standard FC model that consists of two regions, the slope of the linear relation between the distribution of expenditures and the distribution of rms is equal to dλ FC dS FC n = +ϕu −ϕu , with ϕu being the freeness of trade between those two regions. Thus, my ndings with respect to the HME are qualitatively the same as those come from the framework of Martin and Rogers (1995). However, it can be easily seen that trade openness to an external market enhances the HME that takes place within the system of the two regions.
Proposition 2: Comparing the rst derivative of λ with respect to Sn from equation (17) with the one comes from the standard FC model, we can see that dλ Therefore, trade openness to an external market implies stronger HME within the system of the two regions. Intuitively, improved market access with respect to Foreign country intensi es the local price competition within Domestic country by rms located in Foreign country. As a result, dispersion within the regions of Domestic country no longer weakens price competition, and thus, agglomeration forces come from the foreign market dominate.

Diagrammatic Analysis
Analysis of how trade openness to an external market enhances the HME is easily illustrated with the help of Figure 1. It plots the share of industry in North on the vertical axis and the expenditure share in North on the horizontal axis. The solid line depicts the HME for the current model and the dashed line is the HME that comes from the standard FC model. Notice that both solid and dashed lines are linear. The slope of the solid line is equal to ϕu+ δϕ f −ϕu > and intersects the x-axis at ϕu+δϕ f +ϕu+ δϕ f . Similarly, the slope of the dashed line is equal to +ϕu −ϕu > and intersects the x-axis at ϕu +ϕu . Obviously, the solid line is steeper than the dashed line. This shows diagrammatically that trade openness to an external market makes the HME stronger within Domestic country, all else equal. Moreover, both lines pass through the point ( / , / ), regardless of the internal and external freeness of trade. So, any change in ϕu and/or ϕ f rotates the solid line around the midpoint. For example, as trade between Domestic and Foreign country becomes freer (i.e., ϕ f goes up), the solid line gets steeper, while the dashed line remains unchanged. Steeper solid line implies stronger HME. Similarly, as trade gets freer within Domestic country (i.e., ϕu goes up), the solid line gets steeper. This result is the same as the one comes from the standard FC model, all else equal.

Market Forces
As it is shown by Ottaviano (2001), the di erential of the rental rate is zero, positive or negative when the right-hand side of the following expression is zero, positive or negative, respectively. This yields When the internal freeness of trade (i.e., ϕu) is equal to one, the right-hand side is equal to zero. This implies that the rental rates are the same in both regions within Domestic country no matters the spatial distribution of rms. Intuitively, with no internal trade costs, the location of rms is immaterial. An interesting case is when the internal trade is not perfectly free (i.e., ϕu < ). Then,expression (18) shows that the decision of rms to relocate within Domestic country depends on the interaction of two opposing forces: the Market Access E ect (MAE) and the Market Crowding E ect (MCE). The rst term inside the brackets is the MAE and it is positive, since ( + ϕu + δϕ f ) > . This shows the market access advantage of producing in the larger market when trade is not perfectly free. Intuitively, a larger sales market makes the rental rate large, because it makes sales per rm large. This is actually the sale agglomeration force in the model. Comparing the MAE of the current model with the one that comes from the standard FC model, one can see that trade openness to an external market makes the MAE stronger within Domestic country. More speci cally, the MAE of the standard FC model is equal to ( + ϕu)(Sn − / ), which is weaker than the one that comes from the current model that is equal to ( + ϕu + δϕ f )(Sn − / ). Therefore, trade openness to an external market increases the MAE and this implies that the agglomeration force in the model goes up, all else equal.
The second term inside the brackets is the MCE and it is negative, since −( − ϕu) < . This shows the market crowding disadvantage of producing in the large market. Intuitively, more rms in the region shrink sales per rm and hence also the return on capital. This is actually the sale dispersion force in the model. Interestingly, the MCE of the current model is the same as the one that comes from the standard version of the FC model. Thus, trade openness to an external market has no impact on the MCE, and this implies that the dispersion force remains unchanged.
Proposition 3: Trade openness to an external market (i) increases the Market Access E ect in Domestic country, and (ii) has no impact on its Market Crowding E ect.
The proof of Proposition 3 is quite trivial. From expression (18) it can be easily seen that (i) d ( + ϕu + δϕ f )(Sn − / ) /dϕ f > , and (ii) −(λ − / )( − ϕu) is independent of ϕ f . Intuitively, the MAE shows how the spatial distribution of expenditure a ects the spatial distribution of rms, and the MCE shows that the small region (i.e., λ < / ) is more attractive because rms installed there face less competition. These two e ects explain the HME. Since rms are allowed to move within the two regions of Domestic country, but not across countries, the MCE remains unchanged. However, improved external market access reinforces the MAE, and that makes the big region within Domestic country more attractive. This explains why trade openness to an external market enhances the HME within Domestic country.

Conclusion
The HME is well known in the literature, but once we extend to multiple regions, many are unknown. In this paper, I show that improved market access a ects the agglomeration force (i.e., MAE) within Domestic country, while the dispersion force (i.e., MCE) remains unchanged. As a result, trade openness to an external market results in stronger HME within Domestic country. The ndings of the current model could also be applied in the real economy, showing, for example, that Brexit will a ect capital mobility between the core and the periphery of the EU in a particular way. More speci cally, Foreign country can be considered as the UK and Domestic country can be considered as the EU. The big region (i.e., North) represents the core of the EU, while the small region (i.e., South) represents the periphery of the EU. In this case, the model suggests that impaired access from and to the UK will result in weaker HME within the EU countries. Of course, more dimensions should be taken into account in order for one to reach broader conclusions about the impact of Brexit on spatial issues within European economies. In general, this paper sheds light on the impact of improved market access on the domestic HME. More issues could be studied with respect to the HME, including the value chain phenomenon that is taking place inside the EU that favors relocation of the activities in the periphery nurtured by the bettering of the transport system. However, addressing this interesting task is beyond the purview of this paper. Thus, the obtained theoretical ndings may justify the need for further research.
Financial Support: This research received no speci c grant from any funding agency, commercial or nonpro t sectors.

Con ict of Interests Statement:
The authors have no con icts of interest to disclose.