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Most existing theoretical studies on home market effects depend crucially on assumptions of symmetric transportation costs and increasing returns to scale technology. In our model, we remove the home market effect assumptions from the main model used in the literature. Instead, this paper employs a constant returns monopolistic competition model with asymmetric transportation costs. We show that 1) when the home country’s transportation cost is large enough for a given level of the foreign country’s transportation cost, the HME appears in the home country, and 2) the opposite of the HME is observed in the home country as long as the foreign country’s transportation cost is large enough for a given level of the home country’s transportation cost.

Most existing theoretical studies on the home market effect (HME) depend crucially on assumptions of symmetric transportation costs and increasing returns to scale (IRS) (the seminal contribution on the HME is Helpman and Krugman [

In the theoretical literature on HMEs, Davis [^{1}. However, all these studies rely on the assumptions of symmetric transportation costs and IRS to examine the HME. On the other hand, Takahashi [

One possible exception is Johdo [

This paper analyzes the question of whether or not the constant returns model with asymmetric transportation costs exhibits the HME.

In this section, we explain the model that is useful for understanding the role of asymmetric transportation costs in determining the HME. In the next section, we demonstrate that the HME can emerge or disappear depending on the relative size of the home and foreign transportation costs.

We assume a two-country world economy, with a home and a foreign country. The models for the home and foreign countries are the same, and an asterisk is used to denote foreign variables. There are two types of goods, horizontally differentiated goods and a single homogeneous good. The differentiated goods are subject to a monopolistically competitive market structure, whereas the market for the homogeneous good is perfectly competitive. Both the differentiated goods and the homogeneous good are assumed to be produced using a constant-returns technology that requires labor as the only input. The market for labor is perfectly competitive and perfect labor mobility is assumed within each country. The homogeneous good is assumed to be traded without transportation costs, whereas a transportation cost is imposed on the differentiated goods. Monopolistically competitive firms exist continuously in the world in the range, where each firm produces a single differentiated product. Monopolistically competitive firms are mobile across countries, but their owners are not. Hence, all profit flows are distributed to the immobile owners according to the holding shares. In addition, firms in the interval are located in the home country, and the remaining firms are located in the foreign country, where n is endogenous. Therefore, measures the home (foreign) country’s share of firms. Meanwhile, as in Helpman and Krugman [

Preferences are defined over a homogeneous good, named Y, and over differentiated goods, named C. In this paper, the preferences of household in the home country are represented by the following utility function^{2}:

where a is the expenditure share on differentiated goods. Here, we take the price of the homogeneous good as the numéraire. Hence, the price is normalized to one. In addition, in Equation (1), the consumption index C^{i} is defined as follows:

where measures the elasticity of substitution between any two differentiated goods and is the consumption of good j for household i. Here, we assume iceberg transport costs in shipping the differentiated goods between countries. Specifically, units of a differentiated good have to be shipped from the foreign country to the home country for one unit to arrive at its destination. Similarly, units of a differentiated good have to be shipped from the home to the foreign country for one unit to arrive at its destination. Therefore, the asymmetry of transportation costs is characterized by. Then, the consumption price indices are defined as:

where is the price of differentiated goods produced in j. The value of expenditure for household i, E^{i}, is defined as follows:

Then, the household budget constraint can be written as:

where W denotes the nominal wage rate, is the nominal profit flow of firm j located at home (abroad).

Households in the home (foreign) country maximize (1) subject to a given level of expenditure (5) by allocating differentiated goods and Y^{i} optimally. This problem yields:

Here, we define and for convenience. The households are supposed to be symmetric, so we can delete the superscript i from E^{i}. Aggregating the demands in (7) across all households worldwide yields the following market clearing condition for any differentiated product h, ^{3}:

Similarly, for any product f of the foreign located firms, we obtain:

.

(9)

In the monopolistic goods sector, each firm has some monopoly power over pricing and one unit of labor is required to produce one unit of a variety. Because homelocated firm h hires labor domestically, given and n, and subject to (8), home-located firm h faces the following profit-maximization problem:

. By substituting

from Equation (8) into the firm’s nominal profit and then differentiating the resulting equation with respect to, we obtain the following price markup:

Turning to the homogeneous good sector, one unit of labor is required to produce one unit of the homogeneous good. In addition, we assume that some production of the homogeneous good is active in both countries. Hence, the factor-price equalization across countries is ensured because of free trade of the homogeneous good. Therefore, from (10), we obtain:

Substituting (8) and (10) and those of foreign counterparts into the profit flows of the homeand foreign-located firms, and, respectively, we obtain:

The model assumes that firms do not face any relocation costs so that it does not take any time to relocate to another country. For a firm to be indifferent between home and foreign locations after location arbitrage, returns from the two locations must be equalized as follows:

Here, substituting (11) into (3) and (4), respectivelywe have and

. In addition, substituting these equations and (12) into (8) and (9), respectively, we obtain:

Furthermore, from (12) and (13), we obtain. If we substitute (14) and (15) into, we obtain:

Substituting (16) into (14) and considering, we obtain:

where

.

From (12), (13) and (17), we obtain:

By Equations (6) and (18) and because of, we have:

Similarly, for the foreign country, we obtain:

From (17), (19) and (20), we obtain:

where

Substituting (21) into (16) gives:

.^{4} (22)

From (22) and considering, we find the parametric condition required for n to be between 0 and 1 (an interior equilibrium) as follows:

In what follows, we assume that (23) is valid, so that both countries produce the differentiated products.

To explore the pervasiveness of HMEs in the constant returns model, following Helpman and Krugman [

, when, (24)

, when, (25)

, when. (26)

From (24), when the home country’s transportation cost is large enough (large t_{h} or small y_{h}) for a given level of t_{f}, the HME appears in the home country. Meanwhile, Equation (26) shows that the opposite of the HME is observed in the home country as long as the foreign country’s transportation cost is large enough (large t_{f} or small y_{f}) for a given level of t_{h}. The above results imply that whether our model with asymmetric transportation costs can exhibit the HME or the opposite effect of the HME depends on the relative size of the transportation cost between the home and foreign countries.

Next, we consider the relationship between the asymmetric transportation costs and the equilibrium share of firms. Here, for simplicity, we assume. Therefore, if n exceeds, the home (foreign) country has a disproportionally larger (smaller) share of firms. Conversely, if n falls below, the result is the opposite, i.e., the home (foreign) country has a disproportionally smaller (larger) share of firms. From (22), we obtain:

, when, (27)

, when, (28)

, when. (29)

From the above results, if the home country’s transportation cost is larger (smaller) than the foreign country’s transportation cost, then the home country ends up with a disproportionately high (low) share of firms. This is because an increase in t_{h} (or a decrease in y_{h}) leads to and thereby induces some firms to relocate into the home country. Thus, the country that has the larger transportation cost ends up with a disproportionately high share of firms. In contrast, the country that has the smaller transportation cost ends up with a disproportionately low share of firms.

A considerable number of recent theoretical studies have examined the robustness of the HME based on the assumptions of symmetric transportation costs and increasing returns to scale technology. This paper analyzed whether or not the model exhibits the HME after removal of these assumptions using a monopolistic competition model with asymmetric transportation costs. The results indicate that when the home country’s transportation cost is large enough for a given level of the foreign country’s transportation cost, the HME appears in the home country. In addition, we also find that the opposite of the HME is observed in the home country as long as the foreign country’s transportation cost is large enough.

I would like to thank an anonymous referee for helpful comments and suggestions. The author is grateful to have received financial support from Tezukayama University.