International trade, migration and investment with horizontal product differentiation and free entry and exit of firms.

• Author: Vallejo, Hernán
• Pages: 161(14)

Resumen. Este documento construye un modelo de carretera circular del mundo con diferenciación horizontal de producto y libre entrada y salida de firmas, para mostrar que un comercio internacional más libre aumenta el bienestar -con preferencias de variedad ideal- por medio de la explotación de economías de escala y de una mejor asignación de recursos, que todos los países participantes ganan con el comercio y que los países más pequeños tienen más que ganar del libre comercio que los países grandes. La resistencia política a la liberación del comercio, la migración internacional y la inversión extranjera directa también son estudiados con el modelo. Finalmente, el modelo provee una microfundamentación para el uso de curvas de demanda con pendientes constantes y negativas.

Palabras clave: competencia monopolística, diferenciación horizontal de producto, comercio internacional, migración internacional, inversión extranjera directa.

Clasificación JEL: F12, F13.

Abstract. This paper builds a circular road model of the world with horizontal product differentiation and free entry and exit of firms, to show that freer international trade increases welfare --with ideal variety preferences-- through the exploitation of economies of scale and better allocative efficiency, that all participating countries gain from trade, and that smaller countries have more to win from free trade than larger countries. Political resistance to trade liberalization, international migration and foreign direct investment are also analyzed with the model. Finally, the model provides a microfoundation for the use of demand curves with constant and negative slopes.

Key words: monopolistic competition, horizontal product differentiation, international trade, international migration, foreign direct investment.

JEL classification: F12, F13.

1. Introduction

   This paper builds on the circular road model of horizontal product differentiation of Eaton et al. (1975) with free entry and exit of firms, to derive results that can be applied in industrial organization, international trade and political economy.

   The model shows that freer international trade increases welfare -with ideal variety preferences- through the exploitation of economies of scale and improved allocative efficiency, that all participating countries gain from trade, and that smaller countries have more to win from free trade than larger countries. Furthermore, the model explains that there may be adjustment costs when liberalizing trade and thus, political resistance to trade liberalization. International migration can also be analyzed with the model, showing the possibility of suboptimal migration flows and political barriers to the exit of national citizens. The model suggests that foreign direct investment will be welfare improving for the source country in the short run and for the receiving country in the long run.

2. Previous literature

   Many of the insights generated in this paper have been derived before in a monopolistic competition model within a general equilibrium setting, by Lancaster (1979) --with ideal variety preferences-- and by Krugman (1979) --with love of variety preferences--. In fact, the model presented in this paper can be interpreted --at least in part-- as a formal and partial equilibrium representation of the model presented in an intuitive manner by Lancaster (1979). A similar approach, but with some differences in the parameters used and emphasising the effects of tariffs, was followed by Schmitt (1990). Other authors that have written in this area are, among others, Salop (1979), Schmitt (1995), and Boccard and Wauthy (2000).

   The main contributions of this paper are that the results here generated are derived within a partial equilibrium framework, highlighting the different effects of trade in goods between larger and smaller countries, providing insights for the political economy of trade and migration, and exploring the short and long run impacts of foreign direct investment. The paper also provides a microfoundation for the use of demand curves with constant and negative slopes.

3. The model

   3.1. Assumptions and notation

   The basic assumptions of the model presented in this paper are:

   i. The world can be represented as a circular road of extension equal to a, where all countries are located one on top of the other (see Figure 1).

   [FIGURE 1 OMITTED]

   ii. There is one industry (this is a partial equilibrium model).

   iii. The good produced is homogeneous in quality, but not in location.

   iv. There are N producers of the homogeneous good, that represent N varieties of that good in terms of location.

   v. Firms playa two stage game: on the first stage they determine locations, and on the second stage they determine their prices.

   vi. To solve the model by backward induction, in the second stage of the game firms are assumed to be located at a distance [alpha]/N of each other.

   vii. Each firm has the same cost structure, TC = f + ex, where f is the fixed cost and e is the constant marginal cost.

   viii. Consumers are homogeneous and uniformly distributed along the circular road (there are [beta] consumers on every unit of distance of the road, with [beta] > 0).

   ix. Consumers have identical ideal variety preferences and they all consume one unit of the good, as long as the utility they receive from that consumption is non-negative (assuming that u * = 0 when there is no consumption). Thus, the representative consumer will have the following utility function:

   U = u* - p - td (1)

   where

   u* = utility derived from consuming one unit of the good,

   p = unit price of the good,

   t = unit transport cost for the consumers, with t > 0, and

   d = distance to the nearest producer.

   x. There are no international transport costs.

   3.2. Autarky equilibrium

   In this paper, a symmetrical equilibrium is searched. Thus, the second stage of the game identifies what a symmetric Nash...