Optimal export taxes with an endogenous location.

• Author: Hwang, Hong

1. Introduction

   Export tax policy is one of the most debated issues in many developing countries. Those countries that have strong natural advantages in the production of primary commodities (such as agricultural and livestock products, coffee, jute, rubber, and others) have attained at particular times a position as dominant suppliers in international trade. They have often used export taxes on those commodities to obtain foreign exchange and/or government tax revenues (Renaud and Suphaphiphat 1971; Repetto 1972; Gomez-Sabaini 1990). For example, Gomez-Sabaini (1990) provided a detailed analysis of the reasons for the evolution of export taxes in the case of Argentina during the 1932-1987 period and pointed out that, in 1985, the share of export taxes in GDP rose to 1.85%, representing almost 64% of the revenue from foreign trade. Left (1969) followed an exportable surplus approach to develop the notion that export taxes have been used (such as in Brazil) for internal income distribution reasons. Renaud and Suphaphiphat (1971) used a simple econometric analysis to determine the magnitude of the increases in the domestic rice price and paddy price for separate types of rice and paddy as a consequence of the reduction or abolition of the rice export tax.(1) These analyses relied on a setting of either perfect competition or monopoly with constant returns to scale.

   Recent papers on trade policy with increasing returns and imperfect competition have attracted attention because of their relevance to the new protectionism. Some articles going in this direction include Spencer and (1983), Brander and Spencer (1984a, b, 1985), Dixit (1984), Venables (1985), De Meza (1986), Eaton and Grossman (1986), Mai and Hwang (1987), Hwang and Mai (1988, 1991), Rodrik (1989), and others. Eaton and Grossman (1986), in particular, have argued that, whenever there is more than one domestic firm exporting to a foreign market, competition among them is detrimental to home-country social welfare. Hence, an export tax can be used to lower total domestic exports, shifting them closer to the output level with collusion. In this way, an export tax enables the home country to fully exploit its monopoly power in trade.

   All of the above-mentioned studies analyze trade policies in a nonspatial world in which transportation costs between countries are assumed to be zero or insignificant. It is now widely recognized that geographic space is costly and that the world of economic space is underscored by imperfectly competitive markets (Losch 1954; Greenhut 1956; Churchill 1967) and that the level of trade restrictiveness can have important effects on the distribution of production both across countries and across regions within each country. Several recent studies have examined the implications of trade policies in the context of an open spatial economy. These include Benson and Hartigan (1983, 1984, 1987), Brander and Krugman (1983), Brander and Spencer (1987), Horstmann and Markusen (1990), Hatzipanayotou and Heffley (1991), and Anderson, Schmitt, and Thisse (1995). What is perhaps surprising is that none of the above-mentioned papers have their firms choose their locations between two different sites. In this respect, Krugman (1991a, b, 1993) and Krugman and Elizondo (1996) considered a model in which firms are located in a space and in which transportation costs play a critical role. Krugman and Elizondo (1996) formally demonstrated, in particular, that a fall in export taxes decreases the importance of the home relative to the foreign markets and shifts firm location outwards. Their result receives empirical support from Hanson (1997) in the case of Mexico. Nevertheless, all these works have a positive orientation, and it is believed that normative analyses are needed for exploring the welfare implications of trade policies.

   The present paper goes a step further to conduct a normative analysis of an export tax policy and to make a comparison between optimal export taxes with endogenous location and those with exogenous location. More specifically, this paper presents a partial-equilibrium model in which N imperfectly competitive firms produce a homogeneous good for export to another country (i.e., there is no domestic consumption of the good) and in which there is no foreign production taking place. Each firm is assumed simultaneously to make both a Cournot output decision and a spatial location decision within national boundaries. The location decision balances the costs of transporting inputs to the production site against the costs of transporting output abroad. Within this framework, we investigate the impact of an export tax on both equilibrium output and plant location as well as solve the optimal export tax. These results will then be compared with those under an exogenous location. We find that the optimal tax is smaller and that the output effect of a tax increase is larger under an endogenous location as long as production is not constant returns to scale. We also investigate a free-entry version of the model and find that comparisons between exogenous and endogenous locations depend on the convexity/concavity of the demand function.

   The paper is organized as follows. Section 2 of the paper sets forth a simple oligopoly model to derive the optimal export tax rule in the short run in which the number of domestic firms is exogenously given. Section 3 conducts a long-run analysis in which free entry is allowed and in which the number of domestic firms is endogenously determined. Concluding remarks are contained in the final section.

2. Optimal Export Tax

   The analysis in this paper is confined to a partial equilibrium setting and a Weberian triangle space.(2) Assume there are n domestic firms exporting an identical product to a foreign country. Each firm uses two transportable inputs L and K (which are located at A and B, respectively, in the domestic country) in the production of the output q which is sold, across the border C, at the foreign market F henceforth referred to as the foreign markets as pictured in Figure 1. Each firm chooses its optimal production location at E.(3) Define s and z as the distances of E from A and B, respectively, and h as the distance between E and F; 0 is the angle between FE and FA, [Beta] is the angle between FA and FB, and a and b are the lengths of FA and FB, respectively.

   The production function of firm i is specified as

   [q.sup.i] = f([L.sup.i], [K.sup.i]), i = 1, 2, ..., n, (1)

   which is assumed to be homothetic. To simplify our analysis, we first derive the cost function by minimizing total costs subject to a given output level. That is,

   [Mathematical Expression Omitted]

   s.t. [q.sup.i] = f([L.sup.i], [K.sup.i]), (2)

   where w and r are the base prices of L and K at A and B, respectively, and are assumed to be constant; k and rn are the constant transport rates of L and K, respectively; and s and z are the distances from A and B to the locus of production of the final product, respectively. By the law of cosines, the distances from the two input sites to E can be determined in terms of h and [Theta] as follows:

   [s.sup.i] = [-square root of [a.sup.2] + [([h.sup.i]).sup.2] - 2a[h.sup.i]cos [[Theta].sup.i]]

   [z.sup.i] = [-square root of [b.sup.2] + [([h.sup.i]).sup.2] - 2b[h.sup.i]cos([Beta] - [[Theta].sup.i]).] (3)

   Shephard's lemma indicates that cost functions are separable in input prices and output if production functions are homothetic. In other words, the total cost function can be written as

   [Mathematical Expression Omitted], (4)

   where [W.sup.i] = w + k[s.sup.i] and [Mathematical Expression Omitted] are the delivered prices of L and K, respectively, and c is a function of [W.sup.i] and [Mathematical Expression Omitted], which are, in turn, functions of [Theta] and h. Note that each firm's location decision involves the two variables [Theta] and h. However, treating both [Theta] and h as...