Piecemeal oligopoly, exchange rate uncertainty, and trade policy.

• Author: Mesa, Fernando
• Position: Report
• Pages: 161(18)

1. Introduction

   Under assumptions of imperfect competition in external markets and strategic behaviour by firms, prices are not equal to marginal costs, as the competitive markets analysis shows, and lucky firms in some industries may be able to earn returns higher than the opportunity costs of the resources they employ. Indeed, international economists have long recognized that governments can participate in external markets in order to transfer part of foreign firms' potential profits to domestic firms (Brander and Spencer, 1985).

   Eaton and Grossman (1986) provided an integrative treatment of the effects of trade policy on national welfare under imperfect competition. They showed that the results are sensitive to the character of the competition. While export subsidies are desirable in a Cournot market (where competition is based on quantity of output), they are never desirable in a Bertrand market (competition based on price), where an export tax is more appropriate.

   So under specific conditions, a public policy of taxing or subsidizing exports can be a strategic move that tilts the international competition in favour of domestic firms. This outcome increases national welfare as it has a deterrent effect on foreign competition. Yet few studies have attempted to test the effects of government intervention by constructing formal models of trade under uncertainty, both in the market demand and cost functions. This paper extends the new international trade theory by linking theoretical underpinnings with new insights from the real world.

   In contrast to the few models where uncertainty is introduced through external shocks (Cooper and Riezman, 1989; Laussel, 1992; Qiu, 1995; and Caglayan, 2000), this model systematically adds uncertainty directly to the exchange rate. This is an important factor, and it better captures the reality of firms in the international market, which have to include this variable in decisions. (1)

   Klemperer and Meyer (1986) describe the strategic trade policy as an endogenous instrument where firms identify the best type of competition. Its framework is constructed under uncertainty conditions, relayed through an external shock in demand. Klemperer and Meyer's main finding is that firms play a Cournot game if the total cost function is convex, but prefer a Bertrand game if the total cost function is concave. (2)

   Qiu (1995) extends Brander and Spencer (1985) by incorporating the main results derived in Klemperer and Meyer. Qiu introduces a linear-quadratic trade policy to show that a linear export subsidy is strictly dominated by a non-linear subsidy scheme.

   In contrast to the above studies, the present model introduces uncertainty via the exchange rates used by firms and governments. The main finding is that the export tax or the export subsidy decreases as uncertainty in the domestic exchange rate increases. However, if the uncertainty is related to the foreign exchange rate, the export subsidy or the export tax levels could be set higher.

   These results help clarify the debate as to whether public trade policy should be oriented toward subsidising or taxing exports. The answer depends on the type of competition, the level of efficiency and the uncertainty condition that firms face. Whenever the competition is in quantities, efficiency is high, and uncertainty is low, governments should offer subsidies to domestic exporters. When the competition is in price, efficiency is high, and uncertainty is low, government should impose taxes on exports. Such trade policy decisions are the best to maximize social welfare in the economies.

   The elements of the model are as follows. There are three countries: the home country, a foreign country, and a third country that is the sole market for one differentiated product produced in both the domestic country and in the foreign one. In addition, there is only one firm in the domestic country and only one in the foreign country. The level of welfare in the domestic and foreign countries is determined by the profits of the respective firms, net of any government subsidy or tax. The focus of the analysis is on the domestic country's welfare.

   The study restricts its domain to international competition by assuming that there is no demand for the differentiated good in the two producing countries and that the domestic and foreign firms compete only in the third country's market. This artificial assumption neglects the effects of trade policy on the domestic consumer but allows the model to focus on international trade effects as a criterion in the formulation of economic policy.

   The goal is to characterise the Nash equilibrium for a two stage sequential game and to derive the optimum public policy for the domestic country with respect to an export tax or subsidy. In the first stage of the game, the domestic government sets trade policy. In the second stage, the domestic and foreign firms simultaneously choose their output or price levels for the third country's market, given the level of the domestic trade policy intervention. At the end of the period, the uncertainty in the exchange rates is resolved. Using backward induction to analyse the rational Nash equilibrium for the entire game, we consider the second stage of the game first, then consider the initial stage. The domestic government acts as a Stackelberg leader vis-à-vis both the domestic and the foreign firm in setting the subsidy or tax rates. Thus the firms set outputs or prices, taking the subsidy or tax rates as given.

   This paper is divided into four sections. The model framework under uncertainty conditions is constructed in the next section. The international trade policy for the Cournot and the Bertrand market settings are examined in sections 2 and 3, respectively. The relations between the export tax or export subsidy, and changes in the variance of the exchange rate currencies are derived for each type of market. Finally, concluding remarks are made in section 4.

2. The formal framework

   In subsequent sections the optimal public policy is characterised under the presence of oligopolistic competition, where the domestic and foreign firms are both incumbents and sell all of their outputs in the international market.

   To simplify notation, we refer to the firm in the home country as the domestic firm and in the foreign country as the foreign firm. Variables relating to the domestic firm and the foreign firm are identified by subscripts d and f, respectively. Variables associated with the third country are identified by an asterisk. The domestic firm produces the quantity [X.sub.d] and the foreign firm produces the quantity [X.sub.f].

   The linear inverse demand function for differentiated products in the third country is written as

   [P.sup.*.sub.i] = [alpha] - [beta][X.sub.i] - [zeta][X.sub.j], (1)

   where i = d, f; and 0

   We assume that firms have the following cost structures

   [C.sub.i]([X.sub.i]) = [C.sub.i1][X.sub.i] + [1/2] [C.sub.i2] [X.sup.2.sub.i], (2)

   [C.sub.i1] and [C.sub.i2] being parameters. When [C.sub.i2] > 0 firms produce under decreasing returns, and if [C.sub.i2] = 0 firms produce under constant returns. The study does not consider explicitly fixed cost levels since these do not effect the comparative static analysis. Also the increasing returns are not taken into account because the equilibrium of the model might present stability problems.

   The domestic export subsidy is a function of export quantity. In particular, the trade policy has the same mathematical expression used by Qiu (1995), in that is a linear-quadratic scheme. This equation is

   S ([X.sub.d]) = [S.sub.1] [X.sub.d] + [1/2] [S.sub.2] [X.sup.2.sub.d], (3)

   where [S.sub.1] and [S.sub.2] are parameters. If [S.sub.1] [not equal to] 0 and [S.sub.2] = 0 the domestic government pre-commit to a linear scheme, but if [S.sub.1] = 0 and [S.sub.2] [not equal to] 0 the government pre-commit to a non-linear scheme. To simplify the model, the assumption is made that the foreign government is passive, i.e. it does not apply any policy against the domestic government.

   The profit functions under uncertainty for the domestic and foreign firms are

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

   The tilde above the domestic and foreign exchange rates ([[??].sub.d], [[??].sub.f]) refers to uncertain conditions. (3) The same conditions are applied to the profit outcomes [[??].sup.d], [[??].sup.f]). Firms...