A Note on Export Subsidies and Exchange Rate
Benan Zeki Orbay*, Hakan Orbay**
Abstract
This note investigates effects of exchange rate uncertainty on optimal trade policies and market prices within a standard export subsidy model. As exchange rate changes, relative efficiencies of firms in different countries change. In accordance with the conventional result, we show that changes in expected exchange rate effects optimal subsidies through relative costs. In particular, increa in expected depreciation of own currency increas subsidy levels when marginal cost is constant. Introducing import dependency, however, violates this uniform relation, and subsidy levels may decrea with increasing depreciation. Subsidy levels always decrea in import dependency when depreciation is expected. We also show that market price is less nsitive to exchange rates, compared to the free trade ca (no subsidies).
JEL Classifications: F12
左庶长是什么官Key Words: Subsidies, exchange rate uncertainty, cost asymmetry, demand asymmetry.
* Istanbul Technical University, Department of Management Engineering, Macka, 80680, Istanbul, e-mail:*************.tr
**SabanciUniversity,Orhanli,34956,Istanbul,e-mail:**********************
1.Introduction
This note introduces exchange rate uncertainty into a standard export subsidy model. While optimal trade intervention policies have been analyzed under various market structures in the existing international trade literature, effects of exchange rates on optimal policies and resulting market structures have not been considered.
Starting from leading studies of Brander and Spencer (1985) and Eaton and Grossman (1986) in the area, many studies focud on the models analyzing trade and trade policies in countries with oligopolistic markets. The main result of this line of literature is that the optimal trade policies heavily depend on the market structure. Focusing on export subsidies, Meza (1986) and Neary (1994) showed that when subsidies are the optimal policies they should be higher for the more efficient firms. In other words, governments should subsidize the winners more. On the other hand, Bandyopadhyay (1997) found that demand elasticity is also a major determinant of the subsidy level
and this result can be reverd for the inelastic demand ca. Later, Bandyopadhyay et al. (2004) determined that the optimal subsidy level is higher with higher level of cost heterogeneity. There are various other papers looking at the trade policy issues under uncertainty on either demand or cost sides1. The results again vary depending on the environment modeled.
In this paper, we aim to fill a gap by investigating effects of exchange rate uncertainty on optimal subsidy policies and relative price levels with cost and demand asymmetries. Consider a two-country environment, referred to as domestic and foreign, where one firm is located in each country and the firms compete in both countries. In our model, governments t subsidy policies before obrving the actual exchange rate, but taking into account its expected value, e. Firms compete after exchange rate is realized.
With constant marginal costs, we find that the optimal subsidy level of domestic country increas and foreign developed country decreas with e, where exchange is measured in domestic currency per foreign currency. This result is in accordance with conventional results of the existing literature which states that higher cost firms gets less subsidy, as higher e corresponds to a lower relative cost for the domestic
1 For example, e Cooper and Riezman (1989), Qui (1994), Shikumavar (1993), Maggi (1996), Brainard and Martimort (1997), Caglayan and Usman (2004).
country’s firm. However, when import dependency for the domestic firm is considered, where the marginal cost may partially depend on exchange rate, subsidy level could go either way as expected exchange rate increas. Subsidy level is always decreasing in the import dependency parameter if currency value depreciation is expected.
We show that higher cost firm may receive a higher subsidy in equilibrium, which is reminiscent of Bandyopadhyay (1994)’s result . We also show that domestic market price may be decreasing in exchange rate, if intensity of subsidy by the foreign government is high. Otherwi, nsitivity of market price to exchange rate is less compared to the free trade (no subsidy) regime.
2. The Model沈阳游玩攻略
Consider a two-country world, where there is one firm in each country. Following the literature, one of the countries is a developing country and the other is a developed one. The developing country is referred to as domestic country (d ) and the other as foreign country (f ). Both domestic and foreign firms produce the same good, which is sold in both countries, however, domestic firm has hig
her costs due to inferior technology.
We consider a two stage game. In the first stage, governments choo subsidy levels, facing exchange rate uncertainty. In the cond stage, exchange rate is realized and firms enter a Cournot competition in both domestic and foreign markets.
Let e
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~ denote the exchange rate in the cond stage of the game, reprenting value of unit foreign currency in domestic currency. In the first stage, probability
distribution of e
~ is known, and expected exchange rate is denoted by e . For discussion purpos, assume that actual exchange rate in the first stage is 1; hence expected devaluation of domestic currency is reprented by 1e .
Linear demand functions are assumed for both developing and developed countries as follows,
f d j q q Q Q b a p j j j j j j j ,,,21 (1)
where d p and f p are domestic and foreign market prices in each country’s own currency. We refer to the firm residing in the domestic country as firm 1, and the other as firm 2. Thus, 1d q and 1f q denote quantities sold by the domestic firm in
domestic and foreign markets, respectively. We assume constant marginal costs for both firms,
2,1,,)(i q q q q c q C fi di i i i i i . (2) Following the developing country theme, we will assume that domestic firm remains inefficient even with expected devaluation, or e c c 21.
Under the assumptions for both supply and demand sides, the profit functions of domestic and foreign firms can be written as follows;
22222221111111
红海行动主演)( )( d f f d f f d d f d f d f f d d q s q q c q p e q p πq s q q c q p e q p π (3)
where d s and f s are the
subsidies given by
the domestic and foreign countries respectively, and e is the realization of the exchange rate in stage 2. Note that both profit functions are given in own currencies.
Social welfare in each country is given by the sum of consumer surplus and the profit of its firm net of subsidy transfers,
2211CS SW CS SW d f f f f d d d
q s q s (4)
In the first stage, governments t the subsidy level that maximizes expected social welfare in stage 2.
3. Exchange Rate and Subsidy Levels
Solving the last stage of the game, we obtain Cournot-Nash equilibrium quantity levels as follows:
,3~)(2,3~)(2212211d f d d d f d d b e s c c a q b e s c c a q e b s c e c a q e b s c e c a q f
d f f f d f f ~3~)2(~322~)(122121 (5) In th
e first stage, governments maximize expected social welfare. We note that derivative o
f social welfare functions with respect to subsidy levels are as follows,
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d
b e s
c c a s
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d W S d b
e s c c a s d W S
郎世宁d (6) wher
e e
e f ~/1~is the exchange rate expresd in foreign currency per domestic currency. Therefore, the first order conditions 0SW E j j ds d yield, 42)(12c e c a s f d and e
e c c a s d
f 4221. (7) as the optimal subsidy levels. In order obtain (7), one needs to assume congruence of expected values of the two versions of the exchange rate, i.e., e e f
五十度灰无删减版/1, which is
certainly suggested by common n.
We now turn to the effects of exchange rate expectations on subsidy levels. The following proposition immediately follows from (7).
Proposition 1. The subsidy level of the domestic country increas and that of the foreign country decreas as expected exchange rate, e , increas. Intuitively, export subsidies increa welfare through grabbing welfare from the foreign country. Potential welfare to be grabbed increas as the foreign market gets larger, or own firm becomes more efficient. Thus, subsidy levels intensify as the size of the foreign market increas and marginal cost of own firm decreas. The latter is the conve
ntional result in this literature that the higher cost firm gets lower subsidy. From the perspective of the domestic country, devaluation of domestic currency makes both the foreign market relatively larger (f a e ), and the domestic firm relatively more efficient as its cost is given by e c /1in local currency at the foreign market. Conquently, subsidy level of the domestic country increas as expected exchange rate increas. The argument for the foreign country is symmetric.
It is, however, unrealistic to assume that marginal cost of the domestic firm remains constant while domestic currency depreciates. We will therefore extend the model to include possible dependency of the marginal cost to exchange rate nsitivity. In order to avoid confusion, let us re-label domestic firm’s marginal cost as d c , and assume that
