17 RESEARCH ARTICE Optimal Trade Policies for Exporting Countries under the Stackelberg Type of Competition between irms Yordying Supasri and Makoto Tawada* Abstract This paper examines optimal trade policies for the exporting countries whose firms compete in a Stackelberg fashion of oligopoly in the third country. e show that the government of the exporting country whose firm is a Stackelberg leader does not take any intervention and that the welfare of the exporting country is higher when its firm behaves as a follower rather than a leader. Moreover, it is proved that the euilibrium output, profit and welfare of the country whose firm is a Stackelberg follower (leader) becomes euivalent to those of the country in the case where its government acts as a Stackelberg leader (follower) but all firms compete in a Cournot fashion. Keywords: Three-country model, Stackelberg competition, Strategic Trade Policy * Graduate School of Economics, Nagoya University, uro-cho, Chikusa-Ku, Nagoya 464-8601 JAPAN E-mail: mtawada@soec.nagoya-u.ac.jp
Introduction Most studies of strategic trade policies in the three country model invented by Brander and Spencer, 1985 assumed that competitions between governments and between firms are both of the Cournot type, in other words, the simultaneous move. Recently, several studies such as Arvan, 1991 and Ohkawa, Okamura and Tawada, 2002 considered the case where the governments possibly move seuentially in the determination of their optimal trade policy. However, almost none of studies dealt with the case where firms possibly move seuentially. In our present paper, we re-examine the analysis of the optimal trade policies in the case where the governments move simultaneously but the firms act as a Stackelberg duopolist. e can show that the government of the exporting country containing of a Stackelberg leader firm does not take any intervention in trade. Moreover, comparing our results with those of the case where the firms play Cournot competition, we reveal that the levels of export subsidy, output, profit and welfare of the exporting country whose firm is a Stackelberg leader (follower) are smaller (larger) than those of each exporting country in the case where its firm plays Cournot competition. Therefore, although the leader firm usually has an advantage without any government intervention, the follower firm has an advantage under the intervention taken simultaneously by the governments. Moreover, it is proved that the euilibrium output, profit and welfare of the country whose firm is a Stackelberg follower (leader) become euivalent to those of the country in the case where its government acts as a Stackelberg leader (follower) but all firms compete in a Cournot fashion. 18 The remainder of this paper is organized as follows. e describe our main model in section 2. The analysis is presented in section 3. The last section is devoted to our conclusion. Model e consider a trading economy consisting of two exporting countries and one importing country. There is only one tradable good in this economy. There is only one firm in each exporting country and each firm supplies the good only for the importing country. e also assume that there is no consumption in both exporting countries and no production in the importing country, so that the full amount of the good produced by the firm of each exporting country is exported to the importing country. The firm of each exporting country plays Stackelberg competition in the market of the importing country. e call the exporting country whose firm is a Stackelberg leader as country and that whose firm is a Stackelberg follower as country. The demand for the good in the importing country market is represented by the linear demand function Q = A - p, where Q is the demand for the good, p is the good price, and A is a positive parameter expressing the market size. So the inverse demand function of this market is p = A - Q. The cost function is identical to both firms and is, C( i ) = c i where i is the output level of a firm in exporting country i; for i =,, and c is a constant marginal cost. The importing country market is assumed to be sufficiently large, so that A c a > 0. 1 Our present model is the two-stage game. The first stage is that the governments of both exporting countries simultaneously choose 1 e set the model to be as simple as possible, so that we can concentrate on the difference between the timing of firms move.
the levels of the export subsidy to maximize their national welfares under the assumption that the government understands the structure of the industry. The second stage is that, given the level of the export subsidy of each exporting country determined at the previous stage, a Stackelberg leader firm sets its output level first and then, by taking account of the output level of a Stackelberg leader firm a Stackelberg follower firm sets its output level. The sub-game perfect Nash euilibrium is introduced as a solution concept to solve the above two-stage game. Analysis e proceed to the analysis with backward induction to solve the game. At the second stage, a Stackelberg leader firm decides its output level first and then, after observing the output level a Stackelberg leader firm chose, a Stackelberg follower firm decides its own output level. e first focus on the behavior of a Stackelberg follower firm. A Stackelberg follower firm s profit is π = [a - ( + ) + s ], (1) where s is the subsidy to the firm by the government of country. Thus, the profit maximizing output is obtained as a + s = ( ). (2) 2 Next, we focus on the behavior of a Stackelberg leader firm. hen a Stackelberg leader firm decides its output level, it anticipates that a Stackelberg follower firm will choose the output level at (2). Therefore, the profit function of a Stackelberg leader firm can be written as π = π (, ( ). By sub- stituting (2) into this function, a Stackelberg 19 leader firm s profit function can be rewritten as a s + 2s 2 π =, (3) where s is the subsidy to the firm by the government of country. Hence, the euilibrium output of a Stackelberg leader firm is obtained as a s + 2s =. (4) 2 Therefore, substituting (4) into (2), we obtain the euilibrium output of a Stackelberg follower firm as a 2s + 3s =. (5) 4 According to (1), (3), (4) and (5), the profit function of each exporting country can be represented as π i = π i ( si, s j ), i ; j =, ; i j. Now we are going to step into the first stage. At the first stage, given country s export subsidy, the government of country tries to set the level of the export subsidy s so as to maximize its national welfare. ikewise, given country s export subsidy, the government of country tries to set the level of the export subsidy s so as to maximize its national welfare. Since there is no consumption in both exporting countries, the welfare of each exporting country consists of the profit of the firm and the government s net revenue. Consider the welfare of country first. The level of the welfare of country which contains a Stackelberg leader firm can be written as = ( s, s ) = π ( s, s ) s ( s, s )
And it can be transformed into = (s, s ) = [a - (s, s ) - (s, s )] (s, s ). (6) In order to derive s which maximizes, we substitute (4) and (5) into (6) and then maximize (6) with respect to s. The n the optimal level of s is derived as s = 0, (7) from the first order condition of the welfare maximization. The euation (7) is the reaction function of country to the export subsidy of country. Obviously, the optimal policy of country is always non-intervention whatever is the level of subsidy in the other country. Next we consider country s welfare. The level of the welfare of country which contains a Stackelberg follower firm can be written as = ( s, s ) = π ( s, s ) s ( s, s ) And we can rewrite it as [ a ( s, s ) ( s, s )] = ( s, s ) = (s, s ) (8) To obtain the level of s maximizing, substitute (4) and (5) into (8) and then maximize (8) with respect to s. As a result, the optimal s can be expressed as the following reaction function of country. a s = 2 s 3 3. (9) The reaction function of country is dependent on the export subsidy of country. The slope of this reaction function is negative. 20 Since the governments of both exporting countries choose the export subsidy levels simultaneously, we solve (7) and (9) simultaneously with respect to s and s. Then, the optimal levels of export subsidy S of country and are s = 0 and s S = a 3 > 0. rom the above results, the levels of output, profit and welfare at the Cournot euilibrium of country whose firm is a Stackelberg leader are S = a 3, π S = a2 /18, and S = a2 /18, respectively, while the those of country whose firm is a Stackelberg follower are S = a 2, π S = 2 a 4, and S = a2 /12, respectively. These results S S S S S S represent that s > s, >, π > π S S and >. Therefore the following proposition is established. Proposition 1 Consider a three-country model where the firm of each exporting country plays as a Stackelberg duopolist in the market of the importing country and the governments of the exporting countries intervene international trade simultaneously by the use of an export subsidy. Then, (i) the government of the exporting country whose firm is a Stackelberg leader does not take any intervention in trade whatever is the level of the subsidy the other government sets. (ii) In the euilibrium, the levels of export subsidy, output, profit and welfare in the exporting country whose firm is a Stackelberg follower are higher than those of the other country where the firm is a Stackelberg leader. There are two remarks on Proposition 1. The first one is related to (i) of Proposition 1. This assertion implies that the leader firm can take an advantage of the leader in bringing a benefit to the country, so that the government of that country does not need to execute any
subsidization to his firm. This is true for any level of the subsidy the other country sets. Therefore, the timing of the government intervention is not important at all when two firms compete in the way of the Stackelberg duopoly. The second remark is related to (ii) of Proposition 1. This result seems to be interesting in the following sense: It is obvious that, if any government never intervenes in trade, the leader firm can have an advantage rather than the follower firm. Thus, our result (ii) turns over this, by revealing that, if both governments take an action in trade policy simultaneously, the following firm can have an advantage rather than the leader firm. Incidentally we compare the levels of output, profit and welfare of both countries with those in the case where the firms play as a Cournot duopolist. It is widely known by Brander and Spencer (1985) that when both firms play as a Cournot duopolst, each exporting country subsidizes its home firm. By employing the model and assumptions in section 2 to confirm the results of Brander and Spencer (1985), when both firms compete in Cournot fashion, the reaction function of each exporting country is si = a 4 1 4 s j ri ( s j ), i ; j =, ; i j. Thus we can derive the optimal level of export subsidy of each country as s C = a 5. And by this optimal export subsidy, the levels of output, profit and welfare at the Cournot euilibrium of each exporting country in this 21 case are C = 2a 5, π C = 4a 2 /25, and C = 2a 2 /25, respectively. These results yield s < s < s, < <, π < π < π, and < <. Thus, the following proposition is derived. Proposition 2 In a three-country model where both government of exporting countries play simultaneously, the levels of export subsidy, output, profit and welfare of the exporting country whose firm is a Stackelberg leader (follower) are respectively lower (higher) than those of each exporting country when its firm competes in a Cournot fashion. Now we consider a slightly different case where the firm of each exporting country competes in Cournot fashion but the governments intervene in trade seuentially. In this case, we can show that the reaction function of the follower governments is f l s = a 4 1 4 s. Therefore, the optimal export subsidy level of the leader government is s l = a 3, and accordingly, that of the follower government is s f = a 6. e then know that the euilibrium output, profit, welfare levels of the leader government are l = a 2, l 2 π = a 4 and f = a 2 /12, and those of the follower government are f = a 3, f π = a 2 /18, and f = a 2 /18. Therefore, we l f l f l f also derive that s > s, >, π > π l f and >. More interestingly, we can find out that the profit, output and welfare of the country where the firm acts as a Stackelberg leader (follower) are euivalent to those of the country where the government acts as a Stackelberg S f S l follower (leader). That is, =, =, s f S l S f S l π = π, π = π, =, =. Thus we have Proposition 3 In the euilibrium of the three-country model where the governments move simultaneously and the firms move seuentially, the euilibrium output, profit, and welfare of the country whose firm is a Stackelberg leader (follower) are, respectively, the same to those euilibrium values of the country whose government is a Stackelberg follower (leader) in the three country model where the
22 governments move seuentially and the firms move simultaneously. Proposition 3 states that to take an advantage for the government by taking a position of a Stackelberg leader when the firms compete with each other in the Cournot fashion is euivalent for the government to make his firm act as a Stackelberg follower when both governments move simultaneously. Conclusion Most of existing studies of strategic trade policies implicitly assume that the firms are involved in the Cournot type of competition. Thus, we treated the case where the Stackelberg type of competition dominates between firms, and examined how the results on trade policies, firms profits and welfare of each country are affected under our circumstances. As our first result, we showed that, although the optimal trade policies of both governments are a positive subsidy in the case of Cournot competition, the optimal trade policy of the country whose firm is a leader is non-intervention in trade, and so only the other country executes the positive subsidizing policy in our case. As our second result, we found that the country whose firm is a follower attains a higher level of welfare than the other country. This means that in our model, the second mover advantage exists. inally, we examined a case symmetric to our case. That is, both firms compete in a Cournot fashion but the governments move seuentially. Then the result of this case seems to be symmetric. As is presented in Proposition 3, the euilibrium output, profit and welfare of the country whose firm is a Stackelberg leader (follower) coincide with those of the country whose government is a Stackelberg follower (leader). Hence, in view of our second results, we can assert that the leader government exactly has an advantage over the other government when they move seuentially but the firm move simultaneously. More interestingly, if the governments cannot take a leader position and both governments have to move simultaneously, they have an incentive to make their firms take a follower position in the competition between firms. Our analysis can be extended to a two country model treated by Collie, 1994 and price competition of the differentiate goods observed by Dixit, 1984. References Arvan,. (1991). lexibility Versus Commitment in Strategic Trade Policy under Uncertainty. Journal of International Economics. 31, 341 355. Brander, J.A., Spencer, B.J. (1985). Export Subsidies and International Market Share Rivalry. Journal of International Economics. 18, 83 100. Collie, David R. (1994). Endogenous Timing in Trade Policy Games: Should Governments Use Countervailing Duties? eltwirtschaftliches Archiv. 130, 191 209. Dixit, A.K. (1984). International Trade Policy for Oligopolistic Industries. Economic Journal Conference Papers. 94, 1-16. Ohkawa, T., Okamura, M., Tawada, M. (2002). Endogenous Timing and elfare in the Game of Trade Policies under International Oligopoly. In oodland A. (ed.), Economics Theory and International Trades: Essays in Honor of Murray C. Kemp. Edward Elgar.