管理授權下出口補貼與進口關稅之國際寡占策略分析

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(1)國立高雄大學經濟管理研究所碩士論文. 管理授權下出口補貼與進口關稅之國際寡占策略分析 THE STRATEGIC ANALYSIS OF EXPORT SUBSIDY AND IMPORT TARIFF IN INTERNATIONAL OLIGOPOLY WITH MANAGERIAL DELEGATION. 研究生:林育珊撰指導教授:王鳳生博士. 中華民國九十六年六月.

(2) 誌謝終於，來到論文最後部分－致謝辭! 首先，謝謝這兩年來，開啟我研究學習生涯大門的王鳳生老師。這兩年跟在您旁邊做學問的日子，您那源源不絕的點子、做學問的堅持與熱忱、對我們學生的照顧，亦或身為一經濟學者對社會的關懷，無不讓我感到佩服，忙碌之虞，也希望恩師多保重身體。接著要謝謝雅津學姊，任何問題請教學姊，學姊總耐心的為我解答，更在每次的投稿和研討會中，一次又一次的熬夜幫我確認計算過程，特別在此項您說聲謝謝。也謝謝鄭育仁老師、陳師慎老師對論文的多方建議，得以讓論文更加完善。另外謝謝珮瑜姐，您就像大姐姐一樣，對我們這群老師的學生無為不至的照顧，尤其謝謝您，對於我在準備考試期間的鼓勵與關心。還有謝謝鄭大哥，果然不愧為一成功的商場人，在您身上，我學到課本之外的做人處事態度，也謝謝您不吝的與我分享您商場經營之道與人生觀。謝謝欣怡、曉娟、佳涵和兆宏，期盼我們日後在自己的工作崗位上發光發熱，這樣才能讓我們的美食循環越來越豐盛喔。謝謝建成、聖凱、苔琳、泰良，有你們讓研究所生活更充實與快樂，也祝福你們一帆風順。此外，謝謝多年來互相扶持與鼓勵的老友郁婷以及支持和包容著我的啟鴻，願我們夢想都能起飛、實現。最後要謝謝我親愛的爸媽，雖然從研一開始就不斷問我: 這學期會過吧? 到了研二又問: 會畢業吧? 現在，我修完學分、寫完論文，要跟你們說我真的可以畢業了喔！謝謝你們對我無悔的付出，此站旅程才將結束，而前方未知的路途才開始，但我仍會持續地努力，讓你們以我為榮。 . 林育珊謹誌民國96年7月 i .

(3) 管理授權下出口補貼與進口關稅之國際寡占策略分析指導教授：王鳳生博士國立高雄大學應用經濟學系學生:林育珊國立高雄大學經濟管理研究所. 摘要 1985 年，首先由 Brander and Spencer 提出策略性國際貿易理論，隨後，相關議題在文獻中廣為被討論，此方面文章多將廠商視為一極大化利潤目標之決策體，以探討最適貿易政策之訂定。觀察現今企業，公司擁有權乃為股東所有，而由專業經理人負責管理，對經理人而言，比起為股東創造利潤極大化目標，為自己的稱譽而追求公司營收極大或公司產品市場佔有率極大化為目標相較，經理人存在不追求利潤極大化誘因。此論文探討存在擁有權與經營權分離下的企業，當其經理人決策與董事會利潤極大化目標不一致時，其是否會影響政府最適出口補貼與最適進口關稅的訂定，又出口補貼和進口關稅決策如何影響公司經理人在市場上進行競爭時之決策。研究結果發現，經理人追求的目標決策不同，會導致其在市場上進行數量競爭之結果差異。在一雙佔市場，兩國出口至第三國進行競爭模型下，當只有一國進行管理授權，不論其政府是否進行政策干預，另一國政府進行補貼干預時，政策干預與管理授權工具存在替代性。當兩國廠商皆進行授權時，工具替代性效果消失，並且管理授權工具反而使廠商陷入囚犯兩難境界，但市場份額授權下之囚犯兩難境界小於銷售份額授權。此外，重新設定一個兩外國雙佔，本國不生產從事產品進口之競爭模型，比較差異性關稅與單一關稅之差異性，分析結果指出，不論差異性關稅或單一關稅，銷售授權下之關稅稅率最低，Cournot 競爭下之關稅稅率最高。差異性關稅稅率之差異決定於成本差別，且無論何種授權之下，稅. ii.

(4) 率差異皆等於二分之一的成本差異。差異性關稅對低成本廠商較有利，而單一關稅對高成本廠商有利。此外，在差異性關稅下，銷售授權的社會福利及關稅稅收皆高於市場份額授權。. 關鍵字：銷售授權，市場份額授權，關稅，出口補貼. iii.

(5) THE STRATEGIC ANALYSIS OF EXPORT SUBSIDY AND IMPORT TARIFF IN INTERNATIONAL OLIGOPOLY WITH MANAGERIAL DELEGATION Advisor: Dr. Leonard F.S. Wang Department of Applied Economics National University of Kaohsiung Student: Yu-Shan Lin Institute of Economics and Management National University of Kaohsiung. ABSTRACT In many important industries, corporate firms, with the separation of management and ownership, compete in oligopolistic international markets. The managerial performance is the key to the overall performance of the firm. Although prolific studies have been made on strategic trade policy and strategic delegation, respectively, but the implication of optimal trade policy with strategic delegation is still need to be explored. The main purpose are of this thesis are to ask how export subsidy and import tariff policy affect the incentive that are provided by owner to the manager, which in turn affects the managerial decision on quantities, and see how optimal trade policy may be designed in the light of changes in managerial incentive contracts by using backward induction to solve subgame perfect equilibrium.. In export competing model, we demonstrated that in duopoly, when firms take different delegation forms, it will result in different equilibrium outcomes. iv.

(6) Furthermore, when only one firm adopts delegation, whether it is a sales or market-share case, it makes the firm acting as a Stackelberg leader. Delegation and export subsidy is substitutable for profit-shifting purpose. For the case of two-sided delegation, the instrument-substitution ablity of trade policy and managerial delegation disappears, and two export firms are involved in a “Prisoner’s Dilemma”, but market share delegation is in less degree. In the import competing model, we have shown that whether it is discriminatory or uniform tariff, the optimal tariff rate is the highest under Cournot competition, and sales delegation is the least. It also demonstrated that the tariff rate difference equals half of the marginal cost difference, regardless of managerial delegation forms. In addition, we obtained that the social welfare and tariff revenue is higher with sales delegation than market share delegation under discriminatory tariff regime.. Keywords：sales delegation, market share delegation, tariff, export subsidy.. v.

(7) TABLE OF CONTENTS CHAPTER ONE: AN INTRODICTION…………………………………………..….1 1.1 Research Background………………………………………………………….1 1.2 Literature Review……………………………………………………………...2 1.2-1 Strategic Delegation…………………………………………………………2 1.2-2 Strategic Trade Policy………………………...………...………...…………4 1.3 Structure of Thesis…………………………………………………………….5 CHAPTER TWO：MANAGERIAL DELEGATION MODEL……………………….7 2.1 Market Share Delegation………………………………………………………8 2.2 One-Sided Asymmetric Delegation…………………………………………..11 2.3 Concluding Remark……………………………………………………….13 CHAPTER THREE： EXPORT-COMPETING MODEL…………………………...15 3.1 STRATEGIC. TRADE POLICY WITH ONE-SIDED DELEGATION……………………16. 3.1.1 One Country Intervention…………………………………………………..16 3.1.2 Two Countries Intervention………………………………………………...18 3.1.2-1 One-Sided Market Share Delegation…………………………………….18 3.1.2-2 One-Sided Sales Delegation……………………………………………...21 3.2 STRATEGIC TRADE POLICY WITH TWO-SIDED DELEGATION……………………24 3.2.1 One Country Intervention…………………………………………………..24 3.2.2 Two Countries Intervention………………………………………………...24 3.3 Concluding Remark………………………………………………………28 CHAPTER FOUR： Optimal Discriminatory Tariff and Managerial Incentive under Oligopolistic Competition………………………………………………....30 4.1 Basic Model…………………………………………………………………..30 4.2 Discriminatory Tariff………………………………………………………...31 4.3 Uniform Tariff………………………………………………………………..36 4.4 Concluding Remark…………………………………………………………..43 CHAPTER FIVE： CONCLUSIONS……………………………………………….44 REFERENCE………………………………………………………………………. .46. vi.

(8) LIST OF FINGURES Figure 2.1 Game stages of Cournot competition model with market share delegation……………………………………………………………………9 Figure 2.2 Game stages of Cournot competition model with one-side market share delegation…………………………………………………….……………..11 Figure 2.3 When only one firm adopts delegation it acts as Stackelberg leader in output competition………………………………….……………………….12 Figure 3.1 Game stages of export-competing model with one-side market share delegation and one-side intervention………………………………………..16 Figure 3.2 Game stages of sequential export-competing model with one-side market share delegation and two countries intervention……………………………18 Figure 3.3 Game stages of simultaneously export-competing model with one-side market share delegation and one country intervention……………………...20 Figure 3.4 Game stages of sequential export-competing model with one-side sales delegation and two countries intervention…………………………………..22 Figure 3.5 Game stages of simultaneously export-competing model with one-side sales delegation and one country intervention……………………………...23 Figure 3.6 Game stages of export-competing model with two-side market share delegation and one country intervention……………………………………25 Figure 3.7 Game stages of export-competing model with two-side market share delegation and two countries intervention…………………………………..27. vii.

(9) Figure 4.1 Game stages of import-competing model with market share delegation in discriminatory tariff…………………………………………………………32 Figure 4.2 Game stages of import-competing model with sales delegation in discriminatory tariff…………………………………………………………34 Figure 4.3 Game stages of import-competing model with market share delegation in uniform tariff………………………………………………………………..37 Figure 4.4 Game stages of import-competing model with sales delegation in uniform tariff…………………………………………………………………………39. viii.

(10) LIST OF TABLES Table 1.1 Typical delegation models………………………………………………….4 Table 2.1 Compare the new market share form with Jansen et al.(2007)……………13 Table 3.1 Market-share delegation game……………………………………………21 Table 3.2 Sales delegation game……………………………………………………..24 Table 4.1 Change of social welfare under different tariff regime……………………42. ix.

(11) CH APTER ONE: AN INTRODICTION. 1.1 Research Background According to World Trade Report 2005, published by World Trade Organization, “In 2004, the value of world merchandise trade rose by 21 percent, to $8.88 trillion, and that of world commercial services trade by 16 percent, to 2.10 trillion.” International trade plays a more and more important role in modern economics. For some purpose governments prefer to protect domestic industries through a variety of trade policy, tariff and non-tariff barriers, such as import quotas, export subsidy, voluntary export restraint, and etc. A great deal of effort has been on strategic trade policy to discuss optimal trade policy under different product-market competition. While reviews strategic trade policy study, the firm itself viewed as a simple profit-maximizing entity and incentive structure within a firm are treated as exogenous. While in most modern managerial enterprises, the ownership belongs to the Board of Directors and they do not participate in management. That separation of ownership and control imply that they have different objectives. For the owner, he seeks to maximize profit, but for the manager he more concerns with maximizing revenues, quantity, or market share than profits. Review the literatures in the area of strategic delegation; it has been limited to sales delegation cases, until Jansen et al. (2007) presented the case of market share delegation. He points that manager’s objectives are not only focusing on sales revenue but also on product market share rate. In real world, Makoto Ebata, president and CEO of the Hitachi consumer business group on April 18, 2007, said that “As the 1.

(12) number of PDP players is limited, we can expect a big market opportunity”. Hitachi aims to achieve a 20 percent share of the market in fiscal 2010. And in the 50-inch-plus category, the company is aiming for a 30 percent share. Looking at another example, Matsushita Electric Industrial Co., Ltd., the top 1 PDP manufacturers in the fourth quarter of 2006 in the PDP industry, announced in 2005 that it aims to increase its global market share for large-sized plasma display panel TVs to 40 percent share of the market in fiscal 2010. So far only few trade studies have been taken strategic delegation into consideration. Even though in this few literature, their discussion on sales delegation. In order to assess the desirability and the scale of policy intervention in international trade, it is important to understand how trade policies affect intra-firm incentive and vice versa. Hence, this thesis, the main purposes are to ask how export subsidy and import tariff policy affect the incentive provided by owner to the manager, which in turn affect the managerial decision on quantities, and see how optimal trade policy may be designed in the light of changes in managerial incentive contracts by using backward induction to solve subgame perfect equilibrium.. 1.2 Literature Review 1.2-1 Strategic Delegation In the principal-agent industrial organization literature, there are two aspects of managerial incentives analysis, moral hazard and strategic delegation. In the former strand, the manager is an agent dislikes effort, and owner is a principal can not observe the degree of manager’s effort. For the sake of urging agent working hard, 2.

(13) owner designs a contract for the agent based on observables (e.g. profits) that includes effort. This has been applied to the context of international trade policy by Campbell and Vousden (1994) and Horn and Lundgren (Horn et al., 1995). Strategic delegation refers to the design of an incentive payment scheme by the owner to the manager to deal with oligopolistic rivalry in the market, independent of considerations like moral hazard or adverse selection. Schelling (1960) explained the advantage of delegating decision to an agent with a different motivation as a means of making certain action credible. Fershtman and Judd (1987), Sklivas (1987) considered the case of sales delegation (henceforth, FJS). They offer a game-theoretic explanation for managers' nonprofit-maximizing behavior, and examine a two-stage game where in the first stage the owner writes his manager's contract that is publicly announced before market competition, and in the second stage managers decide on output or price in the market. In their models, according to the contract, managers receive a bonus that is proportional to a linear combination of profit and sales. They showed that managerial delegation would significantly affect the competition behaviors of each firms, and the firm could gain the advantage of cost reducing and profit increasing, regardless of the market competition type in quantity or price competition. Recently, Jansen et al. (2007) proposed the case of market share delegation in which the salary of the manager is based on a combination of profit and market share, and demonstrated that it is a dominant strategy in the delegation game. We summarize in Table 1.1.. 3.

(14) Table 1.1 Typical delegation models Delegation version. wage combination. Wage equation. Sales delegation Profits and sales. g i = α i π i + (1 − α i ) pq. i. (FJS, 1987) Market share delegation Profit and market share (Jansen et al., 2007). g. i. = π. i. + α. i. qi Q. 1.2-2 Strategic Trade Policy Apart from strategic delegation, for political or economic policies, government tends to protect domestic firms or courage them to aggress by trade polices, such as tariff, import quota, export subsidy, voluntary export restraint, and etc. The theory of strategic trade policy 1 for oligopolies started with an article by Brander and Spencer (1985), who demonstrated that export subsidy was optimal policy under Cournot duopoly. Eaton and Grossman (1986) showed that under Bertrand duopoly an export tax was optimal. My research is related to strategic trade policy, but there is an important difference. That is not only quantities are set strategically, so are managerial objectives. There are few studies dealing with strategic delegation and optimal trade policy. Das (1997) and Miller and Pazgal (2005) consider three-stage games in which governments choose subsidies, firms’ owners choose incentive schemes for their managers, and then the. 1. According to Handbook of International Economics, it has two meanings. First, strategic trade policy sometimes refers to trade policy that has directly military implications. Secondly, the term strategic is sometimes used simply as a synonym for important; thus strategic trade policy is trade policy targeted toward industries that are so to be important for some reasons. Neither of these definitions is considered further, although an industry that is strategic by one of these definitions might also be strategic in the game theoretical sense used here. 4.

(15) managers compete in the product market. Das (1997) adapt FJS model for analyzing exporting and import-competing industries. He demonstrated that the scale of policy intervention in an oligopolistic export market is reduced, and in an import-competing industry may be reduced or enhanced depending on whether firms compete in quantity or price. Miller and Pazgal (2005) showed that if firms’ owners have sufficient control over their managers’ behavior, then the optimal strategic trade policy does not depend on the mode of product-market competition, i.e., whether firms compete by setting prices or quantities. And Ma (2000) showed that the instrument of managerial incentive in the form of sales delegation as a credible commitment which could substitute for export subsidy and making firm acts as a Stackelberg leader. Lin, Hsu, and Hwang (1999) found that under Cournot competition the board of trustees in modern corporations often initiate incentive schemes designed to push managers to raise output to the Stackelberg leadership level, and price under quotas are necessarily higher than those under tariffs.. 1.3 Structure of Thesis In many important industries, cooperate firms, with separation of management and ownership, compete in oligopolistic international markets. The managerial performance is the key to the overall performance of the firm. Although a large number of studies have been made on strategic trade policy and strategic delegation, respectively, little is known about optimal trade policy with strategic delegation. Furthermore, even the few literatures about strategic delegation and optimal delegation, those literatures has been limited to analysis sales delegation cases. Therefore, the purpose here is to explore further into different strategic delegation 5.

(16) forms and its implications for international trade policy. The remaining chapters are organized as follows. In chapter 2, set the delegation model under Cournot competition. In Chapter 3, we construct export-competing model under quantity competition to analyze optimal subsidy policy. In chapter 4, conduct import-competing model to analyze optimal tariff. Chapter 5, gives the conclusion.. 6.

(17) CHAPTER TWO：MANAGERIAL DELEGATION MODEL. Schelling (1960) explained the advantage of delegating decision to an agent with a different motivation as a means of making certain action credible. In a Cournot oligopoly, Vickers (1985), Fershtman, Judd (1987), and Sklivas (1987) have shown that a firm which delegates to a manager, with utility that depends upon a combination of profits and sales, can increase its profit. Moreover, delegating to a manager concerned about sales as well as profits allows the firm to commit to produce the Stackelberg leader output. Jansen et al. (2007) proposed the case of market share delegation in which the salary of the manager is based on a combination of profit and market share, and demonstrated that it is a dominant strategy in the delegation game. In this chapter, in order for dealing with a three－stages game with export-competing and import-competing models in following chapters, we offer a variation of market share delegation model, which does not harm the spirit of original market share delegation model, and discuss the equivalence of sales delegation and market share delegation. This chapter is organized as follows. The new market share delegation form is presented in section 2.1, and section 2.2 discussed asymmetric delegation model. Section 2.3 concludes this chapter.. 7.

(18) 2.1 Market Share Delegation Considering a duopoly industry, firm 1 and firm 2 are both managerial firms. We assume the duopoly model with linear demand and cost functions. Let inverse demand function p = a − Q , where Q is the sum of the output levels of firms 1 and 2, respectively q1 and q 2 . The cost function is C i (qi ) = cqi , where i = 1,2 . There is a two-stage game in consideration. It is assumed that the market demand is not too small; more precisely, a > c , which ensures positive quantities in equilibrium.. Stage 1: The owner writes and publicly announces a contract with his manager that specifies how the manager will be rewarded. From Jansen et al. (2007), the manager of firm i is paid π i + α i. qi , where α i is an incentive weight, π i and Q. qi stand respectively, for profits and market share. Here, in order to deal with a Q. three-stage game later, specify g i =π i+α i (ln q i − ln q j ) , where i ≠ j. Let k =. qi , Q. then (ln qi − ln q j ) will also be able to measure the market share of firm i , considering f (k ) = ln. k is an increasing function of k . Assume that the owner 1− k. seeks to maximize profit: π i = ( p − c)qi . Stage 2: The managers simultaneously choose their firm’s output to maximize gi . The game is solved by employing the method of backward induction.. 8.

(19) Stage I. Stage II Time. Firm’s owners choose the incentive to the managers.. Managers make choice of quantity simultaneously.. Figure 2.1 Game stages of Cournot competition model with market share delegation. According to the first-order conditions, the equilibrium quantities of the market game satisfy the following system of equations:. α ∂g1 = a − c − 2q1 − q 2 + 1 = 0 q1 ∂q1. (2.1). ∂g 2 α = a − c − q1 − 2q 2 + 2 = 0 ∂q 2 q2 and ∂π 1 ∂q ∂q = 0 ⇔ 1 [a − c − 2q1 − q 2 ] − q1 2 = 0 ∂α 1 ∂α 1 ∂α 1. (2.2). ∂q ∂q ∂π 2 = 0 ⇔ 2 [a − c − q1 − 2q 2 ] − q 2 1 = 0 ∂α 2 ∂α 2 ∂α 2 ⎡ ∂F1 ⎢ where ∂q1 = − 1 det ⎢ ∂α 1 ⎢ ∂F2 ∂α 1 J F ⎢ ⎣ ∂α 1 ⎡ ∂F1 ⎢ ∂q ∂q 2 −1 = det ⎢ 1 ⎢ ∂ F2 ∂α 2 J F ⎢ ⎣ ∂q 1. ∂F1 ⎤ ⎡ ∂F1 ⎢ ∂q ⎥ ∂q 2 , ∂q 2 −1 ⎥ = det ⎢ 1 ⎢ ∂F2 ∂ F2 ⎥ ∂ α 1 J F ⎢ ⎥ ∂q 2 ⎦ ⎣ ∂q1. ∂F1 ⎤ ∂α 1 ⎥ , ⎥ ∂F2 ⎥ ⎥ ∂α 1 ⎦. ∂F1 ⎤ ⎡ ∂F1 ⎢ ∂α ∂α 2 ⎥ , and ∂q1 −1 ⎥ = det ⎢ 2 ⎢ ∂ F2 ∂F2 ⎥ ∂α 2 J F ⎢ ⎥ ∂α 2 ⎦ ⎣ ∂α 2. ∂F1 ⎤ ∂q 2 ⎥ . ⎥ ∂ F2 ⎥ ⎥ ∂q 2 ⎦. 9.

(20) Solving (2.1) and (2.2), incentive solutions and reduced-form solutions of quantities are:. qim =. 1 1 (4 + 2 )(a − c) ; α im = (5 2 − 1)(a − c) 2 . 14 98. (2.3). Substitute them into profit function to obtain. π im =. 1 (10 − 2 )(a − c) 2 . 98. (2.4). 1 Note that, in equilibrium, qim = qimj but α im = α imj , where the superscript m 4. represents our form of market share delegation while mj denotes market share delegation à la Jansen et al. (2007). The new form of market share delegation we are introducing here not only preserves the spirit of Jansen et al. (2007) but also becomes useful in dealing with the three-stage game of concerned issues as well. Fershtman and Judd (1987), Sklivas (1987) considered the case of sales delegation in that according to the contract, managers receive a bonus which is proportional to a linear combination of profit and sales: α iπ i + (1 − α i ) pqi . To compare equilibrium output and profit under market share delegation, sales delegation and simple Cournot solution, we can rank in order qis > qim > qic and π ic > π im > π is where c and s denote simple Cournot and sales delegation respectively. Hence, in duopoly, when firms take different delegation forms, market share or sales delegation, it will result in different equilibrium outcomes.. 10.

(21) 2.2 One-Sided Delegation Assume that firm 1 is a managerial firm in which the ownership and control is separated and firm 2 is an entrepreneurial firm in which the ownership and control is not separated. In stage 2, the manager of firm 1 maximizes g1 =π 1+α 1 (ln q1 − ln q 2 ) . The manager of firm 2 maximizes π 2 = ( p − c)q 2 .. Stage I. Stage II. Time The owner of firm 1 chooses the incentive to his manager.. Firms make choice of quantity simultaneously.. Figure 2.2 Game stages of Cournot competition model with one-side market share. Now, the system (2.1) rewrite as ∂g 1 α = a − c − 2q1 − q 2 + 1 = 0 ∂q1 q1. (2.5). ∂π 1 = a − c − q1 − 2q 2 = 0 ∂q1. In stage 1, for owner 1, we obtain ∂π 1 ∂q ∂q = 0 ⇔ 1 [a − c − 2q1 − q 2 ] − q1 2 = 0 ∂α 1 ∂α 1 ∂α 1 ⎡ ∂F1 ⎢ where ∂q1 = − 1 det ⎢ ∂α 1 ⎢ ∂F2 ∂α 1 J F ⎢ ∂α ⎣ 1. ∂F1 ⎤ ⎡ ∂F1 ⎢ ∂q ∂q 2 ⎥ , ∂ q 2 −1 ⎥ = det ⎢ 1 ⎢ ∂F2 ∂F2 ⎥ ∂α 1 J F ⎢ ⎥ ∂q 2 ⎦ ⎣ ∂q1. (2.6). ∂F1 ⎤ ∂α 1 ⎥ . ⎥ ∂F2 ⎥ ⎥ ∂α 1 ⎦. 11.

(22) Simultaneously solving (2.5) and (2.6), we obtain incentive weight and quantities solutions: 1 2. 1 8. α1 = (a − c) 2 , q1 = (a − c) = 2q 2 .. (2.7). Substituting (2.7) into profit functions, the profit solutions are: 1 8. π 1 = (a − c) 2 = 2π 2 .. (2.8). This result is the same as a Stackelberg leader solution. Hence, in an asymmetric duopoly, if only one firm adopts delegation -whether sales delegation 2 or market share delegation-as long as the other is an entrepreneurial firm, it acts as Stackelberg leader, but with different equilibrium outcome. See Fingure 3, q c < q m < q s .. q2. R1m. R1s. R1c. R2 q1 c. q. q. m. s. q. Figure 2.3 When only one firm adopts delegation it acts as Stackelberg leader in output competition.. 2. See FJS model for sales delegation case. 12.

(23) Proposition 2.1: Regardless of the form of delegation in duopoly, if only one firm. adopts delegation it acts as Stackelberg leader in output competition.. 2.3 CONCLUDING REMARKS In this chapter, it can conclude two points. First, in order to deal with a three-stage game in later chapters, we offer a new market share delegation form, g i =π i+α i (ln qi − ln q j ) , where i ≠ j , to instead the original manager’s salary. function in Jansen et al. (2007). After calculating, the equilibrium, qim = qimj but 1 4. α im = α imj , where the superscript m represents our form of market share delegation while mj denotes market share delegation à la Jansen et al. (2007). The new form of market share delegation we are introducing here not only preserves the spirit of Jansen et al. (2007) but also becomes useful in dealing with the three-stage game of concerned issues as well. We summarized in Table 2.1.. Table 2.1 Compare the new market share form with Jansen et al.(2007). Manager’s salary function. Original Jansen et al.. New market share. (2007) model. delegation form. g i =π i+α i (ln qi − ln q j ). g i =π i+α i (ln qi − ln q j ). qimj =. Outcome. α imj =. 1 (4 + 2 )(a − c) 14. 1 (10 2 − 2)(a − c) 2 49. qim = qimj 1 4. α im = α imj. 13.

(24) Secondly, in an asymmetric duopoly, if only one firm adopts delegation -whether sales delegation or market share delegation-as long as the other is an entrepreneurial firm, it acts as Stackelberg leader in output competition.. 14.

(25) CHAPTER THREE： EXPORT-COMPETING MODEL Brander and Spencer (1985) have shown that export subsidies can appear as attractive weapons because they improve the relative position of the domestic firm in non-cooperative rivalries with other firms, and allow it to expand its “market share”. Delegation of trade policy decisions in a customs union has been considered by Gatsios and Karp (1991, 1995). They show that the countries in a customs union may gain by delegating trade policy to the most aggressive member of customs union. Das (1997) demonstrated that the scale of trade policy intervention with symmetric sales delegation in an oligopolistic export market is reduced, and further argued that any other form of incentive scheme to the managers which is set strategically (via-á-vis those offered by other firms) will have a bearing on optimal trade policy. Ma (2000) showed that the instrument of managerial incentive in the form of sales delegation as a credible commitment which could substitute for export subsidy and making firm acts as a Stackelberg leader. In this chapter, we add market-share delegation into export rivalry model to demonstrate the instrument substitutability between different forms of managerial delegation and export subsidy in both simultaneous and sequential move games. In particular, we show the ranking of optimal export subsidy under different forms of incentive scheme. The chapter is organized as follows. Section 1 and 2 consider an export rivalry model with one-sided and two-sided managerial delegation respectively. Section 3 concludes the paper.. 15.

(26) 3.1 STRATEGIC TRADE POLICY WITH ONE-SIDED DELEGATION 3.1.1 One Country Intervention Extend the model of chapter two to consider the export rivalry model. Assume that are two countries, a home and a foreign country and that each country has one firm producing homogeneous goods, the home firm is a managerial enterprise which is labeled as firm 1 and the foreign firm is an entrepreneurial firm which is labeled as firm 2. Both firms export to a third-country market where they compete in a Cournot duopoly. Assume only the home government decides to provide export subsidy. In such a setting, a three-stage game evolves. Stage 1: the home government chooses specific subsidy s1 to maximize social welfare: w1 = π 1 − s1 q1 , where π 1 = ( p − c)q1 + s1 q1 Stage 2: the owner of firm 1 offers incentive scheme g1 = π 1 + α 1 (ln q1 − ln q2 ) to his manager, but himself choosing α 1 to maximize profit function π 1 . Stage 3: managers simultaneously compete in quantities.. Stage I. Stage II. Stage III. Time. Home government decides the subsidy.. The owner of firm 1 chooses the incentive to the manager.. Firms compete in quantity.. Figure 3.1 Game stages of export-competing model with one-side market share delegation and one-side intervention.. 16.

(27) Now system (2.1) and (2.2) must be rewritten as. α ∂g1 = a − c + s1 − 2q1 − q 2 + 1 = 0 ∂q1 q1 ∂π 2 = a − c − q1 − 2q 2 = 0 ∂q 2. ,. (3.1). ∂π 1 ∂q ∂q = 0 ⇔ 1 [a − c + s1 − 2q1 − q 2 ] − q1 2 = 0 . ∂α 1 ∂α 1 ∂α 1 ⎡ ∂F1 ⎢ where ∂q1 = − 1 det ⎢ ∂α 1 ⎢ ∂F2 ∂α 1 J F ⎢ ⎣ ∂α 1. ∂F1 ⎤ ⎡ ∂F1 ⎢ ∂q ∂q 2 ⎥ , ∂q 2 −1 ⎥ = det ⎢ 1 ⎢ ∂F2 ∂ F2 ⎥ ∂ α 1 J F ⎢ ⎥ ∂q 2 ⎦ ⎣ ∂q1. (3.2). ∂F1 ⎤ ∂α 1 ⎥ . ⎥ ∂F2 ⎥ ⎥ ∂α 1 ⎦. As before, firstly simultaneously solving (3.1) and (3.2) to obtain q1 = q1 ( s1 ) , q 2 = q 2 ( s1 ) and α 1 = α 1 ( s1 ) . Substituting them into stage 1 to maximize social. welfare, the home government decides on the export subsidy. We have s1 = 0 . The other variables can be obtained as follows: 1 8. 1 2. 1 8. α 1 = (a − c) 2 , q1 = (a − c) = 2q 2 , w1 = π 1 = (a − c) 2 = 2w2 = 2π 2 , (3.3) These results imply that when the owner can “manage” the manager by providing a suitable incentive contract, there is no need for government to intervene; it complies with the requirement of export-subsidy prohibition by World Trade Organization, Economic Cooperation and Development, etc. Because of the results (3.3) are identical with (2.7) and (2.8), we have the following proposition. Proposition 3.1: When only the domestic firm’s owner decides on delegation whether. it is sales or market-share case, it makes the domestic firm acting as a Stackelberg leader, export subsidy is no longer needed; hence, delegation and export subsidy is strategically substitutable for profit shifting. 17.

(28) 3.1.2 Two Countries Intervention We now would like to see that both governments intervene while firm 1 is a managerial enterprise with market-share or sales delegation and firm 2 is an entrepreneurial firm.. 3.1.2-1 One-Sided Market Share Delegation Assume that firm 1 is a market-share delegation firm while firm 2 is an entrepreneurial firm. It is a three-stage game to be solved. In stage 1, both governments choose a specific subsidy. si. to maximize social welfare,. wi = π i − si qi ; In stage 2, the owner of firm 1 offers incentive scheme g1 = π 1 + α 1 (ln q1 − ln q2 ). to his manager, but himself choosing α1 to maximize. profit function , π 1 ; In stage 3: managers simultaneously compete in quantities.. Stage I. Stage II. Stage III. Time. Both governments decide the subsidy.. The owner of firm 1 chooses the market share delegation incentive to the manager.. Firms compete in quantity.. Figure 3.2 Game stages of sequential export-competing model with one-side market share delegation and two countries intervention.. We can rewrite equation (2.1) and (2.2) as:. 18.

(29) α ∂g1 = a − c − 2q1 − q 2 + 1 + s1 = 0 ∂q1 q1 ∂π 1 = a − c − q1 − 2q 2 + s 2 = 0 ∂q 2. ,. ∂π 1 ∂q ∂q = 0 ⇔ 1 [a − c + s1 − 2q1 − q 2 ] − q1 2 = 0 . ∂α 1 ∂α 1 ∂α 1. (3.4). (3.5). We first simultaneously solve (3.4) and (3.5) to obtain q1 = q1 ( s1 , s 2 ) , q 2 = q 2 ( s1 , s 2 ) , and α 1 = α 1 ( s1 , s 2 ) . And then substituting them into stage 1 to. maximize social welfare, both governments decide on the export subsidies, s1 = 0 1 and s 2 = (a − c) ; other variables can be obtained as follows: 3. α1 =. 1 1 1 (a − c) 2 , q1 = (a − c) , q 2 = (a − c) , 18 3 2. w1 = π 1 =. 1 1 1 (a − c) 2 , π 2 = (a − c) 2 , w2 = π 2 − s2 q2 = (a − c) 2 . 12 18 4. (3.6). In the case of one-sided market share delegation - firm 1 is a managerial firm, the optimal trade policy of the home country is no intervention, but for foreign government it can take an export subsidy to defend against the profit-shifting. Here, we show that policy intervention and market share delegation exits a relationship of substitution which is been stated in proposition 2, but the welfare of country 2 under export subsidy is higher than country 1 when firm 1 adopts managerial incentive which is mainly because the foreign government pre-commits to policy intervention. Because the export subsidy of home government is substituted by private firm’s delegation, we want to examine the following scenario that in the first stage, firm 1 adopts market-share delegation without government intervention, but the foreign government offers a subsidy to firm 2 simultaneously, and in the second stage both. 19.

(30) firms compete in quantities.. Stage I. Stage II Time. The owner of firm 1 chooses the market share delegation incentive to the manager, and foreign government decides the subsidy, simultaneously.. Managers make simultaneous choice of quantity.. Figure 3.3 Game stages of simultaneously export-competing model with one-side market share delegation and one country intervention.. In stage 2, the system from first order condition is. α ∂g1 = a − c − 2q1 − q 2 + 1 = 0 ∂q1 q1 ∂π 1 = a − c − q1 − 2q 2 + s 2 = 0 ∂q 2. .. (3.7). In stage 1, the system from first order condition is ∂q ∂q ∂π 1 = 0 ⇔ 1 [a − c − 2q1 − q 2 ] − q1 2 = 0 ∂α 1 ∂α 1 ∂α 1 ∂w2 ∂q ∂q = 0 ⇔ 2 [a − c − q1 − 2q 2 ] − q 2 1 = 0 ∂s 2 ∂s 2 ∂s 2. .. (3.8). By simultaneously solving (3.7) and (3.8), we obtain the following results: 9 3 5 1 s 2 = (a − c) , α 1 = (a − c) 2 , q1 = (a − c) , q 2 = (a − c) , 7 98 7 14. 20.

(31) w1 = π 1 =. 25 15 9 (a − c) 2 , w2 = (a − c) 2 . (a − c) 2 , π 2 = 196 196 98. (3.9). Comparing equilibrium outcomes of sequentially chosen and simultaneously chosen instruments in market-share delegation, the welfare effects can be seen from (3.6) and (3.9) which is presented in Table 3.1. Table 3.1 Market-share delegation game Market-share delegation Sequentially chosen instruments Simultaneously chosen instruments. Welfare Comparison w1 =. 1 1 (a − c) 2 < w2 = (a − c) 2 18 12. w1 =. 9 15 (a − c) 2 > w2 = ( a − c) 2 98 196. Proposition 3.2: When the foreign government pre-commits export subsidy to its. entrepreneurial firm, such policy is used to shift profit from the rival firm. The private sector of the home country will provide incentives to its manager that replaces home government intervention. However, if the foreign government and domestic firm can commit simultaneously, the home country performs better than the foreign country when the domestic firm decides on market-share delegation.. 3.1.2-2. One-Sided Sales Delegation. Assume that firm 1 adopts sales delegation instead of market-share delegation while firm 2 is an entrepreneurial firm. In stage 1, both governments choose a specific subsidy si to maximize social welfare wi = π i − s i qi ; In stage 2, the owner of firm 1 offers incentive scheme g1 = α 1π 1 + (1 − α1 ) pq1 to his manager, but himself choosing α1 to maximize profit function π 1 ; In stage 3: managers simultaneously 21.

(32) compete in quantities.. Stage I. Stage II. Stage III. Time. Both governments decide the subsidy.. The owner of firm 1 chooses the sales delegation incentive to the manager.. Firms compete in quantity.. Figure 3.4 Game stages of sequential export-competing model with one-side sales delegation and two countries intervention.. The equilibrium outcomes are obtained as follows: 1 1 1 (a − c) s1 = 0 , s 2 = (a − c) , α 1 = 1 − , q1 = (a − c) , q 2 = (a − c) , 3 3 2 6c w1 = π 1 =. 1 1 1 (a − c) 2 , π 2 = (a − c) 2 , w2 = (a − c) 2 . 4 12 18. (3.10). We get the same results as shown in section 3.1.1; managerial delegation and government intervention are substitutable instruments no matter what form of delegation firm 1 is under. Next, we examine the following scenario that in the first stage, firm 1 adopts sales delegation without government intervention, but the foreign government offers a subsidy to firm 2 simultaneously, and in the second stage both firms compete in quantities.. 22.

(33) Stage I. Stage II Time. The owner of firm 1 chooses the sales delegation incentive to the manager, and foreign government decides the subsidy, simultaneously.. Managers make simultaneous choice of quantity.. Figure 3.5 Game stages of simultaneously export-competing model with one-side sales delegation and one country intervention.. After solving the system of equations, we obtain the following results: 1 2 2 (a − c) s2 = (a − c) , α1 = 1 − , q1 = q2 = (a − c) , w1 = π 1 = (a − c) 2 , 5 5 25 5c. π2 =. 4 2 (a − c) 2 , w2 = (a − c) 2 196 25. (3.11). From (3.9) and (3.11), we can see that when the home firm adopts sales delegation, 1 the foreign government is forced to decide on larger subsidy s 2 = (a − c) than 5 s2 =. 1 (a − c) , the case of home firm who adopts market-share delegation. 7. Comparing equilibrium outcomes of sequentially chosen and simultaneously chosen instruments in sales delegation, the welfare effects can be seen from (3.10) and (3.11) which is presented in Table 3.2.. 23.

(34) Table 3.2 Sales delegation game Sales delegation Sequentially chosen instruments Simultaneously chosen instruments. Welfare Comparison w1 =. 1 1 (a − c) 2 < w2 = (a − c) 2 18 12. w1 = w2 =. 2 (a − c) 2 25. Comparing Table 3.1 and Table 3.2, we have Proposition 3.3: In the sequentially chosen instruments game, sales delegation and. market share delegation is substitutable. In the simultaneously chosen instruments game, sales delegation and export subsidy are substitutable, but market-share delegation is a welfare-dominant strategy.. 3.2 STRATEGIC TRADE POLICY WITH TWO-SIDED DELEGATION 3.2.1. One Country Intervention. Now we consider the case where the home government decides to offer export subsidy to its firm. In stage 1, home government maximizes its social welfare to decide on the subsidy; in stage 2, both firms simultaneously offer incentives to their managers; in stage 3, managers compete in quantities.. 24.

(35) Stage I. Stage II. Stage III. Time Owners choose the incentive to the managers.. Home government decides the subsidy.. Managers compete in quantity.. Figure 3.6 Game stages of export-competing model with two-side market share delegation and one country intervention.. Now, the equation (2.1) and (2.2) can be rewritten as a − c − 2q1 − q 2 + a − c − q1 − 2q 2 +. α1 q1. α2 q2. + s1 = 0 ,. (3.12). =0. and ∂q ∂π 1 ∂q = 0 ⇔ 1 [a − c − 2q1 − q 2 + s1 ] − q1 2 = 0 ∂α 1 ∂α 1 ∂α 1 ∂q ∂q ∂π 2 = 0 ⇔ 2 [a − c − q1 − 2q 2 ] − q 2 1 = 0 ∂α 2 ∂α 2 ∂α 2. .. (3.13). We first simultaneously solve (3.12) and (3.13) to obtain q1 = q1 ( s1 ) , q 2 = q 2 ( s1 ) , α 1 = α 1 ( s1 ) and α 2 = α 2 ( s1 ) . Then substituting them into stage 1 to. maximize social welfare, home government decides on the export subsidy. We can obtain the optimal subsidy s1m =. 1 (5 − 3 2 )(a − c) ; other variables can be obtained 7. as follows: 1 4. α1m = ( 2 - 1)(a - c) 2 , α 2m =. 1 1 (5 2 + 1)(a - c) 2 , q1m = (a − c) , 196 2. 25.

(36) q2m =. 1 1 1 (3 + 2 )(a − c) , π 1m = (2 − 2 )(a − c) 2 , w1m = (4 − 2 )(a − c) 2 , 14 4 28. w2m = π 2m =. 1 (10 + 2 )(a − c) 2 . 196. (3.14). The optimal subsidy and profit under two-sided sales delegation but only the home country intervenes are: s1s = w2s = π 2s =. 1 1 1 (a − c) , π 1s = (a − c) 2 , w1s = (a − c) 2 , 12 12 20. 1 (a − c) 2 . We show that under the market share delegation case, the 18. welfare of the home country and the two firms’ profit are larger than the results of sales delegation case. Because the degree of competitiveness for market-share delegation is less than sales delegation, s1m =. 1 1 (5 − 3 2 )(a − c) > s1s = (a − c) , 7 12. under market share delegation the subsidy is larger than sales delegation for encouraging its firm to be more aggressive. Proposition 3.4: When only one country intervenes, the welfare of both countries. under market share delegation is higher than that of sales delegation.. 3.2.2 Two Countries Intervention Now we consider the case that both governments decide to offer subsidies to their export firms. In stag 1, the home government maximizes its social welfare to decide on the subsidy; in stage 2, both firms simultaneously offer incentives to their managers; in stage 3, managers compete in quantities. Now, the equation (2.1) and (2.2) can be rewritten as. 26.

(37) Stage II. Stage I. Stage III. Time. Both governments decide the subsidies.. Owners choose the incentive to the managers.. Managers compete in quantity.. Figure 3.7 Game stages of export-competing model with two-side market share delegation and two countries intervention.. a − c − 2q1 − q 2 + a − c − q1 − 2q 2 +. α1 q1. α2 q2. + s1 = 0 ,. (3.15). + s2 = 0. and ∂q ∂π 1 ∂q = 0 ⇔ 1 [a − c − 2q1 − q 2 + s1 ] − q1 2 = 0 ∂α 1 ∂α 1 ∂α 1 ∂q ∂q ∂π 2 = 0 ⇔ 2 [a − c − q1 − 2q 2 + s 2 ] − q 2 1 = 0 ∂α 2 ∂α 2 ∂α 2. .. (3.16). We first simultaneously solve (3.15) and (3.16) to obtain q1 = q1 ( s1 , s 2 ) , q 2 = q 2 ( s1 , s 2 ) ,. α 1 = α 1 ( s1 ) , α 1 = α 1 ( s1 , s 2 ) , and α 2 = α 2 ( s1 , s 2 ) . Then. substituting them into stage 1 to maximize social welfare, home government and foreign government decide on the export subsidies to obtain the following results:. sm =. (290 − 127 2 ) (12 − 7 2 ) (88 − 13 2 ) ( a − c) , π m = ( a − c) 2 , w m = (a − c) 2 .(3.17) 23 1058 1058. 27.

(38) In the profit-maximization case of Brander and Spencer (1985), the simple Cournot model is s c = delegation case, s s =. 2 (a − c) and w c = (a − c) 2 . In Das (1997), the sales 25 5. 3 (a − c) and w s = (a − c) 2 . From (3.17), we find that the 49 14. ranking of the optimal subsidy and welfare under simple Cournot, market share and sales delegation is s c > s m > s s and w c > w m > w s . We draw conclusions on this in proposition 3.5. Proposition 3.5: When both firms delegate and governments intervene, the subsidy. and welfare under market share delegation is higher than that of sales delegation. Clearly, in the case of bilateral choices of incentives, the two firms are involved in a “Prisoner’s Dilemma”, but market share delegation is in less degree.. 3.3. CONCLUDING REMARKS In this chapter, we demonstrated that when a domestic firm’s owner decides on. delegation whether it is a sales or market-share case, it makes the domestic firm acting as a Stackelberg leader; delegation and export subsidy is substitutable for profit-shifting. Considering the timing of instrument choice with one-sided delegation, in a sequentially chosen instrument game, the foreign government pre-commits export subsidy to its entrepreneurial firm, such policy is used to shift profit from a rival firm; in consequence, the home government “stays put” without intervention and let the private sector provides incentives to its managers for competing with the foreign rival firm, sales delegation and market share delegation are substitutable. However, in a simultaneously chosen instrument game, the domestic firm and foreign government 28.

(39) commit strategic instruments simultaneously; sales delegation and export subsidy are substitutable, but market-share delegation is a welfare-dominant strategy. Furthermore, for the case of two-sided delegation, the welfare of both countries under market share delegation is higher than that of sales delegation whether one country or two countries intervene. At end, we must point out that in the case of bilateral choices of incentives, two export firms are involved in a “Prisoner’s Dilemma”, but market share delegation is in less degree.. 29.

(40) CHAPTER FOUR: OPTIMAL DISCRIMINITORY TARIFF AND MANAGERIAL INCENTIVE UNDER OLIGOPOLISTIC COMPETITION Brander and Spencer (1984) discussed with the profit-shift effect in imposing tariff. Hwang and Mai (1991) adapted that the optimal structure of discriminatory tariff is determined mainly by the cost differences among the foreign exporting countries, and that the countries with the highest costs will be charged the lowest tariffs. Kuo and Mai (1991) demonstrated that in the short term, import country can increase its social welfare by discriminatory tariff rather than uniform tariff. In this chapter we extend the model of Hwang and Mai (1991) and Kuo and Mai (1991) by adding managerial delegation into consideration to see how it affects the configuration of discriminatory and uniform tariff rate. This chapter is organized as follows. The basic model is presented in section 1. Section 2 and 3 consider discriminatory and uniform tariff, respectively. Section 4 concludes this chapter.. 4.1 Basic Model Consider an oligopolistic industry that spans two countries, 1 and 2. There is only one firm within each country. The domestic country imports a homogeneous product q1 and q 2 from countries 1 and 2, respectively. For simplicity, we assume that this. commodity is not produced in the domestic country. Let inverse demand function in the domestic market is p = a − Q , where Q is the sum of the output levels of firm 1. 30.

(41) and firm 2, respectively, q1 and q 2 . Moreover, assume that the domestic government understand the structure of the industry and is able to set credible tariff on imports in advance of the output decisions by the two foreign firms. Here we consider two cases, specific discriminatory and uniform tariff. The cost function is. C i (qi ) = ci qi , where i = 1,2 . There is a three-stage game in consideration. Stage 1: The domestic government chooses discriminatory or uniform tariff to maximize domestic social welfare. Stage 2: The owners write and publicly announce contract with his manager that specify how manager will be reward, and they non-cooperatively determine the structure of incentive pay to be offered to their managers. Assume that owners seek to maximizes profit: π i = ( p − ci − t i )qi . Stage 3: The managers simultaneously choose their firm’s output to maximize g i . Game is solved by employing the method of backward induction.. 4.2 Discriminatory Tariff Case Ι. Market Share Delegation The tariffs are t1 and t 2 per unit of imports and the quantity of imports are q1 and q 2 so tariff revenue is TR = t1 q1 + t 2 q 2 . We use backward induction to solve the optimal discriminatory tariff. In the third stage, the managers of both foreign countries compete in quantities to maximize their salaries： g i =π i+α i (ln qi − ln q j ) , where. i ≠ j and π i = ( p − ci − t i )qi . In stage two both owners offers incentive scheme 31.

(42) g1 = π 1 + α 1 (ln q1 − ln q2 ) to his manager, but himself choosing α1 to maximize profit function π 1 .. Stage I. Stage III. Stage II. Time. Domestic government decides the discriminatory tariff rate.. Both foreign owners choose the market share delegation incentive to their managers to maximize profit.. Both foreign managers compete in quantity in domestic market.. Figure 4.1 Game stages of import-competing model with market share delegation in discriminatory tariff.. Now system (2.1) and (2.2) must be rewritten as ∂g1 α = a − 2q1 − q 2 − c1 − t1 + 1 = 0 ∂q1 q1. (4.1). ∂g 2 α = a − q1 − 2q 2 − c 2 − t 2 + 2 = 0 ∂q 2 q2. and. ∂q ∂π 1 ∂q = 0 ⇔ 1 [a − c − 2q1 − q 2 − t1 ] − q1 2 = 0 ∂α 1 ∂α 1 ∂α 1 ∂q ∂q ∂π 2 = 0 ⇔ 2 [a − c − q1 − 2q 2 − t 2 ] − q 2 1 = 0 ∂α 2 ∂α 2 ∂α 2 ⎡ ∂F1 ⎢ Where ∂q1 = − 1 det ⎢ ∂α 1 ⎢ ∂F2 ∂α 1 J F ⎢ ⎣ ∂α 1. ∂F1 ⎤ ⎡ ∂F1 ⎢ ∂q ⎥ ∂q 2 , ∂q 2 −1 ⎥ = det ⎢ 1 ⎢ ∂F2 ∂ F2 ⎥ ∂ α 1 J F ⎢ ⎥ ∂q 2 ⎦ ⎣ ∂q1. (4.2). ∂F1 ⎤ ∂α 1 ⎥ , ⎥ ∂F2 ⎥ ⎥ ∂α 1 ⎦. 32.

(43) ⎡ ∂F1 ⎢ ∂q ∂q 2 −1 = det ⎢ 1 ⎢ ∂ F2 ∂α 2 J F ⎢ ⎣ ∂q 1. ∂F1 ⎤ ⎡ ∂F1 ⎢ ∂α ⎥ ∂α 2 , and ∂q1 −1 ⎥ = det ⎢ 2 ⎢ ∂ F2 ∂F2 ⎥ ∂α 2 J F ⎢ ⎥ ∂α 2 ⎦ ⎣ ∂α 2. ∂F1 ⎤ ∂q 2 ⎥ . ⎥ ∂ F2 ⎥ ⎥ ∂q 2 ⎦. We simultaneous solving (4.1) and (4.2) to obtain q1 = q1 (t1 , t 2 ) , q 2 = q 2 (t1 , t 2 ) ,. α 1 = α 1 (t1 , t 2 ) and α 2 = α 2 (t1 , t 2 ). And then substituting them into stage 1 to maximize domestic social welfare, W =. (q1 + q 2 ) 2 + t1 q 1 + t 2 q 2 . 2. ∂W 1 = [(10− 2)a − 6(9 + 4 2)c1 + (44+ 25 2)c2 −13(9 + 4 2)t1 + (79+ 46 2)t 2 ] = 0 ∂t1 98. (4.3). ∂W 1 = [(10− 2)a − 6(9 + 4 2)c2 + (44+ 25 2)c1 −13(9 + 4 2)t 2 + (79+ 46 2)t1 ] = 0 ∂t 2 98. By solving (4.3) to obtain optimal discriminatory tariff. t1dm =. 1 [2(4 − 2 )a + ( 2 − 11)c1 + (3 + 2 )c 2 ] , 28. (4.4a). t 2dm =. 1 [2(4 − 2 )a + ( 2 − 11)c 2 + (3 + 2 )c1 ] . 28. (4.4b). After substitution, we find that. q1dm =. 1 [4(3 + 2 )a − (20 + 9 2 )c1 + (8 + 5 2 )c 2 ] , 56. (4.5a). q 2dm =. 1 [4(3 + 2 )a + (8 + 5 2 )c1 − (20 + 9 2 )c 2 ] , 56. (4.5b). W dm =. 1 [8(3 + 2)a 2 + (20 + 9 2)(c12 + c22 ) − 8(3 + 2)a(c1 + c2 ) − 2(8 + 5 2)c1c2 ] , 112. (4.5c). TRdm =. 1 [8(10 + 2)a 2 + (118+ 51 2)(c12 + c22 ) − 8(10 + 2)a(c1 + c2 ) − 2(78 + 47)c1c2 ] .(4.5d) 784. The superscript m, s, and c denote competition in market share delegation, sales delegation, and simple Cournot competition, and d represents the case of optimal 33.

(44) discriminatory tariff. Moreover, the subscript i denotes quantity competition among the managers.. CaseⅡ. Sales Delegation Now we consider the case of sales delegation.. Stage II. Stage I. Stage III. Time. Domestic government decides the discriminatory tariff rate.. Both foreign owners choose the sales delegation incentive to their managers to maximize profit.. Both foreign managers compete in quantity in domestic market.. Figure 4.2 Game stages of import-competing model with sales delegation in discriminatory tariff.. Now equation (2.1) was rewritten as ∂g1 = a − 2q1 − q 2 − (c1 − t1 )α 1 = 0 ∂q1. (4.6). ∂g 2 = a − q1 − 2q 2 − (c 2 − t 2 )α 2 = 0 ∂q 2. By simultaneously solve (4.6) and (4.2) to obtain q1 = q1 (t1 , t 2 ) , q 2 = q 2 (t1 , t 2 ) ,. α 1 = α 1 (t1 , t 2 ) and α 2 = α 2 (t1 , t 2 ). And then substituting them into stage 1 to maximize domestic social welfare, W =. (q1 + q 2 ) 2 + t1q 1 + t 2 q 2 . 2. ∂W 2 = ( a − 13c1 + 12 c 2 − 28t1 + 22 t 2 ) = 0 ∂t1 25 ∂W 2 = ( a + 12 c1 − 13c 2 + 22 t1 − 28t 2 ) = 0 ∂t 2 25. (4.7). 34.

(45) By solving (4.7) to obtain optimal discriminatory tariff 1 (a + c1 − 2c 2 ) . 6. (4.8). 1 1 q1ds = (a − 2c1 + c 2 ) , q 2ds = (a + c1 − 2c 2 ) . 3 3. (4.9a). 1 W ds = [a 2 + c12 + c 22 − c1c 2 − a(c1 + c 2 )] . 3. (4.9b). t1ds =. 1 (a − 2c1 + c 2 ) , 6. t 2ds =. After substitution, we get. 1 [2a 2 + 5(c12 + c 22 ) − 8c1c 2 − 2a(c1 + c 2 )] . 18. TR ds =. (4.9c). The optimal discriminatory tariffs, quantities, social welfare, and total tariff revenue under Cournot competition are obtained 3 1 1 t1dc = (2a − 3c1 + c 2 ), t 2dc = (2a − 3c 2 + c1 ). 8 8. (4.10a). 1 1 q1dc = (2a − 3c1 + c 2 ) , q1dc = (2a + c1 − 3c 2 ) . 8 8. (4.11b). W dc =. 1 [4a 2 + 3(c12 + c 22 ) − 2c1c 2 − 4a(c1 + c 2 )] . 16. TR dc =. (4.12c). 1 [4a 2 + 5(c12 + c 22 ) − 6c1c 2 − 4a(c1 + c 2 )] . 32. (4.12d). Proposition 4.1: The ranking of optimal discriminatory tariff, tariff revenue and. social. welfare. among. TR ds > TR dm > TR dc , and. different W. ds. >W. delegation dm. >W. dc. forms. are t idc > t idm > t ids. ,. .. 3. See Hwang and Mai (1991) and Kuo and Hwang (1991) for deriving the same results in the case of discriminatory tariffs except in ours b = 1 . 35.

(46) The reason for the results is the following： Jansen et al. (2007) showed that the degree of competition in market share lies between Cournot competition and sales delegation. Hence, the ranking of output is q s > q m > q c . So, for maximization of domestic welfare, domestic government will impose the highest tariff in Cournot competition, and the lowest is in sale delegation.. The tariff rate difference is. t1dm − t 2dm = t1dc − t 2dc = t1ds − t 2ds =. 1 (c 2 − c1 ) . 2. (4.11). Corollary 4.1: From the equation (4.10), we see that domestic government will. charge a higher tariff to the foreign exporting country with a lower marginal cost of production, but the tariff rate difference equals half the marginal cost difference, regardless of the managerial delegation forms.. 4.3 Uniform Tariff Case Ι. Market Share Delegation. Consider the case that the domestic government has less than full discretionary power in setting tariff rates, and sets uniform tariff instead.. 36.

(47) Stage I. Stage II. Stage III. Time. Domestic government decides the uniform tariff rate.. Both foreign owners choose the market share delegation incentive to their managers to maximize profit.. Both foreign managers compete in quantity in domestic market.. Figure 4.3 Game stages of import-competing model with market share delegation in uniform tariff.. Now, equation (2.1) and (2.2) becomes α ∂g 1 = a − 2q1 − q 2 − (c1 − t ) 1 = 0 ∂q1 q1. (4.12). α ∂g 2 = a − q1 − 2q 2 − (c 2 − t ) 2 = 0 ∂q 2 q2 and ∂π 1 ∂q ∂q = 0 ⇔ 1 [a − c − 2q1 − q 2 − t ] − q1 2 = 0 ∂α 1 ∂α 1 ∂α 1. (4.13). ∂q ∂q ∂π 2 = 0 ⇔ 2 [a − c − q1 − 2q 2 − t ] − q 2 1 = 0 ∂α 2 ∂α 2 ∂α 2 ⎡ ∂F1 ⎢ where ∂q1 = − 1 det ⎢ ∂α 1 ⎢ ∂F2 ∂α 1 J F ⎢ ⎣ ∂α 1 ⎡ ∂F1 ⎢ ∂q ∂q 2 −1 = det ⎢ 1 ⎢ ∂ F2 ∂α 2 J F ⎢ ⎣ ∂q 1. ∂F1 ⎤ ⎡ ∂F1 ⎢ ∂q ⎥ ∂q 2 , ∂q 2 −1 ⎥ = det ⎢ 1 ⎢ ∂F2 ∂ F2 ⎥ ∂ α 1 J F ⎢ ⎥ ∂q 2 ⎦ ⎣ ∂q1. ∂F1 ⎤ ∂α 1 ⎥ , ⎥ ∂F2 ⎥ ⎥ ∂α 1 ⎦. ∂F1 ⎤ ⎡ ∂F1 ⎢ ∂α ⎥ ∂α 2 , and ∂q1 −1 ⎥ = det ⎢ 2 ⎢ ∂ F2 ∂F2 ⎥ ∂α 2 J F ⎢ ⎥ ∂α 2 ⎦ ⎣ ∂α 2. ∂F1 ⎤ ∂q 2 ⎥ . ⎥ ∂ F2 ⎥ ⎥ ∂q 2 ⎦. We simultaneously solve (4.12) and (4.13) to get q1 = q1 (t ) , q 2 = q 2 (t ) , α 1 = α 1 (t ) ,. 37.

(48) and α 2 = α 2 (t ). And then substituting them into stage 1 to maximize domestic social welfare, W =. (q1 + q 2 ) 2 + t (q 1 + q 2 ) . 2. ∂W 1 = [2(10 − 2 )a − (10 − 2 )(c1 − c2 ) − 4(19 + 3 2 )t ] = 0 ∂t 98. (4.14). which yields. t um =. 1 (4 − 2 )(2a − c1 − c 2 ) . 28. (4.15). Hence. q1um =. 1 [2(3 + 2 )a − (17 + 8 2 )c1 + (11 + 6 2 )c 2 ] , 28. (4.16a). q 2um =. 1 [2(3 + 2 )a + (11 + 6 2 )c1 − (17 + 8 2 )c 2 ] , 28. (4.16b). W um =. 1 (4 + 2 )(10 + 2 )(−2a + c1 + c 2 ) 2 , 784. (4.16c). TR um =. 1 (4 − 2 )(3 + 2 )(−2a + c1 + c 2 ) 2 . 392. (4.16d). 38.

(49) Case Ⅱ Sales Delegation Now we consider the case of sales delegation.. Stage I. Stage II. Stage III. Time. Domestic government decides the uniform tariff rate.. Both foreign owners choose the sales delegation incentive to their managers to maximize profit.. Both foreign managers compete in quantity in domestic market.. Figure 4.4 Game stages of import-competing model with sales delegation in uniform tariff.. The equation (2.1) and (2.2) rewrite as. ∂g1 = a − 2q1 − q 2 − (c1 − t )α 1 = 0 ∂q1. (4.17). ∂g 2 = a − q1 − 2q 2 − (c 2 − t )α 2 = 0 ∂q 2 and. ∂q ∂q ∂π 1 = 0 ⇔ 1 [a − c − 2q1 − q 2 − t ] − q1 2 = 0 ∂α 1 ∂α 1 ∂α 1 ∂q ∂q ∂π 2 = 0 ⇔ 2 [a − c − q1 − 2q 2 − t ] − q 2 1 = 0 ∂α 2 ∂α 2 ∂α 2 ⎡ ∂F1 ⎢ where ∂q1 = − 1 det ⎢ ∂α 1 ⎢ ∂F2 ∂α 1 J F ⎢ ⎣ ∂α 1. ∂F1 ⎤ ⎡ ∂F1 ⎢ ∂q ⎥ ∂q 2 , ∂q 2 −1 ⎥ = det ⎢ 1 ⎢ ∂F2 ∂ F2 ⎥ ∂ α 1 J F ⎢ ⎥ ∂q 2 ⎦ ⎣ ∂q1. (4.18). ∂F1 ⎤ ∂α 1 ⎥ , ⎥ ∂F2 ⎥ ⎥ ∂α 1 ⎦. 39.

(50) ⎡ ∂F1 ⎢ ∂q ∂q 2 −1 = det ⎢ 1 ⎢ ∂ F2 ∂α 2 J F ⎢ ⎣ ∂q 1. ∂F1 ⎤ ⎡ ∂F1 ⎢ ∂α ⎥ ∂α 2 , and ∂q1 −1 ⎥ = det ⎢ 2 ⎢ ∂ F2 ∂F2 ⎥ ∂α 2 J F ⎢ ⎥ ∂α 2 ⎦ ⎣ ∂α 2. ∂F1 ⎤ ∂q 2 ⎥ . ⎥ ∂ F2 ⎥ ⎥ ∂q 2 ⎦. We simultaneously solve (4.17) and (4.18) to get q1 = q1 (t ) , q 2 = q 2 (t ) , α 1 = α 1 (t ) , and α 2 = α 2 (t ). And then substituting them into stage 1 to maximize domestic social welfare, W =. (q1 + q 2 ) 2 + t (q 1 + q 2 ) . 2. ∂W 2 = (2a − c1 − c2 − 12t ) = 0 , ∂t 25. (4.19). which yields. t us =. 1 ( 2 a − c1 − c 2 ) . 12. (4.20). Hence,. q1us =. 1 1 (2a − 7c1 + 5c 2 ) , q1us = (2a + 5c1 − 7c 2 ) , 6 6. W us =. 1 ( −2 a + c1 + c 2 ) 2 , 12. TR us =. 1 ( −2 a + c1 + c 2 ) 2 . 36. (4.21a). (4.21b). (4.21c). Comparing equilibrium outcomes of optimal uniform tariff, output, welfare, and tariff revenue with the case of Cournot competition,. t uc =. 1 ( 2 a − c1 − c 2 ) , 8. 1 1 q1uc = (2a − 5c1 + 3c 2 ) , q 2uc = (2a + 3c1 − 5c 2 ) , 8 8. (4.22a). (4.22b). 40.

(51) W uc =. 1 ( −2a + c1 + c 2 ) 2 , 16. (4.22c). TR uc =. 1 ( −2 a + c1 + c 2 ) 2 . 32. (4.22d). We then have the following proposition. Proposition 4.2: The ranking of optimal uniform tariff rate, tariff revenue, and social. welfare with different delegation forms are t u c > t um > t us , TR us > TR um > TR uc , and W. us. >W. um. >W. uc. . The ranking is the same as discriminatory case, regardless. of the delegation forms. From propositions 4.1 and 4.2, we obtained the similar results even in the presence of managerial incentive. Corollary 4.2: Regardless of the delegation forms, uniform tariff is favorable for the. low marginal cost of firm, and discriminatory tariff is advantageous to the high marginal cost of firm. For example, by adding equation (4.5a), (4.5b), (4.16a), and (4.16b), we get Q dm ≡ q1dm + q 2dm = Q um ≡ q1um + q 2um =. 1 (3 + 2 )(2a − c1 − c2 ) , the case of market share 14. delegation. It means that the import quantities are the same regardless of discriminatory tariff or uniform tariff.. Further, form demand function,. p = a − q1 − q 2 , we know that the equilibrium price under discriminatory and uniform. tariff are the same. If this assumed that the marginal cost of firm 1 is lower than firm 2, then according to (4.5a), (4.5b), (4.16a), and (4.16b), we can find that q 1dm > q. dm 2. and q 1um > q 2um . By the same token,. 1 Q ds ≡ q1ds + q 2ds = Q us ≡ q1us + q 2us = (2a − c1 − c 2 ) , the case of sales delegation. Uniform 3 41.

(52) tariff is still favorable for the low marginal cost of firm, and discriminatory tariff is advantageous to the high marginal cost firm. The difference of tariff revenue and social welfare under different tariff regimes are 4. W dm − W um = TR dm − TR um =. W ds − W us = TR ds − TR us =. 1 (2 + 2 )(c1 − c 2 ) 2 > 0 , 16. (4.23a). 1 (c1 − c 2 ) 2 > 0 . 4. (4.23b). Table 4.1 Change of social welfare under different tariff regime Market-share Delegation dm um Welfare φ = W − W 1 = (2 + 2 )(c1 − c 2 ) 2 16. Sales Delegation ψ = TR ds − TR us =. φ<ψ. 1 (c1 − c 2 ) 2 4. From Table 4.1, we can further see the change of tariff revenue and social welfare under different tariff regime. Proposition 4.3: Even though Q dm = Q um and Q ds = Q us , social welfare and tariff. revenue is higher under discriminatory tariff than under uniform tariff, regardless of the delegation forms. The social welfare and tariff revenue improve with sales delegation than with market share delegation under discriminatory tariff regime.. 4. The welfare equals tariff revenue plus consumer surplus. But the difference of consumer surplus (CS). equals zero. For example, CS dm =. ( q1dm + q 2dm ) 2 ( q um + q 2um ) 2 and CS um = 1 . And from Corollary 2 2. 2, we have Q dm = Q um , so CS − CS = 0 . Hence, under different tariff regimes, the difference of social welfare equals the difference of tariff revenue. dm. um. 42.

(53) 4.4 Concluding Remark In this paper, we constructed a model un that domestic country does not produce goods, importing from two foreign countries and imposes a discriminatory or uniform tariff on import goods. We demonstrated that whether it is discriminatory or uniform tariff rate, the optimal tariff rate is the highest under Cournot competition, and sales delegation is the least. We also showed that domestic government will charge a higher tariff to the foreign exporting country with a lower marginal cost of production, but the tariff rate difference equals half the marginal cost difference, regardless of managerial delegation forms. Furthermore, we obtained that the social welfare and tariff revenue is higher with sales delegation than market share delegation under discriminatory tariff regime.. 43.

(54) CHAPTER FIVE: CONCLUSIONS This thesis of the main purpose is to examine export subsidy and import tariff policy in international oligopoly with managerial delegation. The results can be dividend into three main parts. In chapter two, in order to deal with three-stages game, we construct a new market share delegation form which not only preserves the spirit of Jansen et al. (2007) but also becomes useful in dealing with the three-stage game of concerned issues as well, and furthermore we showed in a duopoly mode, if only one firm adopt delegation, regardless of market share delegation or sales delegation, it acts as Stackelberg leader. In chapter three, we extend the model in chapter two to apply in international oligopoly and discuss the optimal subsidy policy. Here we demonstrated that delegation and export subsidy is substitutable for profit-shifting. Considering the timing of instrument choice with one-sided delegation, in a sequentially chosen instrument game, the foreign government pre-commits export subsidy to its entrepreneurial firm, such policy is used to shift profit from a rival firm; in consequence, the home government “stays put” without intervention and let the private sector provides incentives to its managers for competing with the foreign rival firm, sales delegation and market share delegation are substitutable. However, in a simultaneously chosen instrument game, the domestic firm and foreign government commit strategic instruments simultaneously; sales delegation and export subsidy are substitutable, but market-share delegation is a welfare-dominant strategy. Furthermore, for the case of two-sided delegation, the welfare of both countries under market share delegation is higher than that of sales delegation whether one country or two countries intervene. At end, we must point out that in the case of bilateral choices of incentives, 44.

(55) two export firms are involved in a “Prisoner’s Dilemma”, but market share delegation is in less degree. In chapter four, we constructed a model that domestic country does not produce goods, importing from two foreign countries and imposes a discriminatory or uniform tariff on import goods. We demonstrated that whether it is discriminatory or uniform tariff rate, the optimal tariff rate is the highest under Cournot competition, and sales delegation is the least. We also showed that domestic government will charge a higher tariff to the foreign exporting country with a lower marginal cost of production, but the tariff rate difference equals half the marginal cost difference, regardless of managerial delegation forms. Furthermore, we obtained that the social welfare and tariff revenue is higher with sales delegation than market share delegation under discriminatory tariff regime.. 45.