Resource Rivalry and Endogenous Lobby

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(1)Japan and the World Economy 18 (2006) 488–511 www.elsevier.com/locate/econbase. Resource rivalry and endogenous lobby Jue-Shyan Wang a,, Hui-wen Koo b, Tain-Jy Chen b a. Department of Public Finance, National Chengchi University, Taipei, Taiwan b Department of Economics, National Taiwan University, Taipei, Taiwan. Received 30 September 2003; received in revised form 11 December 2004; accepted 22 December 2004. Abstract We present a two-sector model to depict the determination of trade preference. The model highlights lobby as a rivalry between sectors in competition for resources where the outcome of the lobby race is determined by each sector’s ability to generate rent at a given welfare cost to the general population. We investigate the relation between the structure of trade protection and the resource endowment. # 2005 Elsevier B.V. All rights reserved. JEL Classification: F13; D72 Keywords: Trade protection; Resource allocation; Auction. 1. Introduction It is increasingly recognized that government interventions in trade are as certain as government impositions of tax. There is also increasing interest among economists to offer an interpretation for this almost universal phenomenon. This can be seen in the voluminous literature known as the political economy of trade (for a survey, see Helpman, 1995).1 One of the most brilliant models is offered by Grossman and Helpman (1994), which depicts the formation of trade policy as the result of an interaction  Corresponding author. Present address: Department of Public Finance, National Chengchi University, 64 Tznan Road, Sector 2, Taipei 11623, Taiwan. Tel.: +886 2 29393091x51538; fax: +886 2 29390074. E-mail address: jswang@nccu.edu.tw (J.-S. Wang). 1 Besides the research cited by Helpman, more traditional literature includes Tullock (1967); Bhagwati (1968, 1980, 1982); Becker (1983, 1985).. 0922-1425/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.japwor.2004.12.003.

(2) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 489. between the government and interest groups. The government is concerned with the welfare of the general population as well as political contributions that can be obtained from interest groups to finance election campaigns to keep itself in power. Interest groups, knowing the government’s need for political support, make contributions to influence the choice of trade policies. In short, it is the government’s need for political support that makes trade intervention inevitable. The government offers ‘trade protection for sale’ to raise funds to keep itself in power. Trade protection is almost a necessary evil in any democracy. If that is the case, then it is interesting to ask whether income levels will make a difference to the level and the structure of trade protection. Will a country’s trade regime come closer to free trade as its per-capita income rises? If so, then at least we may expect all countries ultimately to convert to free trade if their incomes are high enough. We should therefore be patient and understand developing countries’ resistance to trade liberalization programs such as those championed by World Trade Organization. It is also interesting to note that some countries give preference to the export sector, while others favor the import-competing sector and that the preference may also change over time. For example, the focus of US trade policy was to protect weak sectors (importing) before the 1980s, and the focus was shifted to assisting strong sectors (exporting) in securing access to foreign markets. How is this related to the structure of the economy? The purpose of this paper is to offer some answers to these questions. We present a two-sector model in line with Grossman and Helpman’s concept of making political contributions for policy favors.2 The model highlights the rivalry between sectors in competition for policy favors in a game-theoretic setting. Compared to the Grossman and Helpman (1994) paper in which a multi-sector model is adopted to describe the nature of equilibrium, the simplicity of the two-sector model offers several advantages. It allows us to explicitly identify the degree of political contribution as the one that maximizes the lobbyist’s net income while keeping the rival lobby at bay. It allows us to examine the relations between the resource endowment and the structure of protection. An industry may be forced to lobby even if it knows that free trade is a superior outcome. In fact, the rivalry between sectors makes free trade an infeasible political choice. Whether a government adopts a policy in favor of its export sector or importcompeting sector, depends, among other things, on factor intensity and the size of the respective sectors. There is no guarantee that rising incomes will turn a protectionist into a free-trade believer. Growth can make a country deviate away from, or move closer to free trade. In particular, balanced growth, in the sense that both sectors grow at the same rate, will not change the structure of protection, whereas unbalanced growth will. The rest of the paper is organized as follows. The basic model is set up in Section 2. Section 3 characterizes the equilibria of our lobbying game, and compares them with the equilibria in a menu auction which was originally studied by Grossman and Helpman. 2. A similar framework is also applied in some other research. See Cadot et al. (1997); Mitra (1999); Olarreaga (1999); Goldberg and Maggi (1999)..

(3) 490. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. (1994). Then comparative statistics is analyzed in Section 4. The last section concludes with our discussion. 2. The model We consider a small open economy with two goods and three factors. The population of L people provide inelastic labor and among them, two capitalists own specific factors to produce goods 1 and 2, respectively. We use Ki to denote the quantity of the specific factor for good i. 2.1. Consumption Consumers are assumed to have the Leontief utility function:3 uðx1 ; x2 Þ ¼ min fx1 ; x2 g; where xi denotes the consumption of good i. Let good 1 be the numeraire good, p the relative price of good 2 in the domestic market, and I the combined disposable income of all consumers. The aggregate demands for these two goods are: I : (1) x1 ¼ x2 ¼ 1þ p Let yi denote the domestic output of good i. The disposable income is: I ¼ y1 þ py2  Tð pÞ; (2) where Tð pÞ is the tax raised (or subsidy paid) to maintain trade protection. When the domestic price p is set different from the international price p , the government has a tax revenue (or a subsidy payment) of: Tð pÞ ¼ ð p  p Þðx2  y2 Þ: (3) When p > ð < Þ p , there is an import tariff (subsidy) for good 2 if x2 > y2 ; and an export subsidy (tax) for good 2 if x2 < y2 . (1)–(3) imply: y 1 þ p y 2 x1 ¼ x2 ¼ : (4) 1 þ p To simplify the analysis, in the following, we shall assume the tax rate t to be invariant with income: t¼. Tð pÞ : ðy1 þ py2 Þ. (5). 2.2. Production Each good is assumed to be monopolized by the specific factor owner, whose production function is: yi ¼ Ki Lbi i ; 3. bi 2 ð0; 1Þ; i ¼ 1; 2;. Hence, their demand functions and indirect utility functions could be aggregated.. (6).

(4) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 491. where Li denotes the labor input. Though the production technology appears to be increasing returns to scale, this paper does not exploit this property, since Ki is exogenously given in our model. Facing the domestic product price p and wage rate w, capitalist i, who has a Leontief preference, chooses the labor employment to maximize his net real income (in terms of a pair of goods 1 and 2): 8 ð1  tÞ > > ½K1 Lb11  wL1  for i ¼ 1; < max L1 1 þ p pi ð pÞ ¼ ð1  tÞ > > : max ½ pK2 Lb22  wL2  for i ¼ 2: L2 1 þ p In the labor market, the equilibrium wage equates the value of the marginal product of labor in two sectors4: w ¼ b1 K1 L1b1 1 ¼ b2 pK2 L2b2 1 ;. (7). and the market clear condition for labor is: L ¼ L 1 þ L2 :. (8). 2.3. The government For any domestic price p set by the government, the equilibrium wage rate and labor allocation are determined by (7) and (8). The output of each industry yi ð pÞ and the capitalist’s real income pi ð pÞ are then in turn determined. Because the capitalist’s wellbeing hinges upon domestic product price p, each considers tendering offer Ci ði ¼ 1; 2Þ to lobby for a favorable price. To facilitate future analysis, the unit of Ci is set to be a pair of two goods. Following Grossman and Helpman (G&H), we assume the government to be concerned about both the political contributions from lobbyists and social welfare. The latter concern becomes important in view of future elections. From (4), summing up individuals’ utilities, the social welfare V is:5 y1 ð pÞ þ p y2 ð pÞ Vð p; p Þ ¼ : (9) 1 þ p Let a denote the weight the government gives to social welfare. Taking the weight given to political contributions as unity, the government’s utility is: G ¼ max ½C1 þ aVð p1 ; p Þ; C2 þ aVð p2 ; p Þ; aVð p ; p Þ;. a > 0:. The lobby will be formulated as a two-stage game. At the first stage, two capitalists simultaneously propose a package of a domestic price and the political contribution to be tendered: ð pi ; Ci Þ, i ¼ 1; 2. The government then evaluates their proposals. We shall solve the game for its subgame perfect equilibrium (SPE), which consists of no weakly dominated strategies. 4 In general, the wage will not be equal to the value of the marginal product of labor when the labor market is a duopsony. However, our analysis remains valid if one considers a lobbyist in the model as a representative agent of a few suppliers who own the same specific factor and form a lobby group. 5 G&H instead assume wage to be fixed, and their welfare is defined in terms of consumers’ surplus derived from quasilinear utility functions..

(5) 492. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 3. The SPE of the lobbying game In our setting, the lobby race is triggered by a rivalry over limited resources, namely, labor. The profit of capitalist i can be derived as: pi ð pÞ ¼ Vð pÞsi ð pÞð1  bi Þ;. i ¼ 1; 2;. (10). where 1  bi is capitalist i’s share of the sector’s gross product, and si is sector i’s share in GDP: y1 s1 ð pÞ ¼ ; s2 ð pÞ ¼ 1  s1 ð pÞ: (11) y1 þ py2 In (10), the free-trade term p maximizes Vð pÞ, but not si ð pÞ. Fig. 1 illustrates how the domestic price p determines labor allocation, and hence the sector’s share in GDP. If we raise the domestic price p in Fig. 1, capitalist 1 will receive less labor L1, and hence produce less y1 . At the same time, L2 and y2 both increase. The total effect is: Lemma 1. s1 ð pÞ decreases in p, and s2 ð pÞ increases in p. In the following, we shall first explain intuitively how capitalist i designs his package ð pi ; Ci Þ of policy proposal, and then present the technical details. To promote ð pi ; Ci Þ, i has to keep government’s utility, i.e. Ci þ aVð pi Þ, high enough; and at the mean time, to enhance his own utility, pi ð pi Þ  Ci . In view of this, Ci serves as a pure transfer between i and the government and pi should be chosen to maximize the joint utilities Wi : max Wi ð pÞ ¼ pi ð pÞ þ aVð pÞ; i ¼ 1; 2: (12) p. From (10), we can rewrite the joint utilities as: Wi ð pÞ ¼ Vð pÞ½ð1  bi Þsi ð pÞ þ a. Fig. 1. Labor allocation. Note: MPi denotes the marginal product of labor in sector i.. (13).

(6) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 493. Let p¯ i denote the price that maximizes Wi . The following lemma characterizes p¯ i . Its proof is given in the Appendix A. Lemma 2. (a) p¯ 2 > p > p¯ 1 . (b) p1 ð p Þ > p1 ð p¯ 2 Þ and p2 ð p Þ > p2 ð p¯ 1 Þ. It turns out that the party whose p¯ i yields a higher sum of utilities of all players in the ˙ i denote game, including two capitalists and the government, is the successful lobby. Let W this sum: ˙ i  p1 ð p¯ i Þ þ p2 ð p¯ i Þ þ aVð p¯ i Þ; i ¼ 1; 2: (14) W ˙ i and Wi ð p¯ i Þ is i’s opponent’s utility. This is important to i, The difference between W because if his proposed price p¯ i does not harm the opponent’s utility much, the opponent will not react by a strong counter-lobby. The following two propositions provide the necessary and sufficient conditions for SPE involving no weakly dominated strategies. Their proofs are given in the Appendix A. Proposition 1. Let Gi (G j ) denote the government’s payoff if she adopts i’s (j’s) equilibrium proposal. When i wins and j loses in equilibrium, the SPE with no weakly dominated strategy played satisfies the following conditions: Gi ¼ G j ;. (15). pi ¼ p¯ i ;. (16). p j ¼ p¯ j ;. (17). Ci ¼ C j þ aVð p¯ j Þ  aVð p¯ i Þ;. (18). C j  p j ð p¯ j Þ  p j ð p¯ i Þ;. (19). ˙ j; ˙iW W. (20). ˙ j ; p j ð p¯ i Þg  0: ˙i W Let k  min fW  Cj. ˙i W ˙ j < p j ð p¯ i Þ  p j ð p¯ j Þ  p j ð p¯ i Þ þ k; if W < p j ð p¯ j Þ  p j ð p¯ i Þ þ k; otherwise:. (21). ˙ j , j ¼ 3  i, the following strategy profile is an SPE with no ˙iW Proposition 2. When W weakly dominated strategy played: (a) ð pi ; Ci Þ and ð p j ; C j Þ are proposals that satisfy (16)– (19)and (21). (b) Considering any proposals ð pi ; Ci Þ and ð p j ; C j Þ, the government maintains p ¼ p , if aVð p Þ > max fCi þ aVð pi Þ; C j þ aVð p j Þg. Otherwise, it shall accept i’s (j’s) proposal when Ci þ aVð pi Þ  ð < ÞC j þ aVð p j Þ. In equilibrium, not only is the losing party’s profit lower than that in free trade (Lemma 2(b)), the winning lobbyist may also end up with a lower profit after paying his.

(7) 494. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. political donations, and the government turns out to be the sole winner.6 The following corollary shows when this will occur. Its proof is given in the Appendix A. Corollary 1. Let i and j denote the winning and losing sector, respectively. When bi ¼ b j ¼ b, or when bi > b j , either lobbyist ends up with a lower profit than what he earns in free trade. When the precondition of the above corollary does not hold, the winning lobby does have a chance to earn more than under free trade. For instance, consider the case in which b1 ¼ 3=4, b2 ¼ 1=4, a ¼ 1, p ¼ 1, L ¼ 100 and K2 ¼ 10. Suppose the political gifts are at their minimum values, i.e. k ¼ 0 in (21). It can be shown that capitalist 2 is the winning lobby when K1 is either as small as 1 or as large as 161. In the former (latter) case, capitalist 2 earns more (less) profits than under free trade. 3.1. Menu auction This section relates our bidding game to the menu auction studied by G&H. In G&H’s model, lobbyist i proposes a contribution schedule fi ð pÞ that indicates how his political donation will vary with the domestic price to be chosen. Considering these menus, the problem of the government is: max f1 ð pÞ þ f2 ð pÞ þ aVð pÞ: p. Proposition 3. For any SPE in our game with proposals fð p¯ i ; Ci Þgi¼1;2 which involve no weakly dominated strategies, there exists a corresponding SPE in the menu auction, with f fi ð pÞgi¼1;2 constructed as follows:  Ci ; if p ¼ p¯ i for i ¼ 1; 2: (22) fi ð pÞ ¼ 0; otherwise Proof. See the Appendix A.. &. Though our game is closely related to the menu auction as Proposition 3 demonstrates, the literature of menu auction focuses on other equilibria than those depicted in Propositions 1 and 2. In their pioneering study, Bernheim and Whinston (B&W, 1986, pp. 4–6) point out there are multiple equilibria in a menu auction, and they propose the truthful Nash equilibrium (TNE) may be focal. In a TNE, the contribution schedule fi ð pÞ reflects the true preference of bidder i, and it is shown that: (i) Bidder i’s best response correspondence always contains a truthful strategy, so there is no loss to i to restrict himself to playing truthfully. (ii) TNE are coalition-proof. G&H (1994, p. 841) instead consider bidders to use differentiable contribution schedules. In their model, this leads to the same 6. In this case, to lobbyists, it is a game even worse than the contest analyzed by Posner (1975), in which firms compete to become a monopolist, and the rent-seeking expenses just break even with the expected rent..

(8) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 495. measure of trade protection as the TNE predicts, and when evaluating the political contributions, in face of multiple (differentiable) equilibrium schedules, G&H restrict the analysis to the TNE. The contribution schedules derived from the SPE of our game are neither differentiable nor truthful. If we follow B&W’s or G&H’s line of thinking, when holding a menu auction, the government does not expect schedules in (22) to be submitted. In the following, we shall show schedules in (22) yield a higher payoff to the government than the TNE. If the government ever has a choice between our game and the menu auction, it is to its advantage to auction off protection in our way to realize an unlikely result in the menu auction. Let p¯ denote the domestic price realized in the TNE in a menu auction, and n¯ i the net payoff of i in equilibrium, n¯ i  pi ð p¯ Þ  fi ð p¯ Þ. Theorem 2 by B&W characterizes the TNE with the following conditions: ˆ pÞ ¼ p1 ð pÞ þ p2 ð pÞ þ aVð pÞ; (23) p¯ ¼ argmax p Wð and ð¯n1 ; n¯ 2 Þ lies on the Pareto frontier of the following set: fðn1 ; n2 Þ 2 R2 jn1  p1 ð p¯ Þ þ p2 ð p¯ Þ þ aVð p¯ Þ  ðp2 ð p¯ 2 Þ þ aVð p¯ 2 ÞÞð  xÞ; n2  p1 ð p¯ Þ þ p2 ð p¯ Þ þ aVð p¯ Þ  ðp1 ð p¯ 1 Þ þ aVð p¯ 1 ÞÞð  yÞ; n1 þ n2  p1 ð p¯ Þ þ p2 ð p¯ Þ þ aVð p¯ Þ  aVð p Þð  zÞg;. (24). where p¯ i is the price that maximizes Wi ð pÞ in (12). The above result characterizes a different prediction about the trade policy from ours, as demonstrated by the following proposition, the proof for which is given in the Appendix A. Proposition 4. (a) When b1 ¼ b2 ¼ b, p¯ 2 > p ¼ p¯ > p¯ 1 . (b) When b1 < b2 , p¯ 2 > p > p¯ > p¯ 1 . (c) When b1 > b2 , p¯ 2 > p¯ > p > p¯ 1 .7 In a menu auction, the government’s payoff is: Gm ¼ aVð p¯ Þ þ ðp1 ð p¯ Þ  n¯ 1 Þ þ ðp2 ð p¯ Þ  n¯ 2 Þ: Consider an SPE with no weakly dominated strategy played in our game, and let Gi denote the government’s payoff in equilibrium. The following proposition compares the government’s payoff in our game and in the menu auction. The proof is provided in the Appendix A. Proposition 5. Gm < Gi . Comparing (12) and (23), it is easy to see that the total payoff to three players is higher in the menu auction. Proposition 5 still stands, thanks to lobbyists being more generous in donations in our game. This is because in our game a lobbyist bids against one drastic 7. We thank Professor Grossman for providing this result..

(9) 496. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. condition proposed by the opponent; while in a menu auction, even if his ideal condition is not fulfilled, there is a spectrum of possible outcomes.. 4. Comparative statics The analysis in Section 3 shows that the domestic price is always lobbied away from the international price in our game. This section will continue to study how this price distortion changes with the political and economic environment. In the following, we shall first study how capitalist i’s proposed price p¯ i changes with a, p , L, K1 and K2 . We then study which sector becomes in favor as the domestic resources L, K1 and K2 change. 4.1. Individual proposals Proposition 1 states that capitalist i’s proposed price p¯ i maximizes Wi . (9) and (13) together show how the domestic production activities y1 and y2 determine V and hence Wi . In our model, the variable inputs that determine y1 and y2 are labors L1 and L2 . Therefore, to find the domestic price p that maximizes joint utilities Wi , we have to first analyze how p affects the labor allocation. In the following, we shall consider the interior solution. Let z;s denote the derivative of z with respect to s. From (7) and (8), it can be derived that: L1; p ¼ . L1 L2 < 0; p½ð1  b1 ÞL2 þ ð1  b2 ÞL1 . L2; p ¼ L1; p > 0:. With the Cobb–Douglas production function, we then have: y1; p b1 b 2 y 1 y 2 p > 0: < 0; y2; p ¼  y1; p ¼  b1 ð1  b2 Þy1 þ b2 ð1  b1 Þ py2 p. (25). Because two sectors’ lobbied price p¯ i ’s are derived in the same manner, in the following, we shall discuss the case of sector 1 only. The study naturally extends to sector 2. (9), (13) and (25) imply that to maximize W1 , p¯ 1 has to satisfy the following FOC: y1 y2 ðb1 y1 þ b2 py2 Þ ð1 þ p Þ½b1 ð1  b2 Þy1 þ b2 ð1  b1 Þ py2  ( ðy1 þ p y2 Þð1  b1 Þ ð1  b1 Þy1 þ aðy1 þ py2 Þ þ   y1 þ py2 ðy1 þ py2 Þ2 )  b1 b2 ð p  pÞ   ¼ 0:  pðb1 y1 þ b2 py2 Þ . W1; p j p¼ p¯ 1 ¼. (26). p¼ p¯ 1. To see the impact of change in the domestic political environment or the international market conditions on the lobbied price p¯ 1 , we differentiate W1; p with respect to a and p , respectively. Let z;st denote the second derivative of z with respect to s and t. It can be shown that: W1; pa j p¼ p¯ 1 > 0;. W1; p p j p¼ p¯ 1 > 0;. At the interior solution, W1; p p j p¼ p¯ 1 < 0. It follows immediately that:.

(10) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 497. Proposition 6. (a) When the government is more concerned about social welfare, both sectors will propose prices closer to the international level, i.e. when a is larger, p¯ 1 rises, and p¯ 2 falls. (b) When the international price of good 2, p , becomes higher, both p¯ 1 and p¯ 2 become higher. The intuition of Proposition 6 is as follows. From Lemma 2, p¯ 2 > p > p¯ 1 , i.e. each capitalist lobbies to enhance the relative price of his good above the international level. This harms social welfare, and when social welfare becomes a more important concern to the government, both capitalists have to concede to propose a price closer to the international level. On the other hand, for sector i, p¯ i shows the optimal deviation from the international price p . When p becomes higher, we expect p¯ i to be adjusted in the same direction. We now turn to see how the lobbied price p¯ i changes when capitals K1 and K2 grow. To differentiate W1; p in (26) with respect to K1 , we have:   0 if b1 > b2 and a is big enough; (27) W1; pK1 j p¼ p¯1 > 0 otherwise: This implies that   W1; pK1  @ p¯ 1 0 ¼ >0 @K1 W1; p p  p¼ p¯. if b1 > b2 and a is big enough; otherwise:. (28). 1. The intuition is as follows. From Lemma 1, to lower the domestic price p will increase sector 1’s share in GDP, s1 ð pÞ. This has a positive effect on W1 in (13). On the other hand, to lower p further away from the international price p reduces the welfare Vð pÞ, and hence W1 . How low capitalist 1 should push down the domestic price depends upon the trade-off between these two conflicting forces. At p¯ 1 , the marginal effects of these two forces should be equal. When sector 1’s capital K1 grows, MP1 curve in Fig. 1 shifts up, and without lowering the domestic price p, we observe that L1 (L2 ) increases (decreases) and sector 1’s share s1 ð pÞ increases as a result. This implies that although lowering p still helps to enhance sector 1’s share s1 ð pÞ, its effect becomes limited. So, we expect @ p¯ 1 =@K1 > 0. The exceptional case is when b1 > b2 and a is very large. In light of (12), when a ! 1, because the government cares deeply about social welfare, sector 1 cannot propose allowing the domestic price p to deviate from the international price p much, i.e. p¯ 1 ! p . Because Vð pÞ is maximized at p ¼ p , dVð pÞ=d pj p¼ p ¼ 0. That means when a ! 1, dVð pÞ=d pj p¼ p¯ 1 ! 0: the marginal harm a smaller p brings to Vð pÞ is limited. Thus, capitalist 1 could consider enhancing his share s1 ð pÞ by lowering p, especially when this share enhancement is backed up by a production advantage, i.e. when the productivity of labor is higher in sector 1 (b1 > b2 ) and when sector 1’s capital K1 increases. A similar result holds when the capital in sector 2 increases. To differentiate W1; p in (26) with respect to K2 , we have W1; pK2 ¼ W1; pK1 K1 =K2 . That implies:   W1; pK2  @ p¯ 1  0 if b1 > b2 and a is big enough; ¼ (29)  < 0 otherwise: @K2 W1; p p p¼ p¯ 1. In reality, capital in different sectors changes at the same time. Suppose K1 and K2 have the same growth rate: r. For any domestic price p, the labor allocation Li ð pÞ dictated in (7) and (8) does not change after the growth of K1 and K2 . This implies the output yi ð pÞ in (6).

(11) 498. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. grows at the rate r, for i ¼ 1; 2. It follows that the welfare Vð pÞ in (9) grows at the same rate, while sectors’ shares si ð pÞ in (11) stay the same. In total, the joint utility W1 ð pÞ in (13) becomes 1 þ r times its original value for any p. It follows immediately that: Proposition 7. When K1 and K2 grow at the same rate, p¯ 1 and p¯ 2 remain the same. When the growth rate of K1 is larger than that of K2 , we can reason the change of p¯1 in two steps. First, imagine that K1 only grows at the same rate as K2 . From Proposition 7, this causes no change to p¯ 1 . Now, consider K1 continues to grow to its full amount while K2 stays the same; p¯ 1 will then change according to (28). The same thought experiment can be made for all other possible cases, and the results are summarized as follows. Proposition 8. Consider a case in which K1 grows at a higher (lower) rate than K2 . (a) p¯ 1 becomes lower (higher), when b1 > b2 and a is sufficiently large; and in all other conditions, p¯ 1 becomes higher (lower). (b) p¯ 2 becomes lower (higher), when b2 > b1 and a is sufficiently large; and in all other conditions, p¯ 2 becomes higher (lower). Lastly, we shall study the impact of population growth on the lobbied price p¯ i . To differentiate W1; p with respect to L, we have: 8  0 if b1 > b2 and a is small enough; K1 ðb1  b2 Þ < W1; pL j p¼ p¯ 1 ¼ W1; pK1 ¼ 0 if b1 ¼ b2 ; : L < 0 otherwise: This along with (27) implies: Proposition 9. (a) When b1 ¼ b2 , p¯ 1 and p¯ 2 are invariant with the change in labor population L. (b) When b1 > b2 , p¯ 2 increases with L and p¯ 1 increases (decreases) with L, if a is sufficiently small (large). (c) When b2 > b1 , p¯ 1 decreases with L and p¯ 2 increases (decreases) with L, if a is sufficiently large (small). The mechanism behind Proposition 9 is as follows. When b1 ¼ b2 ¼ b, if the population becomes l times the original size, for any domestic price p, from (7) and (8), labor input in each sector becomes l times larger, and output lb times larger. It follows that welfare Vð pÞ increases to lb times the original level, and sectors’ shares si ð pÞ’s remain unchanged. So, Wi ð pÞ is l times that before the population growth, 8 p. The maximum of Wi ð pÞ therefore occurs at the same p¯ i . When b1 < b2 , the productivity of labor in sector 1 is lower than that in sector 2, and when the labor supply L increases, because ½ð@L1 =@LÞ=L1 = ½ð@L2 =@LÞ=L2  ¼ ð1  b2 Þ=ð1  b1 Þ < 1, L1 grows at a smaller rate than L2 . This along with b1 being smaller implies y1 increases at a smaller rate than y2 , and if the domestic price p stays the same, sector 1’s share s1 ð pÞ shrinks. To mitigate this unfavorable change, capitalist 1 will propose to lower the relative price of good 2, p, further. Similarly, when b1 > b2 , an increase in L enhances sector 1’s share s1 ð pÞ, and we expect capitalist 1 to be lax on lowering p to enhance the share, and the harm of price distortion to welfare Vð pÞ will be more of a concern to him. So, we expect p¯ 1 to increase to be closer to the international.

(12) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 499. price. The exceptional case is when a is sufficiently large. As discussed previously, when a ! 1, dVð pÞ=d pj p¼ p¯ 1 ! 0. Since the marginal effect on Vð pÞ is limited, capitalist 1 will consider enhancing his sector share by lowering p, especially when the share enhancement is supported by an advantage in labor employment, i.e. when b1 > b2 and L grows. 4.2. Party in favor, political gifts and domestic price The previous section shows how individual lobbied price changes with the political and economic environment. To understand how the domestic price changes in the end, we have to further study who becomes the winning lobbyist as the environment changes. From ˙ 1 and W ˙ 2 , and from (14), the government will Proposition 1, this leads to a comparison of W set the domestic price to be p¯ 1 when ˙1 W ˙ 2 ¼ Vð p¯ 1 Þ½a þ s1 ð p¯ 1 Þð1  b1 Þ þ ð1  s1 ð p¯ 1 ÞÞð1  b2 Þ W  Vð p¯ 2 Þ½a þ s1 ð p¯ 2 Þð1  b1 Þ þ ð1  s1 ð p¯ 2 ÞÞð1  b2 Þ > 0: Suppose the capital at each sector grows at the same rate: r. From the discussion about Proposition 7, each capitalist will continue lobbying for the same price p¯ i , which results in the same share for sector 1, s1 ð p¯ i Þ. On the other hand, the welfare Vð p¯ i Þ will grow at the ˙1W ˙ 2 above becomes 1 þ r rate r, for i ¼ 1; 2. It then follows that the magnitude of W times the original difference, while its sign remains unchanged. That means the government favors the same capitalist when the capital in each sector grows at a uniform rate. Together with Proposition 7, it implies that: Proposition 10. When K1 and K2 grow at the same rate, the domestic price stays the same. In our model, labor and capital are complementary factors, i.e. @2 yi =@Li @Ki > 0, when capital grows, labor becomes more valuable a resource because its productivity is enhanced, and we expect each capitalist to offer more to compete for labor allocation. (18), (19) and (21) characterize the donations in intervals. It can be easily checked that the bounds of these intervals increase to 1 þ r times the original values when the sectorial capital grows uniformly at rate r. In sum, when the rivalry between two sectors intensifies, we expect the government to receive more political gifts, while no change occurs in the domestic price. The analysis in the previous section shows that when the sectorial capitals K1 and K2 grow at an uneven rate, or when the labor population L grows, there are a few possibilities with which p¯ 1 and p¯ 2 might change. So the share s1 ð p¯ i Þ in the above expression also has a few possibilities to change. To avoid this complexity and to see better how the system works, in the following, we shall focus on simplified cases when b1 ¼ b2 ¼ b. This reduces the condition for p ¼ p¯ 1 to be: ˙1 W ˙ 2 ¼ ½Vð p¯ 1 Þ  Vð p¯ 2 Þð1 þ a  bÞ > 0; W. (30). ˙ 2 hinges upon whether p¯ 1 creates a larger welfare V than ˙ 1 is larger than W i.e. whether W p¯ 2 ..

(13) 500. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. Case 1. When b1 ¼ b2 ¼ b, and labor supply increases from L to lL. Proposition 6(a) states that in this case, p¯ 1 and p¯ 2 both stay unchanged, and the discussion following the ˙1W ˙ 2 in (30) proposition shows that Vð p¯ i ; lLÞ ¼ lb Vð p¯ i ; LÞ, for i ¼ 1; 2. That means W does not change sign after the labor supply increases. So the winner of the lobbying game is the same person as before, and the domestic price remains unchanged. Regarding the political gifts, it can be easily checked that the bounds of Ci and C j become lb times the original values. That means when lobbyists are richer because the resource competed for becomes more bountiful, they are more generous in making political donations. Because the marginal product of labor is assumed to be diminishing, the (bounds of) political gifts will increase with labor population in a decreasing rate. On the other hand, the domestic price is not distorted further as the government benefits more. Case 2. When b1 ¼ b2 ¼ b, and the capital at sector 1 increases from K10 to K1n . Let p¯ oi and p¯ ni denote the price lobbied by i, when K1 is K1o and K1n , respectively. From Proposition 8, p¯ ni > p¯ oi , for i ¼ 1; 2. The change in the domestic price, along with the change in K1 , brings changes to labor allocation and social welfare. Let L1 ð p; K1 Þ denote the labor allocated to sector 1 when the domestic price is p and sector 1 is equipped with capital K1 . The change ˙ 2 has the same sign as the following term: ˙1 W in W ½VðL1 ð p¯ n1 ; K1n Þ; K1n Þ  VðL1 ð p¯ o1 ; K1o Þ; K1o Þ. (31). ½VðL1 ð p¯ n2 ; K1n Þ; K1n Þ  VðL1 ð p¯ o2 ; K1o Þ; K1o Þ:. (32). ˙ 1 =ð1 þ a  bÞ, and can be decomposed into: (31) shows the change of W VðL1 ð p¯ n1 ; K1n Þ; K1n Þ  VðL1 ð p¯ o1 ; K1n Þ; K1n Þ. (33). þVðL1 ð p¯ o1 ; K1n Þ; K1n Þ  VðL1 ð p¯ o1 ; K1o Þ; K1n Þ. (34). þVðL1 ð p¯ o1 ; K1o Þ; K1n Þ  VðL1 ð p¯ o1 ; K1o Þ; K1o Þ:. (35). In (33), K1 is fixed at the new level, and the focus is on how the welfare changes when the domestic price is changed from p¯ o1 to p¯ n1 . Because the new price is raised closer to the international price, and results in a welfare improvement, (33) is positive. In (35), the labor allocation is fixed. Apparently, welfare increases when there is more capital in Section 1. So, (35) is also positive. The sign of (34) is uncertain. When K1 ¼ K1n , welfare V is maximized when L1 ¼ L1 ð p ; K1n Þ. Because p¯ o1 < p and K1o < K1n , L1 ð p¯ o1 ; K1n Þ is greater than L1 ð p ; K1n Þ and L1 ð p¯ o1 ; K1o Þ. The order between L1 ð p ; K1n Þ and L1 ð p¯ o1 ; K1o Þ is uncertain. When the latter is larger, (34) is negative; otherwise, the sign of (34) is uncertain. ˙ 2 =ð1 þ a  bÞ in (32) can be decomposed into the following Similarly, the change of W three effects: VðL1 ð p¯ n2 ; K1n Þ; K1n Þ  VðL1 ð p¯ o2 ; K1n Þ; K1n Þ. (36). þVðL1 ð p¯ o2 ; K1n Þ; K1n Þ  VðL1 ð p¯ o2 ; K1o Þ; K1n Þ þVðL1 ð p¯ o2 ; K1o Þ; K1n Þ  VðL1 ð p¯ o2 ; K1o Þ; K1o Þ:. (37) (38).

(14) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 501. Fig. 2. Labor allocation and deadweight loss. Note: MPo1 and MPn1 denotes the marginal product of labor at sector 1, when K1 ¼ K1o and when K1 ¼ K1n .. The argument that (33) is positive can be applied to show (36) to be negative, and this implies (33)–(36) is positive. We now turn to the comparison between (35) and (38). (38) is positive for the same reason that (35) is positive. What concerns us is the difference between these two positive terms. (35)–(38) can be rearranged to be: ½VðL1 ð p¯ o1 ; K1o Þ; K1n Þ VðL1 ð p¯ o2 ; K1o Þ; K1n Þ  ½VðL1 ð p¯ o1 ; K1o Þ; K1o Þ  VðL1 ð p¯ o2 ; K1o Þ; K10 Þ. The latter term evaluates the impact of labor allocation on welfare when K1 is still K1o . From Lemma 2(a), L1 ð p¯ o2 ; K1o Þ < L1 ð p ; K1o Þ < L1 ð p¯ o1 ; K1o Þ. Either L1 ð p¯ o2 ; K1o Þ or L1 ð p¯ o1 ; K1o Þ causes a deadweight loss, and in terms of good 1, it is the area of 4abc (4cde) when L1 ¼ L1 ð p¯ o2 ; K1o Þ (L1 ¼ L1 ð p¯ o1 ; K1o Þ) as shown in Fig. 2. The former term of (35)–(38) evaluates the deadweight losses resulting from the same labor allocations, but with K1 ¼ K1n in the background. When K1 increases to K1n , more labor than L1 ð p ; K1o Þ should be allocated to sector 1 to achieve efficiency. If L1 ð p ; K1n Þ surpasses L1 ð p¯ o1 ; K1o Þ as depicted in Fig. 2, the deadweight loss is the area of 4 fbh (4gdh) when L1 ¼ L1 ð p¯ o2 ; K1o Þ (L1 ð p¯ o1 ; K1o Þ). A straightforward comparison of these areas shows: ð4 fbh  4gdhÞ  ð4abc  4cdeÞ > 0, and it follows that (35)–(38) > 0. On the other hand, if L1 ð p ; K1n Þ < L1 ð p¯ o1 ; K1o Þ, it can be shown that when K1 ¼ K1n , the deadweight loss becomes larger (smaller) than the area of 4abc (4cde) when L1 ¼ L1 ð p¯ o2 ; K1o Þ (L1 ð p¯ o1 ; K1o Þ). In this case, (35)–(38) is also positive. Lastly, (37) is positive because L1 ð p ; K1n Þ > L1 ð p¯ o2 ; K1n Þ > L1 ð p¯ o2 ; K1o Þ. If (34) is negative, apparently (34)–(37) is negative. If (34) is positive, to repeat the same graphical analysis for (35)–(38), we find (34)–(37) ends with a comparison of two irrelevant areas. This leaves the sign of (34)–(37) uncertain. ˙1 W ˙ 2 can either increase or To summarize, our analysis of (33) through (38) shows W decrease when the capital at sector 1 grows. Fig. 3 presents a simulation result that shows these two possible cases. In the simulation, we set K2 ¼ 10, p ¼ 1, a ¼ 1, b ¼ 1=2, L ¼ 100, and let K1 runs from 1 to 15. In this set of data, capitalist 1 cannot lobby successfully when his capital is less than the opponent’s, i.e. only when K1  K2 , is ˙1W ˙ 2 positive. Fig. 4 shows how the domestic price p changes when K1 increases. W Before K1 reaches 10, the government always protects sector 2, and more so when sector 1 becomes stronger, i.e. p increases with K1 . Once K1 reaches the critical level, the government switches to protect sector 1, and we observe that the domestic price falls sharply below the international price p . In reality, the protected sector changes through.

(15) 502. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. ˙1 W ˙ 2. Fig. 3. Simulation result: W. Fig. 4. Simulation result: the domestic price.. time. Our model shows that it can simply be a result of changes in domestic resources. It is worth noting that although in this special case, the government always protects the exporting sector, when b1 6¼ b2 , the government may protect either the exporting or the importing sector.8 In this case of unbalanced growth, it is uncertain whether the capitalist in the growing sector offers more or less political gifts to lobby. On one hand, labor becomes a more valuable resource to the growing sector, because its productivity is enhanced by more inputs of capital. On the other hand, Eq. (7) shows that the market automatically allocates more labor to the growing sector, thus sector 1 need not distort the domestic price further to lobby for more resources. Actually, Proposition 8 shows that the growing sector will 8 In another simulation, we set b1 to be 1/3 and b2 to be 2/3, while letting all other variables take the same value as in case 2. The government protects sector 1 when K1  12, but sector 1 is not an exporting sector until K1 reaches 35..

(16) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 503. propose a price closer to the free-trade condition. In view of this, capitalist 1 may offer less political gifts because there is less welfare loss to be compensated. To continue with the above simulation setting, we find the government receives more political gifts before K1 increases to 14, and less afterwards. Case 3. b1 ¼ b2 ¼ b, K1 grows at a higher rate than K2 . Suppose K2 grows to be K2 ð1 þ r1 Þ and K1 grows to be K1 ð1 þ r1 þ r2 Þ, where r2 > 0. First consider the halfway case: Ki grows to be Ki ð1 þ r1 Þ, for i ¼ 1; 2. From the previous analysis of case 2, the favored party remains unchanged in this half-way case. Now, fix capital at sector 2 to be K2 ð1 þ r1 Þ and increase capital at sector 1 to K1 ð1 þ r1 þ r2 Þ. We find ourselves back to case 2 above. It is ˙ 2 changes sign, and the identity of the favored party is uncertain. ˙1 W uncertain whether W Lastly, we would like to bring to attention some caveat for the case in which b1 6¼ b2 . Case 2 above leaves us the impression that in a symmetric case (b1 ¼ b2 , and p ¼ 1), the sector with bigger muscle, i.e. equipped with more capital, wins the lobby. What happens if two sectors are endowed with the same capital, say K1 ¼ K2 ¼ 10, and the terms of trade at the international market lean toward neither good, i.e. p ¼ 1, but labor in sector 1 is more productive, i.e. b1 > b2 ? In this case, sector 1 need not be the one with bigger muscle to win the lobby. When b1 b2 , sector 1 does have an edge. For instance, if b1 ¼ 2=3, b2 ¼ 1=3, a ¼ 1 and L ¼ 100, capitalist 1 is the winner of the game. However, if b1 b2 , the capital’s share of profit in sector 1 is much less than that in sector 2, and we expect capitalist 1 to be less motivated to lobby. If we change b1 and b2 in the above data set to be 3/4 and 1/4, respectively, then capitalist 2 becomes the winning lobbyist.. 5. Conclusion In a two-sector model like ours, the sector that is more able to create rent at a lower cost to consumers will win the race for policy favor. At least part of the rent will be transferred to the government as political contributions, however. The winner of the lobby race will not necessarily gain from such a trade preferences, as the political contributions needed to win the race may be higher than the rent, but the winner will necessarily be better off than letting the rival sector dictate the policy. The lobby competition between sectors, driven by the fear that the rival sector will win the favor of the government, makes free trade an infeasible policy choice. Political contribution is tantamount to a bribe to prevent the government from hurting the sector’s interest. The simplicity of the two-sector model, combined with the single-offer auction, means that the lobbyist knows that his policy proposal will be adopted if the contribution he offers is accepted. As usual, rent-seeking activity in our model is unproductive. In general, the sector that commands more intra-marginal gains from resource reallocation while carrying a smaller weight in the consumption bundle will be the winner in the lobby race. The consumption bias is assumed away in our model by a symmetric Leontief utility function. Resource endowment hence plays a central role in the outcome of the lobby game and in the determination of the structure of protection. A country having asymmetric resource.

(17) 504. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. endowments between the sectors will adopt a policy closer to free trade than a country having symmetric endowments of resources between the sectors. Since the former also has a higher tendency to trade if the world consumption pattern is similar, the policy choice resulting from our model will reinforce rather than impede the tendency to trade. Thus a country endowed with asymmetric resources is naturally more open to trade partly because of its need for foreign resources, and partly because it engenders a political process leaning toward freer trade. Political contribution in an asymmetric economy also tends to be small because the smaller sector presents little threat to the dominant sector in the lobby competition. A government with a long-term planning horizon may, however, wish to help the smaller sector grow in order to extract more contributions from the larger sector. The model is intended to depict the policy choice of an incumbent government that values political contributions but is also concerned about the welfare of the general population. It is essentially a mix of the interest group model and the national interest model as described by Baldwin (1989). It ignores the political competition among the candidates who are running for office. If the welfare function of the government portrayed in our model in fact depicts the probability of being elected, then there is no chance for the repressed sector to turn to the opposition by proposing an alternative policy formula with commensurate political contributions, because the opposition will never win the election with this platform and the attached political funds. Therefore, trade policy will never be a debatable issue in the campaign because every party knows which sector should be favored and ‘‘taxed’’ with political gifts to stay in power once it is elected. Only if the winning formula for election changes, e.g., the voters become more aware of their well-being or the effectiveness of campaign funds in swinging votes decreases, will the structure of protection change.. Acknowledgements Financial support from the National Science Council (NSC90-2811-H-001-001) is gratefully acknowledged. We thank Professor Chou, Chien-Fu and the referee for comments and suggestions.. Appendix A Proof of Lemma 2. (a) In view of (13), W1 ð pÞ hinges upon the magnitudes of Vð pÞ and s1 ð pÞ. The social welfare Vð pÞ is maximized when p ¼ p . On the other hand, Lemma 1 shows s1 ð pÞ decreases in p. Therefore, W1 ð pÞ must be maximized at p¯ 1 < p . p¯ 2 > p can be proved similarly. (b) Because s1 ð pÞ decreases in p and p¯ 2 > p , s1 ð pÞ is larger when p is set to be p than p¯ 2 . This, along with Vð p Þ > Vð p¯ 2 Þ, establishes that p1 ð p Þ > p1 ð p¯ 2 Þ, where p1 ð Þ is defined in (10). Similarly, p2 ð p Þ > p2 ð p¯ 1 Þ. &.

(18) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 505. The following lemma is used in the Proof of Propositions 1 and 2. Lemma 3. (a) 8 p > 0, pi ð pÞ > 0, i ¼ 1; 2. (b) lim p ! 1 p1 ð pÞ ¼ lim p ! 0 p2 ð pÞ ¼ 0. Proof. (a) From (9)–(11), we have to show yi ð pÞ > 0 to establish pi ð pÞ > 0. With Cobb–Douglas technology, 8 p > 0, as L1 ðL2 Þ approaches 0, MP1 ð pMP2 Þ in Fig. 1 goes to infinity. So, the labor allocation is always an interior solution. This implies 8 p > 0, yi ð pÞ > 0, for i ¼ 1; 2. (b) From Fig. 1, we observe lim p ! 1 L1 ð pÞ ¼ 0. It implies that lim p ! 1 s1 ð pÞ ¼ 0: On the other hand, the social welfare is bounded: Vð pÞ  Vð p Þ; 8 p > 0: The above two conditions and (10) and (11) imply lim p ! 1 p1 ð pÞ ¼ 0. Similarly, one can show lim p ! 0 p2 ð pÞ ¼ 0. & Proof of Proposition 1. Consider an SPE involving no weakly dominated strategy, in which i, the winner, proposes ð pi ; Ci Þ, and j, the loser, proposes ð p j ; C j Þ. We first establish that Ci > 0: If Ci ¼ 0, the only possible case in which the government will decide in i’s favor is pi ¼ p . Given that i proposes ð p ; 0Þ, j has a better proposal than ð p j ; C j Þ which causes i to lose. From Lemma 2(a), e  ðW j ð p¯ j Þ  W j ð p ÞÞ=2 > 0. If j instead proposes ð p¯ j ; aVð p Þ  aVð p¯ j Þ þ eÞ, the government will switch to accept j’s offer, and j’s payoff will be higher than p j ð p Þ, his payoff when losing to i, by e. This contradicts the notion that losing is j’s best response to i’s equilibrium strategy. We now study the 7 listed conditions in turn. Condition (15): Because i is the winner, Gi  G j . Suppose Gi ¼ G j þ d; d > 0, then i can win with another package, ð pi ; Ci  eÞ where 0 < e < min fCi ; dg, and become better off. This contradicts ð pi ; Ci Þ being i’s best response to j’s equilibrium proposal. So, we must have Gi ¼ G j . Condition (16): Given j’s proposal, suppose i wins with ð pi ; Ci Þ where pi 6¼ p¯ i . Define Ci0  Ci þ aVð pi Þ  aVð p¯ i Þ. We shall show ð p¯ i ; Ci0 Þ is a better response to j’s equilibrium strategy than ð pi ; Ci Þ. We first establish that Ci0 is feasible, i.e. Ci0  0. This is obvious when aVð pi Þ  aVð p¯ i Þ, because Ci > 0. We only have to consider the case when aVð pi Þ < aVð p¯ i Þ. From Lemma 2(a), aVð p¯ i Þ < aVð p Þ:. (A.1). Therefore, aVð pi Þ < aVð p Þ, and for i to persuade the government to lower the social welfare, he must donate more to compensate for this loss: Ci  aVð p Þ  aVð pi Þ: (A.1) and (A.2) together imply Ci0 > 0.. (A.2).

(19) 506. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. By construction, ð p¯ i ; Ci0 Þ yields the same payoff to the government as ð pi ; Ci Þ. So, i can also win with ð p¯ i ; Ci0 Þ. Moreover, i’s net payoff, pi ð p¯ i Þ  Ci0 , will be higher than when winning with ð pi ; Ci Þ. This is because ½pi ð p¯ i Þ  Ci0   ½pi ð pi Þ  Ci  ¼ pi ð p¯ i Þ  ðCi þ aVð pi Þ  aVð p¯ i ÞÞ  ½pi ð pi Þ  Ci  > 0; for pi 6¼ p¯ i. The above reasoning prevents i from proposing a price other than p¯ i in equilibrium. Condition (17): Suppose p j 6¼ p¯ j . Let C0j  C j þ aVð p j Þ  aVð p¯ j Þ:C 0j > 0, for the same reason that Ci0 > 0 above. We shall show ð p¯ j ; C 0j Þ weakly dominates ð p j ; C j Þ. Let G0j denote the government’s payoff when she accepts ð p¯ j ; C0j Þ. By construction, G0j ¼ G j . Therefore, for any proposal ð p0i ; Ci0 Þ by i, either ð p¯ j ; C 0j Þ and ð p j ; C j Þ both beat ð p0i ; Ci0 Þ, or both lose to it. In the former case, ð p¯ j ; C 0j Þ yields a strictly higher payoff to j than ð p j ; C j Þ, for the same logic used when proving condition (16). In the latter case, j gains p j ð p0i Þ with either proposal. Condition (18): Condition (18) follows from conditions (15)–(17). Condition (19): Suppose condition (19) does not hold, then 9 d > 0, such that p j ð p¯ j Þ  C j  d ¼ p j ð p¯ i Þ. Given i’s equilibrium strategy, if j changes to propose ð p¯ j ; C j þ d=2Þ, the government will accept his proposal, because her payoff will become G j þ d=2, higher than Gi ð¼ G j Þ. On the other hand, j’s payoff also becomes higher than when proposing ð p¯ j ; C j Þ and losing to i’s ð p¯ i ; Ci Þ, because   d d p j ð p¯ j Þ  C j þ ¼ p j ð p¯ i Þ þ > p j ð p¯ i Þ: 2 2 This contradicts ð p¯ j ; C j Þ being j’s equilibrium strategy, and establishes the claim. Condition (20): Because Ci > 0, we must have: pi ð p¯ i Þ  Ci  pi ð p¯ j Þ:. (A.3). Otherwise, from (15), given j’s equilibrium strategy, to propose ð p¯ i ; 0Þ makes i lose to j, and leaves i a higher payoff than when winning with ð p¯ i ; Ci Þ. This negates ð p¯ i ; Ci Þ to be a best response to j’s equilibrium strategy. On the other hand, from (18) and (19), Ci  ½p j ð p¯ j Þ þ aVð p¯ j Þ  ½p j ð p¯ i Þ þ aVð p¯ i Þ:. (A.4). ˙iW ˙ j. (A.3) and (A.4) together imply W Condition (21): Condition (21) means C j cannot exceed min fWi ð p¯ i Þ  Wi ð p¯ j Þ; p j ð p¯ j Þg. From (18) and (A.3), we readily have: C j  Wi ð p¯ i Þ  Wi ð p¯ j Þ. Next, suppose C j  p j ð p¯ j Þ. We shall show such C j causes ð p¯ j ; C j Þ to be weakly dominated by ð p¯ j ; 0Þ, in conflict with our pre-condition. We first establish that: G j > aVð p Þ: From (17) and (19), G j  aVð p Þ  p j ð p¯ j Þ þ aVð p¯ j Þ  ðp j ð p¯ i Þ þ aVð p ÞÞ:. (A.5).

(20) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 507. From Lemma 2(b), p j ð p¯ i Þ < p j ð p Þ, so the above inequality can be further developed to be: G j  aVð p Þ > W j ð p¯ j Þ  W j ð p Þ > 0; which establishes the claim. Consider any proposal by i: ð p0i ; Ci0 Þ. If j proposes ð p¯ j ; C j Þ, (A.5) implies that the government will either set p to be p0i ð 6¼ p¯ j Þ or p¯ j. In the former case, j’s payoff is p j ð p0i Þ. If j changes to propose ð p¯ j ; 0Þ, there will be no change to his payoff, since he will remain a loser. In the latter case, ð p¯ j ; C j Þ causes j’s payoff to be negative when C j  p j ð p¯ j Þ. If j instead proposes ð p¯ j ; 0Þ, the domestic price will be either p0i or p, and j’s payoff is strictly positive in either case (Lemma 3(a)). Thus, ð p¯ j ; 0Þ weakly dominates ð p¯ j ; C j Þ. & Proof of Proposition 2. (b) is a straightforward statement of government’s maximizing her utility. Given (b), we shall show proposals in (a) are equilibrium strategies with no weakly dominated proposals. First note that with ð pi ; Ci Þ in (a), the government is better off accepting i’s proposal than maintaining the international price. From (18), (19) and (21), Ci ¼ ½p j ð p¯ j Þ þ aVð p¯ j Þ  ½p j ð p¯ i Þ þ aVð p¯ i Þ þ k; where k is specified in (21). Let Gi denote the government’s utility under i’s proposal: Gi  aVð p¯ i Þ þ Ci ¼ p j ð p¯ j Þ þ aVð p¯ j Þ  p j ð p¯ i Þ þ k:. (A.6). Applying Lemma 1(a) and (b) in turn, we have: Gi > p j ð p Þ þ aVð p Þ  p j ð p¯ i Þ þ k > aVð p Þ which establishes the claim. Next, we shall turn to explain (i) it is not to j’s advantage to outbid i’s offer in (a). (ii) ð p j ; C j Þ depicted in (a) will be rejected. Therefore, j’s strategy in (a) is the best response to i’s. (iii) ð p j ; C j Þ in (a) is not weakly dominated. (i) To outbid i’s offer, ð p j ; C j Þ has to yield a higher utility to the government than ð p¯ i ; Ci Þ, namely: C j þ aVð p j Þ > ½p j ð p¯ j Þ þ aVð p¯ j Þ  ½p j ð p¯ i Þ þ aVð p¯ i Þ þ aVð p¯ i Þ þ k: (A.7) When j’s offer is accepted, his net payoff becomes p j ð p j Þ  C j , and in view of (A.7), we have: p j ð p j Þ  C j < p j ð p j Þ  ½p j ð p¯ j Þ þ aVð p¯ j Þ  p j ð p¯ i Þ  aVð p j Þ  k: Because p j ð pÞ þ aVð pÞ is maximized at p ¼ p¯ j , the above inequality implies: p j ð p j Þ  C j < p j ð p¯ i Þ; i.e. it is better for j to lose to i. (ii) Let G j denote the government’s utility when she accepts j’s proposal in (a). (18) implies that Gi ¼ G j ; and with the government’s choice depicted in (b), she will turn down j’s offer..

(21) 508. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. (iii) In the proof of condition (17) in Proposition 1, it has been shown that ð p j ; C j Þ in (a) weakly dominates any other proposal by j that also yields G j to the government. In the following, we shall show for any ð p0j ; C 0j Þ that yields the government a different utility G0j ð¼ C 0j þ aVð p0j ÞÞ, there exists a proposal ð p0i ; Ci0 Þ by i, to which ð p j ; C j Þ in (a) is a strictly better response for j than ð p0j ; C 0j Þ. Case 1. G0j > G j . From (A.5), maintaining p makes the government worse off than accepting ð p j ; C j Þ in (a) or ð p0j ; C0j Þ. Lemma 3(b) implies that 9 ð p0i ; Ci0 Þ by i such that Ci0 þ aVð p0i Þ < aVð p Þ. Against this proposal, ð p0j ; C 0j Þ yields j a payoff of: p j ð p0j Þ  C0j ¼ p j ð p0j Þ þ aVð p0j Þ  G0j < p j ð p¯ j Þ þ aVð p¯ j Þ  G j ¼ p j ð p¯ j Þ  C j : That is, ð p j ; C j Þ in (a) is a better response to ð p0i ; Ci0 Þ. Case 2. G0j < G j . From (21), p j ð p¯ j Þ  C j > 0. Lemma A.1(b) implies that 9 p0i > 0 such that p j ð p¯ j Þ  C j > p j ð p0i Þ:. (A.8). From (A.5), we can pick e 2 ð0; min fG j  G0j ; G j  aVð p ÞgÞ, and have: Ci0  G j  aVð p0i Þ  e > G j  aVð p Þ  e > 0: By construction, G j > Ci0 þ aVð p0i Þ > max faVð p Þ; G0j g. That means, against ð p0i ; Ci0 Þ, ð p j ; C j Þ in (a) by j will be accepted, and j’s payoff will become p j ð p¯ j Þ  C j . If ð p0j ; C 0j Þ is instead proposed, ð p0i ; Ci0 Þ will be accepted, and j’s payoff will be p j ð p0i Þ. The setup of (A.8) makes ð p j ; C j Þ a better response for j than ð p0j ; C 0j Þ. To repeat step (iii) above, one can similarly establish for i that ð pi ; Ci Þ in (a) is not weakly dominated. To establish i’s strategy in (a) to be a best response to j’s in (a), we shall show (i) among all winning offers, the one in (a) yields i the highest profit. (ii) i is better off by winning with such an offer than by losing to j. (i) Given the opponent’s strategy, the best winning offer ð pi ; Ci Þ for i solves the following problem: max pi ð pi Þ  Ci pi ;Ci. s:t: Ci þ aVð pi Þ  G j. Because the right-hand-side of the constraint, G j , is independent of the choice of ð pi ; Ci Þ, for any pi, the best Ci is the one that holds the constraint in equality. Therefore, with (17), (19) and (21), i’s problem can be simplified to be: max pi ð pi Þ  ½aVð p¯ j Þ þ p j ð p¯ j Þ  p j ð p¯ i Þ þ k  aVð pi Þ pi. This is the same problem as in (12), so pi ¼ p¯ i ; and accordingly, Ci is what stated in (a). With this offer, i’s profit is: ½pi ð p¯ i Þ þ p j ð p¯ i Þ þ aVð p¯ i Þ  ½p j ð p¯ j Þ þ aVð p¯ j Þ  k ˙ j and the definition of k in (21), it is larger than pi ð p¯ j Þ, i.e. i’s ˙iW From the assumption W profit when losing to j. &.

(22) J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. 509. Proof of Corollary 1. We shall show that pi ð p¯ i Þ  Ci < pi ð p Þ. Because p¯ j maximizes W j in (12), we have: pi ð p Þ > pi ð p Þ þ p j ð p Þ þ aVð p Þ  ½p j ð p¯ j Þ þ aVð p¯ j Þ: In view of (10), when b1 ¼ b2 ¼ b, pi ð pÞ þ p j ð pÞ þ aVð pÞ ¼ Vð pÞð1  b þ aÞ; which is maximized when Vð pÞ reaches the maximum, i.e. when p ¼ p . This observation, along with the above inequality, leads to: pi ð p Þ > pi ð p¯ i Þ þ p j ð p¯ i Þ þ aVð p¯ i Þ  ½p j ð p¯ j Þ þ aVð p¯ j Þ: From (18), (19) and (21), the right-hand-side is exactly pi ð p¯ i Þ  Ci þ k, where k is a positive number defined in (21). On the other hand, (10) and (11) imply that: pi ð pÞ þ p j ð pÞ þ aVð pÞ ¼ Vð pÞð1  bi þ a þ ðbi  b j Þs j ð pÞÞ: Because Vð p Þ > Vð p¯ i Þ and s j ð p Þ > s j ð p¯ i Þ (from Lemmas 1 and 2(a)), to repeat the logic above, it can be shown again that pi ð p¯ i Þ  Ci < pð p Þ, when bi > b j . & Proof of Proposition 3. Consider any SPE in our game. Let ið jÞ denote the winner (loser) in this equilibrium. Clearly, with f fk ð pÞgk¼1;2 constructed in (22), the government will choose p ¼ p¯ i , and her and lobbyists’ payoffs stay the same as the equilibrium payoffs in our game. We shall argue that fi ð pÞ in (22) is a best response to f j ð pÞ in the menu auction. The reverse can be similarly established. Given f j ð pÞ, consider a case in which i modifies his menu in (22) to improve his own payoff. Suppose the government still chooses p¯ i after this change, then i can improve his payoff only through a change in fi ð p¯ i Þ. But to increase fi ð p¯ i Þ reduces i’s payoff, and to decrease fi ð p¯ i Þ makes p¯ i a choice strictly inferior to p¯ j to the government. (See (15).) In sum, there is no way to improve i’s payoff with another menu which still keeps p¯ i a chosen price. Now, consider i submitting a menu fi0 ð pÞ different from (22), and makes p0 ð 6¼ p¯ i Þ the government’s choice. If p0 ¼ p¯ j , then i’s payoff is pi ð p¯ j Þ  fi0 ð p¯ j Þ which is in no way higher than pi ð p¯ i Þ  Ci , i’s payoff when he submits fi ð pÞ in (22) instead. Because in our game, given j proposes ð p¯ j ; C j Þ, if i proposes ð p¯ j ; fi0 ð p¯ j ÞÞ, the government will set p ¼ p¯ j and collect C j þ fi0 ð p¯ j Þ. (See (A.5).) This leaves i a payoff of pi ð p¯ j Þ  fi0 ð p¯ j Þ, no higher than pi ð p¯ i Þ  Ci , since ð p¯ i ; Ci Þ is i’s best response to j’s ð p¯ j ; C j Þ in our game. If p0 6¼ p¯ j , we have: aVð p0 Þ þ fi0 ð p0 Þ  aVð p¯ j Þ þ C j þ f j0 ð p¯ j Þ: To repeat logic very similar to that above, one can again negate fi0 ð pÞ being a better menu to i than fi ð pÞ in (22). &.

(23) 510. J.-S. Wang et al. / Japan and the World Economy 18 (2006) 488–511. Proof of Proposition 4. (a) From Lemma 2(a), it suffices to show p¯ ¼ p. When b1 ¼ b2 ¼ b, (23) becomes: p¯ ¼ argmax p ð1  b þ aÞVð pÞ: Clearly, p¯ ¼ p . (b) When b1 < b2 , (23) can be arranged as: p¯ ¼ argmax p Vð pÞ½ðb2  b1 Þs1 ð pÞ þ ð1  b2 þ aÞ: To reapply the logic by which we show p¯ 1 < p in Lemma 2(a), one can establish that ˆ p¯ 1 Þ > Wð ˆ pÞ; 8 p < p¯ 1 , so p¯ < p . It remains to show p¯ > p¯ 1. We shall establish (i) Wð ˆ p¯  p¯ 1 . (ii) dW=d pj p¼ p¯ 1 > 0. It then follows p¯ > p¯ 1 . (i) Lemmas 1 and 2(a) imply that p2 ð pÞ in (10) is strictly less than p2 ð p¯ 1 Þ; 8 p < p¯ 1 . ˆ p¯ 1 Þ > Wð ˆ pÞ; 8 p < p¯ 1 . Moreover, p¯ 1 maximizes p1 ð pÞ þ aVð pÞ. Thus Wð (ii) We already know dðp1 ð pÞ þ aVð pÞÞ=d pj p¼ p¯ 1 ¼ 0. It remains to show dp2 ð pÞ=d pj p¼ p¯ 1 > 0. From Lemma 1, ds2 ð pÞ=d p > 0, and from Lemma 2(a), dVð pÞ=d pj p¼ p¯ 1 > 0. In view of (10), the claim is established. (c) Reasoning similar to that in (b) can be applied to show (c). & Proof of Proposition 5. We first show that in (24), z > x þ y. Only the case b1  b2 will be considered. Similar logic can be applied to the other case. From (24), z  ðx þ yÞ ¼ ½W1 ð p¯ 1 Þ  W1 ð p¯ Þ þ ½W2 ð p¯ 2 Þ  W2 ð p Þ þ ½p2 ð p Þ  p2 ð p¯ Þ: (A.9) From Proposition 4, when b1  b2 , p¯ 2 > p  p¯ > p¯ 1 . This establishes the sum of the first two terms in the right-hand-side of (A.9) to be strictly positive. For the same reason that we establish Lemma 2(b), it can be shown p2 ð p Þ  p2 ð p¯ Þ. Thus z > x þ y. With this inequality, we have n¯ 1 ¼ x, n¯ 2 ¼ y in (24), and Gm ¼ W1 ð p¯ 1 Þ þ W2 ð p¯ 2 Þ  ðp1 ð p¯ Þ þ p2 ð p¯ Þ þ aVð p¯ ÞÞ: From (A.6), we have: Gi  Gm ¼ ðp1 ð p¯ Þ þ p2 ð p¯ Þ þ aVð p¯ ÞÞ  ðpi ð p¯ i Þ þ p j ð p¯ i Þ þ aVð p¯ i ÞÞ þ k > 0: &. References Baldwin, R.E., 1989. The political economy of trade policy. Journal of Economic Perspectives 3 (4), 119–135. Becker, G.S., 1983. A theory of competition among pressure groups for political influence. Quarterly Journal of Economics 48, 371–400. Becker, G.S., 1985. Public policies, pressure groups, and dead weight costs. Journal of Public Economics 28, 329– 347. Bernheim, B.D., Whinston, M.D., 1986. Menu auctions, resource allocation, and economic influence. Quarterly Journal of Economics 101, 1–31..

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