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Domestic trade protection in vertically-related markets
Economic Modelling 28 (2011) 1595–1603
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Economic Modelling j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c m o d
Domestic trade protection in vertically-related markets Kuang-Cheng A. Wang a,⁎, Hui-Wen Koo b, Tain-Jy Chen b a b
Social Science Division, Center for General Education, Chang Gung University, Taiwan Department of Economics, National Taiwan University, Taiwan
a r t i c l e
i n f o
Article history: Accepted 10 February 2011 JEL classification: F12 F13 Keywords: Market structure Vertically-integrated firms Vertically-related markets
a b s t r a c t We consider trade policy in a setting where home country firms are fully dependent on vertically-integrated foreign firms for supplies of a key input. We find that vertically-integrated firms' strategic considerations play an important role and that, in particular, a tariff on final goods may either increase or decrease the domestic price of final goods. The import of final goods is always taxed to extract and shift rents from foreign firms, while the import of intermediate goods can be either taxed or subsidized. The market structure is shown to be an important consideration when making trade policy. © 2011 Elsevier B.V. All rights reserved.
1. Introduction In the global trade system, developing countries have always played the role of exporters of raw materials or processors of final products. Colombia, Cuba and Brazil, for example, belong to the former category, while China and the Four Asian Newly Industrialized Countries belong to the latter. On the other hand, firms in developed countries are usually large, vertically integrated, and control and sell technologies necessary for producing key intermediate inputs as well as the final goods. An example of such cases is the market for cellular phones in China. In these years, the Chinese domestic market has gradually become the most important market in the world. Motorola, Nokia and Sony Ericsson are the main foreign suppliers of cellular phones in China, with a collective total market share of about 85% in 2001, and 70% in 2002, with the rest of the market being taken up by 12 domestic Chinese firms dependent on their foreign competitors to supply core components, such as ICs and LCDs.1 Another example is the TFT-LCD industry, in which there are several vertically-integrated (thereafter VI) firms in the market, including LG-Philips, Samsung, Sharp, NEC and Hitachi. On the other hand, there are quite a few downstream assembling firms: AUO, Chi-Mei, Hann Star, Quanta, Chunghwa in Taiwan and SVA-NEC, Boe-Hydis in China. The VI firms
⁎ Corresponding author at: Social Science Division, Center for General Education, Chang Gung University, 259 Wen-Haw 1st Rd., Kwei-Shan Tao-Yua, 33302, Taiwan. Tel.: +886 3 211 8800x3298; fax: +886 3 211 8458. E-mail address: [email protected] (K.-C.A. Wang). 1 The detailed information of the market of cellular phones in China can be found in http://search.cei.gov.cn. 0264-9993/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2011.02.022
not only compete with downstream firms in the TFT-LCD market, but also sell key components for the assembly of TFT-LCDs to downstream firms. For instance Sharp, NEC and Hitachi sell drive ICs to their downstream competitors. The purpose of this paper is to examine how developing countries can protect their downstream firms in the domestic market, when domestic firms must import a key intermediate input from vertically-integrated foreign firms to undertake production. In the literature, the vertically-related market has been a widely discussed topic. The pioneering paper in the literature is that of Greenhut and Ohta (1979). They set up a successive oligopoly model and compared the equilibrium intermediate and final prices of goods between all firms, non-integrated and integrated firms alike. Following Greenhut and Ohta's successive oligopoly model, much later literature further researched related topics of market foreclosure or strategic spin-offs, for example Salinger (1988), Schrader and Martin (1998), Higgens (1999), Lin (2006), and Matsushima (2006). In international trade theory, there is also much literature focusing on the vertically-related market, such as the works of Spencer and Jones (1991, 1992), Ishikawa and Lee (1997), Ishikawa and Spencer (1999) and Wang and Chiou (2004). In these works, Spencer and Jones (1991) study the trade policies of exporting countries when firms based in those countries compete with firms in the importing countries, which also hosts the market for the final goods, while Ishikawa and Spencer (1999) and Wang and Chiou (2004) focus on export subsidies of two exporting countries when these two countries export finished goods to vertically-related market of a third country. The difference between Ishikawa and Spencer (1999) and Wang and Chiou (2004) is mainly in market structures. The study in Ishikawa and Spencer (1999) assumes that there are a group of upstream and downstream firms in these two exporting countries, while Wang and
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Chiou (2004) assume that there are a group of VI firms in one exporting country and a group of downstream firms with lower production cost in the other exporting country. This indirectly means that Ishikawa and Spencer (1999) and Wang and Chiou (2004) both allow that the number of independent upstream (downstream) firms or the number of VI firms can vary to characterize different market structures in both exporting countries. However, Spencer and Jones (1992) and Ishikawa and Lee (1997) focus on the importing country's policies if the importing country faces a foreign VI firm or foreign vertically-decentralized firms (i.e., one independent upstream and one independent downstream firms) and the domestic firms and foreign firms compete in the domestic intermediate and final goods markets. The main difference between these two papers is that Spencer and Jones (1992) study how the trade policies of the domestic country affect foreign firm(s)'s pricing in the intermediate goods market and domestic social welfare, while Ishikawa and Lee (1997) emphasize “the backfire effect”. Ishikawa and Lee's study points out that if the domestic country imposes a prohibited tax on intermediate or final import goods, it may hurt domestic upstream and (or) downstream firms due to structural changes in the market. They refer to this phenomenon as the ‘Backfire effect’. Thus, an overview of the literature reveals a trend to consider market structures when studying relative trade issues. Representing the actual situation more realistically and responding to the expansion of the literature, we build up a more general vertically-related model to discuss how the importing country's trade policies affect both upstream and downstream market prices and what are the importing country's optimal trade policies under different market structures. We arrive at some broad conclusions. First, VI firms' strategic effect plays an important role in our general vertically-related model. The strategic effect follows the finding of Salop and Scheffman (1983, 1987), which states that a VI firm may gain from raising its rivals' costs even at some expense to itself. The strategic effect is also mentioned by Spencer and Jones (1991, 1992). We find that the VI firms' strategic effect lessens as the number of foreign VI firms increases. Second, this strategic effect shows that an increase of the tariff on intermediate goods increases both prices in both domestic upstream and downstream markets. But an increase of the tariff on final goods may either increase or decrease both prices in domestic upstream and downstream markets, with the result depending on the relative ratio of the number of domestic independent downstream firms to foreign VI firms. The case of an increase in the final goods' tariff lowering the domestic price of the final goods is a special case that violates general economic intuitions. Some of our findings supplement those of Spencer and Jones (1992), who authored the paper most relevant to our own. In our model, the optimal trade policy would impose a tariff on final goods, but whether to subsidize or impose a tariff on intermediate goods depends on market structures between home and foreign countries. This method of considering differences in market structure between different countries has many advantages, and we can look ahead to considering relations between China and the U.S., or China and Japan, and so on, where market structures may be remarkably different. In addition, our results indicate that market structure seems not to be ignored and makes clear the necessity of our study. The paper is organized as follows. Section 2 outlines the setting of the model. In Section 3, we derive the Cournot equilibrium in the upstream and downstream industries, when the tariffs (subsidies) on intermediate goods and final goods are given. Section 4 solves the optimal tariffs so as to maximize the social welfare of the home country. Section 5 offers some conclusions.
Fig. 1. The market structure.
goods. In the home country, there are M downstream firms, indexed from 1 to M, that import intermediate goods and process them into final goods. These L + M suppliers of final goods are engaged in Cournot competition in the home country's market. The domestic demand for final goods is a linear form: P = P ðY Þ = a−bY;
a;bN0;
ð1Þ
where P and Y denote the price and quantity of final goods, respectively. To simplify the analysis, we assume that one unit of an intermediate good can be transformed into one unit of a final good at a constant marginal cost (MC) of ch in the home country and cf in the foreign country. The MC of producing the intermediate good, cI, is assumed to be constant. In the following, we assume a − cI − ch N 0 and a − cI − cf N 0 in order to exclude the possibility of corner solutions under free trade. Following Ishikawa and Lee (1997) and Ishikawa and Spencer (1999), we have three stages of decisions in our game. In the first stage, the government of the home country commits to imposing a specific import tariff on the intermediate good (s), and a specific import tariff on the final good (t). We allow s to be negative to cover the case of an import subsidy. In stage two, taking the import tariffs as given, the foreign VI firms decide the levels of output of intermediate goods and conduct Cournot competition among them. We assume that all the foreign VI firms commit to their quantities of intermediate goods; that is, there is a Cournot–Nash equilibrium in the intermediate-good market. In the third stage, taking the price of intermediate goods as given, L foreign VI firms and M domestic firms compete to sell final goods to the domestic market on the basis of Cournot competition. This means that the market for final goods in stage 3 involves a Cournot–Nash equilibrium in which L foreign VI firms and M domestic firms set their optimal outputs, and the subgame-perfect equilibrium will incorporate this three stages of decision.2 These suppliers of final goods bear different costs. Let r be the price of intermediate goods determined in the second stage. The MC of producing final goods for domestic firms is ch + r. On the other hand, foreign integrated firms use self-supplied materials to produce final goods, and so their MC is cI + cf. Let xj and y j denote the sales of intermediate goods and final goods by foreign firm j, respectively. Let π jD and π jU denote a foreign VI firm's downstream and upstream profit. The objective of a foreign VI firm is: j
max π = π x ;y j
j
jD
+π j
jU
j j = Py − cI + cf + t y j
+ rx −ðcI + sÞx ; j = 1;…;L:
ð2Þ
2. The model The model setting is illustrated in Fig. 1. There are L foreign VI firms, indexed from 1 to L, that produce both intermediate and final
2 Please see pp. 156 in Spencer and Jones (1991) and pp. 203 in Ishikawa and Spencer (1999).
K.-C.A. Wang et al. / Economic Modelling 28 (2011) 1595–1603
Let yi denote the outputs by a domestic firm. A domestic firm will: i
i
i
max π = Py −ðch + r Þy ; i = 1;…;M
ð3Þ
yi
1597
3.2. The intermediate goods market The derived demand for the intermediate goods is obtained by summing up yi across M domestic downstream firms. We shall consider its inverse:
In the following, we shall solve the game backward to obtain the equilibria.
D r = r t; cI ; ch ; cf ; X ;
3. The equilibrium in the upstream and downstream industries
where XD stands for the quantity demanded. The inverse demand function has some key characteristics. First, the slope of the derived demand is negative:rX = 1/Myir b 0. Second, when foreign firms' MC of final goods increases (decreases), the derived demand curve will shift outward (inward): rt = rcI = rcf = − yit/yir N 0. That is, facing weaker foreign firms, domestic downstream firms will become more competitive in the final goods market and their demand for intermediate goods will increase accordingly. Third, an increase (decrease) of domestic firms' MC will cause the derived demand to shift inward: rch = − ychi/yir = − 1. On the other hand, in the market for intermediate goods, a foreign supplier solves the following problem,
Given the tariffs s and t, we shall solve the last two stages of our model and examine how the specific tariffs affect the equilibrium. 3.1. The final goods market In the final goods market, there are M + L firms engaged in Cournot competition. The sales of final goods by a domestic downstream firm, yi, and by a VI firm, yj, can be determined by the market demand in Eq. (1) and the F.O.C.s of the profit maximization problems listed in Eqs. (2) and (3). The F.O.C.s are: jD j = 0; πy j = PY y + P− cI + cf + t i
ð4Þ
i
πyi = PY y + ðP−ðch + r ÞÞ = 0:
ð5Þ
The following S.O.C.s and stability conditions are assumed to hold globally3: i
i
πjD b πjD b 0; y jy j y j yi
πyi yi b πyi y j b 0 ; i
jD
i
ð6Þ
jD
Δ = πyi yi πy j y j −πyi y j πy j yi N 0:
ð7Þ i
j
The equilibrium outputs of domestic and foreign firms, y and y , are affected by the price of intermediate goods (r), tariff on final goods (t) and the production cost (cI, ch and cf). From Eqs. (6) and (7), their effects are as follows:
i
i
yr = ych =
πjD y jy j Δ
j
j
j
b 0; yt = ycI = ycf =
πiyi yi
i
i
i
i
yt = ycI = ycf =
−πyi y j Δ
j
j
N 0; yr = ych =
Δ
b 0;
−πjD y j yi Δ
ð8Þ
N 0:
ð9Þ
Eq. (8) shows that an increase of MC will cause production to decrease and Eq. (9) shows the effect of an increase of MC of the counterpart country's firms. Because yi and y j are strategic substitutes in our model, an increase of foreign (domestic) firms' MC will cause the final goods outputs of domestic (foreign) firms to increase. When domestic firms' MC or foreign firms' MC increases, the equilibrium total outputs in the domestic market always decrease: i
j
Yr = Ych = Myr + Lyr = =
PY L b 0: Δ
PY M i j b 0 and Yt = YcI = Ycf = Myt + Lyt Δ ð10Þ
3 If the final goods demand function is linear or not too convex, S.O.C.s and stability conditions will hold globally. See Appendix A for the detail of these conditions. The S.O. C.s and stability conditions will be satisfied in the linear demand case.
j
jD
ð11Þ
j
j
max π = π ðr Þ + rx −ðcI + sÞx ; xj
j = 1;…;L;
ð2′Þ
where the downstream profit π jD(r) is solved in stage three. A VI firm has to consider the impact on both its upstream and downstream profit when it sells the intermediate goods. The F.O.C. of Eq. (2′) is, dπ j dπ jD ðr Þ ∂r j = + ðr−cI −sÞ + x = 0: dx j ∂x j dx j
ð12Þ
Using Eq. (4), the first term of Eq. (12) can be written as4: jD
jD
dπ ∂π ∂r = ∂r ∂x j dx j i 1 h = − P− cI + cf + t Myir + ðL−1Þyrj b0 Myir
ð13Þ
Joint control of the two exports gives a VI firm the addition of the ‘strategic effect’ shown in Eq. (13). This total strategic effect is negative and consists of three items. The first item in the right hand side in Eq. (13) is the profit margin of a VI firm in the final goods market. The larger the profit margin, the larger the magnitude of the strategic effect, and a VI firm will sell fewer intermediate goods in this case. The second term measures how opponent firms' outputs change with the price of intermediate goods and it is negative since Yr b 0. Because yir b 0 and yrj N 0, roughly speaking, the absolute value of the second term increases with M and decreases with L. The latter is a result of the fact that when L increases, there are more other VI firms to free ride the benefit resulting from a raised r. It indicates the strategic effect of a VI firm has externality, and an increase of L discourages every VI firm from curbing sales of intermediate goods.5 The third term is the slope of the derived demand. A VI firm is less willing to sell intermediate goods when it faces a steeper derived demand curve. Thus, as shown by Eq. (12), there are two effects to decide a VI firm's intermediate goods selling, one is the strategic effect (the first term of Eq. (12)) and the other is marginal profit from selling 4 There are different settings in literature when a VI firm sells intermediate goods into the intermediate goods market. Greenhut and Ohta (1979) and Salinger (1988) think that VI firms will not intervene into the intermediate goods market in a vertically related market. Schrader and Martin (1998) consider that a VI firm trades in the intermediate goods market with a ‘Cournot belief’. The setting here is followed by Spencer and Jones (1991, 1992), Higgens (1999) and Wang and Chiou (2004). 5 If L = M = 1, the first and second terms will degenerate to the case of Spencer and Jones (1991, 1992).
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intermediate goods in the upstream market (the second and last terms of Eq. (12)). In the previous discussion, we ignored how the change of M and L affects yir and yrj. We also ignore the interplay between the last two terms, both of which depend on market structure parameters. In the following, we shall take all this into account and calculate the strategic effect when the demand for final goods is linear. In this case, by Eqs. (A.3) and (A.4) the strategic effect of a VI firm is, a− t + cI + cf −bLx j dπjD = −2 b 0; ð1 + LÞ2 dx j
ð14Þ
and by Eqs. (12) and (A.4), the sales of intermediate goods are:
x
j
h i M ðL−1Þða−cI Þ−ð1 + LÞ2 ðch + sÞ + 2 + L + L2 cf + t = : b ð1 + LÞ3 + 1 + L2 M ð15Þ
Proposition 1. The magnitude of the strategic effect for a VI firm to curb sales of intermediate goods decreases with the number of foreign firms and is independent of the number of domestic downstream firms in a linear demand case. Proof. Differentiating Eq. (14) with L and M respectively, we obtain: ∂
dπjD 2 a−t−cI −cf −bðL−1Þx j j dx = 2 N 0; ∂L ð1 + LÞ3 jD
∂
dπ dx j = 0: ∂M □
This strategic effect comes from raising domestic downstream firms' (rivals') costs, as shown in Salop and Scheffman (1983, 1987) and defined by Spencer and Jones (1991, 1992). Here, Proposition 1 in our model indicates that the effect will decrease as the number of VI firms increases, but is independent of variation in the number of its downstream rival firms. It must be noted that Eq. (13) shows that M would affect the strategic effect, but M disappears in Eq. (14). The reason is that the effects of M offset each other in a linear demand case. Substituting t = s = 0 into Eq. (15), we have Proposition 2. Under the free trade policies and a linear demand, (1) if cf ≤ ch(cf N ch)where there is only one VI firm, the VI firm will (not) foreclose the intermediate goods market; (2) if cf ≥ ch and L ≥ 2, then the foreign VI firms always sell intermediate goods to domestic downstream firm(s) (xj * N 0). When there is only a VI firm in the market, it will have two choices: foreclosing the intermediate goods market, or not. If the VI firm forecloses the intermediate goods market, it can realize monopoly profits. If it chooses not to foreclose, it can gain upstream profits from selling intermediate goods but the downstream profits will decrease because there will be a group of downstream firms competing with the VI firm. In a linear demand case, Proposition 2(1) shows that the threshold to foreclose is dependent on the relative size of cf to ch. When cf N ch, domestic downstream firms have a comparative advantage to produce final goods. The VI firm's profit from the rent of double marginalization and the sales of final goods is larger than its monopoly rent from market foreclosure. On the other hand, the profit from foreclosing is larger than the profit from both selling in the intermediate goods and final goods markets if cf ≤ ch. Proposition 2
(2) shows how the strategic effect affects the behavior of a VI firm in the vertically-related market. First, we know that the strategic effect causes a VI firm to sell less intermediate goods than a pure upstream firm. Second, as shown in Proposition 1, when L increases, VI firm's strategic consideration decreases and the VI firm shows a greater tendency to sell intermediate goods to rival downstream firms. Thus, when L N 2, the strategic effect is less than the one in L = 1, and VI firms will not foreclose the intermediate market even if domestic downstream firms have less comparative advantage in the production of final goods (i.e., the case of cf = ch shown in Proposition 2(2)).6 Spencer and Jones (1992) indicate that a VI firm has a greater tendency to foreclose the upstream market (or sell less intermediate goods) than a pure upstream firm because the VI firm should consider the impact on its downstream profits of selling intermediate goods.7 Here, we further show that this impact will decrease and that VI firms tend not to foreclose the intermediate market as L increases. Proposition 2 discusses the impact of strategic effect on the behavior of the VI firm(s) based on the VI firms' foreclosure of upstream market. However, as shown in Eq. (12), the equilibrium value of xj * is dependent on both the strategic effect and marginal profit from the upstream market. To analyze this, differentiating Eq. (15) with M and L respectively, we have: Proposition 3. Suppose the demand for final goods is linear. (1) When there are more domestic downstream firms, the VI firms sell more intermediate goods, that is, ∂ xj */∂ M N 0. (2) When cf = ch, ∂ xj */∂ L N 0 if L ≤ 2 and ∂ xj */∂ L b 0 if L N 2; (3) xj * increases with t and decreases with s. The intuition behind the first part of Proposition 3 is clear. From Proposition 1, increasing M has no effect on the strategic effect. Thus an increase in M only changes the marginal revenue of a VI firm in the upstream market, and causes xj * to increase. The sign of ∂xj */∂L is ambiguous because when the number of VI firms increases, both the magnitude of the strategic effect and the marginal revenue in the upstream market reduce. The former causes xj * to increase and the latter causes xj * to decrease. Where cf =ch, if L≤2, xj * increases with L because the change in strategic effect dominates the change in the revenue. If L N 2, the opposite takes place. Proposition 3(3) is easy to obtain from Eq. (15). It is easy to obtain that xj *will decreases with s and increase with t from Eq. (15). These are respectively because: (1). for a VI firm, a decrease of s reduces its marginal cost to sell intermediate goods; (2). an increase of t not only reduces the magnitude of the strategic effect, but also increases the marginal revenue of intermediate goods because the demand for intermediate goods will expand. The price of intermediate goods can be derived from Eq. (15) and Eq. (A.4):
r =
1 fð1 + 3L + M Þa ð1 + LÞ3 + 1 + L2 M 2 3 2 + L + 2L + L + LM + L M s 2 LðM þ 1 LÞ t + cf + L ð3 + L + M ÞcI
ð16Þ
ð1 + Lð2 + L MÞM Þch g: Differentiating Eq. (16) with s and with t respectively, we have: dr4 ∂r4 ∂x j4 L + 2L2 + L3 + LM + L2 M = = N 0; j4 ds ð1 + LÞ3 + 1 + L2 M ∂x ∂s
ð17Þ
dr4 ∂r 4 ∂r 4 ∂xj4 LðL−1−MÞ : = + L = D4 dt ∂t ∂t ∂X ð 1 + L Þ3 + 1 + L2 M |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} ð + Þ
ð18Þ
ð−Þ
6 In fact, when L gets larger, from Eq. (15) we can find that VI firms will still not foreclose even if cf b ch. 7 See Spencer and Jones (1992), pp.39–40.
K.-C.A. Wang et al. / Economic Modelling 28 (2011) 1595–1603 4
Proposition 4. Suppose the demand for final goods is linear. (1). Increasing the tariff on intermediate goods (decreasing the subsidy), s, causes the price of intermediate goods to increase (∂ r*/∂ s N 0). (2). WhenL ≥ (b)M + 1, increasing the tariff on final goods, t, also causes the price of intermediate goods to increase (decrease). The intuition behind part (1) of Proposition 4 is simple. A tax on the trade of intermediate goods will naturally raise their market price, but the story behind part (2) is a little complicated. First, an increase of t shifts the derived demand curve outward and causes the price of intermediate goods to increase. This effect is shown in the term ∂r*/∂ tof Eq. (18). Second, ∂ x j */∂ tN 0 from part (3) of Proposition 3. Because ∂r*/∂ XD * is the slope of derived demand, which is negative, the second term in Eq. (18) is negative. If there is no strategic effect, the first term always dominates the second term in Eq. (18) because an increase of t directly causes a higher derived demand for intermediate goods and the increase of x j* caused by increasing t (∂ xj */∂ t) is indirectly induced by this higher derived demand. Thus, r* increases with t. If we consider the strategic effect, whether the first or the second term is more important depends on the market structure (L and M). If L = 1, the strategic effect is strongest where L≥1 from Proposition 1. But the strategic effect will be lessened if t increases (from Eq. (14), d2π jD/dxjdt = 2/(1 + L)2N0), and this causes the monopolistic VI firm to sell more intermediate goods and results in the second term dominating the first term in Eq. (18). Thus, we can see that an increase of t always causes r* to decrease if L = 1 from part (2) of Proposition 4. When L increases, there are two consequences for VI firms' strategic effect. First, the strategic effect is less prominent. Second, the magnitude of the decrease in strategic effect by an increase in t decreases with L (d3π jD/ dxjdtdL = − 4/(1 + L)3 b 0). These two statements mean that an increase of x j caused by a higher t will be less when L increases. Thus, the first term will dominate the second term in Eq. (18) if L is higher. In our model, the threshold of L is M + 1.8 Part (2) of Proposition 4 shows that the first term dominates (or is dominated by) the second term in Eq. (18) if L ≥ (b)M + 1. In the case of linear demand, Spencer and Jones (1992) also get ∂ r*/∂ t b 0 when L = M = 1.9 But we further indicate that the relation between r* and t could be reversed when L N M+ 1. This is mainly because the impact of t on the strategic effect decreases with L. Because an increase of t may increase or decrease the price of intermediate goods, this encourages us to learn how changes of t and s affect the final goods price. Substituting Eq. (16) into Eqs. (A.5) and (A.6) and using Eq. (1), we can get total final equilibrium outputs, Y*:
Y =
L 2 ð1 + LÞ + LM ða−cI Þ−ðLM + M Þðs + ch Þ b ð1 + LÞ3 + 1 + L2 M 2 − ð1 + LÞ −M t + cf : ð19Þ
Z
x
dY 4 = Yt dt ð−Þ
1599
2 − ð1 + LÞ −M 4 4 dr : + Yr = b ð1 + LÞ3 + 1 + L2 M ð−Þ dt
ð21Þ
ð?Þ
From Eqs. (20) and (21), we have: Proposition 5. Suppose the demand for final goods is linear. (1). When the tariff (subsidy) on intermediate goods s increases (decreases), p fewer ffiffiffiffiffi final goods will be produced. (2). When L≥ðbÞ M−1, an increase in t causes the domestic price of final goods, P*, to increase (decrease). Raising s increases the price of intermediate goods (Proposition 4) and hence decreases total output of final goods as a result. The intuition for part (2) of Proposition 5 is as follows. When t increases, foreign firms become less competitive in the downstream market, and we expect y j * to shrink and yi * to expand. When r is fixed, the total output will decrease (Yt b 0). How r will change with t is not clear as shown in Proposition 4. From part (2) of Proposition 4, we know that dr*/dt b 0if L b M + 1. In this case, the second term in Eq. (21) is positive. We find that the second term dominate the first term pffiffiffiffiwill ffi when L is less than the threshold M−1. Notice that P* usually increases with t in traditional trade theory, but in our model when pffiffiffiffiffi L b M−1, the opposite takes place. This special phenomenon is induced by VI firm's strategic effect. When t increases, the strategic effect causes VI firms to sell more xj. This will lead r to reduce, and P* to further reduce because domestic downstream firms have cheaper marginal costs.11 Fig. 2 shows how the tariff affects the prices of intermediate and final goods. From Fig. 2, we find that contrary to the literature on trade theory, increasing the tariff on final goods does not necessarily raise the price of final goods in the domestic market. We have not found that the final goods price decreases with the tariff on final goods in theoretic literature until now. This result shows that the market structure in the vertically-related market is a key issue when we study strategic trade theory, and we should take note of, and review the role of strategic tariffs in the vertically-related market. For these reasons, the next section is concerned with the optimal tariffs. 4. The optimal tariffs In this section, we study the optimal tariffs for the domestic government. The domestic social welfare consists of producers' surpluses (Mπi *(yi *, y j *, x j *)), the tariff revenue (the final good tariff revenue, tLy j * and theintermediate good tariff revenue, sMyi *), and Y* consumers' surpluses ∫0 P(Y)dY − P(Y *)Y * . Thus, the social welfare function of the home country can be shown as W ðs; t Þ = Mπ
i4
i
j
y ;y ;x
j
+ tLy
j
i Y4 + sMy + ∫ P ðY ÞdY−P Y Y ; 0
ð22Þ 10
Differentiating Eq. (19) with s and t respectively, we have :
dY −LM ðL + 1Þ dr b 0; = Yr = ds b ð1 + LÞ3 + 1 + L2 M ð−Þ ds
ð20Þ
ð + Þ
8 The change of the number of L and M will affect VI firms' upstream marginal profit from selling intermediate goods. But this is not the crucial factor to decide the sign of Eq. (18) because the first term always dominates the second term in Eq. (18) if there is no strategic effect. Therefore we skip the discussion of the variation of VI firms' upstream marginal profit. 9 See Spencer and Jones (1992, pp.46), Proposition 5(i). The result of Proposition 4 (1),∂ r*/∂ s N 0 is consistent with Spencer and Jones's result which can be seen in Spencer and Jones (1992, pp. 50), Proposition 6. 10 For the sign of Yr* and Yt*, see Eq. (10).
11 The story of the TV set industry in mainland China may serve as an example of this surprising possibility. Mainland Chinese TV producers are like the domestic producers in our model, who have to completely rely on imports of iconoscopes to manufacture TV sets. According to the data from the Almanac of China's Domestic Trade (2000, pp. 126–127), in 1999, the domestic prices of 29-inch and 21-inch color TV sets were as low as $250 and $125 respectively, while the Statistic Almanac of China's Customs (2000, p. 1157) reported the average import price of color TVs to be as high as $320. According to the Customs Import and Export Tariff of the People's Republic of China (1999), since 1997, the import tariffs of color TVs and color TV iconoscopes have been 35% and 18%, respectively, but the high tariffs did not seem to enhance the domestic TV set prices. Our analysis suggests that it might be that high tariffs caused foreign VI firms to stay away from mainland China's TV set market. When these foreign firms reduced the sales of final products, they might have priced the intermediate goods, iconoscopes, low, and this might have caused the TV set prices in the market to come down. In fact, the Almanac of China's Economy (2000, p. 261) reported that in 1999, the market share of the top ten domestic TV firms was about 80%.
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Fig. 2. The relationship between tariffs and prices.
where yi *, yj * and xj * depend on s and t, and Y* = Myi * + Lyj *. Differentiating Eq. (22) with respect to t and s respectively, we have:
t =
s =
i i i j + Ly + sM dydt − dP M −y dr + y dP Y dt dt dt j
−L dydt
j M −yi dr + y j dP Y + Myi + tL dyds − dP ds ds ds i
−M dyds
;
:
ð23Þ
ð24Þ
Eq. (23) exhibits the factors to determine the tariffs on final goods. The first term in the numerator of Eq. (23) is the rent shifting effect, originally defined by Brander and Spencer (1985).12 That is, an increase in t will shift rents from foreign VI firms to M domestic firms. This effect involves both the change of P and the change of r. The second term in the numerator of Eq. (23) shows the rent extracted from foreign VI firms. The third term in the numerator of Eq. (23) shows the interplay between t and s. Compared with the case in s = 0, this indicates t will be higher (lower) if s N (b)0 because tariff revenue from (a subsidy, or expenditure on) intermediate goods increases with t. The last term represents concerns with consumers' surpluses. It is easy to check if M = 0, t* = (Pt − 1)Y/Yt. This is the case in Brander and Spencer (1984) where there is only the rent extracting effect. The factors to decide s are similar, so we shall show the discussion of them later. In a linear demand case, t* and s* can be solved from Eqs. (23) and (24),13
t =
h i 2 2 3 2 ð1 + LÞ + 2LM ða−cI −ch Þ− 2ð1 + LÞ + −2 + L + L M cf −ch 4 + 2L½5 + 2M + Lð4 + L + M + LMÞ
;
ð25Þ
s =
M + 1−L2 2L a−cI −cf + 2 + 3L + L2 cf −ch 4 + 2L½5 + 2M + Lð4 + L + M + LMÞ
: ð26Þ
With the result of Eq. (25), we find: Proposition 6. When domestic downstream firms import intermediate goods, the home country always imposes a tariff on final goods; that is, t* N 0 in the linear demand case. The proof of Proposition 6. See Appendix A. In the linear demand case, the first term of the numerator of Eq. (23) is positive. Moreover, the rent shifting and extracting effects will dominate the concern about consumers' surpluses and a possible increase in subsidy expenditure on intermediate goods. Note that the rent shifting effect here is more important than traditionally considered, because an increase in t in our model can shift foreign VI firms' focus away from final goods market to intermediate goods market, and domestic downstream firms can get a better position as a result. 12 The definition of ‘rent shifting’ is that ‘The central idea is that it is to the advantage of a country to capture a large share of the production of profit-earning imperfectly competitive industries.’ Please see Brander and Spencer (1985). 84, line 9 to line 11. 13 In the linear demand case, the S.O.C.s conditions will hold and s and t are strategic complements. See Appendix A.
On the other hand, the government may either tax or subsidize the imports of intermediate materials as the following proposition suggests. Proposition 7. Suppose the demand for final goods is linear. If M N (b) L2 − 1, then s* N (b)0 when yi*, yj* N 0. The proof of Proposition 7. See Appendix A. In the linear demand case, the rent shifting effect (the first term in the numerator of Eq. (24)) is negative because domestic firms do not produce intermediate inputs in our model and a tax on exporting intermediate goods lowers the profits of domestic firms. Where the rent extracting effect (the second term in the numerator of Eq. (24)) is positive, the interplay effect between t and s (the third term in the numerator of Eq. (24)) is positive due to t*N0 and dy j */dsN 0, and the last term in the numerator of Eq. (24) is negative because an increase of s hurts social welfare. This means that the only reason to tax intermediate goods is to extract rents from the intermediate goods market and to help raise rents extracted from the final goods market (because of the interplay effect between t and s). Foreign VI firms' rents in both intermediate and final good markets are, in fact, high when L is relatively smaller than M. That is why the home country will tax (subsidize) intermediate goods only if MN (b)L2 −1 in Proposition 7. We should note that domestic governments usually taxes on import goods from the viewpoint of strategic trade, but Proposition 7 points out that if the number of domestic firms is relatively smaller than the number of foreign VI firms, a domestic government should subsidize intermediate import goods.14 In other words, the market structure in the vertically-related market plays an important role when domestic government decides whether to tax or subsidize intermediate goods. A change of M can support the intuition above. Differentiating s* and t* with respect to M., we find from Eqs. (25) and (26) that: ∂s ð1 + LÞð2 + ðL−1ÞLÞ = ∂M 2½2 + Lð5 + 2M + Lð4 + L + M + LMÞÞ2 h i 2 cf −ch N 0; 2L a−cI −cf + 2 + 3L + L
ð27Þ
h i ðL−2ÞLð1 + LÞ3 2L a−cI −cf + 2 + 3L + L2 cf −ch ∂t N N =− 0 if 2 L: b b ∂M 2½2 + Lð5 + 2M + Lð4 + L + M + LMÞÞ2
ð28Þ The proof of the sign of ∂ s*/∂ M and ∂ t*/∂ M. See Appendix A. Eqs. (27) and (28) indicate that s* increases and t* decreases with M. The intuition is the same as the one for Propositions 6 and 7. When M increases, the final goods market becomes more competitive, and foreign VI firms earn economic rents mainly in the market of 14 In this model, t* − s* N 0 is always satisfied. From Propositions 6 and 7, we know that t* N 0 ≥ s* if M ≤ L2 − 1. Subtracting Eq. (26) from Eq. (25), we can find that:
t −s =
1 V2 1 + L 1 + L + L2 + M a−cI −cf 2½2 + 2Lð5 + 2M + Lð4 + L + M + LM ÞÞ : + cf −ch ð1 + LÞ½−2 + Lð−1 + Lð2 + L−MÞÞg
When M N L2 − 1 and cf ≤ cf ( cf is the upper bound of cf and is defined in Eq. (A.7)), we can find that t* − s* N 0.
K.-C.A. Wang et al. / Economic Modelling 28 (2011) 1595–1603
intermediate goods. Thus, the best way to extract their rents is to increase s. On the other hand, as the market of final goods becomes more competitive and fewer rents can be extracted and shifted in this market, we expect t* to decrease in general. Eq. (28) shows that ∂t*/∂MN 0 when L=1. The intuition for this special case is as follows: When there is only one foreign VI firm, all benefit from raising domestic firms' costs accrues to the foreign firm itself (there is no free-rider effect), and this VI firm tends to cut the supply of intermediate goods. To correct this, the domestic government can raise t to weaken the foreign firm's competitiveness in the final goods market in order to shift this VI firm's business interest back to the sale of intermediate goods. If L=M=1, cf ≥ch and the domestic firm can produce intermediate inputs, Spencer and Jones (1992) found that domestic governments will subsidize imported intermediate goods under free trade condition.15 Our sufficient condition for subsidizing intermediate goods is not as restricted as Spencer and Jones's. In this model, if L=M=1 and t=0, the domestic government always subsidizes intermediate goods whatever cf ≥ch or cf ≤ch.16 The reason is that in addition to a generalized market structure, our model and Spencer and Jones's differ in that our domestic firms cannot produce intermediate inputs on their own. This difference induces the rent shifting effect (the first term in the numerator of Eq. (24)) is always negative in our model because there is no rent to shift in the upstream market. In other words, a domestic government are more likely to subsidize intermediate goods in our model than in that of Spencer and Jones. From this viewpoint, we can further infer that tariffs on intermediate and final import goods will be higher if domestic firms can produce intermediate inputs by themselves.17 This also means that
1601
although domestic firms are not permitted to produce intermediate goods by themselves in our model, this model still applies without a loss of generality.
5. Conclusion Developing countries usually play the role of processing final goods in the global trade system. It is thus quite important to examine how they protect domestic industries that face fierce international competition. Using the framework of Spencer and Jones (1991, 1992) with a flexible market structure, we have studied import tariffs (subsidies) on the intermediate goods and final goods markets. We also focus on how optimal tariffs are affected by the market structure. In our model, we find that the strategic effect for a VI firm plays an important role. This strategic effect, coming from raising the costs borne by rivals, will decrease as the number of VI firms increases. This result shows that the strategic effect has some externality. To protect domestic firms and to extract rents from foreign firms, the imports of final goods are always taxed, but imports of intermediate goods can be taxed or subsidized, depending on the market structure. A surprising finding is that a tariff increase on final goods may lower the domestic price of intermediate goods and final goods. This is because a tariff on final goods directs the vertically integrated firms to focus on the production of intermediate goods, leading to a lower price of intermediate goods, which trickles down the price of final goods.
Appendix A Comparative static analyses on final goods outputs Taking the total differential of F.O.C.s, Eqs. (4) and (5), we obtain: jD
j
jD
i
i
j
i
i
πy j yi dy + πy j yi dy = dt; πyi y j dy + πyi yi dy = dr; j jD j i i i i jyj = PYYLy + PY(L + 1)b0, πyjyi = PYYMy + PYMb0, πyiyi = PYYMy + PY(M + 1)b0 and πyiyj = PYYLy + PYLb0 if the demand function is linear where πyjD
or not too convex. The stability condition is Δ = PYYPYY + PY2(L + M + 1)N0. Thus, we have, yir =
πjD y jy j Δ
b 0; ytj =
πiyi yi Δ
b 0; yit =
−πiyi y j Δ
N 0;
yrj =
−πjD y j yi Δ
N 0:
Using the same method, we can have ycih = yir b 0, ycjI = ycjf = ytj b 0, yciI = ycif = yit N 0 and ycjh = yrj N 0. Stage 3's market equilibriums in the linear demand function Using Eqs. (1), (4) and (5), we have,
i
y =
j
y =
15 16 17
a + L cf + cI + t −ðL + 1Þðch + r Þ bðL + M + 1Þ
;
a + M ðr + ch Þ−ðM + 1Þ cf + cI + t bðL + M + 1Þ
ðA:1Þ
:
See Spencer and Jones (1992, pp. 43), Proposition 3. Under L = M = 1 and t = s = 0, ∂ W/∂ s = − (5(a − cI − cf) − 2(cf − ch))/50b and yj * = (5(a − cI − cf) − 2(cf − ch))/13b. yj *N0 if and only ∂ W/∂ s b 0. Because s and t are strategic complements (see Appendix A (Eq. (A.8)), an increase of s will cause to an increase of t.
ðA:2Þ
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Summing up two equations below across all firms, the total sales of final goods and their market price are, respectively: aðL + M Þ−L cI + cf + t −Mðch + r Þ
Y=
bðL + M + 1Þ a + L cI + cf + t + M ðch + r Þ
P=
L+M+1
;
:
Thus the downstream profit of a VI firm and the domestic firm's profit can be respectively derived to be: jD
π
=
i
π =
2 a + Mðr + ch Þ−ðM + 1Þ cf + cI + t bðL + M + 1Þ2
;
2 a + L cf + cI + t −ðL + 1Þðch + rÞ
: bðL + M + 1Þ2 Summing up Eq. (A.1) across M domestic downstream firms, the inverse derived demand function is,
r=
a + L cI + cf + t L+1
−ch −
bðL + M + 1Þ D X : ðL + 1ÞM
ðA:3Þ
ðA:4Þ
The proof of Proposition 6 Substituting Eq. (16) into (A.1) and (A.2), we can have equilibrium outputs of domestic firm i, yi *, and equilibrium outputs of foreign firm j, yj *. They are: h i L ðL−1Þða−cI Þ−ðL + 1Þ2 ðs + ch Þ + 2 + L + L2 t + cf ; y = b ð1 + LÞ3 + 1 + L2 M i
y
j
2 2 ð1 + LÞ + M a−cI −t−cf + LM + L M s + ch −t−cf = : b ð1 + LÞ3 + 1 + L2 M
ðA:5Þ
ðA:6Þ
Case 1: yj * N 0. Substituting t* of Eq. (25) and s* of Eq. (26) into Eq. (A.6), we have the upper bound of cf when yj * N 0: 2ðL + 1Þða−cI Þ + 2 + L + L2 Mch cf = : 2ð1 + LÞ + 2 + L + L2 M
ðA:7Þ
Suppose t* ≤ 0. From Eq. (25), we have: h i 2 ð1 + LÞ2 + 2LM ða−cI Þ + ðL−2Þð1 + LÞ2 Mch cf ≥ Ncf ; 2ð1 + LÞ2 + −2 + L + L3 M which contradicts with our presumption that y j N 0. Case 2: y j * = 0: Under the assumption that a − cI − cf N 0, if the home country wants to deter foreign VI firms from importing final goods, then t* must be positive. The S.O.C.s conditions of optimizing s and t From Eq. (22), we will have, h i 2 2 Lð1 + LÞ M 2ð1 + LÞ + ð2 + Lð2L−1ÞÞM Wss = − b0; 2 b ð1 + LÞ3 + 1 + L2 M h i M2 −L ð1 + LÞ4 ð2 + LÞ + 2ð2 + Lð3 + Lð7 + Lð5 + 3LÞÞÞÞM + 2 + L 1 + 2L 2 + L + L2 Wtt = b0; 2 2b ð1 + LÞ3 + 1 + L2 M Wst = Wts =
LM½2ð1 + MÞ + Lð5 + M + Lð7 + 3M + Lð7 + 3L + 2ð1 + LÞM ÞÞÞ N 0; 2b ð1 + LÞ3 + 1 + L2 M
Wss Wtt −Wst Wts =
2L2 M ½2 + Lð5 + 2M + Lð4 + L + M + LMÞÞ N 0: 2 b2 ð1 + LÞ3 + 1 + L2 M
ðA:8Þ
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The proof of Proposition 7 (1). When yj *, yi * N 0, Eq. (A.5) provides the right formula for yi *. Substituting s* and t* into Eq. (A.5), we find the upper bound of ch for yi * N 0 to be:
ch =
2Lða−cI Þ + 2 + L + L2 cf ð1 + LÞð2 + LÞ
:
ðA:9Þ
We wish to show that the sign of s* is the same as M + 1 − L2. Suppose the contrary holds. It then follows from Eq. (26) that ch ≥ch , which contradicts our presumption that yi * N 0.
The sign of ∂ s*/∂ M and ∂ t*/∂ M Suppose if the sign of ∂ s*/∂ M in Eq. (27) is non-positive, using Eq. (A.9), then one will find ch ≥ch . This contradicts yi * N 0. Similar logic can be applied to determine the sign of ∂ t*/∂ M. References Brander, J., Spencer, B.J., 1984. Trade warfare: tariffs and cartels. Journal of International Economics 16, 227–242. Brander, J., Spencer, B.J., 1985. Export subsides and international market share rivalry. Journal of International Economics 18, 83–100. Greenhut, M.L., Ohta, H., 1979. Vertical integration of successive oligopolists. The American Economic Review 69 (1), 137–141. Higgens, R.S., 1999. Competitive vertical foreclosure. Managerial and Decision Economics 20, 229–237. Ishikawa, J., Lee, K.D., 1997. Backfiring tariffs in vertically related markets. Journal of International Economics 42, 395–423. Ishikawa, J., Spencer, B.J., 1999. Rent-shifting export subsidies with an imported intermediate product. Journal of International Economics 48 (2), 199–232. Lin, P., 2006. Strategic spin-offs of input division. European Economic Review 50, 977–993.
Matsushima, N., 2006. Industry profits and free entry in inputs markets. Economics Letters 93, 329–336. Salinger, M.A., 1988. Vertical mergers and market foreclosure. Quarterly Journal of Economics 103, 345–356. Salop, S.C., Scheffman, D.T., 1983. Raising rivals' cost. The American Economic Review 73, 267–271. Salop, S.C., Scheffman, D.T., 1987. Cost raising strategy. Journal of Industrial Economics 36, 19–34. Schrader, A., Martin, S., 1998. Vertical market participation. Review of Industrial Organization 13, 321–331. Spencer, B.J., Jones, R.W., 1991. Vertical foreclosure and international trade policy. The Review of Economic Studies 58, 153–170. Spencer, B.J., Jones, R.W., 1992. Trade and protection in vertically related markets. Journal of International Economics 32, 31–55. Wang, K.-C.A., Chiou, J.-C., 2004. Strategic trade policies in the vertically-related market. Academia Economic Papers 32, 369–391.
Contents lists available at ScienceDirect
Economic Modelling j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c m o d
Domestic trade protection in vertically-related markets Kuang-Cheng A. Wang a,⁎, Hui-Wen Koo b, Tain-Jy Chen b a b
Social Science Division, Center for General Education, Chang Gung University, Taiwan Department of Economics, National Taiwan University, Taiwan
a r t i c l e
i n f o
Article history: Accepted 10 February 2011 JEL classification: F12 F13 Keywords: Market structure Vertically-integrated firms Vertically-related markets
a b s t r a c t We consider trade policy in a setting where home country firms are fully dependent on vertically-integrated foreign firms for supplies of a key input. We find that vertically-integrated firms' strategic considerations play an important role and that, in particular, a tariff on final goods may either increase or decrease the domestic price of final goods. The import of final goods is always taxed to extract and shift rents from foreign firms, while the import of intermediate goods can be either taxed or subsidized. The market structure is shown to be an important consideration when making trade policy. © 2011 Elsevier B.V. All rights reserved.
1. Introduction In the global trade system, developing countries have always played the role of exporters of raw materials or processors of final products. Colombia, Cuba and Brazil, for example, belong to the former category, while China and the Four Asian Newly Industrialized Countries belong to the latter. On the other hand, firms in developed countries are usually large, vertically integrated, and control and sell technologies necessary for producing key intermediate inputs as well as the final goods. An example of such cases is the market for cellular phones in China. In these years, the Chinese domestic market has gradually become the most important market in the world. Motorola, Nokia and Sony Ericsson are the main foreign suppliers of cellular phones in China, with a collective total market share of about 85% in 2001, and 70% in 2002, with the rest of the market being taken up by 12 domestic Chinese firms dependent on their foreign competitors to supply core components, such as ICs and LCDs.1 Another example is the TFT-LCD industry, in which there are several vertically-integrated (thereafter VI) firms in the market, including LG-Philips, Samsung, Sharp, NEC and Hitachi. On the other hand, there are quite a few downstream assembling firms: AUO, Chi-Mei, Hann Star, Quanta, Chunghwa in Taiwan and SVA-NEC, Boe-Hydis in China. The VI firms
⁎ Corresponding author at: Social Science Division, Center for General Education, Chang Gung University, 259 Wen-Haw 1st Rd., Kwei-Shan Tao-Yua, 33302, Taiwan. Tel.: +886 3 211 8800x3298; fax: +886 3 211 8458. E-mail address: [email protected] (K.-C.A. Wang). 1 The detailed information of the market of cellular phones in China can be found in http://search.cei.gov.cn. 0264-9993/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2011.02.022
not only compete with downstream firms in the TFT-LCD market, but also sell key components for the assembly of TFT-LCDs to downstream firms. For instance Sharp, NEC and Hitachi sell drive ICs to their downstream competitors. The purpose of this paper is to examine how developing countries can protect their downstream firms in the domestic market, when domestic firms must import a key intermediate input from vertically-integrated foreign firms to undertake production. In the literature, the vertically-related market has been a widely discussed topic. The pioneering paper in the literature is that of Greenhut and Ohta (1979). They set up a successive oligopoly model and compared the equilibrium intermediate and final prices of goods between all firms, non-integrated and integrated firms alike. Following Greenhut and Ohta's successive oligopoly model, much later literature further researched related topics of market foreclosure or strategic spin-offs, for example Salinger (1988), Schrader and Martin (1998), Higgens (1999), Lin (2006), and Matsushima (2006). In international trade theory, there is also much literature focusing on the vertically-related market, such as the works of Spencer and Jones (1991, 1992), Ishikawa and Lee (1997), Ishikawa and Spencer (1999) and Wang and Chiou (2004). In these works, Spencer and Jones (1991) study the trade policies of exporting countries when firms based in those countries compete with firms in the importing countries, which also hosts the market for the final goods, while Ishikawa and Spencer (1999) and Wang and Chiou (2004) focus on export subsidies of two exporting countries when these two countries export finished goods to vertically-related market of a third country. The difference between Ishikawa and Spencer (1999) and Wang and Chiou (2004) is mainly in market structures. The study in Ishikawa and Spencer (1999) assumes that there are a group of upstream and downstream firms in these two exporting countries, while Wang and
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Chiou (2004) assume that there are a group of VI firms in one exporting country and a group of downstream firms with lower production cost in the other exporting country. This indirectly means that Ishikawa and Spencer (1999) and Wang and Chiou (2004) both allow that the number of independent upstream (downstream) firms or the number of VI firms can vary to characterize different market structures in both exporting countries. However, Spencer and Jones (1992) and Ishikawa and Lee (1997) focus on the importing country's policies if the importing country faces a foreign VI firm or foreign vertically-decentralized firms (i.e., one independent upstream and one independent downstream firms) and the domestic firms and foreign firms compete in the domestic intermediate and final goods markets. The main difference between these two papers is that Spencer and Jones (1992) study how the trade policies of the domestic country affect foreign firm(s)'s pricing in the intermediate goods market and domestic social welfare, while Ishikawa and Lee (1997) emphasize “the backfire effect”. Ishikawa and Lee's study points out that if the domestic country imposes a prohibited tax on intermediate or final import goods, it may hurt domestic upstream and (or) downstream firms due to structural changes in the market. They refer to this phenomenon as the ‘Backfire effect’. Thus, an overview of the literature reveals a trend to consider market structures when studying relative trade issues. Representing the actual situation more realistically and responding to the expansion of the literature, we build up a more general vertically-related model to discuss how the importing country's trade policies affect both upstream and downstream market prices and what are the importing country's optimal trade policies under different market structures. We arrive at some broad conclusions. First, VI firms' strategic effect plays an important role in our general vertically-related model. The strategic effect follows the finding of Salop and Scheffman (1983, 1987), which states that a VI firm may gain from raising its rivals' costs even at some expense to itself. The strategic effect is also mentioned by Spencer and Jones (1991, 1992). We find that the VI firms' strategic effect lessens as the number of foreign VI firms increases. Second, this strategic effect shows that an increase of the tariff on intermediate goods increases both prices in both domestic upstream and downstream markets. But an increase of the tariff on final goods may either increase or decrease both prices in domestic upstream and downstream markets, with the result depending on the relative ratio of the number of domestic independent downstream firms to foreign VI firms. The case of an increase in the final goods' tariff lowering the domestic price of the final goods is a special case that violates general economic intuitions. Some of our findings supplement those of Spencer and Jones (1992), who authored the paper most relevant to our own. In our model, the optimal trade policy would impose a tariff on final goods, but whether to subsidize or impose a tariff on intermediate goods depends on market structures between home and foreign countries. This method of considering differences in market structure between different countries has many advantages, and we can look ahead to considering relations between China and the U.S., or China and Japan, and so on, where market structures may be remarkably different. In addition, our results indicate that market structure seems not to be ignored and makes clear the necessity of our study. The paper is organized as follows. Section 2 outlines the setting of the model. In Section 3, we derive the Cournot equilibrium in the upstream and downstream industries, when the tariffs (subsidies) on intermediate goods and final goods are given. Section 4 solves the optimal tariffs so as to maximize the social welfare of the home country. Section 5 offers some conclusions.
Fig. 1. The market structure.
goods. In the home country, there are M downstream firms, indexed from 1 to M, that import intermediate goods and process them into final goods. These L + M suppliers of final goods are engaged in Cournot competition in the home country's market. The domestic demand for final goods is a linear form: P = P ðY Þ = a−bY;
a;bN0;
ð1Þ
where P and Y denote the price and quantity of final goods, respectively. To simplify the analysis, we assume that one unit of an intermediate good can be transformed into one unit of a final good at a constant marginal cost (MC) of ch in the home country and cf in the foreign country. The MC of producing the intermediate good, cI, is assumed to be constant. In the following, we assume a − cI − ch N 0 and a − cI − cf N 0 in order to exclude the possibility of corner solutions under free trade. Following Ishikawa and Lee (1997) and Ishikawa and Spencer (1999), we have three stages of decisions in our game. In the first stage, the government of the home country commits to imposing a specific import tariff on the intermediate good (s), and a specific import tariff on the final good (t). We allow s to be negative to cover the case of an import subsidy. In stage two, taking the import tariffs as given, the foreign VI firms decide the levels of output of intermediate goods and conduct Cournot competition among them. We assume that all the foreign VI firms commit to their quantities of intermediate goods; that is, there is a Cournot–Nash equilibrium in the intermediate-good market. In the third stage, taking the price of intermediate goods as given, L foreign VI firms and M domestic firms compete to sell final goods to the domestic market on the basis of Cournot competition. This means that the market for final goods in stage 3 involves a Cournot–Nash equilibrium in which L foreign VI firms and M domestic firms set their optimal outputs, and the subgame-perfect equilibrium will incorporate this three stages of decision.2 These suppliers of final goods bear different costs. Let r be the price of intermediate goods determined in the second stage. The MC of producing final goods for domestic firms is ch + r. On the other hand, foreign integrated firms use self-supplied materials to produce final goods, and so their MC is cI + cf. Let xj and y j denote the sales of intermediate goods and final goods by foreign firm j, respectively. Let π jD and π jU denote a foreign VI firm's downstream and upstream profit. The objective of a foreign VI firm is: j
max π = π x ;y j
j
jD
+π j
jU
j j = Py − cI + cf + t y j
+ rx −ðcI + sÞx ; j = 1;…;L:
ð2Þ
2. The model The model setting is illustrated in Fig. 1. There are L foreign VI firms, indexed from 1 to L, that produce both intermediate and final
2 Please see pp. 156 in Spencer and Jones (1991) and pp. 203 in Ishikawa and Spencer (1999).
K.-C.A. Wang et al. / Economic Modelling 28 (2011) 1595–1603
Let yi denote the outputs by a domestic firm. A domestic firm will: i
i
i
max π = Py −ðch + r Þy ; i = 1;…;M
ð3Þ
yi
1597
3.2. The intermediate goods market The derived demand for the intermediate goods is obtained by summing up yi across M domestic downstream firms. We shall consider its inverse:
In the following, we shall solve the game backward to obtain the equilibria.
D r = r t; cI ; ch ; cf ; X ;
3. The equilibrium in the upstream and downstream industries
where XD stands for the quantity demanded. The inverse demand function has some key characteristics. First, the slope of the derived demand is negative:rX = 1/Myir b 0. Second, when foreign firms' MC of final goods increases (decreases), the derived demand curve will shift outward (inward): rt = rcI = rcf = − yit/yir N 0. That is, facing weaker foreign firms, domestic downstream firms will become more competitive in the final goods market and their demand for intermediate goods will increase accordingly. Third, an increase (decrease) of domestic firms' MC will cause the derived demand to shift inward: rch = − ychi/yir = − 1. On the other hand, in the market for intermediate goods, a foreign supplier solves the following problem,
Given the tariffs s and t, we shall solve the last two stages of our model and examine how the specific tariffs affect the equilibrium. 3.1. The final goods market In the final goods market, there are M + L firms engaged in Cournot competition. The sales of final goods by a domestic downstream firm, yi, and by a VI firm, yj, can be determined by the market demand in Eq. (1) and the F.O.C.s of the profit maximization problems listed in Eqs. (2) and (3). The F.O.C.s are: jD j = 0; πy j = PY y + P− cI + cf + t i
ð4Þ
i
πyi = PY y + ðP−ðch + r ÞÞ = 0:
ð5Þ
The following S.O.C.s and stability conditions are assumed to hold globally3: i
i
πjD b πjD b 0; y jy j y j yi
πyi yi b πyi y j b 0 ; i
jD
i
ð6Þ
jD
Δ = πyi yi πy j y j −πyi y j πy j yi N 0:
ð7Þ i
j
The equilibrium outputs of domestic and foreign firms, y and y , are affected by the price of intermediate goods (r), tariff on final goods (t) and the production cost (cI, ch and cf). From Eqs. (6) and (7), their effects are as follows:
i
i
yr = ych =
πjD y jy j Δ
j
j
j
b 0; yt = ycI = ycf =
πiyi yi
i
i
i
i
yt = ycI = ycf =
−πyi y j Δ
j
j
N 0; yr = ych =
Δ
b 0;
−πjD y j yi Δ
ð8Þ
N 0:
ð9Þ
Eq. (8) shows that an increase of MC will cause production to decrease and Eq. (9) shows the effect of an increase of MC of the counterpart country's firms. Because yi and y j are strategic substitutes in our model, an increase of foreign (domestic) firms' MC will cause the final goods outputs of domestic (foreign) firms to increase. When domestic firms' MC or foreign firms' MC increases, the equilibrium total outputs in the domestic market always decrease: i
j
Yr = Ych = Myr + Lyr = =
PY L b 0: Δ
PY M i j b 0 and Yt = YcI = Ycf = Myt + Lyt Δ ð10Þ
3 If the final goods demand function is linear or not too convex, S.O.C.s and stability conditions will hold globally. See Appendix A for the detail of these conditions. The S.O. C.s and stability conditions will be satisfied in the linear demand case.
j
jD
ð11Þ
j
j
max π = π ðr Þ + rx −ðcI + sÞx ; xj
j = 1;…;L;
ð2′Þ
where the downstream profit π jD(r) is solved in stage three. A VI firm has to consider the impact on both its upstream and downstream profit when it sells the intermediate goods. The F.O.C. of Eq. (2′) is, dπ j dπ jD ðr Þ ∂r j = + ðr−cI −sÞ + x = 0: dx j ∂x j dx j
ð12Þ
Using Eq. (4), the first term of Eq. (12) can be written as4: jD
jD
dπ ∂π ∂r = ∂r ∂x j dx j i 1 h = − P− cI + cf + t Myir + ðL−1Þyrj b0 Myir
ð13Þ
Joint control of the two exports gives a VI firm the addition of the ‘strategic effect’ shown in Eq. (13). This total strategic effect is negative and consists of three items. The first item in the right hand side in Eq. (13) is the profit margin of a VI firm in the final goods market. The larger the profit margin, the larger the magnitude of the strategic effect, and a VI firm will sell fewer intermediate goods in this case. The second term measures how opponent firms' outputs change with the price of intermediate goods and it is negative since Yr b 0. Because yir b 0 and yrj N 0, roughly speaking, the absolute value of the second term increases with M and decreases with L. The latter is a result of the fact that when L increases, there are more other VI firms to free ride the benefit resulting from a raised r. It indicates the strategic effect of a VI firm has externality, and an increase of L discourages every VI firm from curbing sales of intermediate goods.5 The third term is the slope of the derived demand. A VI firm is less willing to sell intermediate goods when it faces a steeper derived demand curve. Thus, as shown by Eq. (12), there are two effects to decide a VI firm's intermediate goods selling, one is the strategic effect (the first term of Eq. (12)) and the other is marginal profit from selling 4 There are different settings in literature when a VI firm sells intermediate goods into the intermediate goods market. Greenhut and Ohta (1979) and Salinger (1988) think that VI firms will not intervene into the intermediate goods market in a vertically related market. Schrader and Martin (1998) consider that a VI firm trades in the intermediate goods market with a ‘Cournot belief’. The setting here is followed by Spencer and Jones (1991, 1992), Higgens (1999) and Wang and Chiou (2004). 5 If L = M = 1, the first and second terms will degenerate to the case of Spencer and Jones (1991, 1992).
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intermediate goods in the upstream market (the second and last terms of Eq. (12)). In the previous discussion, we ignored how the change of M and L affects yir and yrj. We also ignore the interplay between the last two terms, both of which depend on market structure parameters. In the following, we shall take all this into account and calculate the strategic effect when the demand for final goods is linear. In this case, by Eqs. (A.3) and (A.4) the strategic effect of a VI firm is, a− t + cI + cf −bLx j dπjD = −2 b 0; ð1 + LÞ2 dx j
ð14Þ
and by Eqs. (12) and (A.4), the sales of intermediate goods are:
x
j
h i M ðL−1Þða−cI Þ−ð1 + LÞ2 ðch + sÞ + 2 + L + L2 cf + t = : b ð1 + LÞ3 + 1 + L2 M ð15Þ
Proposition 1. The magnitude of the strategic effect for a VI firm to curb sales of intermediate goods decreases with the number of foreign firms and is independent of the number of domestic downstream firms in a linear demand case. Proof. Differentiating Eq. (14) with L and M respectively, we obtain: ∂
dπjD 2 a−t−cI −cf −bðL−1Þx j j dx = 2 N 0; ∂L ð1 + LÞ3 jD
∂
dπ dx j = 0: ∂M □
This strategic effect comes from raising domestic downstream firms' (rivals') costs, as shown in Salop and Scheffman (1983, 1987) and defined by Spencer and Jones (1991, 1992). Here, Proposition 1 in our model indicates that the effect will decrease as the number of VI firms increases, but is independent of variation in the number of its downstream rival firms. It must be noted that Eq. (13) shows that M would affect the strategic effect, but M disappears in Eq. (14). The reason is that the effects of M offset each other in a linear demand case. Substituting t = s = 0 into Eq. (15), we have Proposition 2. Under the free trade policies and a linear demand, (1) if cf ≤ ch(cf N ch)where there is only one VI firm, the VI firm will (not) foreclose the intermediate goods market; (2) if cf ≥ ch and L ≥ 2, then the foreign VI firms always sell intermediate goods to domestic downstream firm(s) (xj * N 0). When there is only a VI firm in the market, it will have two choices: foreclosing the intermediate goods market, or not. If the VI firm forecloses the intermediate goods market, it can realize monopoly profits. If it chooses not to foreclose, it can gain upstream profits from selling intermediate goods but the downstream profits will decrease because there will be a group of downstream firms competing with the VI firm. In a linear demand case, Proposition 2(1) shows that the threshold to foreclose is dependent on the relative size of cf to ch. When cf N ch, domestic downstream firms have a comparative advantage to produce final goods. The VI firm's profit from the rent of double marginalization and the sales of final goods is larger than its monopoly rent from market foreclosure. On the other hand, the profit from foreclosing is larger than the profit from both selling in the intermediate goods and final goods markets if cf ≤ ch. Proposition 2
(2) shows how the strategic effect affects the behavior of a VI firm in the vertically-related market. First, we know that the strategic effect causes a VI firm to sell less intermediate goods than a pure upstream firm. Second, as shown in Proposition 1, when L increases, VI firm's strategic consideration decreases and the VI firm shows a greater tendency to sell intermediate goods to rival downstream firms. Thus, when L N 2, the strategic effect is less than the one in L = 1, and VI firms will not foreclose the intermediate market even if domestic downstream firms have less comparative advantage in the production of final goods (i.e., the case of cf = ch shown in Proposition 2(2)).6 Spencer and Jones (1992) indicate that a VI firm has a greater tendency to foreclose the upstream market (or sell less intermediate goods) than a pure upstream firm because the VI firm should consider the impact on its downstream profits of selling intermediate goods.7 Here, we further show that this impact will decrease and that VI firms tend not to foreclose the intermediate market as L increases. Proposition 2 discusses the impact of strategic effect on the behavior of the VI firm(s) based on the VI firms' foreclosure of upstream market. However, as shown in Eq. (12), the equilibrium value of xj * is dependent on both the strategic effect and marginal profit from the upstream market. To analyze this, differentiating Eq. (15) with M and L respectively, we have: Proposition 3. Suppose the demand for final goods is linear. (1) When there are more domestic downstream firms, the VI firms sell more intermediate goods, that is, ∂ xj */∂ M N 0. (2) When cf = ch, ∂ xj */∂ L N 0 if L ≤ 2 and ∂ xj */∂ L b 0 if L N 2; (3) xj * increases with t and decreases with s. The intuition behind the first part of Proposition 3 is clear. From Proposition 1, increasing M has no effect on the strategic effect. Thus an increase in M only changes the marginal revenue of a VI firm in the upstream market, and causes xj * to increase. The sign of ∂xj */∂L is ambiguous because when the number of VI firms increases, both the magnitude of the strategic effect and the marginal revenue in the upstream market reduce. The former causes xj * to increase and the latter causes xj * to decrease. Where cf =ch, if L≤2, xj * increases with L because the change in strategic effect dominates the change in the revenue. If L N 2, the opposite takes place. Proposition 3(3) is easy to obtain from Eq. (15). It is easy to obtain that xj *will decreases with s and increase with t from Eq. (15). These are respectively because: (1). for a VI firm, a decrease of s reduces its marginal cost to sell intermediate goods; (2). an increase of t not only reduces the magnitude of the strategic effect, but also increases the marginal revenue of intermediate goods because the demand for intermediate goods will expand. The price of intermediate goods can be derived from Eq. (15) and Eq. (A.4):
r =
1 fð1 + 3L + M Þa ð1 + LÞ3 + 1 + L2 M 2 3 2 + L + 2L + L + LM + L M s 2 LðM þ 1 LÞ t + cf + L ð3 + L + M ÞcI
ð16Þ
ð1 + Lð2 + L MÞM Þch g: Differentiating Eq. (16) with s and with t respectively, we have: dr4 ∂r4 ∂x j4 L + 2L2 + L3 + LM + L2 M = = N 0; j4 ds ð1 + LÞ3 + 1 + L2 M ∂x ∂s
ð17Þ
dr4 ∂r 4 ∂r 4 ∂xj4 LðL−1−MÞ : = + L = D4 dt ∂t ∂t ∂X ð 1 + L Þ3 + 1 + L2 M |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} ð + Þ
ð18Þ
ð−Þ
6 In fact, when L gets larger, from Eq. (15) we can find that VI firms will still not foreclose even if cf b ch. 7 See Spencer and Jones (1992), pp.39–40.
K.-C.A. Wang et al. / Economic Modelling 28 (2011) 1595–1603 4
Proposition 4. Suppose the demand for final goods is linear. (1). Increasing the tariff on intermediate goods (decreasing the subsidy), s, causes the price of intermediate goods to increase (∂ r*/∂ s N 0). (2). WhenL ≥ (b)M + 1, increasing the tariff on final goods, t, also causes the price of intermediate goods to increase (decrease). The intuition behind part (1) of Proposition 4 is simple. A tax on the trade of intermediate goods will naturally raise their market price, but the story behind part (2) is a little complicated. First, an increase of t shifts the derived demand curve outward and causes the price of intermediate goods to increase. This effect is shown in the term ∂r*/∂ tof Eq. (18). Second, ∂ x j */∂ tN 0 from part (3) of Proposition 3. Because ∂r*/∂ XD * is the slope of derived demand, which is negative, the second term in Eq. (18) is negative. If there is no strategic effect, the first term always dominates the second term in Eq. (18) because an increase of t directly causes a higher derived demand for intermediate goods and the increase of x j* caused by increasing t (∂ xj */∂ t) is indirectly induced by this higher derived demand. Thus, r* increases with t. If we consider the strategic effect, whether the first or the second term is more important depends on the market structure (L and M). If L = 1, the strategic effect is strongest where L≥1 from Proposition 1. But the strategic effect will be lessened if t increases (from Eq. (14), d2π jD/dxjdt = 2/(1 + L)2N0), and this causes the monopolistic VI firm to sell more intermediate goods and results in the second term dominating the first term in Eq. (18). Thus, we can see that an increase of t always causes r* to decrease if L = 1 from part (2) of Proposition 4. When L increases, there are two consequences for VI firms' strategic effect. First, the strategic effect is less prominent. Second, the magnitude of the decrease in strategic effect by an increase in t decreases with L (d3π jD/ dxjdtdL = − 4/(1 + L)3 b 0). These two statements mean that an increase of x j caused by a higher t will be less when L increases. Thus, the first term will dominate the second term in Eq. (18) if L is higher. In our model, the threshold of L is M + 1.8 Part (2) of Proposition 4 shows that the first term dominates (or is dominated by) the second term in Eq. (18) if L ≥ (b)M + 1. In the case of linear demand, Spencer and Jones (1992) also get ∂ r*/∂ t b 0 when L = M = 1.9 But we further indicate that the relation between r* and t could be reversed when L N M+ 1. This is mainly because the impact of t on the strategic effect decreases with L. Because an increase of t may increase or decrease the price of intermediate goods, this encourages us to learn how changes of t and s affect the final goods price. Substituting Eq. (16) into Eqs. (A.5) and (A.6) and using Eq. (1), we can get total final equilibrium outputs, Y*:
Y =
L 2 ð1 + LÞ + LM ða−cI Þ−ðLM + M Þðs + ch Þ b ð1 + LÞ3 + 1 + L2 M 2 − ð1 + LÞ −M t + cf : ð19Þ
Z
x
dY 4 = Yt dt ð−Þ
1599
2 − ð1 + LÞ −M 4 4 dr : + Yr = b ð1 + LÞ3 + 1 + L2 M ð−Þ dt
ð21Þ
ð?Þ
From Eqs. (20) and (21), we have: Proposition 5. Suppose the demand for final goods is linear. (1). When the tariff (subsidy) on intermediate goods s increases (decreases), p fewer ffiffiffiffiffi final goods will be produced. (2). When L≥ðbÞ M−1, an increase in t causes the domestic price of final goods, P*, to increase (decrease). Raising s increases the price of intermediate goods (Proposition 4) and hence decreases total output of final goods as a result. The intuition for part (2) of Proposition 5 is as follows. When t increases, foreign firms become less competitive in the downstream market, and we expect y j * to shrink and yi * to expand. When r is fixed, the total output will decrease (Yt b 0). How r will change with t is not clear as shown in Proposition 4. From part (2) of Proposition 4, we know that dr*/dt b 0if L b M + 1. In this case, the second term in Eq. (21) is positive. We find that the second term dominate the first term pffiffiffiffiwill ffi when L is less than the threshold M−1. Notice that P* usually increases with t in traditional trade theory, but in our model when pffiffiffiffiffi L b M−1, the opposite takes place. This special phenomenon is induced by VI firm's strategic effect. When t increases, the strategic effect causes VI firms to sell more xj. This will lead r to reduce, and P* to further reduce because domestic downstream firms have cheaper marginal costs.11 Fig. 2 shows how the tariff affects the prices of intermediate and final goods. From Fig. 2, we find that contrary to the literature on trade theory, increasing the tariff on final goods does not necessarily raise the price of final goods in the domestic market. We have not found that the final goods price decreases with the tariff on final goods in theoretic literature until now. This result shows that the market structure in the vertically-related market is a key issue when we study strategic trade theory, and we should take note of, and review the role of strategic tariffs in the vertically-related market. For these reasons, the next section is concerned with the optimal tariffs. 4. The optimal tariffs In this section, we study the optimal tariffs for the domestic government. The domestic social welfare consists of producers' surpluses (Mπi *(yi *, y j *, x j *)), the tariff revenue (the final good tariff revenue, tLy j * and theintermediate good tariff revenue, sMyi *), and Y* consumers' surpluses ∫0 P(Y)dY − P(Y *)Y * . Thus, the social welfare function of the home country can be shown as W ðs; t Þ = Mπ
i4
i
j
y ;y ;x
j
+ tLy
j
i Y4 + sMy + ∫ P ðY ÞdY−P Y Y ; 0
ð22Þ 10
Differentiating Eq. (19) with s and t respectively, we have :
dY −LM ðL + 1Þ dr b 0; = Yr = ds b ð1 + LÞ3 + 1 + L2 M ð−Þ ds
ð20Þ
ð + Þ
8 The change of the number of L and M will affect VI firms' upstream marginal profit from selling intermediate goods. But this is not the crucial factor to decide the sign of Eq. (18) because the first term always dominates the second term in Eq. (18) if there is no strategic effect. Therefore we skip the discussion of the variation of VI firms' upstream marginal profit. 9 See Spencer and Jones (1992, pp.46), Proposition 5(i). The result of Proposition 4 (1),∂ r*/∂ s N 0 is consistent with Spencer and Jones's result which can be seen in Spencer and Jones (1992, pp. 50), Proposition 6. 10 For the sign of Yr* and Yt*, see Eq. (10).
11 The story of the TV set industry in mainland China may serve as an example of this surprising possibility. Mainland Chinese TV producers are like the domestic producers in our model, who have to completely rely on imports of iconoscopes to manufacture TV sets. According to the data from the Almanac of China's Domestic Trade (2000, pp. 126–127), in 1999, the domestic prices of 29-inch and 21-inch color TV sets were as low as $250 and $125 respectively, while the Statistic Almanac of China's Customs (2000, p. 1157) reported the average import price of color TVs to be as high as $320. According to the Customs Import and Export Tariff of the People's Republic of China (1999), since 1997, the import tariffs of color TVs and color TV iconoscopes have been 35% and 18%, respectively, but the high tariffs did not seem to enhance the domestic TV set prices. Our analysis suggests that it might be that high tariffs caused foreign VI firms to stay away from mainland China's TV set market. When these foreign firms reduced the sales of final products, they might have priced the intermediate goods, iconoscopes, low, and this might have caused the TV set prices in the market to come down. In fact, the Almanac of China's Economy (2000, p. 261) reported that in 1999, the market share of the top ten domestic TV firms was about 80%.
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K.-C.A. Wang et al. / Economic Modelling 28 (2011) 1595–1603
Fig. 2. The relationship between tariffs and prices.
where yi *, yj * and xj * depend on s and t, and Y* = Myi * + Lyj *. Differentiating Eq. (22) with respect to t and s respectively, we have:
t =
s =
i i i j + Ly + sM dydt − dP M −y dr + y dP Y dt dt dt j
−L dydt
j M −yi dr + y j dP Y + Myi + tL dyds − dP ds ds ds i
−M dyds
;
:
ð23Þ
ð24Þ
Eq. (23) exhibits the factors to determine the tariffs on final goods. The first term in the numerator of Eq. (23) is the rent shifting effect, originally defined by Brander and Spencer (1985).12 That is, an increase in t will shift rents from foreign VI firms to M domestic firms. This effect involves both the change of P and the change of r. The second term in the numerator of Eq. (23) shows the rent extracted from foreign VI firms. The third term in the numerator of Eq. (23) shows the interplay between t and s. Compared with the case in s = 0, this indicates t will be higher (lower) if s N (b)0 because tariff revenue from (a subsidy, or expenditure on) intermediate goods increases with t. The last term represents concerns with consumers' surpluses. It is easy to check if M = 0, t* = (Pt − 1)Y/Yt. This is the case in Brander and Spencer (1984) where there is only the rent extracting effect. The factors to decide s are similar, so we shall show the discussion of them later. In a linear demand case, t* and s* can be solved from Eqs. (23) and (24),13
t =
h i 2 2 3 2 ð1 + LÞ + 2LM ða−cI −ch Þ− 2ð1 + LÞ + −2 + L + L M cf −ch 4 + 2L½5 + 2M + Lð4 + L + M + LMÞ
;
ð25Þ
s =
M + 1−L2 2L a−cI −cf + 2 + 3L + L2 cf −ch 4 + 2L½5 + 2M + Lð4 + L + M + LMÞ
: ð26Þ
With the result of Eq. (25), we find: Proposition 6. When domestic downstream firms import intermediate goods, the home country always imposes a tariff on final goods; that is, t* N 0 in the linear demand case. The proof of Proposition 6. See Appendix A. In the linear demand case, the first term of the numerator of Eq. (23) is positive. Moreover, the rent shifting and extracting effects will dominate the concern about consumers' surpluses and a possible increase in subsidy expenditure on intermediate goods. Note that the rent shifting effect here is more important than traditionally considered, because an increase in t in our model can shift foreign VI firms' focus away from final goods market to intermediate goods market, and domestic downstream firms can get a better position as a result. 12 The definition of ‘rent shifting’ is that ‘The central idea is that it is to the advantage of a country to capture a large share of the production of profit-earning imperfectly competitive industries.’ Please see Brander and Spencer (1985). 84, line 9 to line 11. 13 In the linear demand case, the S.O.C.s conditions will hold and s and t are strategic complements. See Appendix A.
On the other hand, the government may either tax or subsidize the imports of intermediate materials as the following proposition suggests. Proposition 7. Suppose the demand for final goods is linear. If M N (b) L2 − 1, then s* N (b)0 when yi*, yj* N 0. The proof of Proposition 7. See Appendix A. In the linear demand case, the rent shifting effect (the first term in the numerator of Eq. (24)) is negative because domestic firms do not produce intermediate inputs in our model and a tax on exporting intermediate goods lowers the profits of domestic firms. Where the rent extracting effect (the second term in the numerator of Eq. (24)) is positive, the interplay effect between t and s (the third term in the numerator of Eq. (24)) is positive due to t*N0 and dy j */dsN 0, and the last term in the numerator of Eq. (24) is negative because an increase of s hurts social welfare. This means that the only reason to tax intermediate goods is to extract rents from the intermediate goods market and to help raise rents extracted from the final goods market (because of the interplay effect between t and s). Foreign VI firms' rents in both intermediate and final good markets are, in fact, high when L is relatively smaller than M. That is why the home country will tax (subsidize) intermediate goods only if MN (b)L2 −1 in Proposition 7. We should note that domestic governments usually taxes on import goods from the viewpoint of strategic trade, but Proposition 7 points out that if the number of domestic firms is relatively smaller than the number of foreign VI firms, a domestic government should subsidize intermediate import goods.14 In other words, the market structure in the vertically-related market plays an important role when domestic government decides whether to tax or subsidize intermediate goods. A change of M can support the intuition above. Differentiating s* and t* with respect to M., we find from Eqs. (25) and (26) that: ∂s ð1 + LÞð2 + ðL−1ÞLÞ = ∂M 2½2 + Lð5 + 2M + Lð4 + L + M + LMÞÞ2 h i 2 cf −ch N 0; 2L a−cI −cf + 2 + 3L + L
ð27Þ
h i ðL−2ÞLð1 + LÞ3 2L a−cI −cf + 2 + 3L + L2 cf −ch ∂t N N =− 0 if 2 L: b b ∂M 2½2 + Lð5 + 2M + Lð4 + L + M + LMÞÞ2
ð28Þ The proof of the sign of ∂ s*/∂ M and ∂ t*/∂ M. See Appendix A. Eqs. (27) and (28) indicate that s* increases and t* decreases with M. The intuition is the same as the one for Propositions 6 and 7. When M increases, the final goods market becomes more competitive, and foreign VI firms earn economic rents mainly in the market of 14 In this model, t* − s* N 0 is always satisfied. From Propositions 6 and 7, we know that t* N 0 ≥ s* if M ≤ L2 − 1. Subtracting Eq. (26) from Eq. (25), we can find that:
t −s =
1 V2 1 + L 1 + L + L2 + M a−cI −cf 2½2 + 2Lð5 + 2M + Lð4 + L + M + LM ÞÞ : + cf −ch ð1 + LÞ½−2 + Lð−1 + Lð2 + L−MÞÞg
When M N L2 − 1 and cf ≤ cf ( cf is the upper bound of cf and is defined in Eq. (A.7)), we can find that t* − s* N 0.
K.-C.A. Wang et al. / Economic Modelling 28 (2011) 1595–1603
intermediate goods. Thus, the best way to extract their rents is to increase s. On the other hand, as the market of final goods becomes more competitive and fewer rents can be extracted and shifted in this market, we expect t* to decrease in general. Eq. (28) shows that ∂t*/∂MN 0 when L=1. The intuition for this special case is as follows: When there is only one foreign VI firm, all benefit from raising domestic firms' costs accrues to the foreign firm itself (there is no free-rider effect), and this VI firm tends to cut the supply of intermediate goods. To correct this, the domestic government can raise t to weaken the foreign firm's competitiveness in the final goods market in order to shift this VI firm's business interest back to the sale of intermediate goods. If L=M=1, cf ≥ch and the domestic firm can produce intermediate inputs, Spencer and Jones (1992) found that domestic governments will subsidize imported intermediate goods under free trade condition.15 Our sufficient condition for subsidizing intermediate goods is not as restricted as Spencer and Jones's. In this model, if L=M=1 and t=0, the domestic government always subsidizes intermediate goods whatever cf ≥ch or cf ≤ch.16 The reason is that in addition to a generalized market structure, our model and Spencer and Jones's differ in that our domestic firms cannot produce intermediate inputs on their own. This difference induces the rent shifting effect (the first term in the numerator of Eq. (24)) is always negative in our model because there is no rent to shift in the upstream market. In other words, a domestic government are more likely to subsidize intermediate goods in our model than in that of Spencer and Jones. From this viewpoint, we can further infer that tariffs on intermediate and final import goods will be higher if domestic firms can produce intermediate inputs by themselves.17 This also means that
1601
although domestic firms are not permitted to produce intermediate goods by themselves in our model, this model still applies without a loss of generality.
5. Conclusion Developing countries usually play the role of processing final goods in the global trade system. It is thus quite important to examine how they protect domestic industries that face fierce international competition. Using the framework of Spencer and Jones (1991, 1992) with a flexible market structure, we have studied import tariffs (subsidies) on the intermediate goods and final goods markets. We also focus on how optimal tariffs are affected by the market structure. In our model, we find that the strategic effect for a VI firm plays an important role. This strategic effect, coming from raising the costs borne by rivals, will decrease as the number of VI firms increases. This result shows that the strategic effect has some externality. To protect domestic firms and to extract rents from foreign firms, the imports of final goods are always taxed, but imports of intermediate goods can be taxed or subsidized, depending on the market structure. A surprising finding is that a tariff increase on final goods may lower the domestic price of intermediate goods and final goods. This is because a tariff on final goods directs the vertically integrated firms to focus on the production of intermediate goods, leading to a lower price of intermediate goods, which trickles down the price of final goods.
Appendix A Comparative static analyses on final goods outputs Taking the total differential of F.O.C.s, Eqs. (4) and (5), we obtain: jD
j
jD
i
i
j
i
i
πy j yi dy + πy j yi dy = dt; πyi y j dy + πyi yi dy = dr; j jD j i i i i jyj = PYYLy + PY(L + 1)b0, πyjyi = PYYMy + PYMb0, πyiyi = PYYMy + PY(M + 1)b0 and πyiyj = PYYLy + PYLb0 if the demand function is linear where πyjD
or not too convex. The stability condition is Δ = PYYPYY + PY2(L + M + 1)N0. Thus, we have, yir =
πjD y jy j Δ
b 0; ytj =
πiyi yi Δ
b 0; yit =
−πiyi y j Δ
N 0;
yrj =
−πjD y j yi Δ
N 0:
Using the same method, we can have ycih = yir b 0, ycjI = ycjf = ytj b 0, yciI = ycif = yit N 0 and ycjh = yrj N 0. Stage 3's market equilibriums in the linear demand function Using Eqs. (1), (4) and (5), we have,
i
y =
j
y =
15 16 17
a + L cf + cI + t −ðL + 1Þðch + r Þ bðL + M + 1Þ
;
a + M ðr + ch Þ−ðM + 1Þ cf + cI + t bðL + M + 1Þ
ðA:1Þ
:
See Spencer and Jones (1992, pp. 43), Proposition 3. Under L = M = 1 and t = s = 0, ∂ W/∂ s = − (5(a − cI − cf) − 2(cf − ch))/50b and yj * = (5(a − cI − cf) − 2(cf − ch))/13b. yj *N0 if and only ∂ W/∂ s b 0. Because s and t are strategic complements (see Appendix A (Eq. (A.8)), an increase of s will cause to an increase of t.
ðA:2Þ
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K.-C.A. Wang et al. / Economic Modelling 28 (2011) 1595–1603
Summing up two equations below across all firms, the total sales of final goods and their market price are, respectively: aðL + M Þ−L cI + cf + t −Mðch + r Þ
Y=
bðL + M + 1Þ a + L cI + cf + t + M ðch + r Þ
P=
L+M+1
;
:
Thus the downstream profit of a VI firm and the domestic firm's profit can be respectively derived to be: jD
π
=
i
π =
2 a + Mðr + ch Þ−ðM + 1Þ cf + cI + t bðL + M + 1Þ2
;
2 a + L cf + cI + t −ðL + 1Þðch + rÞ
: bðL + M + 1Þ2 Summing up Eq. (A.1) across M domestic downstream firms, the inverse derived demand function is,
r=
a + L cI + cf + t L+1
−ch −
bðL + M + 1Þ D X : ðL + 1ÞM
ðA:3Þ
ðA:4Þ
The proof of Proposition 6 Substituting Eq. (16) into (A.1) and (A.2), we can have equilibrium outputs of domestic firm i, yi *, and equilibrium outputs of foreign firm j, yj *. They are: h i L ðL−1Þða−cI Þ−ðL + 1Þ2 ðs + ch Þ + 2 + L + L2 t + cf ; y = b ð1 + LÞ3 + 1 + L2 M i
y
j
2 2 ð1 + LÞ + M a−cI −t−cf + LM + L M s + ch −t−cf = : b ð1 + LÞ3 + 1 + L2 M
ðA:5Þ
ðA:6Þ
Case 1: yj * N 0. Substituting t* of Eq. (25) and s* of Eq. (26) into Eq. (A.6), we have the upper bound of cf when yj * N 0: 2ðL + 1Þða−cI Þ + 2 + L + L2 Mch cf = : 2ð1 + LÞ + 2 + L + L2 M
ðA:7Þ
Suppose t* ≤ 0. From Eq. (25), we have: h i 2 ð1 + LÞ2 + 2LM ða−cI Þ + ðL−2Þð1 + LÞ2 Mch cf ≥ Ncf ; 2ð1 + LÞ2 + −2 + L + L3 M which contradicts with our presumption that y j N 0. Case 2: y j * = 0: Under the assumption that a − cI − cf N 0, if the home country wants to deter foreign VI firms from importing final goods, then t* must be positive. The S.O.C.s conditions of optimizing s and t From Eq. (22), we will have, h i 2 2 Lð1 + LÞ M 2ð1 + LÞ + ð2 + Lð2L−1ÞÞM Wss = − b0; 2 b ð1 + LÞ3 + 1 + L2 M h i M2 −L ð1 + LÞ4 ð2 + LÞ + 2ð2 + Lð3 + Lð7 + Lð5 + 3LÞÞÞÞM + 2 + L 1 + 2L 2 + L + L2 Wtt = b0; 2 2b ð1 + LÞ3 + 1 + L2 M Wst = Wts =
LM½2ð1 + MÞ + Lð5 + M + Lð7 + 3M + Lð7 + 3L + 2ð1 + LÞM ÞÞÞ N 0; 2b ð1 + LÞ3 + 1 + L2 M
Wss Wtt −Wst Wts =
2L2 M ½2 + Lð5 + 2M + Lð4 + L + M + LMÞÞ N 0: 2 b2 ð1 + LÞ3 + 1 + L2 M
ðA:8Þ
K.-C.A. Wang et al. / Economic Modelling 28 (2011) 1595–1603
1603
The proof of Proposition 7 (1). When yj *, yi * N 0, Eq. (A.5) provides the right formula for yi *. Substituting s* and t* into Eq. (A.5), we find the upper bound of ch for yi * N 0 to be:
ch =
2Lða−cI Þ + 2 + L + L2 cf ð1 + LÞð2 + LÞ
:
ðA:9Þ
We wish to show that the sign of s* is the same as M + 1 − L2. Suppose the contrary holds. It then follows from Eq. (26) that ch ≥ch , which contradicts our presumption that yi * N 0.
The sign of ∂ s*/∂ M and ∂ t*/∂ M Suppose if the sign of ∂ s*/∂ M in Eq. (27) is non-positive, using Eq. (A.9), then one will find ch ≥ch . This contradicts yi * N 0. Similar logic can be applied to determine the sign of ∂ t*/∂ M. References Brander, J., Spencer, B.J., 1984. Trade warfare: tariffs and cartels. Journal of International Economics 16, 227–242. Brander, J., Spencer, B.J., 1985. Export subsides and international market share rivalry. Journal of International Economics 18, 83–100. Greenhut, M.L., Ohta, H., 1979. Vertical integration of successive oligopolists. The American Economic Review 69 (1), 137–141. Higgens, R.S., 1999. Competitive vertical foreclosure. Managerial and Decision Economics 20, 229–237. Ishikawa, J., Lee, K.D., 1997. Backfiring tariffs in vertically related markets. Journal of International Economics 42, 395–423. Ishikawa, J., Spencer, B.J., 1999. Rent-shifting export subsidies with an imported intermediate product. Journal of International Economics 48 (2), 199–232. Lin, P., 2006. Strategic spin-offs of input division. European Economic Review 50, 977–993.
Matsushima, N., 2006. Industry profits and free entry in inputs markets. Economics Letters 93, 329–336. Salinger, M.A., 1988. Vertical mergers and market foreclosure. Quarterly Journal of Economics 103, 345–356. Salop, S.C., Scheffman, D.T., 1983. Raising rivals' cost. The American Economic Review 73, 267–271. Salop, S.C., Scheffman, D.T., 1987. Cost raising strategy. Journal of Industrial Economics 36, 19–34. Schrader, A., Martin, S., 1998. Vertical market participation. Review of Industrial Organization 13, 321–331. Spencer, B.J., Jones, R.W., 1991. Vertical foreclosure and international trade policy. The Review of Economic Studies 58, 153–170. Spencer, B.J., Jones, R.W., 1992. Trade and protection in vertically related markets. Journal of International Economics 32, 31–55. Wang, K.-C.A., Chiou, J.-C., 2004. Strategic trade policies in the vertically-related market. Academia Economic Papers 32, 369–391.