A Comparison of Optimal Tariffs and Welfare under No Lobbying, Domestic Lobbying and Domestic-foreign Lobbying

1 Introduction

In recent years, lobbying as a common phenomenon has played an important role in influencing trade policymaking. For instance, in 2009, more than 580 principals from some 137 countries participated in lobbying US policymakers, with the total spending in lobbying exceeding 484 million dollars, and most of them are from Asia. In 2009, Toyota spent about 5.2 million dollars in lobbying the US government, which is seven times more than its 1999 lobbying expenditure. Tata Consultancy Services and USINPAC from India and Lenovo, Huawei and Haier from China also lobby the US government for their benefits. On the other hand, the domestic firms in the US also lobby the US government actively. Google's lobbying expenditure in 2009 was $4.03 million, up by 44% as compared to 2008. Microsoft, HP, Tyco Electronics and MOTOROLA are also active lobbyists.

Among the foreign lobbyists, Chinese firms are very active in the eyes of the US government. According to the US political contribution database (opensecrets.org), the lobbying expenditure of Huawei and ZTE Corporation in 2012 reached $1.04 million and $90,000, respectively. In 2011, the lobbying spends of them are $425,000 and $182,000, respectively. There are also other Chinese firms such as Lenovo, China National Offshore Oil Corporation (CNOOC) and Wanxiang Group that began to participate in lobbying foreign countries more frequently in recent years (Figure 1). For example, in 2004, by lobbying the US government, Lenovo successfully initiated an acquisition of IBM global PC business valued at $1.25 billion. In 2013, CNOOC enhanced its lobbying to US congress to prepare for the acquisition of Nexen valued at $15.1 billion. Wanxiang Group spends $140,000 in lobbying in 2013 and is ready to take over American battery manufacturer A123 Systems.

The prevalent lobbying activities have aroused the great interests of many scholars, and numerous related literature has emerged concerning the effect of lobbying on trade policy. Although the literature dealing with the lobbying behaviour from the domestic firms has been abundant ever since Grossman and Helpman (1994),1 papers concerning foreign lobbying in determining trade policymaking have been relatively few, and most of them are empirical studies. For example, Mitchell (1995) found that from 1987 to 1988, the political contribution from foreign lobbying accounted for 5.6 per cent of the total corporate political contribution, and he stated that the lobbying of foreign firms is as intensive as that of domestic firms. Gawande et al. (2006) found that foreign lobbying on average decreases the most-favoured-nation (MFN) tariff applied by the United States, and they also showed that foreign firms’ lobbying to reduce the MFN tariff is still effective while the domestic firms lobby the government to increase the tariff. Kee et al. (2007) found that foreign lobbying power would significantly influence the preferential market access granted by the US. In fact, Silva (2011) found that the lobbying of Latin American exporters and US importers plays an important role in determining the preferential market access granted by the US.

In international trade, the major goal of foreign lobbying is to push for freer trade policy, such as cutting the tariff, whereas domestic firms aim to derive the government's trade protection. If the trade policy is affected by both foreign and domestic lobbying, we then wonder whether and what type of the lobbying-induced trade policy can improve domestic welfare. To this end, we construct a simple duopoly model and conduct a comparison of the optimal tariff choices and welfare consequences under three different scenarios: no lobbying, domestic lobbying, that is, only domestic firms participate in lobbying the domestic government, and domestic-foreign lobbying, that is, both domestic and foreign firms are active and compete with each other in lobbying the domestic government.

We find the following results: as compared to the case of no lobbying and the case of domestic lobbying, the domestic-foreign lobbying achieves the lowest tariff, if the relative effectiveness of foreign lobbying is sufficiently high. Moreover, if the relative effectiveness of foreign lobbying is high enough, the welfare under domestic-foreign lobbying achieves the highest social welfare, but if the effectiveness is relatively low, the welfare under domestic-foreign lobbying would be lower than that under the social optimum or even that under domestic lobbying, when the government is sufficiently avaricious and the product differentiation between the goods of the two firms is sufficiently small.

Our results imply that the domestic-foreign lobbying may contribute to a freer trade in the domestic country, and lobbying competition may be one of the strongest forces pushing for trade liberalisation when the relative lobbying effectiveness of foreign firms is high enough.

Our findings lend some support to the evidence in the real world. For example, in 2005, the Chinese firm, CNOOC, failed in merging with the ninth largest oil corporation in US, Unacol, as its competitor in US, Chevron Group, convinced the US government and investors that the safest option for Unacol was to be merged by a domestic company. In addition, in 2012, Huawei failed to access the US market because of the lobbying of its competitors in US such as Cisco Systems, and Huawei was refused for the reason of threatening US national security. Such barriers or oppositions to foreign lobbying, to a large extent, are associated with the worries about the adverse welfare effects on US. However, our results suggest that the prevalent lobbying competition between Asian firms and US firms in the USA may improve the welfare for USA.

Our model has the structure of a common agency problem: to induce a government (a common agent) to act on their behalf, firms (principals) offer the government payment schedules, which link non-negative transfers to each action the government might take. Foreign firms lobby for free trade of exports, whereas import-competing domestic firms lobby for protection from imports. Our approach draws on Bernheim and Whinston (1986) and Dixit et al. (1997), who characterise the equilibrium for a class of common agency problems. The approach has been largely applied to examine lobbying behaviours of domestic firms towards the formation of trade policy. For example, Grossman and Helpman (1994) consider the determination of tariffs across sectors, Chang (2005) examines trade policy under monopolistic competition, and Kayalica and Lahiri (2007) explore national policies towards foreign domestic investment. Bombardini (2008) and Bombardini and Trebbi (2012) also analyse firm-level contribution decisions. An exception is Konishi et al. (1999), who analyse the government's choice between a voluntary export constraint and a tariff in the presence of lobbying by both domestic and foreign firms; but they focus on the policymaker's choice between voluntary export constraints and tariffs, but their results are derived under the setting of Cournot competition and they pay little attention to other types of competition such as Bertrand, and production differentiation between firms is absent in their model.

This study extends the previous studies of trade protection by considering different oligopolistic competition modes, that is, Cournot duopoly and differentiated Bertrand duopoly. Specifically, we explore the optimal trade policy chosen by the domestic government under domestic-foreign lobbying and compare its welfare consequence with that of domestic lobbying and the social optimum (no lobbying). The model set-ups that are most related to ours are Kikuchi (1998) and Kagitani (2009). Kikuchi (1998) explored how optimal trade policy is affected by the competition modes without considering the lobbying behaviour from firms, while Kagitani (2009) extended the Kikuchi model to investigate the scenario of domestic lobbying. In contrast to these two papers, our model further incorporates the lobbying competition between domestic and foreign firms and its impact on the domestic trade policymaking and domestic social welfare under both oligopolistic quantity and price competition, which are absent in the above two papers.

The rest of the paper is organised as follows. Section 2 presents the setting of the model. Section 3 derives the politically determined tariff and welfare effect of domestic-foreign lobbying under Cournot competition and makes comparisons with the no-lobbying case and the domestic lobbying case. Section 3.1 verifies the results under differentiated Bertrand competition. Section 3.2 states the concluding remarks.

2 Basic Model

Consider a duopoly model in a domestic market. There are two countries, domestic and foreign. Each country has only one firm producing a homogeneous good. The domestic firm produces good X, while the foreign firm produces good Y. The foreign firm exports its product to the domestic market and competes with the domestic firm there. We assume that the marginal cost of the domestic firm and that of the foreign firm are 1 and c, respectively. A quantity tariff t is imposed on the exports from the foreign firm by the domestic government.

We assume that a representative consumer in the domestic market possesses a quasi-linear preference and maximise:

(1)

where , x and y are the consumption amount of good X and good Y, respectively, and p_d and p_f denote the prices of good X and good Y in the domestic market, respectively.

By maximising 1, we can derive the following inverse demand functions:

(2)

(3)

where the subscripts d and f denote the domestic firm and the foreign firm, respectively.

From 2 and 3, we can derive the two firms’ profit functions, respectively:

(4)

(5)

In the absence of lobbying (called no-lobbying case hereinafter), we define the domestic social welfare function as the sum of the domestic firm's profit, consumer surplus and the tariff revenue:

(6)

Now let us consider the political lobbying case. Firms lobby to gain or retain a comparative advantage over their business rivals or to avoid a comparative disadvantage (Reich, 2007). The tariff is determined through the interaction between the two firms and the government. The domestic and foreign firms offer a contribution schedule C_i (t) where i  =  d, f, and C_i (t) ≥ 0, to influence the government's policy decision. The contribution schedules are assumed differentiable. Clearly, the domestic firm aims to increase the tariff imposed on the foreign firm while the foreign firm's strategic goal is the opposite. The resulting pay-offs for the firms are:

(7)

(8)

Now, we can define the domestic social welfare function in the presence of lobbying, which, in addition to the profit of the domestic firm, the amount of consumer surplus and the level of tariff revenue, also includes the foreign contributions reaching the domestic country. This is because foreign contributions represent a net transfer of income to the domestic country.2

(9)

where θ(0 ≤ θ ≤ 1) captures the difference (loss) between the amount of foreign contributions spent by the foreign firm and the amount received by the policymakers (the amount reaching their campaign coffers). Thus, θ measures the effectiveness of the foreign lobbying. We offer several interpretations. To start with, we can think of such loss as the additional transport costs that foreign firms generally have to spend when compared with domestic firms. Alternatively, we can think of it as the additional costs of hiring local agents that are more able because the effectiveness of foreign lobbying under most cases is no greater than that of domestic lobbying (Qiu, 2008). Clearly, θ = 0 denotes the trivial case in which the contributions from the foreign firm completely ‘dissipate’ along the way. Of course, the foreign firm will simply not contribute in such a situation. Hereinafter, we restrict our attention to the case where θ > 0.

On the other hand, there is a self-interested incumbent government in the domestic country. To win the election, the government will set the tariff to maximise the number of votes obtained. As the vote depends on the public endorsement and campaign funds, the government cares about not only the political contributions received from the domestic and foreign firms, but also the level of net social welfare in the domestic market. It should be noted that in the presence of lobbying, part of the contributions from the foreign firm enter the domestic country and become part of domestic social welfare. Hence, we specify the government's objective function as follows:

(10)

where λ(>1) denotes the weight that policymakers attach to the contributions.3 Clearly, contributions from different firms are receiving different de facto weights, with those from the domestic firm (C_d) receiving a weight of λ – 1 and those from the foreign firm (C_f) receiving a weight of λθ.

Given the firms’ contribution schedules, the government chooses tariff t to maximise its objective function. It should be noted that there are four cases: (i) both firms do not lobby the government; (ii) only the domestic firm lobbies the government; (iii) only the foreign firm lobbies the government;4 and (iv) both firms lobby the government.

Clearly, in case (i), the domestic government's objective function will be reduced to 6, and we denote the optimal tariff chosen by the government in this case by t₀ and call it the no-lobbying case.

In case (ii), the objective function of the government will be reduced to

(11)

and we denote the optimal tariff chosen by the government in this case by t_p and call it the domestic lobbying case.

In case (iii), the objective function of the government will be:

(12)

and we denote the optimal tariff of the government in this case by t_q and call it the foreign lobbying case.

In case (iv), the objective function of the government is exactly 9, and we denote the optimal tariff by t_b and call it domestic-foreign lobbying case.

Our model can have multiple subgame perfect Nash equilibria. In the following analysis, we restrict our focus to the truthful Nash equilibrium, supported by truthful contribution functions that everywhere reflect the true preferences of the two firms. A truthful contribution function for firm i, i = d, f, rewards the government for every change in the action by exactly the amount of change in the firm's pay-off, provided that the payment both before and after the change is strictly positive (Dixit et al., 1997). We denote the truthful contribution functions of the two firms, respectively, by

(13)

and

(14)

where t_q is the optimal tariff chosen by the government in the foreign firm lobbying case. Thus, π_d(t_q) is the reservation pay-off of the domestic firm, and π_f(t_p) is similarly defined and represents the reservation pay-off of the foreign firm.

We then consider a simple three-stage game. In stage one, the two firms simultaneously provide the government with their campaign contribution schedules. In stage two, the government sets the tariff imposed on the foreign firm. In stage three, both firms compete in the domestic market à la Cournot (Bertrand), and they choose their outputs (prices) according to the tariff level. Backward induction method is adopted to solve this game.

3 Tariff and Welfare Comparisons under Cournot Duopoly

We consider the Cournot competition in this section, that is, in the third stage, the two firms engage in output competition.

We first look at the third stage. By calculating the first-order conditions of the two firms, we derive the following Cournot equilibrium outputs:

(15)

(16)

Thus, the corresponding prices of the two firms are as follows:

(17)

The equilibrium profits of the two firms are given by:

(18)

(19)

Substituting 15-19 into 6, we get

(20)

The social welfare in the case of domestic-foreign lobbying is:

(21)

In the second stage, the domestic government sets the tariff imposed on the foreign firm. There are four cases:

First, if there is no political contribution, that is, the no-lobbying case, the government will set the tariff to maximise the social welfare function as specified in 6, namely, dW⁰/dt = 0, from which we can derive

(22)

Then we move on to consider the domestic lobbying case. Given the government's possible reaction, the domestic firm will provide the government with a campaign contribution schedule. The domestic firm confronts the following constraint:

(23)

Equation 23 means that the domestic firm must guarantee the government the utility level that the government could obtain in the case of no lobbying. In this way, the government will be willing to accept the domestic firm's contribution schedule. As the domestic firm will try to contribute as little as possible, this inequality must be binding. Thus, the domestic firm will maximise

(24)

Therefore, in equilibrium, the optimal tariff level must satisfy

(25)

From 25, we can derive the optimum tariff t_p under the domestic lobbying case:

(26)

In the foreign lobbying case, the incumbent government will choose a tariff to maximise 11. Similarly, the optimal tariff of the government must satisfy

(27)

From 27, we derive the optimal tariff t_q under the foreign lobbying case:

(28)

Finally, we consider the domestic-foreign lobbying case, that is, both firms lobby the government simultaneously. The incumbent government will choose tariff to maximise 9, and the optimal tariff of the government must satisfy:

(29)

From 29, we can derive the optimum tariff t_b:

(30)

Now, we can calculate π_d(t_p) and π_f(t_q) Substituting π_d(t_p) and π_f(t_q) into 13 and 14, respectively, we get

(31)

(32)

Substituting 31 and 32 into 21, we get the social welfare function in the case of domestic-foreign lobbying:

(33)

Now, we move on to compare t₀, t_p, and t_b. We will consider the following two cases.

3.1 Case 1: The Foreign Firm is More Efficient than the Domestic Firm, that is c < 1

We first compare t₀ and t_p:

(34)

Obviously, as long as λ ≠ 1, 34 is larger than zero, which immediately implies that t₀ < t_p. This result demonstrates that when goods X and Y are homogeneous, the tariff under the scenario of domestic lobbying is always higher than the social optimum.

Then, we move to compare t_p and t_b, and t_b and t₀, respectively:

(35)

(36)

We assume that a = 100 in our comparisons hereinafter. In Table 1, we give the ranges of λ in which t_p > t_b and t_b < t₀. The first row denotes the effectiveness of foreign lobbying. We find that θ must be lower than 0.7 to ensure that both firms lobby the government. The second row gives conditions for the occurrence of lobbying5 (range of λ) corresponding to different values of θ. Rows 3 and 4 show the ranges of λ such that t_b < t_p and t_b < t₀, respectively. Taking row 3 and column 3 for example, (1, 1.5) denotes when θ = 0.1 and 1 < λ < 1.5, lobbying occurs and t_p is greater than t_b; otherwise, when θ = 0.1 and 1.5 < λ < 2, lobbying occurs but t_p is greater than t_b. We can summarise the pattern implied by Table 1 as the following two results:

Table 1. Tariff Comparison When c < 1

Foreign lobbying effectiveness		θ = 0.1	θ = 0.2	θ = 0.3	θ = 0.4	θ = 0.5	θ = 0.6	θ = 0.7
Conditions for Lobbying to occur		λ < 2	λ < 2.1	λ < 2.5	λ < 1.9	λ < 1.5	λ < 1.25	λ < 1.06
Results	tb < tp	(1, 1.5)	(1, 1.5)	(1, 1.5)	(1, 1.5)	(1, 1.5)a	(1, 1.25)a	(1, 1.06)a
	tb < t0	(1, 1.05)	(1, 1.1)	(1, 1.2)	(1, 1.25)	(1, 1.3)	(1, 1.25)a	(1, 1.06)a

Note:

• ^a indicates that t_p > t_b or t_b > t₀ holds for the full range of λ in which lobbying occurs.

Result 1: When lobbying occurs t_p > t_b always holds if the foreign lobbying effectiveness is relatively high, that is, θ ≥ 0.5; otherwise t_p < t_b if θ < 0.5 and λ is relatively large.

Result 2: When lobbying occurs, t_b < t₀ always holds if the foreign lobbying effectiveness is relatively high, that is, θ ≥ 0.6; otherwise, t_b > t₀ if θ < 0.6 and λ is relatively large.

Results 1 and 2 imply that when goods X and Y are homogeneous and the foreign lobbying effectiveness is sufficiently high, the tariff under domestic-foreign lobbying is smaller than both the social optimum and that under domestic lobbying. The intuition behind it will be demonstrated after discussing case 2.

We then move on to compare W(t₀), W(t_p), and W*(t_b). First, we find that

(37)

Obviously, as long as λ > 1, 37 is less than zero, which immediately implies that W(t_p) < W(t₀). This result demonstrates that when goods X and Y are homogeneous, the welfare under the scenario of domestic lobbying is always lower than the social optimum.

Now, we make another two comparisons: W(t_p) and W*(t_b), and W*(t_b) and W(t₀). The results are given in Table 2, which are similar to Table 1.

Table 2. Welfare Comparison When c < 1

Foreign lobbying effectiveness		θ = 0.1	θ = 0.2	θ = 0.3	θ = 0.4	θ = 0.5	θ = 0.6	θ = 0.7
Conditions for Lobbying to occur		λ < 2	λ < 2.1	λ < 2.5	λ < 1.9	λ < 1.5	λ < 1.25	λ < 1.06
Results	w*(tb) > W(tp)	(1, 1.5)	(1, 1.5)	(1, 1.5)	(1, 1.5)	(1, 1.5)a	(1, 1.25)a	(1, 1.06)a
	w*(tb) > W(t0)	(1, 1.1)	(1, 1.2)	(1, 1.4)	(1, 1.45)	(1, 1.4)	(1, 1.25)a	(1, 1.06)a

Note:

• ^a indicates that w*(t_b) > W(t_p) or w*(t_b) > W(t₀) holds for the full range of λ.

Result 3: When lobbying occurs, W*(t_b) > W(t_p) always holds if the foreign lobbying effectiveness is relatively high, that is, θ ≥ 0.5; otherwise, W*(t_b) < W(t_p), if θ < 0.5 and λ is relatively large.

Result 4: When lobbying occurs, W*(t_b) > W(t₀) always holds if the foreign lobbying effectiveness is relatively high, that is, θ ≥ 0.6; otherwise, W*(t_b) < W(t₀), if θ < 0.6 and λ is relatively large.

4 Tariff and Welfare Comparisons under Differentiated Bertrand Duopoly

In this section, we discuss the differentiated Bertrand competition, that is, in the third stage, the two firms engage in price competition.

The model setup is similar to Section 2. However, as the two firms produce heterogeneous goods, we assume that the marginal costs of the two firms are equal and without loss of generality, are normalised to be zero.6 We then define the consumer surplus as follows:

(38)

We assume that 0 < b < 1, where b is the measure of product differentiation between the two firms. 0 < b < 1 implies that the two products are substitutes and the inverse demand for each differentiated good is more sensitive to its own supply than that of the opponent.

Therefore, the inverse demand function would be:

(39)

(40)

We can derive the two firms’ profit functions, respectively:

(41)

(42)

The rest of the model setting is the same as in Section 2.

We first consider the third stage. By calculating the first-order conditions of the two firms, we derive the following Bertrand equilibrium prices:

(43)

(44)

Thus, the corresponding outputs of the two firms are:

(45)

(46)

The equilibrium profits of the two firms are given by:

(47)

(48)

Substituting 43-48 in 6, we get the social welfare function of the domestic country in the case of no lobbying and that under the domestic lobbying:

(49)

With 49, we can also derive the corresponding social welfare in the case of domestic-foreign lobbying:

(50)

Using the same method as in Section 3, we can calculate the corresponding t₀, t_p and t_b under differentiated Bertrand competition:

(51)

(52)

(53)

Now we can calculate π_d(t_p) and π_f(t_q). By substituting them into 13 and 14, respectively, we get and , which can be further used to calculate W*(t).

From Result 5, we conclude that the results in Section 3 largely remain to hold under price competition. Moreover, we can also show that if the relative effectiveness of foreign lobbying is sufficiently high, lobbying competition between the domestic and the foreign firms not only contributes to freer trade but also improves the welfare of the domestic country. However, in the case where the effectiveness of foreign lobbying is relatively low, the welfare under the domestic-foreign lobbying would be lower than that under social optimum or even that under domestic lobbying, should the government be sufficiently avaricious and the product differentiation between the goods of the two firms is sufficiently small.

5 Conclusion

In this study, we find that lobbying competition between the domestic and foreign firms may contribute to a freer trade in the domestic country. Moreover, as compared to the case of no lobbying and the case of domestic lobbying, the domestic-foreign lobbying may probably realise the highest welfare for the domestic country. In other words, lobbying competition may be one of the strongest forces pushing for trade liberalisation. This happens primarily because it is easier for foreign lobbies to compensate the government for the distortions associated with changes in trade policy, as contributions from the foreign lobbies may receive a heavier weight than domestic contributions.

Our findings may have some implications for the current trade policies adopted by US government. Many Asian foreign firms are denied access to the US market because US domestic firms dominate the Asian foreign firms in the lobbying competition, which can be largely accrued to the low effectiveness of foreign lobbying, for example, lack of experience and ability, and the US government's worries over welfare worsening effect generated by such lobbying competition.

We conclude by noting some limitations of our results. First, we have restricted our attention to tariffs to gauge the impact of lobbying on the political process. In the real world, the government holds a wide selection of policy tools. It is possible to examine how the optimal tariffs and the corresponding social welfare may be affected by each of these policies in the presence of lobbying. Second, it would also be interesting to consider the case in which the weights that the government attaches to firm contributions are endogenously determined.