Government-induced production commitment vs. import-tariff under endogenous entry of foreign firms

ABSTRACT

Governments often have direct or indirect control over domestic production to develop or protect their domestic industries that have cost disadvantages against foreign firms. We investigate the welfare effects of such a production control policy when domestic firms face the free entry of foreign firms. We consider the production control policy as the government inducing domestic firms to commit to some target output levels before the foreign entry, and compare the resulting domestic social welfare with that under an import tariff. We show that when the products are homogeneous, the production control policy yields higher domestic welfare than any level of import tariff, even if the production control policy aims to maximize domestic industry profits rather than overall domestic welfare. We also show that when the products are differentiated, the superiority of the production control policy crucially depends on the degree of product differentiation. The results suggest a benefit of maintaining the government's control over domestic production even after opening the domestic market, particularly for homogeneous products.

KEYWORDS:

• Developing countries
• economic development
• imperfect competition
• open economy
• trade barriers
• tariffs

JEL CLASSIFICATIONS:

• F12
• F13
• L11
• L52
• O24

Acknowledgements

We especially thank Yibing Ding, Federico Etro, Kenji Fujiwara, Junichi Haraguchi, Keisaku Higashida, Hong Hwang, Masayo Kani, Toshihiro Matsumura, Noriaki Matsushima, Masaki Nakabayashi, Cong Pan, Ulrike Schaede, Tsuyoshi Toshimitsu, Yuta Yasui, the participants at International Workshop on Global Competition and Innovation, Contract Theory Workshop, and the seminars at Jilin University, Kansai University, Kyoto Sangyo University, National Taiwan University, Osaka University, The University of Tokyo, and University of California, San Diego for helpful discussions and comments. We also thank the editor and two anonymous referees for constructive comments and suggestions. We gratefully acknowledge financial support from the Japan Society for the Promotion of Science (JSPS KAKENHI 15H03355, 16J00067, 19H01494).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Such a system has also been observed in Africa (e.g. Botswana) and, historically, in Europe (Leftwich 1995). Generally, our context is about state interventions to protect less efficient domestic industries. The policies may be relevant to both agricultural and industrial policies.

2 Since theoretically the target output levels can also be attained by the appropriate levels of production subsidies given to domestic firms, our analysis includes this indirect production control as well. See Footnote 23.

3 In the context of economic reform, in contrast to the ‘gradualist’ approach in China and Vietnam, Russia and some Eastern European countries adopted a ‘big bang’ or ‘shock therapy’ approach, where they rapidly privatized domestic industry and reduced state control over domestic enterprises. Our tariffication case could be interpreted as this latter approach.

4 For instance, developmental states commonly include industrial policies that focus on some industries to push economic development (Woo-Cumings 1999). Such a policy may care about a particular industry's profit for some extent. We include these biased cases in order to show that the superiority of the control policy is robust even if the policy fails to maximize welfare and is assumed to be biased.

5 The endogenous entry approach now has wide use in the industrial organization literature. See, for example, Etro (2004, 2008, 2010), Matsumura and Kanda (2005), Ino and Matsumura (2012), and Žigić (2012). See Etro (2014a) for the comprehensive survey of this approach.

6 In Section 5, we discuss the implications of our results for domestic industry restructuring after market liberalization and the debate on the openness of Japanese markets from the end of the last century.

7 Etro (2014b) notes that if a production subsidy is available, the optimal production subsidy is one large enough to completely deter foreign entry and there is no need for an import tariff, in a homogeneous-product market that simply assumes a single domestic firm and identical constant marginal costs for all firms. If we regard the domestic production subsidy as an indirect policy instrument to control domestic production, his simple example can be viewed as a special case within our framework. Our framework for homogeneous products is general in that it includes multiple domestic firms and allows for cost differences between domestic and foreign firms under convex cost functions, and thus, considers both interior (entry accommodation) and corner (entry deterrence) solutions.

8 For a seminal work on mixed oligopoly, see De Fraja and Delbono (1989), and for partial privatization, see Matsumura (1998). For Stackelberg models in a free-entry mixed market, see Ino and Matsumura (2010).

9 Matsumura (2003) and Chang (2005) also consider the case of a state-owned firm as a Stackelberg leader vis-a-vis foreign firms, but the authors assume that the number of foreign firms is exogenously fixed.

10 Domestic firms' entry is exogenous. For example, strong state control over domestic firms is difficult for new entrants. If the government allows free entry of domestic firms as well as foreign firms without any control, all domestic firms are forced out of the market because domestic firms are less efficient than foreign firms. However, our production control policy that controls the fixed number of domestic incumbents contributes to improve the welfare (see Proposition 3.1 and Figure 2). This implies that the government has an incentive to regulate the number of domestic firms and control their production. Previous studies on international trade adopt a similar market structure, where a fixed number of domestic firms face foreign firms' free entry (e.g. Lahiri and Ono 1998a; Kayalica and Lahiri 2007; Etro 2014b).

11 We adopt the linear-demand structure because we would like to focus on the welfare effect of each policy, especially through domestic industry protection. With non-linear demand, an import-tariff policy generates an additional welfare benefit by decreasing the effective import price, which we discuss in more detail in Section 3.3. In the literature on trade policy under imperfect competition, many studies focus on a linear demand structure (e.g. Venables 1985; Horstmann and Markusen 1986; Lahiri and Ono 1998b; Bagwell and Staiger 2012).

12 To identify the pure effect of the production control policy, we analyze the production control policy separately from the import-tariff policy. See Section 3.3 for a discussion of the case where the government uses both policies simultaneously.

13 In this study, we neglect the integer problem of the number of foreign firms entering the market.

14 Hillman (1982) postulates that the government's objective to choose some trade policy is a function of the gain in the interest group's profits and the loss in consumer welfare from the trade policy (political support function). Considering the equilibrium outcomes without the policy as given, our formula $V\left(\mathbf{q}\right)$ is a linear specification of the political support function.

15 Note that this is not the first-best planning because the government cannot control foreign firms and the policy's objective is not pure welfare maximization.

16 See Footnote 23 for more detail.

17 If the superiority of the production control policy holds to the welfare-maximizing level of the tariff, it holds more so to any level of tariff. For homogeneous products, in Proposition 3.2, we show that domestic welfare under a biased production control policy is higher than that under any import tariff rate. Therefore, this result indeed holds, regardless of the government's objective for the tariff policy.

18 Sufficiency for the first-order condition immediately follows the fact that the second-order condition is globally satisfied from our assumptions. Sufficiency for the zero-profit condition comes from the fact that equilibrium profit of a foreign firm strictly decreases in n in the third stage.

19 Note that the following analysis allows for a corner equilibrium ($n^{\ast }\left(Q_D\right)=0$ and $q^{\ast }\left(Q_D\right)=0$) as well as an interior equilibrium given by (3(3) $\begin{array}{rl}& p\left(Q^{\ast }\right)q^{\ast }-c\left(q^{\ast }\right)-f=0\end{array}$(3) ) and (4(4) $\begin{array}{rl}& p\left(Q^{\ast }\right)+p^{\mathrm{\prime }}\left(Q^{\ast }\right)q^{\ast }-c^{\mathrm{\prime }}\left(q^{\ast }\right)=0\end{array}$(4) ).

20 This is because the profit of the first foreign marginal entrant is positive by $p\left(0\right)=a>c^{\mathrm{\prime }}\left(0\right)$.

21 Assumption 3.3 is unnecessary to obtain the results for the production control policy in this subsection, but necessary for Lemma 3.2(i) on the import-tariff policy in the next subsection. See also footnotes 25 and 28.

22 More formally, we obtain $C^{\mathrm{\prime }}\left(Q_D\right)$ by summing up the inverse functions of $c_1^{\mathrm{\prime }},\dots ,c_m^{\mathrm{\prime }}$ unless a marginal cost is constant; that is, defining $I\left(y\right)=\{i\in \{1,\dots ,m\left\}|c_i^{\mathrm{\prime }\mathrm{\prime }}\right(q_i)\ne 0\mathrm{w}\mathrm{h}\mathrm{e}\mathrm{n}{c}_i^{\mathrm{\prime }}(q_i)=y\}$ and $F\left(y\right)=\sum _{i\in I\left(y\right)}{c}_i^{\mathrm{\prime }-1}\left(y\right)$, we obtain $C^{\mathrm{\prime }}\left(Q_D\right)=min\left[F^{-1}\right(Q_D),c_1^{\mathrm{\prime }}(Q_D),\dots ,c_m^{\mathrm{\prime }}(Q_D\left)\right]$. Since we allow for cost heterogeneity among domestic firms, $C^{\mathrm{\prime }}\left(Q_D\right)$ may be kinked as drawn in Figures 2 and A2 below.

23 The equilibrium outcomes under the production control policy analyzed here can be implemented as an equilibrium under the production-subsidy policy. Suppose that under the control policy, the equilibrium levels of the domestic firms' outputs are $(q_1^{\ast },\dots ,q_m^{\ast })$, the number of the foreign firms is $n^{\ast }$, and if $n^{\ast }>0$, the foreign firm's output is $q^{\ast }$. Consider that the government sets a production subsidy for each domestic firm $s_i\in \mathbb{R}$ ($i=1,\dots ,m$) instead of $q_i$ in the first stage, and $q_i$ is chosen by firm i itself in the third stage. For $i\in \{1,\dots ,m\}$ such that $q_i^{\ast }=0$, set a sufficiently small (negative) $s_i$ that results in $q_i=0$ (e.g. $s_i<c_i^{\mathrm{\prime }}\left(0\right)-a$). For $i\in \{1,\dots ,m\}$ such that $q_i^{\ast }>0$, set $s_i=-p\left(Q^{\ast }\right)-p^{\mathrm{\prime }}\left(Q^{\ast }\right)q_i^{\ast }+c_i^{\mathrm{\prime }}\left(q_i^{\ast }\right)$, where $Q^{\ast }=Q^{\ast }\left(0\right)$ when $n^{\ast }>0$ (entry accommodation) and $Q^{\ast }=\sum _{i=1}^m{q}_i^{\ast }$ when $n^{\ast }=0$ (entry deterrence). Then, we can check that the given outcomes $(q_1^{\ast },\dots ,q_m^{\ast })$, $n^{\ast }$, and $q^{\ast }$ are also an equilibrium under this subsidy policy.

24 Note that $Q_D^{\ast }\left(\alpha \right)$ is not unique when $C^{\mathrm{\prime }}\left(Q_D\right)$ is constant at $p\left(Q^{\ast }\right(0\left)\right)$ for some range of $Q_D$.

25 To be precise, Assumption 3 guarantees $Q_D^{\ast }\left(1\right)=Q^{\ast }\left(0\right)$. Since we have $Q_D^{\ast }\left(1\right)\ge Q^{\ast }\left(0\right)$ even without Assumption 3, to show Proposition 3.1(iii), this fact is redundant.

26 Under our setting, the third-stage game has a unique equilibrium. Therefore, there are no other equilibria than the one we focus on here. Refer to, among other studies, Vives (2001, Chapter 4), which provides a sufficiently general explanation of the conditions for the Cournot model with heterogeneous costs to have a unique equilibrium. Furthermore, we can show in the third-stage equilibrium that the profit of a foreign firm is strictly negative if n is sufficiently large. Thus, an equilibrium number of foreign firms exists in the second stage.

27 This case is just for illustration. Our formal analysis proceeds without assuming interior solutions and $t\ge 0$.

28 Assumption 3.3 guarantees $n^T\left(0\right)>0$. This fact is relevant for Proposition 3.2 below. Without Assumption 3.3, we could have $n^T\left(0\right)=0$, especially when m is extremely large.

29 Note that as stated in Lemma 3.2(ii), the output of each foreign firm is neutral relative to the tariff rate (i.e. $d{q}^T\left(t\right)/dt=0$), which is due to our linear demand assumption. The tariff induces each foreign firm to reduce its output by increasing its marginal cost, but it simultaneously encourages its production by reducing the number of entrants. With linear demand, these two contrary effects are cancelled out exactly.

30 Proposition 3.2 implies that when $p\left(Q^{\ast }\right(0\left)\right)\le C^{\mathrm{\prime }}\left(0\right)$, $W^{\ast }\left(Q_D^{\ast }\right)=W^T\left(0\right)$ if t=0 and $W^{\ast }\left(Q_D^{\ast }\right)>W^T\left(t\right)$ for all $t\ne 0$.

31 In this section, we show the welfare superiority of the production control policy without deriving the optimal import-tariff rate. In the supplementary material, we present a parametric example to demonstrate our result after deriving the optimal policy levels under both production control and import-tariff policies.

32 Lemma 3.1 and Proposition 3.1 hold as long as the demand function satisfies $p^{\mathrm{\prime }}\left(Q\right)<0$ and $p^{\mathrm{\prime }\mathrm{\prime }}\left(Q\right)q+p^{\mathrm{\prime }}\left(Q\right)<0$ for all Q such that $p\left(Q\right)>0$ and for all $q\in (0,Q)$. The latter condition ensures that each firm's marginal revenue is decreasing in its rivals' outputs.

33 Etro (2014b) shows that the welfare-maximizing tariff level is positive when demand is linear but that it can be negative when demand is highly convex.

34 Žigić (2012) considers an endogenous number of followers under product differentiation in a closed economy model with a similar linear demand and cost structure as in our study.

35 More precisely, if there are multiple domestic firms, the following two additional welfare effects arise and make our analysis complicated. On the one hand, a variety of products are supplied by domestic firms, which alleviates the loss of product variety due to restricted foreign entry under the production control. In this effect, the production control policy becomes more likely to welfare-dominate the import-tariff/subsidy policy. On the other hand, under free entry with product differentiation, the effect of collusion among domestic firms, which is induced by biased production control, is revived. Therefore, the production control policy becomes less likely to dominate the import-tariff/subsidy policy. Nevertheless, regarding the former effect, our results in this section would be qualitatively unchanged. Assuming a single domestic firm can purify our analysis by eliminating the latter qualitatively different effect and focusing on the effect of product variety.

36 Note also that for $f\ge f_T\left(b\right)$, the optimal tariff rate is not unique and any tariff rate that is high enough to deter foreign entry is optimal.

37 $W_P^{\ast }=W^T$ holds for $b=b_P\left(f\right)$ and for $(b,f)$ such that $b>1/2$ and $f=a^2/4$, whereas $W_W^{\ast }=W^T$ holds for $b=b_W\left(f\right)$.

38 Note that $(4-\sqrt{10})/3\approx 0.279$ in Figure 3(a) and $\hat{b}\approx 0.212$ in Figure 3(b).

39 While we assume that the government commits to its policy before firms' entry and production decisions, a government's (in)ability to commit is also an important issue. The international trade literature has discussed this issue since the pioneering work of Carmichael (1987). See Žigić (2011) for more recent works on this issue.

40 More precisely, in this interpretation, the $q_i$s are the upper limits on production up to which firms can produce with zero marginal cost and the $c_i$s are the cost for installing capacity for $i=1,\dots ,m+n$. If the firms end up producing outputs such that the capacity constraints are binding in the subsequent competition stage, a pure strategy equilibrium with the surplus-maximizing rationing rule will yields a similar outcome to the production control policy. See Vives (2001, Chapter 5) as for competition under capacity constraint.

41 Several studies analyze the effects of price ceilings under imperfect competition. For example, Molho (1995) and Chang (2004) explore the effects of price ceilings in a closed economy under Cournot and Stackelberg oligopoly, respectively. Matsushima (2008) focuses on a monopolist's location choice between two countries and analyzes how imposing a binding price ceiling in one country affects the location choice and overall social welfare.

42 See Grossman and Helpman (1994) for the political mechanism wherein the government endogenously pays special attention to particular sectoral interests when it uses import tariffs.

43 More precisely, while domestic welfare under the welfare-maximizing import tariff is increasing in m, domestic welfare under the optimal production control policy for given α remains constant, regardless of m. While the former is because firms' competition under the import tariff intensifies as m increases, the latter is because the production control policy induces domestic firms to coordinate and operate as a single firm, irrespective of m. Thus, the welfare-reducing effect of the production control policy here corresponds to the welfare benefit of competition under the import tariff, which is eliminated under the production control policy.

44 Although Figure 2 depicts and exemplifies the case in which t>0 and all the equilibrium outcomes are strictly positive, the following proof is valid for all cases, including those in which t<0 or some outcomes are zero.

Additional information

Funding

We gratefully acknowledge financial support from the Japan Society for the Promotion of Science (JSPS KAKENHI 15H03355, 16J00067, 19H01494).