Cooperation among rival firms raises serious skepticism among economists, policymakers, and legal experts, since it generally hurts consumers. We show that this may not be the case in an open economy with strategic foreign direct investment (FDI). Under Cournot competition, increased cooperation among firms reduces the domestic welfare, but it may benefit the consumers by attracting FDI. Under Bertrand competition with differentiated goods, increased cooperation may increase consumer surplus, and it may increase or decrease the domestic welfare by attracting FDI.
Hinweise
We thank two anonymous referees and the editor, Lawrence J. White, for extremely helpful comments and suggestions. We thank Madhuri H. Shastry for research assistance and helping us with Figs. 1 and 2. The usual disclaimer applies.
1 Introduction
Cooperation among rival firms raises serious skepticism among economists, policymakers, and legal experts. In the absence of significant synergic benefits, firms’ gains from cooperation come at the expense of consumers (Farrell & Shapiro, 1990), and create concerns for antitrust authorities. However, this view generally ignores the nonproduction activities of firms, such as innovation (Jacquemin & Slade, 1989). The Schumpeterian view suggests that cooperation between competing firms may benefit consumers due to its favorable effects on innovation (Schumpeter, 1943). However, there are concerns about the adverse effects of firms’ cooperation on innovation (Arrow, 1962; Gilbert & Tom, 2001; and Gilbert, 2006).
Recent papers show that there can be channels other than innovation through which product-market cooperation may benefit consumers. Symeonidis (2008) and Mukherjee (2010) show that product-market cooperation may benefit consumers in the presence of input market imperfection. Deltas et al. (2012) show that cooperation among competing firms may benefit consumers due to the “home market principle”, which gives the cartel members preference for supplying their home markets. Mukherjee and Sinha (2019) show that cooperation among firms might benefit consumers in the presence of strategic trade policies.
Anzeige
We provide in this paper a new channel for the favorable effect of product-market cooperation for consumers: We show that cooperation among rival firms may benefit consumers in the presence of strategic foreign direct investment (FDI), which is an important phenomenon in today’s world (see, e.g., UNCTAD, 2006).
On the one hand, increased cooperation tends to reduce consumer surplus by contracting outputs under both export and FDI regimes. On the other hand, it tends to increase consumer surplus by attracting FDI: This increases cost efficiency in the industry by eliminating the trade (transport and other) cost, which helps to expand output. We show the conditions under which the latter effect dominates the former and cooperation among rival firms benefits consumers. We show it under both Cournot and Bertrand competition.
The positive effect of increased cooperation on consumer surplus can only happen if the increased cooperation leads to FDI, and the increase in cooperation is not significant. However, if either greater cooperation does not induce FDI or the increase in cooperation is significant, then we have the standard adverse effects of cooperation on consumers.
Although increased cooperation among rival firms may benefit consumers by attracting FDI, we find that it reduces aggregate domestic welfare under Cournot competition but it may decrease or increase aggregate domestic welfare under Bertrand competition.1 Since the profit of the foreign firm is not included in the aggregate domestic welfare calculation, the effects of FDI on domestic welfare following greater cooperation depends on the relative strengths of higher consumer surplus and lower domestic profit under FDI as compared to the export alternative.
Anzeige
There is a paper by Mukherjee and Sinha (2016), which does not consider cooperation among firms but shows that under Cournot competition greater product differentiation–which affects the intensity of competition–may benefit consumers by attracting FDI. Unlike this paper, they find that greater product differentiation increases domestic welfare by attracting FDI. Hence, how competition is affected–through greater cooperation among rival firms or by wider product differentiation–may be important for welfare implications.
There is a literature on cross ownership or common ownership among firms, where each firm will maximise its total profit earned from its shareholdings in different firms. See Ghosh and Morita (2017), Backus et al., (2019, 2021), López and Vives (2019), Vives (2020), Vives and Vravosinos (2023), and Mukherjee (2023) for a representative sample of the recent literature on cross or common ownership. Since the parameter of cooperation that is used in our analysis can reflect cross ownership or common ownership arrangements, our paper contributes to this literature by focusing on the international context.
The remainder of the paper is organized as follows: Sect. 2 describes the model and derives the results for Cournot competition with homogenous goods. Section 3 discusses the case of Bertrand competition with differentiated goods. Section 4 concludes.
2 The Model and the Results: Cournot Competition
Assume that there is a foreign firm (firm 1), which competes with a domestic firm (firm 2) in the domestic market with a homogeneous product. The inverse market demand function is P = 1–q, where P is price and q is the total output. Firm 1 can serve the domestic market through export or through FDI. While export requires a per-unit trade cost:t;FDI requires a fixed investment: F. We normalize the marginal costs of production for both firms to zero.
Consider the following game: At stage 1, firm 1 decides whether to export or to undertake FDI. At stage 2, the firms decide whether to cooperate in the product market. Hence, the investment decision of the foreign firm is taken as given at the time of the decision with respect to firm cooperation. At stage 3, the firms choose their outputs simultaneously, and the profits are realized. We solve the game through backward induction.
For cooperation, we follow Symeonidis (2000, 2008), Mukherjee (2010), and Mukherjee and Sinha (2019) and assume that, while taking the production decision, each firm gives \(\alpha \in [0,1)\) weight on the competitor’s profit. Hence, \(\alpha\) represents the degree of cooperation: \(\alpha = 0\) implies no cooperation; while \(\alpha = 1\) implies complete cooperation. To avoid corner solution where only one firm produces under cooperation, we restrict our attention to \(\alpha < 1\). We will consider that the cooperative behavior among firms remains the same under both export and FDI by firm 1.
The term \(\alpha\) is the “coefficient of cooperation”, as introduced by Cyert and DeGroot (1973). It can be justified by referring to some implicit dynamic models of collusion, where the reduced‐form representation of the dynamic game represents the product market competition of our paper. Alternatively, it can capture the situations with different “conjectural variations”, which thereby incorporate a wide range of competition.2 It may also reflect cross or common ownership arrangements.
The purpose of our paper is to show the effects of cooperation; hence, we consider α as an exogenous parameter. This may be justified if significant changes in the intensity of competition are the outcome of exogenous institutional changes–such as the introduction of an effective cartel policy (Symeonidis, 2000, 2008).
There could be several ways to model cooperation among firms. We chose to model it by following the “coefficient of cooperation” introduced by Cyert and DeGroot (1973). An alternative way might be to consider complete cooperation or joint profit maximization. This case follows from our analysis as a special case when \(\alpha = 1\).
If the firms cooperate in stage 2, under the export regime, firms 1 and 2 maximize \([(1 - q - t)q_{1} + \alpha (1 - q)q_{2} ]\) and \([(1 - q)q_{2} + \alpha (1 - q - t)q_{1} ]\) to determine their respective outputs.3
The profits of both firms increase with higher \(\alpha\): Both firms prefer to cooperate in stage 2 if firm 1 exports in stage 1.
If the firms cooperate in stage 2, under FDI, firms 1 and 2 maximize \([(1 - q)q_{1} + \alpha (1 - q)q_{2} - F]\) and \([(1 - q)q_{2} + \alpha (1 - q)q_{1} - F]\) to determine the respective outputs.4
Proposition 1 (i) is the standard tariff-jumping argument: FDI allows firm 1 to save the trade cost. Hence, it will do FDI if the cost associated with FDI is not too high.
If cooperation among firms increases, it helps to increase the profits of the firms under both export and FDI by firm 1. However, the foreign firm gets a greater share of that increased profit in the FDI regime because, in the FDI regime, it shares the market equally with Firm 2, whereas it has a smaller share of the market under export due to the presence of the trade cost. Therefore, increased cooperation is relatively more valuable to the foreign firm under FDI. As a result, increased cooperation increases firm 1’s incentive for FDI, which thus leads to Proposition 1 (ii).
Although cooperation increases the profits of firm 2 when it does not change firm 1’s mode of operation (export or FDI), cooperation can reduce firm 2’s profit if it changes firm 1’s mode of operation from export to FDI. Unless \(\alpha\) increases significantly, a higher \(\alpha\) that induces FDI reduces the profit of firm 2 compared to a lower \(\alpha\) that encourages firm 1 to export. Even if firm 2 realizes that cooperation will reduce its profit by inducing FDI, cooperation still occurs, since cooperation ex-post FDI by firm 1 increases firm 2’s profit. Hence, firm 1 correctly anticipates that firm 2 will cooperate ex-post FDI by firm 1. This possibility of cooperation can encourage firm 1 to undertake FDI, and the firms cooperate ex-post FDI by firm 1.
2.1 The Effect of \(\alpha\) on Consumer Surplus
For a given \(\alpha\), the total output and consumer surplus under the export regime by firm 1 are respectively
In line with the common understanding, if a change in \(\alpha\) does not affect firm 1’s decision on FDI, consumer surplus decreases with higher \(\alpha\). Further, for any given \(\alpha\), consumer surplus is higher under FDI than under export.
The interesting situation occurs if increased cooperation induces FDI by firm 1. We consider this possibility in the following proposition:
Proposition 2
If an increase in \(\alpha\) from \(\alpha_{0}\) to \(\alpha_{1}\) attracts FDI, the consumer surplus is higher under \(\alpha_{1}\) compared to \(\alpha_{0}\) for \(t > \frac{{2(\alpha_{1} - \alpha_{0} )}}{{3 + \alpha_{1} }} \equiv t^{*}\).
Proof
We get from (7) and (8) that \(\left. {CS^{CF*} } \right|_{{\alpha = \alpha_{1} }} > \left. {CS^{Cx*} } \right|_{{\alpha = \alpha_{0} }}\) if \(t > \frac{{2(\alpha_{1} - \alpha_{0} )}}{{3 + \alpha_{1} }} \equiv t^{*}\).
Intuitively, since FDI helps to save the trade cost, for a given \(\alpha\), the total outputs of the firms and the consumer surplus are higher under FDI compared to export. Hence, even if an increase in \(\alpha\) tends to reduce consumer surplus by reducing total output, if a slight increase in \(\alpha\) induces the foreign firm to switch from export to FDI, there will be a range of t where the total output will expand and the consumer surplus will be higher under FDI than under export.
2.2 The Effect of \(\alpha\) on Domestic Welfare
Domestic welfare, which is the sum of consumer surplus and profit of the domestic firm, is \(SW^{Cx*} = \frac{(1 + \alpha + t)(1 - \alpha + t(1 + \alpha ))}{{(1 - \alpha )(3 + \alpha )^{2} }} + \frac{{(2 - t)^{2} }}{{2(3 + \alpha )^{2} }}\) under export and \(SW^{CF*} = \frac{(1 + \alpha )}{{(3 + \alpha )^{2} }} + \frac{2}{{(3 + \alpha )^{2} }}\) under FDI by firm 1.
We get.
\(\begin{aligned} SW^{Cx*} - SW^{CF*} = & \underbrace {{\left[ {\frac{(1 + \alpha + t)(1 - \alpha + t(1 + \alpha ))}{{(1 - \alpha )(3 + \alpha )^{2} }} - \frac{(1 + \alpha )}{{(3 + \alpha )^{2} }}} \right]}}_{Difference\,\,in\,\,domestic\,\,firm^{\prime}s\,\,profit} + \underbrace {{\left[ {\frac{{(2 - t)^{2} }}{{2(3 + \alpha )^{2} }} - \frac{2}{{(3 + \alpha )^{2} }}} \right]}}_{Difference\,\,in\,\,consumer\,\,surplus} \\ = & \underbrace {{\frac{{t\left( {2 + t + \alpha + t\alpha + \alpha^{2} } \right)}}{{\left( {1 - \alpha } \right)\left( {3 + \alpha } \right)^{2} }}}}_{Domestic\,\,firm^{\prime}s\,\,gain\,\,in\,\,profit} + \underbrace {{\frac{{ - \left( {4 - t} \right)t}}{{2\left( {3 + \alpha } \right)^{2} }}}}_{Loss\,\,of\,\,\,consumer\,\,surplus} \\ = & \frac{t}{{\left( {3 + \alpha } \right)^{2} }}\left[ {\frac{{\left( {3 + \alpha } \right)\left( {t + 2\alpha } \right)}}{{2\left( {1 - \alpha } \right)}}} \right] = \frac{t(t + 2\alpha )}{{2(1 - \alpha )(3 + \alpha )}} > 0. \\ \end{aligned}\) Hence, for any given \(\alpha\), domestic welfare is always lower under FDI than under export by firm 1. FDI creates higher consumer surplus as compared to the export regime by increasing total output. However, this gain in total output under FDI comes at the expense of lower output by and lower profit of the domestic firm and higher output by and higher profit of the foreign firm. The foreign firm’s profit does not appear in domestic welfare, and the gain in consumer surplus is not enough to compensate for the loss of domestic profit. This is similar to Collie (1996), who showed in the absence of cooperation that unilateral trade liberalization reduces the domestic welfare under Cournot competition if the foreign firm is not more cost efficient than the domestic firm.
Since greater cooperation reduces domestic welfare under FDI by causing the transfer of some domestic output and profit from firm 2 to firm 1, it is then immediate from the above discussion that if greater cooperation among firms induces FDI by the foreign firm, it reduces the domestic welfare. Hence, we get the following proposition:
Proposition 3
Under Cournot competition with homogenous goods, if greater cooperation among firms induces FDI, it reduces domestic welfare.
3 Bertrand Competition
The purpose of this section is to show that greater cooperation among firms may benefit the consumers by attracting FDI even under Bertrand competition. However, unlike Cournot competition, we will find that greater cooperation may also increase domestic welfare by attracting FDI.
We consider a differentiated goods industry that involves two firms. Assume that the inverse demand function that is faced by the ith firm is \(P_{i} = 1 - q_{i} - \gamma q_{j}\), \(i,j = 1,2,\,\,i \ne j\), where: \(P_{i}\) is the ith firm’s price; \(q_{i}\) is the ith firm’s output; and \(q_{j}\) is the jth firm’s output. The term \(\gamma \in [0,1]\) shows the degree of horizontal product differentiation between the products of firms 1 and 2. The products are perfect substitutes for \(\gamma = 1\), and they are isolated monopolies for \(\gamma = 0\). For our analysis, we will focus on \(\gamma \in (0,1)\) to avoid the well-known Bertrand paradox at \(\gamma = 1\) and to avoid the absence of competition between the firms at \(\gamma = 0\).
We consider a game similar to that under Cournot competition with the exception that now the firms compete as Bertrand duopolists. To save space, we mainly report the relevant expressions, and ignore the mathematical details.
We assume \(t < \frac{{\left( {1 - \gamma } \right)\left( {1 - \alpha \gamma } \right)\left( {2 + \gamma + \alpha \gamma } \right)}}{{2 - \left( {1 + \alpha^{2} } \right)\gamma^{2} }} \equiv \overline{\overline{t}} (\alpha )\), which ensures that the outputs of both firms are always positive.
and \(\overline{\overline{t}} (\alpha ) < \widehat{t}\).5 Hence, as is true under Cournot competition, greater cooperation among firms increases the incentive for FDI.
Now consider the effects on consumer surplus: If firm 1 exports, consumer surplus is
It can be found that \(\frac{{\partial CS^{Bx*} }}{\partial \alpha } < 0\), \(\frac{{\partial CS^{BF*} }}{\partial \alpha } < 0\), and \(CS^{BF*} > CS^{Bx*}\) for a given \(\alpha\). Hence, as is true under Cournot competition, higher \(\alpha\) may increase consumer surplus by attracting FDI by firm 1.
Finally, consider the effects on domestic welfare. If firm 1 exports, domestic welfare is
We can get \(SW^{Bx*} \frac{ \ge }{ < }SW^{BF*}\) depending on the parameter values. Hence, unlike Cournot competition, where \(SW^{Cx*} > SW^{CF*}\) holds and higher \(\alpha\) always reduces domestic welfare by attracting FDI, we get under Bertrand competition that a higher \(\alpha\) may increase domestic welfare by attracting FDI if \(SW^{Bx*} < SW^{BF*}\) in the relevant range of parameters.
As an illustration, we provide two diagrams: Fig. 1 assumes that \(\gamma = 0.5\) and \(t = 0.2\). For these parameter values we get \(SW^{Bx*} < SW^{BF*}\).
Fig. 1
The effects of \(\alpha\) on consumer surplus and welfare for \(\gamma = 0.5\) and \(t = 0.2\) where \(SW^{Bx*} < SW^{BF*}\)
×
Figure 2 assumes \(\gamma = 0.75\) and \(t = 0.2\). Here \(SW^{Bx*} \frac{ \ge }{ < }SW^{BF*}\) and the welfare curves intersect at\(\alpha =0.41323\).
Fig. 2
The effects of \(\alpha\) on consumer surplus and welfare for \(\gamma = 0.75\) and \(t = 0.2\) where \(SW^{Bx*} \frac{ \ge }{ < }SW^{BF*}\)
×
In the absence of cooperation, Clarke and Collie (2003) showed that unilateral trade liberalization under Bertrand competition increases domestic welfare. Our result of \(SW^{Bx*} < SW^{BF*}\) in Fig. 1 is in line with that result, where the gain in consumer surplus dominates the loss of domestic profit under FDI compared to export.
However, if the products are more similar, as in Fig. 2, the ranking of domestic welfare under export and FDI can be different if \(\alpha\) is high. If \(\gamma = 0.75\), FDI reduces the domestic profit significantly as compared to the export regime. Now, if \(\alpha\) is sufficiently high, significant cooperation among firms does not let the consumer surplus under FDI to increase by very much compared to export. In this situation, the gain in consumer surplus is dominated by the loss of domestic profit under FDI, which makes \(SW^{BF*} < SW^{Bx*}\).
4 Conclusion
In the presence of strategic FDI where a foreign firm chooses between exporting or engaging in FDI, we show that increased cooperation among rival firms increases the attractiveness of FDI. Greater cooperation may also increase consumer surplus by attracting FDI. This happens under both Cournot and Bertrand competition in the product market. While greater cooperation under Cournot competition reduces domestic welfare by attracting FDI, greater cooperation under Bertrand competition may increase or decrease domestic welfare by attracting FDI.
Since the lower marginal cost under FDI helps the foreign firm to have a higher market share under FDI as compared to exporting, greater cooperation is more beneficial for the foreign firm under FDI compared to exporting, which increases the incentive for FDI. Hence, a slightly greater level of cooperation may increase consumer surplus by attracting FDI, which helps to increase the total output under FDI compared to the export regime.
Any marginal-cost-reducing investment by a firm that yields a payoff that is more responsive to cooperation than the status quo payoff may have similar results. Thus, greater cooperation may benefit consumers by inducing such cost-reducing investment. This happens as long as the decrease in marginal cost is sufficient and the consumer surplus is sufficiently responsive to a lower marginal cost. Strategic cost-reducing R&D investment is a situation where this result may happen. The FDI example in this paper is another demonstration of this effect.
The broader takeaway message is that cooperation can lead to efficient investments that increase the size of the potential pie enough to make both investors and consumers better off. The paper demonstrates this result in the context of FDI. However, since higher FDI following higher cooperation can hurt the domestic firm, the effects on domestic welfare are not immediate and may depend on the type of product market competition, as has been shown here.
It is well-known under a general demand function that a lower cost of a firm increases its output and the total output but decreases the output of the rival firm. Hence, it must be clear that the basic mechanism behind our results–which is proved under linear demand functions and depends on the effects of a lower marginal cost on the outputs of the firms–is not dependent on the type of demand functions.
We hope that our theoretical analysis will encourage some empirical analysis: For example, examining the effects of cooperation among firms on FDI and price. One may test whether increased cooperation among domestic and foreign firms increases the likelihood of FDI and a lower price. Alternatively, one can empirically analyze whether FDI is more likely to be observed in situations with more international cross-ownership or common ownership and whether it reduces price. This requires a thorough empirical analysis to understand the causal relationship–whether FDI causes more cooperation as predicted by other models in Industrial Organization, due to symmetric cost and collusion (e.g., Leahy & Pavelin, 2003; Sinha, 2018) or more cooperation increases FDI as has been established in this paper.
Declarations
Conflict of interest
The authors declare no competing interests.
Funding
No funding was received for conducting this research.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Cooperation may reduce the profit of the domestic firm if it attracts FDI. We explain below why cooperation occurs even if it reduces the profit of the domestic firm by attracting FDI.
Since the FDI decision is sunk at the time of cooperation, we believe that it is more natural to not put the weight \(\alpha\) on F. The results will not change even if one puts the weight \(\alpha\) on the overall net profit inclusive of F.
