Cross-Border Mergers & Acquisitions Policy in Service Markets

Abstract

We provide facts showing that in service markets: (i) restrictions on foreign direct investment (FDI) are under reform, (ii) cross-border Mergers & Acquisitions dominate as the entry mode of FDI, and (iii) there is often a high market concentration. Based on these facts, we present a model for analyzing cross-border merger and acquisition policy in liberalized service markets taking into account efficiency and market power effects. Our findings suggest that a merger policy, but not a discriminatory policy towards foreigners, seems warranted. Moreover, policies ensuring competition for domestic target firms seem warranted. In this vein, harmonization of the EU takeover regulations may particularly benefit assets owners in countries with many target firms.

Appendix: The linear-quadratic Cournot model

In the Linear-Quadratic Cournot model, we capture that different types of investment have different effects on firms’ production costs, which allows to us derive explicit solutions for the optimal behavior by firms in all stages of the game, and characterize welfare effects. We model the oligopoly interaction in period three as Cournot competition in homogenous services. Investments in new assets in period two reduce the firm’s marginal cost. The profit for firm i can be written:

$$ \pi _{i}(\mathbf{q,\kappa ,}l)=R_{i}(\mathbf{q,\kappa ,}l)-\frac{\mu \kappa _{i}^{2}}{2}-G_{i}, \label{DirectProfit} $$

(22)

where R _i  = (P − c _i )q _i is the service market profit and we assume costs to be quadratic in new assets, κ _i . Firms face the inverse demand $P=a-\frac{1}{s}\sum_{i=1}^{N}q_{i}$, where a > 0 is a demand parameter, s may be interpreted as the size of the market and N is the total number of firms in the market. Investments in new capital reduce a firm’s marginal cost in a linear fashion $c_{i}=\bar{c}_{i}-\theta \kappa _{i},$ where θ is a positive constant measuring how effectively investments in new capital κ _i in stage two reduce the marginal cost. For simplicity, we assume that all firms share the same investment technology, θ and μ. Asymmetries between firms are captured by the intercept term, $\bar{c}_{i}$, which measures the impact on firm i’s absolute efficiency level of the possession of all other assets prior to investment in new assets, κ _i , in stage 2. Making a distinction between firm types, we have:

$$ \bar{c}_{G}=c,\text{ \ \ \ \ }\bar{c}_{A}=c+\tilde{c}_{A}-\gamma \bar{k}, \text{ \ \ \ \ \ }\bar{c}_{d}=c+\tilde{c}_{d}-\bar{k}.\text{\ } \label{MC-intercepts} $$

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Hence, we assume existing assets $\bar{k}$ and new assets κ _i to be imperfect substitutes. The complementarity parameter γ again shows the effect of adding foreign firms’ firm-specific assets to domestic assets k ₀. Similarly, we capture other cost asymmetries by including $\tilde{c}_{A}$ and $\tilde{c}_{d}$.

From Eq. 2, $\frac{\partial R_{i}}{\partial q_{i}}=P-c_{i}-q_{i}=0$ from which optimal quantities q ^∗(κ,l) are derived. In stage two, Eq. 3 implies that $\frac{d\pi _{i}}{d\kappa _{i}}=\frac{ \partial R_{i}}{\partial \kappa _{i}}+\sum_{j\neq i}^{T}\frac{\partial R_{i} }{\partial q_{j}}\frac{dq_{j}}{d\kappa _{i}}-F_{i}^{\prime }=0$, where optimal investments are given from $\kappa _{i}^{\ast }(l)=\frac{\theta }{ \mu }q_{i}^{\ast }\tfrac{2N}{N+1}.$ Solving for stage 2 investments κ ^∗(l) and stage 3 sales q ^∗(l), we have the reduced-form profits π _i (l). It can be shown that these profits take the form $\pi _{i}(q,\kappa ,l)-\frac{\mu \kappa _{i}^{2}}{2}=\frac{1}{s}(q_{i}^{\ast }(l))^{2}\left[ 1-\frac{2\eta }{9}\right] -G_{i}$, where $\eta =s\frac{ \theta ^{2}}{\mu }$. Table 1 gives the explicit expression for the LQC model. Finally, Fig. 8 shows a numerical solution of the model given in Section 3.3.1.

Table 1 Equilibrium quantities and profits as functions of ownership structure

Fig. 8

Numerical solution in the Linear-Quadratic Cournot model for the case of low entry barriers in Section 3.3.1. Parameter values at G _G  = 0.1,G _A  = G _E  = 0, $\bar{k}=1,\Lambda =s=5,M=4$ and $\tilde{c}_{A}=\tilde{c}_{d}=0$