Related party transactions, agency problem, and exclusive effects

Abstract

This paper examines the incentives for, and economic impact of related-party transactions (RPTs) by controlling shareholders (CSHs) of corporate groups. We analyze a theory model of RPTs transacted on ‘market terms’ by two affiliate firms in a group, one of which belongs to an upstream and the other to a downstream market. We show that RPTs of this kind, although non-advantageous to the CSH of the group in terms of transfer price, may be abusive in that they serve the interests of the CSH by sacrificing minority shareholders. This is due to the exclusive effects of such RPTs. We show that a CSH has a strong incentive to exclude upstream rivals for his/her own sake rather than the group’s when he/she is allowed to implement such RPTs. The results shed light on regulation of RPTs: distortions of RPTs arise not only from unfair transfer-pricing but also from large transaction volume. This further implies that competition policies regarding the leverage of market power and anti-competitive vertical mergers may be applied to regulate harmful RPTs.

Appendix

1.1 Proof of Proposition 2

Proof

Since the sign of the effect of s on $\Pi _A$ is trivial, it suffices to show that $\Pi _E$ is increasing in s. Suppose first that s is the interior point of an interval I(N). Then, ${\hat{N}}(s)$ is fixed and $\Pi _E$ is differentiable near s. Letting ${\hat{N}}(s)=N_0$, we have

$$\begin{aligned} \frac{\partial \Pi _1}{\partial s}&= \frac{(a-c)^2}{(N_0+1)^2}\cdot \left( -\lambda _A+\lambda _A N_0\right) >0 \end{aligned}$$

Now, suppose that s is at the left end of an interval ${\hat{N}}(s)=N_0$. Then, for sufficiently small $\epsilon >0$, noting that $\Lambda$ is continuous in s and $N_0 \ge {\underline{N}}\ge 2$,

$$\begin{aligned}&\Pi _1(s+\epsilon , {\hat{N}}(s+\epsilon ))-\Pi _1(s, {\hat{N}}(s))\\&\quad = \Pi _1(s+\epsilon , N_0-1)-\Pi _1(s, N_0)\\&\quad =(a-c)^2\left[ \frac{\Lambda (s+\epsilon )+\lambda _A(s+\epsilon )(N_0-1)}{N_0^2}-\frac{\Lambda (s)+\lambda _AsN_0}{(N_0+1)^2}\right] \\&\quad \rightarrow (a-c)^2\left[ \frac{\Lambda (2N_0+1)}{N_0^2(N_0+1)^2}+\frac{\lambda _As(N_0^2-N_0-1)}{N_0^2(N_0+1)^2}\right] \\&\quad >0 \end{aligned}$$

as $\epsilon$ approaches to zero, which completes the proof. $\square$

1.2 Proof of Proposition 3

Proof

The function $\Gamma /(\lambda _A+\lambda _B)$ can be rewritten as

$$\begin{aligned} \frac{\Gamma }{\lambda _A+\lambda _B}&=\frac{\lambda _A^2}{(1+\theta _A)(\lambda _A+\lambda _B)}\\&=\frac{(2+2\theta _B +\theta _A)^2}{\left( 4+5\theta _A+5\theta _B+4\theta _A\theta _B+\theta _A^2 +\theta _B^2\right) \left( 4+4\theta _A+4\theta _B+3\theta _A\theta _B\right) }, \end{aligned}$$

which decreases in $(\theta _A, \theta _B)$ unless $\theta _B$ is near zero. Thus, it has a global maximum less than 1/4 near the origin. Then, we have

$$\begin{aligned}\frac{\sigma \Gamma }{\lambda _A+\lambda _B}<\frac{1}{4} \Leftrightarrow (2N^2+4N+1) \sigma \Gamma -(N^2 +N-1)(\lambda _A +\lambda _B)<0,\end{aligned}$$

which in turn implies $\Psi <0$ for all N. $\square$

1.3 Proof of Lemma 4

Proof

In the upstream market, with the inverse residual demand in equation (4) and given the number of firm N, the upstream firm $i=2, 3, \ldots , N$ maximizes the following operating profit:

$$\begin{aligned} \pi _i (q_{i}, Q_{-i}) = \left( a- c-\frac{Q}{\Lambda }\right) q_i. \end{aligned}$$

(18)

The first order condition gives the following implicit best response functions:

$$\begin{aligned} a-c-\frac{Q_{-i} +2q_i}{\Lambda } = 0, \end{aligned}$$

(19)

for all $i = 2, \ldots , N$. By the same token, for the upstream affiliate of the group, firm 1, we have the following implicit best response function:

$$\begin{aligned} a -c_1 -\frac{Q_{-1} +2q_1}{\Lambda } = 0. \end{aligned}$$

(20)

Solving the simultaneous equations, the equilibrium quantity and price are

$$\begin{aligned} {\hat{Q}} = \frac{\Lambda (Na-(N-1)c-c_1)}{N+1}=\frac{\Lambda (Na-Nc-\Delta )}{N+1}, \end{aligned}$$

(21)

$$\begin{aligned} {\hat{w}} = \frac{a+(N-1)c +c_1}{N+1}=\frac{a+Nc +\Delta }{N+1}. \end{aligned}$$

(22)

Then, in equilibrium, the quantity produced by each upstream firm is as follows:

$$\begin{aligned} {\hat{q}}_i = \frac{\Lambda (a-2c+c_1)}{N+1}=\frac{\Lambda (a-c +\Delta )}{N+1},\;\;\;\; i= 2, \ldots , N \end{aligned}$$

(23)

$$\begin{aligned} {\hat{q}}_1 = \frac{\Lambda (a+(N-1)c-Nc_1)}{N+1} = \frac{\Lambda (a-c-N\Delta )}{N+1}. \end{aligned}$$

(24)

Now, the equilibrium output by each firm (${\hat{q}}_i$), the market output (${\hat{Q}}$), and the equilibrium price (${\hat{w}}$) are given by

$$\begin{aligned} {\hat{q}}_i = {\left\{ \begin{array}{ll}\frac{\Lambda (a-c +\Delta )}{N+1}, &{} \text {if}\;\; i= 2, \ldots , N\\ \frac{\Lambda (a-c -N\Delta )}{N+1}, &{} \text {if}\;\; i=1, \end{array}\right. } \end{aligned}$$

(25)

$$\begin{aligned} {\hat{Q}} = \frac{\Lambda (Na-Nc -\Delta )}{N+1}, \end{aligned}$$

(26)

$$\begin{aligned} {\hat{w}} = \frac{a+Nc +\Delta }{N+1}, \end{aligned}$$

(27)

In equilibrium, the operating profit from market transaction of the affiliate and non-affiliates are, respectively

$$\begin{aligned} \pi _i = ({\hat{w}} -c)q_i=\frac{\Lambda \left( a-c +\Delta \right) ^2}{(N+1)^2},\;\;\;\; i= 2, \ldots , N \end{aligned}$$

(28)

$$\begin{aligned} \pi _1^{MKT} = ({\hat{w}}-c_1)q_1=\frac{\Lambda \left( a-c-N\Delta \right) ^2}{(N+1)^2} \end{aligned}$$

(29)

For the entrant, there is an additional operating profit from RPTs, which is

$$\begin{aligned} \pi _1^{RPT} = ({\hat{w}}-c_1)sq_A =\frac{\lambda _A (a-c-N\Delta )(Na-Nc -\Delta )s}{(N+1)^2} \end{aligned}$$

(30)

The Nash equilibrium number of firms, ${\hat{N}}$, is determined by the following inequalities.

$$\begin{aligned} \frac{\Lambda \left( a-c +\Delta \right) ^2}{({\hat{N}}+2)^2} < f \le \frac{\Lambda \left( a-c +\Delta \right) ^2}{({\tilde{N}}+1)^2} \end{aligned}$$

(31)

or

$$\begin{aligned} ({\hat{N}}+1)^2 \le \frac{\Lambda \left( a-c +\Delta \right) ^2}{f}< ({\hat{N}}+2)^2. \end{aligned}$$

(32)

$\square$