$$ \begin{aligned}&U_{mn}=\alpha G^{\prime\prime}+\gamma(1-P(n))G^{\prime\prime}-\gamma P_{n}G^{\prime}-C_{mn}\\&U_{mm}U_{nn}-U_{mn}{}^{2}=\{(\alpha+\gamma(1-P(n)))G^{\prime\prime}-C_{mm}\}\{(\alpha+\gamma(1-P(n)))G^{\prime\prime}-2\gamma P_{n}G^{\prime}-C_{nn}+E_{nn}\}\\&-\{(\alpha+\gamma(1-P(n)))G^{\prime\prime}-\gamma P_{n}G^{\prime}-C_{mn}\}^{2}\\&=-C_{mn}{}^{2}+C_{mm}C_{nn}-C_{mm}E_{nn}++2\gamma C_{mm}P_{n}G^{\prime}-2\gamma C_{mn}P_{n}G^{\prime}-\gamma{}^{2}P_{n}{}^{2}G^{\prime}^{2}\\&-\alpha C_{mm}G^{\prime\prime}-\gamma C_{mm}G^{\prime\prime}+\gamma P(n)C_{mn}G^{\prime\prime}+2\alpha C_{mn}G^{\prime\prime}+2\gamma C_{mn}G^{\prime\prime}-2\gamma P(n)C_{mn}G^{\prime\prime}-\alpha C_{nn}G^{\prime\prime}-\gamma C_{nn}G^{\prime\prime}\\&+\gamma P(n)C_{nn}G^{\prime}+\alpha E_{nn}G^{\prime\prime}+\gamma E_{mn}G^{\prime\prime}-\gamma P(n)E_{nn}G^{\prime\prime}>0\\ \end{aligned} $$

となる $ ^{11} $ 。これより、

(5)式：

$$ m_{\alpha}=\frac{-C_{mn}G+C_{nn}G-E_{nn}G+\gamma P_{n}G^{2}+\tau(C_{mn}P_{n}-\alpha P_{n}G^{\prime}-\gamma P_{n}G^{\prime}+\gamma P_{n}^{2}G+\gamma P(n)P_{n}G^{\prime})}{-C_{mn}^{2}+C_{mn}C_{nn}-C_{mm}E_{nn}+2\gamma C_{mm}P_{n}G-2\gamma C_{mn}P_{n}G-\gamma^{2}P_{n}^{2}G^{2}-\alpha C_{mm}G^{\prime}-\gamma C_{mm}G^{\prime}+\gamma P(n)C_{mm}G^{\prime}}\\+2\alpha C_{mn}G^{\prime}+2\gamma C_{mn}G^{\prime}-2\gamma P(n)C_{mn}G^{\prime}-\alpha C_{nn}G^{\prime}-\gamma C_{nn}G^{\prime}+\gamma P(n)C_{nn}G+\alpha E_{nn}G^{\prime}+\gamma E_{nn}G^{\prime}-\gamma P(n)E_{nn}G^{\prime} $$

(6)式：

$$ \begin{aligned}n_{\alpha}=&\frac{C_{mm}G-C_{mn}G-\gamma P_{n}G^{2}+\tau(-C_{mm}P_{n}+\alpha P_{n}G^{\prime}+\gamma P_{n}G^{\prime}-\gamma P(n)P_{n}G^{\prime})}{-C_{mn}^{2}+C_{mm}C_{nn}-C_{mm}E_{nn}+2\gamma C_{mm}P_{n}G-2\gamma C_{mn}P_{n}G-\gamma^{2}P_{n}^{2}G^{2}-\alpha C_{mm}G^{\prime}-\gamma C_{mm}G^{\prime}+\gamma P(n)C_{mm}G^{\prime}}\\&+2\alpha C_{mn}G^{\prime}+2\gamma C_{mn}G^{\prime}-2\gamma P(n)C_{mn}G^{\prime}-\alpha C_{nn}G^{\prime}-\gamma C_{nn}G^{\prime}+\gamma P(n)C_{nn}G+\alpha E_{nn}G^{\prime}+\gamma E_{nn}G^{\prime}-\gamma P(n)E_{nn}G^{\prime}\end{aligned} $$

となる。また、

(7)式：

$$ \begin{aligned}m_{\gamma}=&\frac{\begin{aligned}(1-P(n))C_{mn}G+(1-P(n))C_{nn}G-(1-P(n))E_{nn}G+\gamma P(n)G^{2}\\+G(m+n)(C_{mn}P_{n}+\gamma P_{n}^{2}G-\alpha P_{n}G^{\prime}-\gamma(1-P(n))P_{n}G^{\prime})\end{aligned}}{-C_{mn}^{2}+C_{mm}C_{nn}-C_{mm}E_{nn}+2\gamma C_{mm}P_{n}G-2\gamma C_{mn}P_{n}G-\gamma^{2}P_{n}^{2}G^{2}-\alpha C_{mm}G^{\prime}-\gamma C_{mm}G^{\prime}+\gamma P(n)C_{mm}G^{\prime}}\\&+2\alpha C_{mn}G^{\prime}+2\gamma C_{mn}G^{\prime}-2\gamma P(n)C_{mn}G^{\prime}-\alpha C_{nn}G^{\prime}-\gamma C_{nn}G^{\prime}+\gamma P(n)C_{nn}G+\alpha E_{nn}G^{\prime}+\gamma E_{nn}G^{\prime}-\gamma P(n)E_{nn}G^{\prime}\end{aligned} $$

(8)式：

$$ n_{\gamma}=\frac{G(m+n)(-C_{mm}P_{n}+\alpha P_{n}G^{\prime}+\gamma(1-P(n))P_{n}G^{\prime})+((1-P(n))C_{mm}-(1-P(n))C_{mn})G+\gamma(1-P(n))P_{n}G^{2}}{-C_{mn}^{2}+C_{mm}C_{nn}-C_{mm}E_{nn}+2\gamma C_{mm}P_{n}G-2\gamma C_{mn}P_{n}G-\gamma^{2}P_{n}^{2}G^{2}-\alpha C_{mm}G^{\prime}-\gamma C_{mm}G^{\prime}+\gamma P(n)C_{mm}G^{\prime}}\\+2\alpha C_{mn}G^{\prime}+2\gamma C_{mn}G^{\prime}-2\gamma P(n)C_{mn}G^{\prime}-\alpha C_{nn}G^{\prime}-\gamma C_{nn}G^{\prime}+\gamma P(n)C_{nn}G+\alpha E_{nn}G^{\prime}+\gamma E_{nn}G^{\prime}-\gamma P(n)E_{nn}G^{\prime} $$

となる。これより、τが十分に大であれば、 $ m_{\alpha}>0 $ 、 $ n_{\alpha}<0 $ であることが分かる。

つまり、経営者の持株比率を増やすほど、合法的活動 m を増加させ、不法行為 n を減らすことになる。次に、 $ m_{\gamma} $ と $ n_{\gamma} $ については、正か負かは定まらない $ ^{12} $ 。特に $ n_{\gamma} $ が正の場合