Profit sharing, labour share and financial structure

Abstract

In this paper, we study the effects of the Profit-Sharing rule on an oligopolistic economy. Many believed that the Japanese economy was strong because Japan adopted the Profit-Sharing rule (or the Japanese management system) in the 1980s. However, Japan was trapped in a prolonged recession after the collapse of the bubble economy in the 1990s. The Japanese management system and its regulated financial system have come under criticism as factors of the crisis. We derive a condition that a firm and its union adopt the Profit-Sharing rule voluntarily and construct a macrodynamic model of financial instability. We demonstrate in this study that the Profit-Sharing rule in Japan further stabilises the economy when the financial structure of the economy is already stable.

Appendix

1.1 (Case A) Both firms (first and second mover) adopt the profit sharing rule

$$ w_{1}^{A} = \frac{{ - a + 4\bar{w}}}{3},\;w_{2}^{A} = \frac{{ - a + 7\bar{w}}}{6},\;\theta_{1}^{A} = \frac{2 + \alpha }{3},\;\theta_{2}^{A} = \frac{1 + \alpha }{2} $$

(39a)

$$ v_{1}^{A} = \frac{{(1 - \alpha )(a - \bar{w})^{2} }}{12b},v_{2}^{A} = \frac{{(1 - \alpha )(a - \bar{w})^{2} }}{18b} $$

(39b)

$$ u_{1}^{A} = \frac{{\alpha (\alpha - \bar{w})^{2} }}{12b},u_{2}^{A} = \frac{{(a - \bar{w})^{2} }}{18b} $$

(39c)

1.2 (Case B) Firm 1 (first mover) chooses the Profit-Sharing rule and Firm 2 (second mover) adopts the conventional Non-Profit-Sharing

$$ \begin{aligned} w_{1}^{B} & = \frac{{ - a (2 - \alpha ) + 2(5 - \alpha )\bar{w}}}{8 - \alpha },w_{2}^{B} = \frac{{3\alpha a(16 - 5\alpha )\bar{w}}}{2(8 - \alpha )}, \\ \theta_{1}^{B} & = \frac{{\alpha^{2} + 2\alpha + 4}}{8 - \alpha },\quad \theta_{2}^{B} = 0. \\ \end{aligned} $$

(40a)

$$ v_{1}^{B} = \frac{{(\alpha^{2} + 3\alpha - 4)(a - \bar{w})^{2} }}{4b(\alpha - 8)},v_{2}^{B} = \frac{{(\alpha - 2)^{2} (a - \bar{w})^{2} }}{{b(\alpha - 8)^{2} }} $$

(40b)

$$ u_{1}^{B} = \frac{{\alpha (\alpha + 4)(a - \bar{w})^{2} }}{4b(8 - \alpha )},u_{2}^{B} = \frac{{3\alpha (2 - \alpha )(a - \bar{w})^{2} }}{{2b(\alpha - 8)^{2} }} $$

(40c)

1.3 (Case C) Firm 1 (first mover) chooses the conventional Non-Profit-Sharing and Firm 2 (second mover) adopts the Profit-Sharing rule

$$ w_{1}^{C} = \frac{{\alpha a + (6 - \alpha )\bar{w}}}{6},w_{2}^{C} = \frac{{ - (6 + \alpha )a + (30 + \alpha )\bar{w}}}{24},\theta_{1}^{C} = 0,\,\theta_{2}^{C} = \frac{1 + \alpha }{2}, $$

(41a)

$$ v_{1}^{C} = \frac{{(\alpha - 2)^{2} (a - \bar{w})^{2} }}{64b},v_{2}^{C} = \frac{{(1 - \alpha )(6 + \alpha )^{2} (a - \bar{w})^{2} }}{288b}, $$

(41b)

$$ u_{1}^{C} = \frac{{(2 - \alpha )\alpha (a - \bar{w})^{2} }}{48b},u_{2}^{C} = \frac{{\alpha (6 + \alpha )(a - \bar{w})^{2} }}{288b} $$

(41c)

1.4 (Case D) Both firms (first and second movers) adopt conventional Non-Profit-Sharing

$$ \begin{aligned} w_{1}^{D} = \frac{{\alpha (\alpha + 4)a - (\alpha^{2} + 6\alpha - 16)\bar{w}}}{2(8 - \alpha )}, \hfill \\ w_{2}^{D} = \frac{{\alpha (\alpha^{2} + 2\alpha + 16)a - (\alpha^{3} + 2\alpha^{2} + 24\alpha - 64)\bar{w}}}{8(8 - \alpha )},\;\theta_{1}^{D} = 0,\,\theta_{2}^{D} = 0, \hfill \\ \end{aligned} $$

(42a)

$$ v_{1}^{D} = \frac{{(\alpha^{2} + 2\alpha - 8)^{2} (a - \bar{w})^{2} }}{576b},v_{2}^{D} = \frac{{(\alpha^{3} + 12\alpha - 32)^{2} (a - \bar{w})^{2} }}{{144b(\alpha - 8)^{2} }}, $$

(42b)

$$ u_{1}^{D} = \frac{{\alpha (\alpha - 2)\left( {\alpha + 4} \right)^{2} (a - \bar{w})^{2} }}{48b(\alpha - 8)},u_{2}^{D} = \frac{{\alpha \left( {\alpha - 2} \right)(\alpha^{2} + 2\alpha + 16)^{2} (a - \bar{w})^{2} }}{{96b(\alpha - 8)^{2} }}. $$

(42c)