Effects of Corporation Tax Rates on Factory Locations Through the Function of the Transfer Price

Abstract

In the globalized economy, a firm that is planning to establish a new factory must pay attention to new factors that were not previously recognized as a location factor: corporation tax and interest rates. In addition, a firm comes to consider a new function that works between factories located in different countries, the function of the transfer price of the intermediate goods. Taking corporation tax rates and the transfer price into consideration, this chapter explains how a firm determines a new factory’s location in a large geographical area. In the explanation, some chaotic phenomena are used, and the usefulness of the phenomenon in a firm’s location selections is clarified..

Appendix: Equations Used in the Gradient Dynamics

The terms of ∂Y/∂x, ∂Y/∂y, and ∂Y/∂mp contained in Eqs. 5.15a, 5.15b, and 5.15c are shown by following Eqs. 5.A1, 5.A2, and 5.A3:

$$ \begin{array}{l}\partial Y/\partial x=0.18\;\left[-{A}^{-1.25}{Q}^{1.25}{t}_m\right[\ \left\{{\left({p}_2+{t}_m{d}_2\right)}^{0.5}/{\left({p}_1+{t}_m{d}_1\right)}^{0.5}\right\}\left(x\hbox{--} {x}_1\right)/{d}_1\\ {}\kern4em +\left\{{\left({p}_1+{t}_m{d}_1\right)}^{0.5}/{\left({p}_2+{t}_m{d}_2\right)}^{0.5}\right\}\left(x+{x}_2\right)/{d}_2-tgx\ Q/{d}_4\\ {}\kern4em +Q\left(-{t}_g\left(x/{d}_4\right)\hbox{--} {t}_e\left(x/{d}_3\right)\right)\Big]=0\end{array} $$

(5.A1)

$$ \begin{array}{l}\partial Y/\partial y=0.18\left[ - {A}^{-1.25}{Q}^{1.25}{t}_m\right[\ \left\{{\left({p}_2+{t}_m{d}_2\right)}^{0.5}/{\left({p}_1+{t}_m{d}_1\right)}^{0.5}\right\}\left(y+{y}_1\right)/{d}_1\\ {}\kern4.2em +\left\{{\left({p}_1+{t}_m{d}_1\right)}^{0.5}/{\left({p}_2+{t}_m{d}_2\right)}^{0.5}\right\}\left(y+{y}_2\right)/{d}_2-tg\left(y-1\right)Q/{d}_4\\ {}\kern4.2em +Q\left(-{t}_g\left(\left(y\hbox{--} {y}_4\right)/{d}_4\right)-{t}_e\left(\left(y-{y}_3\right)/{d}_3\right)\right)\Big]=0\end{array} $$

(5.A2)

$$ \begin{array}{l}\partial Y/\partial mp=0.18\Big[\left(Q-99mp/{\left(582409-900mp\right)}^{0.5}\right)\\ {}\kern4.9em +\left(99mp/{\left(582409-900*mp\right)}^{0.5}\right){t}_g\left(x/{d}_4\right)\\ {}\kern4.9em +\left(99mp/{\left(582409-900mp\right)}^{0.5}\right){t}_e\left(x/{d}_3\right)\Big)\\ {}\kern4.9em +2.5*0.5{A}^{-1.25}{\left({p}_2+{t}_m{d}_2\right)}^{0.5}{\left({p}_1+{t}_m{d}_1\right)}^{0.5}Q\left){}^{0.25}\right)\Big)\\ {}\kern4.9em \hbox{--} 0.18\left[-Q-99\left(600-Q\right)\right)/{\left(582409-900*mp\right)}^{0.5}\\ {}\kern4.9em +\left(0.7425{\left(2+Q\right)}^2\right)/{\left(582409-900*mp\right)}^{0.5}\\ {}\kern4.9em +(21.78Q)/{\left(582409-900*mp\right)}^{0.5}\\ {}\kern4.9em +\Big(0.3267\left(2+Q\right)*\left(-206+{\left(582409-900*mp\right)}^{0.5}\right)/\\ {}\kern5.5em {\left(582409-900*mp\right)}^{0.5}+99mp/{\left(582409-900mp\right)}^{0.5}\left]\right]=0.\end{array} $$

(5.A3)