Corporation Tax Games: An Application of Linear Cost Games to Managerial Cost Accounting

Abstract

Everybody knows that any Government, as a social institution, is concerned to provide and ensure a stable legal framework within which the investors can perform their capital investment in an environment of legal certainty that allows them to reduce their costs. Its primary function is to secure some form of cooperative benefit. Motivated by the Spanish Tax system, in this paper, we present an application of linear cost games to a corporate tax reduction system: corporation tax games. We prove that the grand coalition is always stable in the sense of the core.

Appendix

As we pointed out in Section 4, if an investor decides not to cooperate with the Government, he takes a chance to receive a financial penalty,⁶ whose amount depends on several factors and calculation can be relatively complicated. To show how the amount of the penalty would be obtained, without incurring excessive artificiality, we’ll stick to the simplified situation most suited to our situation. To do this we consider the concepts that we define next.

Let $\mathbb{B}$ be “penalty basis”, consisting of the amount not entered for committing infringement and P _HP the damage to Public Finances, a variable that is obtained by dividing the basis of the penalty among the defrauded amount.⁷

The base rates to consider are ξ _G , ξ _CR y ξ _per . The first, ξ _G , reflects the degree of infringement, and so it starts with a minimum value and increases with the severity of the offense.

$$\displaystyle{ \xi _{G} = \left \{\begin{array}{ccc} 0.50, && \mbox{ minor infringement} \\ 0.01 \cdot \left (50 +\xi _{CR} +\xi _{per}\right ), && \mbox{ mayor infringement} \\ 0.01 \cdot \left (100 +\xi _{CR} +\xi _{per}\right ),&&\mbox{ very serious infringement} \end{array} \right. }$$

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The second, ξ _CR has to be added only in case of recidivism.⁸

$$\displaystyle{ \xi _{CR} = \left \{\begin{array}{ccc} 5, && \mbox{ minor infringement} \\ 15,&& \mbox{ mayor infringement} \\ 25,&&\mbox{ very serious infringement} \end{array} \right. }$$

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The latter, ξ _per , reflects the damage caused to Public Finances.

$$\displaystyle{ \xi _{per} = \left \{\begin{array}{ccc} 10,&& 10 <P_{HP} \leq 25 \\ 15,&& 25 <P_{HP} \leq 50 \\ 20,&& 50 <P_{HP} \leq 75 \\ 25,&&75 <P_{HP} \leq 100 \end{array} \right.\qquad with\;P_{HP} = \frac{\mathbb{B}} {B_{i}}\cdot 100 }$$

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To simplify ξ _per , we define the following unit step function, $a \in \mathbb{R}$,

$$\displaystyle{ u\left (t - a\right ) = \left \{\begin{array}{ccc} 0,&&0 <t \leq a\\ 1, & & t> a \end{array} \right. }$$

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and then,

$$\displaystyle{ \xi _{per} = 10 \cdot u\left (P_{HP} - 10\right ) + 5 \cdot \left [u\left (P_{HP} - 25\right ) + u\left (P_{HP} - 50\right ) + u\left (P_{HP} - 75\right )\right ] }$$

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We analyse next how to encourage the offender to accept the sanction.

Let t _a be the time allowed to pay the penalty fee, and t the time actually paid, both measured in days. The variable γ reflects some reductions by acceptance of the sanction. The amount to be paid will be reduced by a percentage γ ₁ if the fraudster agree with the penalty.

$$\displaystyle{ \gamma _{1} = \left \{\begin{array}{ccc} 30&& \mbox{ agreement} \\ 50&&\mbox{ records with agreement} \\ 0 && \mbox{ another case} \end{array} \right. }$$

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Besides this amount it is still reduced by 25% if the total income of the remaining amount of the penalty in time, and also waiving the application for review or appeal against the sanction is made.

$$\displaystyle{ \gamma _{2} = 25\cdot u\left (t - t_{a}\right )\cdot \delta \qquad with\;\delta = \left \{\begin{array}{ccc} 0,&& \mbox{ sanction is claimed}\\ 1, & &\mbox{ sanction not claimed} \end{array} \right. }$$

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Hence,

$$\displaystyle{ \gamma = \left (1 - \frac{\gamma _{1}} {100}\right ) \cdot \left (1 - \frac{\gamma _{2}} {100}\right ) }$$

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and finally, we obtain the penalty (or interest charge) coefficient

$$\displaystyle{ \alpha ^{{\ast}} =\xi _{ G} \cdot \gamma. }$$

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