Transfer pricing under global adoption of destination-based cash-flow taxation

Abstract

The idea that the problem of transfer price manipulation vanishes under global adoption of destination-based cash-flow taxation (DBCFT) is based on how firms behave in perfectly competitive or monopolistic markets. We show that the neutralizing effect DBCFT has on transfer price incentives can fail once multinational firms are multi-market oligopolists. Under imperfect competition, a multinational will delegate output decisions to its affiliates so that its transfer price can have a strategic role through its influence on competitors’ actions. Even if all countries adopt DBCFT, transfer prices will not equal arm’s length prices, and they will vary with changes in corporate tax rates.

Appendix: comparative statics

1.1 Appendix A. Comparative statics with respect to q on stage-2 quantities when affiliate A is the producer

Totally differentiating first-order conditions (4) yields

$$\begin{aligned} \left( \begin{array}{ccc} r_A^{\prime \prime }-c^{\prime \prime }&{}-c^{\prime \prime }&{}0 \\ 0&{}(1-t_B)\frac{\partial ^2 r_B}{\partial Q_B^2}&{}(1-t_B)\frac{\partial ^2 r_B}{\partial Q_B^* \partial Q_B}\\ 0&{}\frac{\partial ^2 r_B^*}{\partial Q_B \partial Q_B^*}&{}\frac{\partial ^2 r_B^*}{\partial Q_B^{*2}} \end{array} \right) \cdot \left( \begin{array}{c}\textrm{d}Q_A\\ \textrm{d}Q_B\\ \textrm{d}Q_B^* \end{array}\right) = \left( \begin{array}{c} 0\\ \textrm{d}q\\ 0\end{array} \right) . \end{aligned}$$

(19)

Let E denote the 3x3 matrix in (19). $|E| < 0$ at any locally stable stage-2 equilibrium.

Solving (19) yields

$$\begin{aligned} \frac{\textrm{d}Q_A}{\textrm{d}q}= & {} c^{\prime \prime }\cdot \frac{\partial ^2 r_B^*}{\partial Q_B^{*2}} \bigg / |E| \ge 0 \nonumber \\ \frac{\textrm{d}Q_B}{\textrm{d}q}= & {} \frac{r_A^{\prime \prime }-c^{\prime \prime }}{|E|}\cdot \frac{\partial ^2 r_B^*}{\partial Q_B^{*2}}\le 0, \text {and} \nonumber \\ \frac{\textrm{d}Q_B^*}{\textrm{d}q}= & {} \frac{-\textrm{d}Q_B}{\textrm{d}q} \cdot \frac{\partial ^2 r_B^*/\partial Q_B \partial Q_B^*}{\partial ^2 r_B^*/\partial Q_B^{*2}}. \end{aligned}$$

(20)

Similar analysis shows that $\textrm{d}Q_i/\textrm{d}t_A=0$ and $\textrm{d}Q_i/\textrm{d}t_B=(q^*/(1-t_B)) \cdot \textrm{d}Q_i/\textrm{d}q$ for $Q_i \in \lbrace Q_A,Q_B,Q_B^* \rbrace$.

1.2 Appendix B Comparative statics with respect to the tax rates on $q^*$ when affiliate A is the sole producer

Totally differentiating (5), with all expressions evaluated at $q^*$, yields

$$\begin{aligned} \frac{\textrm{d}^2 \Pi }{\textrm{d} q^2}\textrm{d}q^*+c^\prime \cdot \frac{\textrm{d}Q_B}{\textrm{d}q} \textrm{d}t_A+\frac{\textrm{d}^2 \Pi }{\textrm{d} t_B \textrm{d} q} \textrm{d}t_B =0, \end{aligned}$$

(21)

where

$$\begin{aligned} \frac{\textrm{d}^2\Pi }{\textrm{d}q^2}=\frac{\partial ^2 \Pi }{\partial Q_A \partial q} \cdot \frac{\textrm{d}Q_A}{\textrm{d}q} +\frac{\partial ^2 \Pi }{\partial Q_B \partial q} \cdot \frac{\textrm{d}Q_B}{\textrm{d}q}+ \frac{\partial ^2 \Pi }{\partial Q_B^* \partial q} \cdot \frac{\textrm{d}Q_B^*}{\textrm{d}q}+\frac{\partial ^2 \Pi }{\partial q^2} \end{aligned}$$

(22)

and

$$\begin{aligned} \frac{\textrm{d}^2\Pi }{\textrm{d}t_B \textrm{d}q}=\frac{\partial ^2 \Pi }{\partial Q_A \partial q} \cdot \frac{\textrm{d}Q_A}{\textrm{d}t_B} +\frac{\partial ^2 \Pi }{\partial Q_B \partial q} \cdot \frac{\textrm{d}Q_B}{\textrm{d}t_B}+ \frac{\partial ^2 \Pi }{\partial Q_B^* \partial q} \cdot \frac{\textrm{d}Q_B^*}{\textrm{d}t_B}+\frac{\partial ^2 \Pi }{\partial t_B \partial q}. \end{aligned}$$

(23)

The $\textrm{d}t_A$ term in (21) consists only of the direct effect of a change in $t_A$ on (5) because $\textrm{d}Q_A/\textrm{d}t_A=0$. The $\textrm{d}t_B$ term in (21) includes indirect terms because $\textrm{d}Q_i/\textrm{d}t_B \ne 0$ and $\partial ^2 Q_i/\partial t_B \partial q \ne 0$, where $Q_i \in \lbrace Q_A,Q_B,Q_B^* \rbrace$. From part A of this appendix, we know that $\textrm{d}Q_i/\textrm{d}t_B=(q/(1-t_B))\textrm{d}Q_i/\textrm{d}q$ which also implies that

$$\begin{aligned} \frac{\partial ^2 Q_i}{\partial t_B \partial q}= \frac{q}{1-t_B}\frac{\partial ^2 Q_i}{\partial q^2}+\frac{1}{1-t_B}\frac{\partial Q_i}{\partial q}. \end{aligned}$$

(24)

Substituting (24) into (23) then implies

$$\begin{aligned} \frac{\textrm{d}^2\Pi }{\textrm{d}t_B \textrm{d}q}=\frac{q}{1-t_B}\frac{\textrm{d}^2\Pi }{\textrm{d}q^2}-\frac{(1-t_A)c^\prime }{1-t_B}\frac{\partial Q_B}{\partial q}. \end{aligned}$$

(25)

According to (25), an increase in $t_B$ generates two opposing effects on the marginal profitability of transfer pricing. The first effect reflects a decrease in the marginal benefits of using the transfer price to influence the B affiliate’s market share, while the second effect reflects a cost savings for the B affiliate from lowering its output in response to a higher transfer price.

Solving Eq. (21) we obtain

$$\begin{aligned} \frac{\textrm{d}q^*}{\textrm{d}t_A}=\frac{-c^\prime \cdot \frac{\textrm{d}Q_B}{\textrm{d}q}}{\partial ^2 \Pi /\partial q^2}<0 \end{aligned}$$

(26)

and

$$\begin{aligned} \frac{\textrm{d}q^*}{\textrm{d}t_B}=-\frac{q^*}{1-t_B}+\frac{(1-t_A)c^\prime }{1-t_B}\frac{\partial Q_B}{\partial q}\frac{1}{\textrm{d}^2 \Pi /\textrm{d}q^2}. \end{aligned}$$

(27)

Because of the opposing effects identified in (25), the sign of $dq^*/dt_B$ is ambiguous.

1.3 Appendix C. Comparative statics with respect to the tax rates on the amount of mis-pricing when affiliate A is the producer

Equation (6) defines not only the equilibrium transfer price but the amount of mis-pricing. We denote the amount of mis-pricing by $\Delta (t_A,t_B) \equiv q^*-(1-t_A)c^\prime (Q_A(q^*)+Q_B(q^*))$.

Direct calculation shows that

$$\begin{aligned} \frac{\partial \Delta _A}{\partial t_A}=c^\prime +\frac{\textrm{d}q^*}{\textrm{d}t_A}-(1-t_A)c^{\prime \prime } \cdot \frac{\textrm{d}(Q_A+Q_B)}{\textrm{d}q} \cdot \frac{\textrm{d}q^*}{\textrm{d}t_A} \end{aligned}$$

(28)

and

$$\begin{aligned} \frac{\partial \Delta }{\partial t_B}=\frac{\textrm{d}q^*}{\textrm{d}t_B}-(1-t_A)c^{\prime \prime } \cdot \frac{\textrm{d}(Q_A+Q_B)}{\textrm{d}q} \cdot \frac{\textrm{d}q^*}{\textrm{d}t_B}. \end{aligned}$$

(29)

From (20),

$$\begin{aligned} \frac{\textrm{d}(Q_A+Q_B)}{\textrm{d}q}= \frac{r_A^{\prime \prime }}{|E|} \cdot \frac{\partial ^2 r_B^*}{\partial Q_B^{*2}}<0. \end{aligned}$$

(30)

Inequality (30) implies that the strategic effect on the amount of mis-pricing has the same sign as $dq^*/dt_x$ for $x \in \lbrace A,B \rbrace$. Holding $t_A$ fixed, an increase in $q^*$ decreases $Q_A+Q_B$. The reduction in multinational production lowers the multinational’s marginal cost and increases the amount of mis-pricing. However, an increase in $t_A$ reduces the optimal transfer price and creates a negative strategic effect. At the same time, the direct effect of an increase in $t_A$ increases the amount of mis-pricing as it lowers marginal cost holding all quantities fixed. Thus, the sign of $\partial \Delta _A /\partial t_A$ is ambiguous. An increase in $t_B$ only generates a strategic effect. The effect on the amount of mis-pricing will be ambiguous given the ambiguous effect of $t_B$ on $q^*$.

1.4 Appendix D. Comparative statics with respect to $q^*$ on stage-2 quantities when affiliate B is the producer

Totally differentiating first-order conditions (4) yields

$$\begin{aligned} \left( \begin{array}{ccc} (1-t_{A})r_A^{\prime \prime }&{}0&{}0 \\ -c^{\prime \prime }&{}\frac{\partial ^2 r_B}{\partial Q_B^2}-c^{\prime \prime }&{}\frac{\partial ^2 r_B}{\partial Q_B^* \partial Q_B}\\ 0&{}\frac{\partial ^2 r_B^*}{\partial Q_B \partial Q_B^*}&{}\frac{\partial ^2 r_B^*}{\partial Q_B^{*2}} \end{array} \right) \cdot \left( \begin{array}{c}\textrm{d}Q_A\\ \textrm{d}Q_B\\ \textrm{d}Q_B^* \end{array}\right) = \left( \begin{array}{c} \textrm{d}q\\ 0\\ 0\end{array} \right) . \end{aligned}$$

(31)

Let E denote the 3x3 matrix in (31). $|E| < 0$ at any locally stable stage-2 equilibrium. Solving (31) yields

$$\begin{aligned} \frac{\textrm{d}Q_A}{\textrm{d}q}= & {} \left( \left[ \frac{\partial ^2 r_B}{\partial Q_B^2}-c^{\prime \prime }\right] \frac{\partial ^2 r_B^*}{\partial Q_B^{*2}}-\frac{\partial ^2 r_B}{\partial Q_B^* \partial Q_B} \frac{\partial ^2 r_B^*}{\partial Q_B \partial Q_B^*}\right) \bigg / |E| =\frac{1}{(1-t_A)r_A^{\prime \prime }} <0 \nonumber \\ \frac{\textrm{d}Q_B}{\textrm{d}q}= & {} c^{\prime \prime } \frac{\partial ^2 r_B^*}{\partial Q_B^{*2}} / |E| \ge 0, \text {and} \nonumber \\ \frac{\textrm{d}Q_B^*}{\textrm{d}q}= & {} -c^{\prime \prime } \frac{\partial ^2 r_B^*}{\partial Q_B \partial Q_B^*} \bigg / |E| \le 0 \quad \text {if }Q_B \text {and}Q_B^* \text {are strategic substitutes} \end{aligned}$$

(32)

Furthermore, we have

$$\begin{aligned} \frac{\textrm{d}(Q_A+Q_B)}{\textrm{d}q}= \left( \frac{\partial ^2 r_B}{\partial Q_B^2} \frac{\partial ^2 r_B^*}{\partial Q_B^{*2}}-\frac{\partial ^2 r_B}{\partial Q_B^* \partial Q_B} \frac{\partial ^2 r_B^*}{\partial Q_B \partial Q_B^*}\right) / |E|. \end{aligned}$$

(33)

Because the term in parentheses in (33) can be positive or negative, the sign of $\textrm{d}(Q_A+Q_B)/dq$ is ambiguous. A larger transfer price will result in the multinational selling less in country B. At the same time, the diseconomies of scope between $Q_A$ and $Q_B$ will result in the multinational selling more in country A.

Similar analysis shows that $\textrm{d}Q_i/\textrm{d}t_B=0$ and $\textrm{d}Q_i/\textrm{d}t_A=(q^*/(1-t_A)) \cdot \textrm{d}Q_i/\textrm{d}q$ for $Q_i \in \lbrace Q_A,Q_B,Q_B^* \rbrace$.

1.5 Appendix E. Comparative statics with respect to the tax rates on $q^*$ when affiliate B is the sole producer

Totally differentiating (14), with all expressions evaluated at the equilibrium transfer price $q^*$, yields

$$\begin{aligned} \frac{\textrm{d}^2 \Pi }{\textrm{d}q^2}\textrm{d}q^*+\frac{\textrm{d}^2 \Pi }{\textrm{d}t_A \textrm{d}q} \textrm{d}t_A+ \frac{\textrm{d}^2\Pi }{\textrm{d}t_B \textrm{d}q} \textrm{d}t_B =0 \end{aligned}$$

(34)

where

$$\begin{aligned} \frac{\textrm{d}^2 \Pi }{\textrm{d}t_B \textrm{d}q}=c^\prime \cdot \frac{\partial Q_A}{\partial q}-\frac{\partial r_B}{\partial Q_B^*}\cdot \frac{\partial Q_B^*}{\partial q} \end{aligned}$$

(35)

and

$$\begin{aligned} \frac{\textrm{d}^2 \Pi }{\textrm{d}t_A \textrm{d}q}=\frac{q}{1-t_A} \frac{\textrm{d}^2 \Pi }{\textrm{d}q^2}- \frac{(1-t_B)}{1-t_A} \frac{\textrm{d}^2 \Pi }{\textrm{d}t_B \textrm{d}q}. \end{aligned}$$

(36)

When $Q_B$ and $Q_B^*$ are economic and strategic substitutes or economic and strategic complements, $d^2 \Pi /dt_B dq<0$ and (34) implies

$$\begin{aligned} \frac{\textrm{d}q^*}{\textrm{d}t_B}=\frac{-\textrm{d}^2 \Pi /\textrm{d}t_B \textrm{d}q}{\textrm{d}^2 \Pi /\textrm{d}q^2}<0 \end{aligned}$$

(37)

and

$$\begin{aligned} \frac{\textrm{d}q^*}{\textrm{d}t_A}=\frac{-\textrm{d}^2 \Pi /\textrm{d}t_A \textrm{d}q}{\textrm{d}^2 \Pi /\textrm{d}q^2}. \end{aligned}$$

(38)

Defining the amount of mis-pricing by $\Delta _B(t_A,t_B) \equiv q^*-(1-t_B)c^\prime (Q_A(q^*)+Q_B(q^*))$, direct calculation yields

$$\begin{aligned} \frac{\partial \Delta _B}{\partial t_A}= & {} \frac{\textrm{d}q^*}{\textrm{d}t_A}-(1-t_B)c^{\prime \prime } \cdot \frac{\textrm{d}(Q_A+Q_B)}{\textrm{d}q} \cdot \frac{\textrm{d}q^*}{\textrm{d}t_A}. \end{aligned}$$

(39)

$$\begin{aligned} \frac{\partial \Delta _B}{\partial t_B}= & {} c^\prime +\frac{\textrm{d}q^*}{\textrm{d}t_B}-(1-t_A)c^{\prime \prime } \cdot \frac{\textrm{d}(Q_A+Q_B)}{\textrm{d}q} \cdot \frac{\textrm{d}q^*}{\textrm{d}t_B} \end{aligned}$$

(40)

We can rewrite these equations as

$$\begin{aligned} \frac{\partial \Delta _B}{\partial t_A}=\beta _B\cdot \frac{\textrm{d}q^*}{\textrm{d}t_A} \quad \text {and} \quad \frac{\partial \Delta _B}{\partial t_B}=c^\prime +\beta _B\cdot \frac{\textrm{d}q^*}{\textrm{d}t_B} \end{aligned}$$

(41)

where

$$\begin{aligned} \beta _B\equiv 1-(1-t_B)c^{\prime \prime } \cdot \frac{\textrm{d}(Q_A+Q_B)}{\textrm{d}q} \cdot \frac{\textrm{d}q^*}{\textrm{d}t_A}. \end{aligned}$$

(42)

There is only a direct effect following a change in $t_A$, whereas there is a direct and an indirect effect following a change in $t_B$.