Market size, product differentiation and bidding for new varieties

Abstract

We analyse a firm’s investment decision in a regional economy composed of two countries. The firm already manufactures a horizontally differentiated good in the region, and we determine the firm’s equilibrium location choice for the new good and the welfare consequences of fiscal competition between the two countries. We find that the firm’s location decision is efficient. Fiscal competition does not affect the location of production but merely redistributes rents between the firm and the taxpayers of the host country. As far as we know, the tax competition literature has not previously addressed the issue of product differentiation.

Appendices

Appendix 1: Inverse demand systems and consumer surplus

We discuss here the quasi-linear utility function from which inverse demand systems are derived, and we show how we calculate countries’ consumer surplus when the MNE introduces the new variety into the region. We implicitly assume that the representative agent in each country i has a quasi-linear preference of the form:

$$\begin{aligned} U^{i}=\left\{ \begin{array}{ll} q_{1}^{i}-\frac{1}{2}q_{1}^{i2}+m &{} \text {(only good 1 available)} \\ \left( q_{1}^{i}+q_{2}^{i}\right) -\frac{1}{2}\left( q_{1}^{i2}+2bq_{1}^{i}q_{2}^{i}+q_{2}^{i2}\right) +m &{} \text {(both goods 1 and 2 available)} \end{array} \right. \text {,} \end{aligned}$$

where m is a homogenous numéraire good; $0\le b\le 1$.

It is easy to confirm that the inverse-demand systems when the MNE produces and sells both varieties in the region (expression 1) are derived from maximizing $U^{i}=\left( q_{1}^{i}+q_{2}^{i}\right) -\frac{1 }{2}\left( q_{1}^{i2}+2bq_{1}^{i}q_{2}^{i}+q_{2}^{i2}\right) +m$ subject to the budget constraint. Each country’s representative agent receives consumer surplus equal to:

$$\begin{aligned} cs^{i}=\left( q_{1}^{i}+q_{2}^{i}\right) -\frac{1}{2}\left( q_{1}^{i2}+2bq_{1}^{i}q_{2}^{i}+q_{2}^{i2}\right) -p_{1}^{i}q_{1}^{i}-p_{2}^{i}q_{2}^{i}. \end{aligned}$$

The smaller country A has a single consumer, while the larger country B has N consumers. Consequently, country B’s total consumption surplus is equal to N times its representative agent’s consumer surplus.

Appendix 2: Alternative views on product differentiation

Suppose that the representative consumers in each country have different perception of the substitutability of the two products produced by the firm. We argue that, as in the basic model, FDI competition does not change the MNE’s location choice. Without loss of generality, we examine the case where the representative consumer in the smaller country considers the two goods to be distinct, with a product-differentiation parameter $b_{S}=0$, while the representative consumer in the larger country still treats them as being substitutes, with a product-differentiation parameter $b_{L}>0$.

The larger country’s market remains the same as in the basic model. However, the MNE gets more profits per capita in the smaller country’s market irrespective of its location choice, while the smaller country’s net benefit under FDI is greater than in the basic model. That is because the representative consumer is now prepared to pay more for the two goods. As a result, the MNE’s equilibrium profits depend upon its location choice as follows:

$$\begin{aligned} \begin{array}{c} \pi _{B}^{**}=\frac{N}{2\left( 1+b\right) }+\frac{\left( 1-\tau \right) ^{2}}{2} \\ \pi _{A}^{**}=\frac{1+\left( 1-\tau \right) ^{2}}{4}+\frac{N}{ 4\left( 1-b^{2}\right) }\left[ 1+\left( 1-\tau \right) ^{2}-2b\left( 1-\tau \right) \right] \end{array} ; \end{aligned}$$

and each country’s net benefits under FDI become:

$$\begin{aligned} \Delta W^{B}= & {} \frac{N\tau }{8\left( 1-b^{2}\right) }\left[ 2-\tau -2b\right] \\ \Delta W^{A}= & {} \frac{\tau \left( 2-\tau \right) }{8}. \end{aligned}$$

It turns out that:

$$\begin{aligned} \pi _{A}^{**}>\pi _{B}^{**}\Leftrightarrow N^{**}< \frac{\left( 2-\tau \right) \left( 1-b^{2}\right) }{2-\tau -2b}; \end{aligned}$$

and

$$\begin{aligned} \Delta W^{A}>\Delta W^{B}+\left( \pi _{B}^{**}-\pi _{A}^{**}\right) \Leftrightarrow N^{**}<\frac{\left( 2-\tau \right) \left( 1-b^{2}\right) }{2-\tau -2b}. \end{aligned}$$

Hence, we obtain the same result as in the basic model, in that competition for FDI does not change the MNE’s location choice. That is because our model has a linear demand system and constant marginal costs. As a result, in equilibrium, the difference between two countries’ net benefits under FDI and the difference between two location-specific profit levels are proportional. We doubt whether this result would change in the more general case where $b_{S}\ne b_{L}\ne 0$.

In order to overturn the result in the basic model, we may need to introduce asymmetry between the competing countries from the supply side, such as only one country having a problem of unemployment (Barros and Cabral 2000) or where one country has a local firm competing with the FDI (Bjorvatn and Eckel 2006).

Appendix 3: The effects of a local production tax/subsidy

Consider the case where countries compete for the investment of the MNE’s new variety by subsidizing/taxing the MNE’s local production of the variety. An export subsidy would never be used by a government because it may be only justified in an environment of international oligopolistic competition.

When the MNE chooses to make investments in the larger country B, the operating profits it receives are:

$$\begin{aligned} \pi _{B}= & {} N\left[ \left( 1-q_{1}^{B}-bq_{2}^{B}-c\right) q_{1}^{B}+\left( 1-bq_{1}^{B}-q_{2}^{B}-c\right) q_{2}^{B}+s_{B}q_{2}^{B}\right] \\&+\left( 1-q_{1}^{A}-bq_{2}^{A}-c-\tau \right) q_{1}^{A}+\left( 1-bq_{1}^{A}-q_{2}^{A}-c-\tau \right) q_{2}^{A}, \end{aligned}$$

where $s_{B}$ is country B’s local production tax/subsidy and c is the marginal cost of producing each variety. It can be shown that:

$$\begin{aligned} q_{1}^{A}= & {} q_{2}^{A}=\dfrac{1-c-\tau }{2\left( 1+b\right) }, \\ p_{1}^{A}= & {} p_{2}^{A}=\dfrac{1+c+\tau }{2}; \\ q_{1}^{B}= & {} \dfrac{\left( 1-c\right) -b\left( 1-c+s_{B}\right) }{2\left( 1-b^{2}\right) }, q_{2}^{B}=\dfrac{\left( 1-c+s_{B}\right) -b\left( 1-c\right) }{2\left( 1-b^{2}\right) }, \\ p_{1}^{B}= & {} \dfrac{1+c}{2}, p_{1}^{B}=\dfrac{1+c-s_{B}}{2}. \end{aligned}$$

Consequently, when the MNE chooses to locate the production of the new variety in country B, its equilibrium operating profits are:

$$\begin{aligned} \pi _{B}^{*}= & {} \dfrac{1}{4\left( 1-b^{2}\right) }\left[ N\left( 1-c\right) ^{2}+N\left( 1-c+s_{B}\right) ^{2}-2bN\left( 1-c\right) \left( 1-c+s_{B}\right) \right] . \\&+\frac{\left( 1-c-\tau \right) ^{2}}{2\left( 1+b\right) }. \end{aligned}$$

If country B chooses not to provide a local production subsidy, we have:

$$\begin{aligned} \pi _{B}^{**}=\dfrac{1}{2\left( 1+b\right) }\left[ N\left( 1-c\right) ^{2}+\left( 1-c-\tau \right) ^{2}\right] . \end{aligned}$$

Similarly, when the MNE chooses to produce the new variety in the smaller country A, the operating profits it receives are:

$$\begin{aligned} \pi _{A}= & {} N\left[ \left( 1-q_{1}^{B}-bq_{2}^{B}-c\right) q_{1}^{B}+\left( 1-bq_{1}^{B}-q_{2}^{B}-c-\tau \right) q_{2}^{B}\right] \\&+\left( 1-q_{1}^{A}-bq_{2}^{A}-c-\tau \right) q_{1}^{A}+\left( 1-bq_{1}^{A}-q_{2}^{A}-c\right) q_{2}^{A}+s_{A}q_{2}^{A}, \end{aligned}$$

where $s_{A}$ is country A’s local production tax/subsidy and c is the marginal cost of producing each variety. It can be shown that:

$$\begin{aligned} q_{1}^{A}= & {} \dfrac{\left( 1-c-\tau \right) -b\left( 1-c+s_{A}\right) }{2\left( 1-b^{2}\right) }, q_{2}^{A}=\dfrac{\left( 1-c+s_{A}\right) -b\left( 1-c-\tau \right) }{2\left( 1-b^{2}\right) }, \\ p_{1}^{A}= & {} \dfrac{1+c+\tau }{2}, p_{2}^{A}=\dfrac{1+c-s_{A}}{2}; \\ q_{1}^{B}= & {} \dfrac{\left( 1-c\right) -b\left( 1-c-\tau \right) }{2\left( 1-b^{2}\right) }, q_{2}^{B}=\dfrac{\left( 1-c-\tau \right) -b\left( 1-c\right) }{2\left( 1-b^{2}\right) }, \\ p_{1}^{B}= & {} \dfrac{1+c}{2}, p_{1}^{B}=\dfrac{1+c+\tau }{2}. \end{aligned}$$

Consequently, when the MNE chooses to locate the production of the new variety in country A, its equilibrium operating profits are:

$$\begin{aligned} \pi _{A}^{*}= & {} \dfrac{1}{4\left( 1-b^{2}\right) }\left[ N\left( 1-c\right) ^{2}+N\left( 1-c-\tau \right) ^{2}-2bN\left( 1-c\right) \left( 1-c-\tau \right) \right] \\&+\dfrac{1}{4\left( 1-b^{2}\right) }\left[ \left( 1-c-\tau \right) ^{2}+\left( 1-c+s_{A}\right) ^{2}-2b\left( 1-c-\tau \right) \left( 1-c+s_{A}\right) \right] . \end{aligned}$$

If country A chooses not to offer a local production subsidy, we have:

$$\begin{aligned} \pi _{A}^{**}=\dfrac{\left( N+1\right) }{4\left( 1-b^{2}\right) } \left[ \left( 1-c\right) ^{2}+\left( 1-c-\tau \right) ^{2}-2b\left( 1-c\right) \left( 1-c-\tau \right) \right] . \end{aligned}$$

It is clear from the above that when both countries do not engage in FDI competition, the MNE will choose to invest in the smaller country if and only if

$$\begin{aligned} \pi _{A}^{**}>\pi _{B}^{**}\Longleftrightarrow b^{**}>\frac{\left( N-1\right) \left( 2-2c-\tau \right) }{2\left[ N\left( 1-c\right) -\left( 1-c-\tau \right) \right] }; \end{aligned}$$

(A3.1)

and vice versa.

It is not obvious that the necessary and sufficient condition under which $\pi _{A}^{*}>\pi _{B}^{*}$ coincides with condition (A3.1) above. As a result, policy competition may change the FDI location choice when the policy instrument used affects the MNE’s marginal decisions.