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Network externalities, trade costs, and the choice of commodity taxation principle

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Abstract

This paper provides a new explanation for the choice of commodity tax principle when introducing network externalities into the intra-industry trade model. First, regardless of the destination or origin principle, when the network externalities are strong (weak), the optimal commodity tax rate in the presence of network externality is positive (negative) and higher (lower) than that without network externality. Second, the interplay between network externalities and trade costs affects the difference in commodity tax rates, influencing the differences in firms’ profits, consumer surplus, tax revenues, and social welfare. Third, if the origin principle’s commodity tax rate is higher (lower) than the destination principle’s, the origin principle’s social welfare level is lower (higher) than the destination principle’s.

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Notes

  1. Katz and Shapiro (1985) consider that a consumer’s utility level comes not only from the quantity of the good consumed by the consumer but also increases with the number of others who consume the good. The following are potential sources of the positive consumption externality: (1) the direct physical effect of the increase in the number of purchasers of the product, such as the network externality of an increase in the number of mobile phone; (2) the indirect effect, for example, when the number of PCs of similar type purchased increases, so will the number and type of software provided to the PCs; (3) when a purchased good is durable, the availability of post-purchase services usually increases with the number of consumers of the durable good.

  2. Haufler et al. (2005) assume an oligopolistic market for Good 1. For simplicity, they assume that the production of Good 1 requires a fixed cost, and the fixed cost is such that only one firm in each country will make positive profits. Therefore, the domestic and foreign firm forms a duopoly in their respective countries. We omit the fixed cost, since it plays no role in the analysis of this paper.

  3. In reality, \(c = 0\) implies redefining the consumer’s basic willingness to pay for Good 1 as the amount that the consumer’s basic willingness to pay for Good 1 exceeds the constant marginal cost \(c\).

  4. The traditional literature usually treats trade cost \(s\) as the transportation cost.

  5. The domestic and the foreign firms’ total outputs of Good 1 are, respectively, \(x + x^{*}\) and \(y + y^{*}\).

  6. In this paper, we treat Good 1, which is produced by both domestic and foreign firm, as two brands.

  7. With \(Z = (x + x^{*} ) + (y + y^{*} )\), it implies that the products of both \(X\) and \(Y\) firms are fully compatible. Fujiwara (2011a, 2011b) demonstrates, regardless of the Good 1’s compatibility, the decrease in trade costs and tariffs has a significant impact on social welfare levels when network externalities are present. Similarly, we assume that Good 1 is fully compatible, and that only considering the network externalities does not affect the results.

  8. To avoid the possibility of corner solutions where all consumers buy the product, this paper follows the assumption of Katz and Shapiro (1985) that there is no lower bound on the basic willingness to pay \(r\). We thank the reviewer for this comment.

  9. Following Katz and Shapiro (1985), when consumers buy Good 1 from firms \(X\) and \(Y\), \(p - nZ\) and \(p^{*} - nZ\) are respective of the expected hedonic price of Good 1, the price adjusted for the network externality sizes.

  10. To compare with most traditional literature, this paper specifies a specific tax rather than an ad valorem tax.

  11. Brander (1981) mentions oligopolistic firms compete in a Cournot fashion, so each firm considers the output of other firms to be given, and each firm’s strategy is naïve under Cournot competition. In reality, oligopolistic firms are unlikely to use this strategy, so such an assumption is vulnerable to be criticized. However, since the cost of gathering and processing information is prohibitively expensive, very sophisticated strategies are unlikely to be implemented. Limiting our attention to a simple strategy is not necessarily a drawback.

  12. The subscripts represent the partial derivatives.

  13. The equilibrium prices, \(\hat{p}^{D}\) and \(\hat{p}^{*D}\), are not always positive. This is because we normalize the unit cost to zero, thus a negative price corresponds to a price below unit cost. As long as the firms can make a positive profit per unit after tax in a particular market, i.e., there is a sufficiently large negative tax (subsidy), they will produce a positive output for that market. We appreciate the reviewer for this insight.

  14. Please see Appendix 1 for conditions of \(\hat{y}^{D} = \hat{x}^{*D} > 0\).

  15. The aim of extracting a foreign firm’s profit is to increase the market share of the domestic firm and shift some tax burden onto foreigners.

  16. Please see Appendix 2 for conditions of \(\hat{y}^{O} = \hat{x}^{*O} > 0\).

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Acknowledgments

We appreciate an anonymous referee for their insightful comments and suggestions on an earlier version of this paper. This paper’s findings, interpretations, and conclusions are entirely those of the authors. All remaining errors are ours.

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Authors and Affiliations

  1. Department of Public Finance, Feng Chia University, Taichung, Taiwan

    Tsaur-Chin Wu

  2. Department of Public Finance and Taxation, National Taichung University of Science and Technology, Taichung, Taiwan

    Chih-Ta Yen

  3. Department of Accounting, National Taiwan University, Taipei, Taiwan

    Hsiu-Wei Chang

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  1. Tsaur-Chin Wu
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  2. Chih-Ta Yen
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Correspondence to Chih-Ta Yen.

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Appendices

Appendix 1

\(\hat{y}^{D} = \hat{x}^{*D} > 0\) if and only if one of the following four conditions holds:

$$\begin{gathered} 0 \le n < \frac{{{13} - \sqrt {97} }}{{8}} \quad{\text{and}}\quad s < \frac{2(3 - 2n)}{{8n^{2} - 24n + 9}}, \hfill \\ \frac{{{13} - \sqrt {97} }}{{8}} < n < \frac{{{3(2} - \sqrt 2 {)}}}{{4}}\quad{\text{and}}\quad\frac{2(3 - 2n)}{{8n^{2} - 24n + 9}} < s, \hfill \\ \frac{3}{{2}} < n < \frac{{{3(2} + \sqrt 2 {)}}}{{4}} \quad{\text{and}}\quad s < \frac{2(3 - 2n)}{{8n^{2} - 24n + 9}}, \hfill \\ \frac{{{3(2} + \sqrt 2 {)}}}{{4}} < n < \frac{{{13} + \sqrt {97} }}{{8}}. \hfill \\ \end{gathered}$$

Appendix 2

\(\hat{y}^{O} = \hat{x}^{*O} > 0\) if and only if one of the following four conditions holds:

$$\begin{gathered} 0 \le n < \frac{{{7} - \sqrt {{1}7} }}{{8}}\quad {\text{and}}\quad s < \frac{{2({1} - n)}}{{{4}n^{2} - {8}n + {3}}}, \hfill \\ \frac{{{7} - \sqrt {{1}7} }}{{8}} < n < \frac{{1}}{{2}}\quad {\text{and}}\quad\frac{{2({1} - n)}}{{{4}n^{2} - {8}n + {3}}} < s, \hfill \\ {1} < n < \frac{{{7 + }\sqrt {{1}7} }}{{8}}\quad{\text{and}}\quad s < \frac{{2({1} - n)}}{{{4}n^{2} - {8}n + {3}}}, \hfill \\ \frac{{{7 + }\sqrt {{1}7} }}{{8}} < n < \frac{{3}}{{2}} \quad{\text{and}}\quad\frac{{2({1} - n)}}{{{4}n^{2} - {8}n + {3}}} < s. \hfill \\ \end{gathered}$$

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Wu, TC., Yen, CT. & Chang, HW. Network externalities, trade costs, and the choice of commodity taxation principle. Int Tax Public Finance 30, 1203–1224 (2023). https://doi.org/10.1007/s10797-022-09740-2

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