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A Simple Model of Foreign Brand Penetration with Multi-Product Firms

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Abstract

Trade liberalization through economic integration and decreasing transport and communication costs has resulted in increasing penetration of foreign brands, a phenomenon that has raised concerns among domestic producers. In fact, in the wake of trade liberalization, there has been not only a proliferation of foreign brands, but also a widening of varieties within each imported brand. This chapter addresses both of these phenomena, using a simple model of import penetration with competition among multi-product firms to analyze short run, medium run, and long run effects of decreased trade costs on product diversity (both in brand names and in varieties), relative prices, and relative profits.

Prof. Kikuchi, formerly with the Graduate School of Economics, Kobe University, Kobe, Japan, has since passed away.

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Notes

  1. 1.

    See Bilkey and Nes (1982) for a review of this literature. They reported that both empirical observations and experimental studies indicate that the country-of-origin has a considerable influence on the quality perceptions of a product. Consumers in more developed countries (MDCs) tend to evaluate their own country's products more favorably. Cultural affinity may also play a role in the evaluation of foreign goods. For example, Indian students rated British products higher than did Taiwanese students. Perceived risk seems to have an inverse relationship with level of economic development. Toys made in the E.U. are considered safer than toys imported from less developed countries (LDCs).

  2. 2.

    In our model, we capture the country-of-origin effect by nesting the utility function, such that goods are grouped by country-of-origin, see Eq. (8). We do not assume bias in favor of any product group, though this can be done by simply giving different weights to them in Eq. (8).

  3. 3.

    Matsuyama (1995) considers only single-product firms in each of two industries, and focuses on the distinction between the intra-industry elasticity of substitution and the inter-industry elasticity of substitution. Allanson and Montagna (2005) consider a single industry consisting of multi-product firms, each specializing in a brand and choosing the range of varieties for each brand. Neither paper deals with trade issues.

  4. 4.

    Thus, Eckel (2009) assumes that each retailer sells all products. While Eckel focuses on retailing, one could argue that the concept of intermediation relates to both wholesaling and retailing. In general, wholesalers tend to be more specialized in terms of brands, while retailers tend to offer many brands, though there are exceptions (e.g., specialized retail shops such as Gap, Benetton, L'Occitane, Sony, Apple, Louis Vuitton, as well as specialized car dealers). Our model abstracts from the wholesaler/retailer distinction, and makes the simplifying assumption that each intermediary is the sole distributor of varieties bearing the same brand name.

  5. 5.

    Nevertheless, the response of relative price is monotone: a permanent fall in trade costs by x per cent will lead in the medium run to a fall in the relative price of imported goods by γx per cent, where γ > 1, and the long run fall in relative price is by qγx per cent, where q > 1.

  6. 6.

    Using a different mechanism, Dhingra (2011) finds a similar impact of trade liberalization with product innovation in a multi-product setting. Lorz and Wrede (2009) obtain a somewhat similar type of adjustment (at least in spirit) made by multi-product firms in response to trade liberalization.

  7. 7.

    In an early contribution, Bond (1986) developed a two-sector model in which firms in one sector are heterogeneous due to differences in the level of ability among entrepreneurs. See, also, Schmitt and Yu (2001) and Yu (2002).

  8. 8.

    In what follows, the terms "an entrepreneur" and "one unit of entrepreneurship" are used interchangeably.

  9. 9.

    Note that \( I_{f} \) is an interval, and \( n_{f} \) is the length of that interval. Loosely speaking, the former is a set of elements, and the latter is the measure of the number of elements in that set.

  10. 10.

    Our assumption that consumers have preferences for brands (equivalently here for firms) is borrowed from Allanson and Montagna (2005). An alternative approach would be to follow Bernard et al. (2011) who postulate that preferences are over products (such as shoes, hats etc.) and over varieties, where products are aggregates over varieties, and each multi-product firm produces. Under that approach, consumers do not care about brand names. Our assumption captures the fact that consumers care about brand names. It seems to play an important role for our result on non-monotonicity (Proposition 1).

  11. 11.

    Note that the group price indices \( P_{f} \) and \( P_{h} \) reflect not only the price of individual items but also the range of varieties available to consumers.

  12. 12.

    Recall our assumption that domestic firms in the differentiated good sector do not export.

  13. 13.

    Recall that to supply one unit of the product to the consumer, the firm must ship \( t_{i} \) units.

  14. 14.

    If \( \alpha > \sigma \) (substitutability between two brands is greater than between two varieties within a brand), gross profit of a brand would be convex in the number of varieties within that brand. Then each brand would have an incentive to increase its varieties without limit, an implausible situation.

  15. 15.

    Although the mechanism is different, Dhingra (2011) finds similar impacts of trade liberalization on product/process innovations. See also Lorz and Wrede (2009) for a somewhat similar type of adjustment.

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Correspondence to Ngo Van Long .

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Appendix

Appendix

Derivation of Eq. (34).

$$ \left( {\hat{r}_{f} } \right)^{LR} = - \frac{(\varepsilon - 1)(\sigma - 1)}{\sigma - \varepsilon }\hat{t} - \frac{(\alpha - \varepsilon )(\sigma - 1)}{(\alpha - 1)(\sigma - \varepsilon )}\left( {\hat{s}_{f} } \right) $$

Then, we use the following relationship:

$$ \hat{s}_{f} = - \left[ {\frac{(\sigma - 1)(\varepsilon - 1)(\alpha - 1)}{(\sigma - \varepsilon )(\alpha - \varepsilon )}} \right]\hat{t} $$

The result follows immediately.

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Kikuchi, T., Van Long, N. (2014). A Simple Model of Foreign Brand Penetration with Multi-Product Firms. In: Acharyya, R., Marjit, S. (eds) Trade, Globalization and Development. Springer, India. https://doi.org/10.1007/978-81-322-1151-8_5

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