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Multinationals: Too Many or Too Few?— The Proximity–concentration Trade-off

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Abstract

The paper builds an analytically tractable model that illustrates the “proximity–concentration trade-off” involved in horizontal multinationals. For low trade costs, firms are single-plant firms, for intermediate costs, some are single-plant firms whereas others are multinationals, for large trade costs, firms are multinationals. Because of the modeling strategy, the model is suited for a welfare analysis of multinationals. It shows that too many firms choose to concentrate their production in only one location. Also, for some transport costs, a reduction in transport costs worsens welfare.

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Notes

  1. For instance, the Treaty on the European Union claims that it is essential to promote trans-European networks (see Vickerman et al. 1999).

  2. These costs are voluntarily reduced through policies of free movement of capital, through harmonization of legislation.... They are involuntarily reduced through the development of the new information and communication technologies, which makes it easier for a firm to communicate with affiliates located in other countries.

  3. In Helpman et al. (2004), costs are assumed to be heterogeneous. As a result, national and multinational firms may coexist. However, as discussed below, heterogeneity does not permit to study welfare in a non controversial manner.

  4. An exception in the analysis of the welfare effects of multinationals is found in the excellent book by Barba-Navaretti and Venables (2004)(Section 3.4). However they consider a coexistence of national and multinational firms, which is not compatible with the assumption of free entry that they use. Also, they exogenously change the number of multinationals and assume that entry is free for national firms. They do not consider that this change affects the profits of multinationals (and is therefore not compatible with zero profits for multinationals) and they do not examine how this change in profits affects welfare. Thus, the welfare analysis of multinationals is still to be done.

  5. See Charlot et al. (2006). Mirrlees (1972) and Wildasin (1986) also show that utilitarism may lead to awkward results in spatial models.

  6. If sizes were different, the number of firms would differ across countries. The price levels would also differ across countries (lower in the country that hosts the larger number of firms) and individuals would have different levels of welfare according to the country in which they live. The same holds if productivity and/or costs were different across countries: agents would get different earnings.

  7. In a different framework with tax competition, Davies (2005) shows that externalities through price levels play an important role for welfare analysis. A country that taxes wages earned by workers of a multinational do not consider the negative effect that this tax have on consumers of other countries through the increase of prices of the goods sold by the multinational to these countries.

  8. These costs can be associated with the duration of transportation. For that duration, the good is not available for consumption, which is clearly a cost for fashion and perishable products.

  9. See Picard et al. (2004) for a general discussion on the role played by the location of capital owners on firms’ location.

  10. Subscripts in capitals denote variables related to multinationals.

  11. Items (1), (2), (4) hinge on the symmetric conditions imposed in the model.

  12. \(\Phi _{2}-\Phi _{1}=2\sigma \left( \sigma -\mu \right) \left( g-f\right) ^{2}N^{2}/\left\{ \mu \left( 2L-gN\right) \left[ \mu \left( 2L-gN\right) +\sigma N\left( g-f\right) \right] \right\} >0\)

  13. \(\mu _{1}\equiv \left[\sigma \left( 1-\mu \right) \right] ^{1-\mu }\left[ \mu \left( \sigma-1\right) \right] ^{\mu }/\left[ 2\left( \sigma -\mu \right) \right]\)

  14. In a first best, a planner would also choose the prices and, maybe, the total number of varieties if he/she can choose it.

  15. The formula give the optimal location of plants when the values are positive, i.e., for intermediate trade costs. \(\hat{N}_{t}=0\) for low trade costs and \(\hat{N}_{t}=N\) for large trade costs.

  16. Technically, setting N t  = N and N r  = N s  = 0 in the welfare expression gives \(2_{{\mu _{1} }} {\left( {2L - Ng} \right)}N^{{\frac{\mu }{{\sigma - 1}}}} \) which is independent of Φ.

  17. The exact values are \(g_{1}\equiv 2\left[\left( \sigma -\mu \right) fN+L\mu \left( 1-\Phi \right) \right] /\left\{ N\left[ 2\sigma -\mu \left(1+\Phi \right) \right] \right\}\) and \(g_{2}\equiv \left[ fN\sigma \left( 1+\Phi \right) +2L\mu \left(1-\Phi \right) -2\mu fN\right] /\left[ N\left( \sigma -\mu \right) \left( 1+\Phi \right) \right]\).

  18. To prove this analytically, use the expression of welfare when N t  = N and N r  = N s  = 0. In the previous section this expression was shown to be \(2\mu _{1}\left( 2L-Ng\right) N^{\frac{\mu }{\sigma -1}}\) which clearly decreases with the communication costs g.

  19. Technically, setting N t  = 0 and N r  = N s  = N/2 in the welfare expression gives \(2_{{\mu _{1} }} {\left( {2L - Nf} \right)}{\left[ {{N{\left( {1 + \Phi } \right)}} \mathord{\left/ {\vphantom {{N{\left( {1 + \Phi } \right)}} 2}} \right. \kern-\nulldelimiterspace} 2} \right]}^{{\frac{\mu }{{\sigma - 1}}}} \) which is independent of g.

  20. Technically, setting \(N_{t}=N_{t}^{\ast }\), \(N_{r}=\left(N-N_{t}^{\ast }\right) /2\), N s  = N r in the welfare expression gives Eq. 6. This expression increases with g if and only if \(g>g_{3}\equiv f+\mu \left( 2L-fN\right) \left( 1-\Phi \right)\) \(\left(1+\Phi \right) ^{-1}\left( \sigma -1\right) ^{-1}N^{-1}\) which is larger than g 2.

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Authors and Affiliations

  1. FUNDP–University of Namur, 8 Rempart de la Vierge, 5000, Namur, Belgium

    Eric Toulemonde

  2. CORE–Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Eric Toulemonde

  3. IZA, Bonn, Germany

    Eric Toulemonde

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  1. Eric Toulemonde
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Correspondence to Eric Toulemonde.

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I thank an anonymous referee for useful comments.

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Toulemonde, E. Multinationals: Too Many or Too Few?— The Proximity–concentration Trade-off. Open Econ Rev 19, 203–219 (2008). https://doi.org/10.1007/s11079-007-9019-7

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