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Abstract
This paper establishes a duopoly model to investigate the impacts of asymmetric absorptive capacity and asymmetric production cost on international technology licensing by an outside patent-holder. We find that, irrespective of fixed fee and royalty licensing, the patent-holder may adopt exclusively licensing if the difference in the absorptive capacity of two firms is large enough; otherwise, it will license to both firms. Surprisingly, such international licensing may be welfare-reducing if the difference in absorptive capacities between two licensees is large enough.
Acknowledgements
We appreciate comments from two anonymous reviewers, the members in Hong Hwang’s International Trade Workshop, Toshihiro Matsumura, Noriaki Matsushima, Daisuke Shimizu. However, all errors remain ours.
Notes
1. Please see Kamien (Citation1992) and Bagchi and Mukherjee (Citation2014) for a complete survey on this literature.
2. The commonly known East Asian ‘economic miracles’ as it seems consistent with empirical observations of successful trade, industrial and other policies that promoted technological and economic growth (Kováć and Žigič Citation2014).
3. The importance of absorptive capacity has been emphasized in the literature, such as Keller (Citation1996), Glass and Saggi (Citation1998) and Ishikawa and Horiuchi (Citation2012). Keller (Citation1996) thinks that to implement technologies invented abroad requires that more skills must be built up by domestic workers and managers, i.e. the absorptive capacity of the economy. Thus, technology is only implementable as the labor force has built up the corresponding skills. Glass and Saggi (Citation1998) discuss how the quality of technology transferred through foreign direct investment is linked to innovation and imitation when the absorptive capacity of LDCs is limited. Ishikawa and Horiuchi (Citation2012) address that technology spillovers crucially depend on the South firm’s capacity to absorb the North firm’s technology.
4. Chang, Hwang, and Peng (Citation2016) also suggests importance of cost asymmetry in the context of international trade and licensing.
5. Kabiraj and Marjit (Citation2003), Mukherjee and Pennings (Citation2006), Ghosh and Saha (Citation2008), Sinha (Citation2010), Tsai and Yang (Citationforthcoming) and Kuo, Lin, and Peng (Citation2016) examine the welfare effect of international technology under different scenarios, such as the tariff policy, export trade policy, asymmetric production cost and vertical product differentiation model.
6. If the patent holder is domestic, the rent-extracting effect will disappear and the domestic social welfare never worsens.
7. . When
, the quantities firm H become negative. It means that firm H will exit the industry if β is larger than
.
8. In previous literature, these two kinds of licensing regimes are the most widely discussed, so we follow the literature, only to explore the case of fixed-fee and royalty.
9. For how the patent-holder exactly charges the fixed fee under the fixed fee regime, please see Appendix 1.
10. Here, ,
, and
.
11. Provided that , and ɛL = 0.5, we can find the critical value
. Given θ ∊ [2.5678,3], then the firm H’s unit cost is still higher than firm L’s unit cost if both firms accept the license. However, under these parameters, the patent-holder would like to license firm H exclusively since θ > θH.
12. It is certainly more profitable for the patent-holder to license the new technology to firm L than to firm H by means of a royalty when θ < 1.
13. In this case, we require .
14. The critical values can be found as follows, and it can be either an interior or corner solution, depending on the value of parameters: and
. Similar to footnote 7, suppose
and β = 1.1, then
if ɛL = 0.95, and
if ɛL = 0.85.
15. In this case, we require .
16. The critical values can be obtained: , and
. In order to prove the existence of those critical values and boundary value, suppose
and ɛL = 0.5; we then can calculate
and
when β = 1.6, and
and
when β = 1.4.
17. The detailed mathematical derivation of equilibrium outcomes under fixed-fee and royalty are available from the authors upon request.
18. Here we draw this figure by given a = 10, c = 4, and ɛL = 0.5.
19. For instance, given , the two firms’ profits are respectively
,
, and both can be clearly see that the profits are lower than before licensing.
20. Notice that, from the Equation (Equation13.4(13.4) ), the welfare will not change if the patent-holder set up a corner royalty rate (i.e. r = ɛH); hence, here we draw this figure by given a = 10, c = 2., and ɛL = 0.5., in order to ensure the patent-holder will set up an interior royalty rate if the patent-holder chooses to license to firm H only.
21. Thanks for an anonymous referee to point out the patent holder may not choose royalty in the areas D3 and D4. However, in this paper , the main point is not the optimal licensing contract but the impact of the international licensing on the welfare. Through a series of mathematical derivation, we can prove that in the areas D3 and D4, the patent holder will prefer fixed-fee, if she can choose using what kind of the licensing contract (i.e. fixed-fee or royalty). About this proof, interested people can privately request from the authors.