Abstract
This research analyzes the impacts of acquiring vertically two-tier cost-saving foreign technologies through licensing on the home economy’s industry profit, consumer surplus, and social welfare. It is found that upstream (downstream) licensing only leads to higher social welfare than the two-tier licensing if the downstream innovation size is small (large) — that is, acquiring more licensed foreign technologies at different tiers in vertically related markets may worsen the domestic welfare. The above results still hold in leader–follower competition under the two-tier licensing regime and even for the case where this two-tier cost-saving technology is present within the home economy itself.
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Notes
Kamien and Tauman (1986) indicate that an outside licensor prefers a fixed-fee to royalty licensing. A series of studies have subsequently shown that an outside licensor may prefer royalty licensing under different settings; e.g., Kamien et al. (1992), Muto (1993), Sen and Tauman (2007), Chang et al. (2013a, b), and Bagchi and Mukherjee (2014). On the other hand, Wang (1998) and Kamien and Tauman (2002) show that an inside licensor prefers a royalty to fixed- fee licensing, with extensions made by such as Arya and Mittendorf (2006), Mukherjee and Pennings (2006), Kitagawa et al. (2014), Chen (2017) and Sen et al. (2021). Although these papers all discuss issues related to technology licensing, they do not consider vertically related markets.
Our model is related to Marjit (1990) where better technology licensing may not take place. His paper differs from ours in several ways. Marjit (1990) considers insider licensing with a one-tier market. Our paper, however, considers outsider licensing with a two-tier market. In addition, our paper examines licensing issues from the perspective of social welfare, such as whether or not foreign technology licensing via more market tiers can increase domestic social welfare.
In order to obtain clear results in the social welfare comparison, we assume that the demand function is linear.
We extend the basic model by assuming the technology is owned by domestic patentees in Sect. 5.
In this subsection, patentees U* and D* simultaneously decide their licensing contracts. Furthermore, our model is extended to consider leader–follower competition in the licensing decision.
In general, licensing contracts are stipulated for a long run but pricing is for a short run. This is why the paper assumes that licensing is made before the pricing of the intermediate goods. This assumption is crucial to our findings: The rent-extracting effect which is the core of the analysis does not exist if the price of the intermediate good is determined prior to the downstream licensing. We are very grateful to a reviewer for raising this point.
Similar optimal licensing contract is derivable even if the demand function is assumed to be nonlinear.
For the incentive compatibility constraint,\({\pi }_{UD}^{D}\ge {\pi }_{N}^{D}\), firm D accepts licensing if \({c}^{D}-{\varepsilon }^{D}+{r}_{UD}^{D}+{w}_{UD}\le {c}^{D}+{w}_{N}\). Therefore, the upper limit of \({r}_{UD}^{D}\) is \({w}_{N}-{w}_{UD}+{\varepsilon }^{D}\). After licensing, firm U’s and firm D’s marginal costs, drop by the amount of \({\varepsilon }^{U}\) and \({\varepsilon }^{D}-{r}_{UD}^{D}\) respectively. Therefore, by (6) and (7), the input price decreases with a difference of \({w}_{UD}-{w}_{N}=-\left({\varepsilon }^{U}/2\right)+\left[({\varepsilon }^{D}-{r}_{UD}^{D})/2\right]\). By substituting the upper limit of \({r}_{UD}^{D}\) into the above equation, we obtain that \({w}_{N}-{w}_{UD}={\varepsilon }^{U}\); i.e., \({r}_{\mathit{UD}}^{D}={\varepsilon }^{U}+{\varepsilon }^{D}\).
We can easily prove that the ranking of the two critical values, \({\widehat{\varepsilon }}^{D}\) under the UDL regime and \({\widetilde{\varepsilon }}^{D}\) under the DL regime, is \({\widehat{\varepsilon }}^{D}\)<\({\widetilde{\varepsilon }}^{D}\). Thus, we take the range, \({\varepsilon }^{D}\le {\widehat{\varepsilon }}^{D}\), to be the corner solution case.
The proof is available from the authors upon request.
Corollary 1 shows that \({w}_{D}\ge {w}_{N}>{w}_{U}\), implying that the distortion from double marginalization is lower under the UL regime than the DL or no-licensing regime. However, under the DL regime, firm U has an incentive to raise the input price since firm D undergoes cost reduction after licensing. In this context, patentee D* would raise the royalty rate to extract firm U’s profit. Consequently, the industry profit ranking depends on the innovation sizes. We have \(\Delta {\Pi }_{U}>\Delta {\Pi }_{D}\) if \({\varepsilon }^{D}={\varepsilon }^{U}=\varepsilon\).
If both the upstream and downstream firms are integrated into a mega monopoly, then the two-tier licensing, of course, is socially more desirable than any other one-tier licensing.
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Appendix
Appendix
This appendix is to prove Proposition 6.
The equilibrium value of CSi and SWi, where i = N, UD, U, D, and \(\theta \equiv a-{c}^{U}-{c}^{D}\) and the difference in industry profits between licensing and no licensing are as follows.
\(\begin{gathered} CS_{i} \quad CS_{N} = \frac{{\theta^{2} }}{32},\quad \quad \quad \quad \;\;\;CS_{UD} = \left\{ \begin{gathered} \frac{{(\theta + \varepsilon^{U} + \varepsilon^{D} )^{2} }}{72},\quad if \varepsilon^{D} > \hat{\varepsilon }^{D} {, } \hfill \\ CS_{N} ,\quad \quad \quad \quad \quad \,if \varepsilon^{D} \le \hat{\varepsilon }^{D} , \hfill \\ \end{gathered} \right. \hfill \\ \;CS_{U} = \frac{{(\theta + \varepsilon^{U} )^{2} }}{32},\quad \quad CS_{D} = \left\{ \begin{gathered} \frac{{(\theta + \varepsilon^{D} )^{2} }}{72},\quad if \varepsilon^{D} > \tilde{\varepsilon }^{D} , \hfill \\ CS_{N} ,\quad \quad \quad if \varepsilon^{D} \le \tilde{\varepsilon }^{D} , \hfill \\ \end{gathered} \right. \hfill \\\quad\quad \varepsilon_{1}^{D} = \frac{{\left( {\theta + \varepsilon^{U} } \right)}}{2} , \;\;\;\varepsilon_{2}^{D} = \frac{{\left( {\theta + 3\varepsilon^{U} } \right)}}{2}, \hfill \ \hat{\varepsilon }^{D} = \frac{{\left( {\theta - 2\varepsilon^{U} } \right)}}{2},\;\;\tilde{\varepsilon }^{D} = \frac{\theta }{2}. \hfill \\ \end{gathered}\) |
\(\begin{gathered} \Delta \Pi_{i} \quad \Delta \Pi_{UD} = 0,\quad\quad \quad\quad \quad\quad \quad\quad \quad\quad \quad\quad \quad\quad \quad\quad \quad\quad \quad\quad \hfill \\ \quad \quad \;\;\Delta \Pi_{U} = \frac{{\varepsilon^{U} \left( {\varepsilon^{D} + 2\theta } \right)}}{16},\quad \quad \Delta \Pi_{D} = \frac{{\left( {5\theta + 2\varepsilon^{D} } \right)\left( {2\varepsilon^{D} - \theta } \right)}}{72}. \hfill \\ \end{gathered}\) |
\(\begin{gathered} SW_{i} \quad SW_{N} = \frac{{7\theta^{2} }}{32},\quad \quad SW_{UD} = \left\{ \begin{gathered} \frac{{(\theta + \varepsilon^{U} + \varepsilon^{D} )^{2} }}{72} + \frac{{3\theta^{2} }}{16},\quad if \varepsilon^{D} > \hat{\varepsilon }^{D} , \hfill \\ SW_{N} ,\quad \quad \quad \quad \quad \quad \quad \;\;\,if \varepsilon^{D} \le \hat{\varepsilon }^{D} , \hfill \\ \end{gathered} \right. \hfill \\SW_{U} = \frac{{(\theta + \varepsilon^{U} )^{2} }}{32} + \frac{{2\theta^{2} + (\theta + \varepsilon^{U} )^{2} }}{16},\quad \quad\quad \quad\quad \quad\quad \quad\quad \quad\quad \hfill \\ SW_{D} = \left\{ \begin{gathered} \frac{{(\theta + \varepsilon^{D} )^{2} }}{72} + \frac{{17\theta^{2} + 16\theta \varepsilon^{D} + 8\varepsilon^{D}}^{2}}{144},\quad \,if \varepsilon^{D} > \tilde{\varepsilon }^{D} , \hfill \\ SW_{N} ,\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \;if \varepsilon^{D} \le \tilde{\varepsilon }^{D} . \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}\) |
From Proposition 5, we have \(C{S}_{U}>\left(\le \right)C{S}_{UD}\) if \({\varepsilon }^{D}<\left(\ge \right){\varepsilon }_{1}^{D}\), and \({\Delta \Pi }_{U}>0\) and \(\Delta {\Pi }_{UD}=0\). On one hand, if \({\varepsilon }^{D}<{\varepsilon }_{1}^{D}\), we have \(S{W}_{U}>S{W}_{UD}\). On the other hand, if \({\varepsilon }^{D}\ge {\varepsilon }_{1}^{D}\), we have \(C{S}_{U}\le C{S}_{UD}\), and \(\Delta {\Pi }_{U}>\Delta {\Pi }_{UD}=0\), but the gap between the industry profits and consumer surplus still depends on \({\varepsilon }^{D}\). Hence, \(S{W}_{U}>\left(\le \right)S{W}_{UD}\) if \({\varepsilon }^{D}<\left(\ge \right)3\sqrt{{\theta }^{2}+6\theta {\varepsilon }^{U}+3{{\varepsilon }^{U}}^{2}}/2-{\varepsilon }^{U}-\theta\). Following the same step, we can compare the social welfare between the DL regime and the UDL regime as follows: \(S{W}_{D}<\left(\ge \right)S{W}_{UD}\) if \({\varepsilon }^{D}<\left(\ge \right) \sqrt{{36\theta }^{2}+5{{\varepsilon }^{U}}^{2}}/4 +\) \({\varepsilon }^{U}/4-\theta .\) Similarly, \(S{W}_{U}\ge \left(<\right)S{W}_{D}\) if \({\varepsilon }^{D}<\left(\ge \right){ \varepsilon }_{w}^{D} \equiv\) \(3\sqrt{25{\theta }^{2}+30\theta {\varepsilon }^{U}+15{{\varepsilon }^{U}}^{2}}/10-\theta\).
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Tsao, KC., Hu, JL., Hwang, H. et al. More licensed technologies may make it worse: a welfare analysis of licensing vertically two-tier foreign technologies. J Econ 139, 71–88 (2023). https://doi.org/10.1007/s00712-023-00818-x
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DOI: https://doi.org/10.1007/s00712-023-00818-x